The volume of the pyramid is approximately 574,533.33 cubic meters.
To find the volume of a pyramid, you use the formula: V = (1/3) × base area × height, where B is the area of the base and h is the height of the pyramid.
Given that the side length of the square base is 140 m and the height is 91 m.
Since the base of the pyramid is a square with a side length of 140 m, we can find its area by multiplying the side lengths: B = 140m x 140m = 19,600 square meters.
By calculating this expression, you'll find the volume of the pyramid.
Now we can plug in the values for B and h into the formula: V = (1/3)(19,600 square meters)(91 meters) = 574,533.33 cubic meters.
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Kubin Company’s relevant range of production is 25,000 to 33,500 units. When it produces and sells 29,250 units, its average costs per unit are as follows: Average Cost per Unit Direct materials $ 8. 50 Direct labor $ 5. 50 Variable manufacturing overhead $ 3. 00 Fixed manufacturing overhead $ 6. 50 Fixed selling expense $ 5. 00 Fixed administrative expense $ 4. 00 Sales commissions $ 2. 50 Variable administrative expense $ 2. 00 Required: 1. For financial accounting purposes, what is the total amount of product costs incurred to make 29,250 units? 2. For financial accounting purposes, what is the total amount of period costs incurred to sell 29,250 units? 3. For financial accounting purposes, what is the total amount of product costs incurred to make 33,500 units? 4. For financial accounting purposes, what is the total amount of period costs incurred to sell 25,000 units? (For all requirements, do not round intermediate calculations. )
1. Total amount of product costs
2. Total amount of period costs incurred
3. Total amount of product costs
4. Total amount of period costs
For the relevant range of production of units total amount of product and period cost as per units are,
Total amount of product costs for 29,250 units is $687,375.
Total amount of period costs incurred for 29,250 units is $58,511.50
Total amount of product costs for 33,500 units is equal to $787,250.
Total amount of period costs for 25,000 units is equal to $50,011.50.
Average Cost per Unit Direct materials = $ 8. 50
Direct labor = $ 5. 50
Variable manufacturing overhead = $ 3. 00
Fixed manufacturing overhead = $ 6. 50
Fixed selling expense = $ 5. 00
Fixed administrative expense = $ 4. 00
Sales commissions = $ 2. 50
Variable administrative expense = $ 2. 00
Total unit produced = 29,250 units,
Total product costs
= (Direct materials + Direct labor + Variable manufacturing overhead + Fixed manufacturing overhead) x Number of units produced
= ($8.50 + $5.50 + $3.00 + $6.50) x 29,250
= $23.50 x 29,250
= $687,375
The total amount of product costs incurred to make 29,250 units is $687,375.
Total period costs
= Fixed selling expense + Fixed administrative expense + Sales commissions + (Variable administrative expense x Number of units sold)
= $5.00 + $4.00 + $2.50 + ($2.00 x 29,250)
= $5.00 + $4.00 + $2.50 + $58,500
= $58,511.50
The total amount of period costs incurred to sell 29,250 units is $58,511.50
For the number of units produced changed to 33,500.
Total product costs
= (Direct materials + Direct labor + Variable manufacturing overhead + Fixed manufacturing overhead) x Number of units produced
= ($8.50 + $5.50 + $3.00 + $6.50) x 33,500
= $23.50 x 33,500
= $787,250
The total amount of product costs incurred to make 33,500 units is $787,250.
The number of units sold changed to 25,000.
Total period costs
= Fixed selling expense + Fixed administrative expense + Sales commissions + (Variable administrative expense x Number of units sold)
= $5.00 + $4.00 + $2.50 + ($2.00 x 25,000)
= $5.00 + $4.00 + $2.50 + $50,000
= $50,011.50
The total amount of period costs incurred to sell 25,000 units is $50,011.50.
Therefore, the total amount of the product and period cost for different situations are,
Total amount of product costs is equal to $687,375.
Total amount of period costs incurred is equal to $58,511.50
Total amount of product costs is equal to $787,250.
Total amount of period costs is equal to $50,011.50.
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I need help with this question can you help?
Answer:
The Correct answer is sinA/3.2=sin110°/4.6
three bolts and three nuts are in a box. two parts are chosen at random. find the probability that one is a bolt and one is a nut.
The probability of picking one bolt and one nut is 1/2 or 50%.
To find the probability that one is a bolt and one is a nut, we need to use the formula for calculating the probability of two independent events happening together: P(A and B) = P(A) × P(B)
Let's first calculate the probability of picking a bolt from the box:
P(bolt) = number of bolts / total number of parts = 3/6 = 1/2
Now, let's calculate the probability of picking a nut from the box:
P(nut) = number of nuts / total number of parts = 3/6 = 1/2
Since the events are independent, the probability of picking a bolt and a nut in any order is:
P(bolt and nut) = P(bolt) × P(nut) + P(nut) × P(bolt)
P(bolt and nut) = (1/2) × (1/2) + (1/2) × (1/2)
P(bolt and nut) = 1/2
Therefore, the probability of picking one bolt and one nut is 1/2 or 50%.
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the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
To find the probability that one chosen part is a bolt and the other chosen part is a nut, we need to use the formula for probability:
Probability = (number of desired outcomes) / (total number of outcomes)
There are two ways we could choose one bolt and one nut: we could choose a bolt first and a nut second, or we could choose a nut first and a bolt second. Each of these choices corresponds to one desired outcome.
To find the number of ways to choose a bolt first and a nut second, we multiply the number of bolts (3) by the number of nuts (3), since there are 3 possible bolts and 3 possible nuts to choose from. This gives us 3 x 3 = 9 total outcomes.
Similarly, there are 3 x 3 = 9 total outcomes if we choose a nut first and a bolt second.
Therefore, the total number of desired outcomes is 9 + 9 = 18.
The total number of possible outcomes is the number of ways we could choose two parts from the box, which is the number of ways to choose 2 items from a set of 6 items. This is given by the formula:
Total outcomes = (6 choose 2) = (6! / (2! * 4!)) = 15
Putting it all together, we have:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 18 / 15
Probability = 1.2
However, this answer doesn't make sense because probabilities should always be between 0 and 1. So we made a mistake somewhere. The mistake is that we double-counted some outcomes. For example, if we choose a bolt first and a nut second, this is the same as choosing a nut first and a bolt second, so we shouldn't count it twice.
To correct for this, we need to subtract the number of outcomes we double-counted. There are 3 outcomes that we double-counted: choosing two bolts, choosing two nuts, and choosing the same part twice (e.g. choosing the same bolt twice). So we need to subtract 3 from the total number of desired outcomes:
Number of desired outcomes = 18 - 3 = 15
Now we can calculate the correct probability:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 15 / 15
Probability = 1
So the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
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Part B
Based on your construction, what do you know about ΔABD and ΔBCD?
The construction and the resulting triangles are interesting because they allow us to explore the properties of perpendicular lines and the angles they form.
Now, let's look at the two triangles that are formed as a result of this construction - ΔABD and ΔBCD. Since line BD is perpendicular to line AC, we know that angle ABD and angle CBD are both right angles. This is because any line that is perpendicular to another line forms a right angle with that line.
Now, let's look at the other sides of the triangles. In ΔABD, we have side AB, which is different from side BC in ΔBCD. Similarly, in ΔBCD, we have side CD, which is different from side AD in ΔABD.
So, although the two triangles share a common side (BD), they have different lengths for their other sides. This means that the two triangles are not congruent, since congruent triangles must have the same length for all their sides.
However, we can still find some similarities between the two triangles. For example, since angle ABD and angle CBD are both right angles, we know that they are congruent. Additionally, we can use the fact that angle ADB is congruent to angle CDB, since they are alternate interior angles formed by a transversal (line BD) intersecting two parallel lines (line AC and the line perpendicular to it passing through point B).
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Complete Question:
Draw a line through point B that is perpendicular to line AC Label the intersection of the line and line AC as point D. Take a screenshot of your work, save it, and insert the image in the space below.
Part B
Based on your construction, what do you know about ΔABD and ΔBCD?
cuantos números
primos son a la vez la suma y la diferencia
Answer: there is only one number
Answer:
Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.
Espero haber ayudado :D
Answer every question. Pick one option for each question. Show your work.
1. Over one week, a snack booth at a fair sold 362 cans of soft drinks for $1.75 each and
221 hot dogs for $2.35 each. Which calculation will give the total sales of soft drinks and
hot dogs?
A. 362(2.35) + 221(1.75)
B. 221(2.35) + 362(2.35)
C. 221(1.75) + 362(1.75)
D. 362(1.75) + 221(2.35)
what is the degree of the polynomial 8 x to the power of 5 plus 4 x cubed minus 5 x squared minus 9 ?
Out of these powers, the highest is 5.
Therefore, the degree of the polynomial is 5.
The degree of a polynomial is the highest power of the variable in the polynomial. In the given polynomial, the highest power of x is 5,
so the degree of the polynomial is 5.
The degree of a polynomial is the highest power of the variable (x) in the expression.
In the polynomial you provided:
[tex]8x^5 + 4x^3 - 5x^2 - 9[/tex]
Let's identify the terms and their respective powers of x:
[tex]8x^5[/tex]has a power of 5.
[tex]4x^3[/tex]has a power of 3.
[tex]-5x^2[/tex] has a power of 2.
-9 is a constant term, so there is no power of x.
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The cost of 1 cup of tea and 6 cakes is £13. The cost of 1 cup of tea and 4 cakes is £9 a) How much do 2 cakes cost? b) How much does 1 cake cost?
The answers are:
a) 2 cakes cost £5
b) 1 cake costs £2.5.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.
To find the cost of 1 cupcake, we need to subtract the cost of the tea from the total cost of 3 cupcakes:
3 cupcakes + 1 tea = £9
3 cupcakes = £9 - 1 tea = £9 - £1.5 (assuming the cost of 1 tea is the same in both cases) = £7.5
1 cupcake = £7.5 ÷ 3 = £2.5
So 2 cupcakes would cost:
2 cupcakes = 2 × £2.5 = £5
Therefore, the answers are:
a) 2 cakes cost £5
b) 1 cake costs £2.5.
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An industrial/organizational psychologist has been consulting with a company that runs weekend job-seeking workshops for the unemployed. She collected data on several issues related to these workshops and, after conducting statistical tests, obtained statistically significant findings. She needs to find a way to evaluate effect size so that she can make recommendations to the company. One of the psychologist's findings is that 18 months after the workshop, a sample of 81 job seekers who received training on using the Internet to find job listings worked more than 30 hours per week an average of 8. 7 months in the last year, with a standard deviation of 4. 1. The typical job seeker works 7. 4 months. The psychologist finds that the estimated Cohen's d is _____, the t statistic is 2. 83, and r^2 is ______. Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a ______ treatment effect. Using r^2 and the extension of Cohen's guidelines for interpreting the effect size using r^2, there is a ______ treatment effect. Another one of the psychologist's findings is that a sample of 81 job seekers who received training on interview skills scored an average of 8. 1 as measured on a 9-point job search motivation scale, with a standard deviation of. 8. The typical job seeker scores 7. 4 points. She finds that the estimated Cohen's d is _____, the t statistic is 7. 78, and r^2 is _____ Using Cohen's d and Cohen's guidelines for interpreting the effect size with the estimated Cohen's d, there is a treatment effect. Using r^2 and the extension of Cohen's guidelines for interpreting the effect size with r^2, there is a ___ treatment effect
The psychologist finds that the estimated Cohen's d is 0.32, the t statistic is 2. 83, and r² is 0.073. Using r² and the extension of Cohen's guidelines for interpreting the effect size using r², there is a small treatment effect. job seeker finds that the estimated Cohen's d is 0.88, the t statistic is 7. 78, and r² is 0.479.Using r² and the extension of Cohen's guidelines for interpreting the effect size with r², there is a large treatment effect
To calculate the estimated Cohen's d, we use the formula
d = (M - M0) / SD
where M is the mean of the treatment group (job seekers who received training on using the Internet to find job listings), M0 is the mean of the control group (typical job seeker), and SD is the pooled standard deviation of the two groups. Using the given values, we have
M = 8.7 months
M0 = 7.4 months
SD = 4.1 months
So, d = (8.7 - 7.4) / 4.1 = 0.32
Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.32, there is a small treatment effect.
To calculate r², we use the formula
r² = t² / (t² + df)
where t is the t statistic, df is the degrees of freedom (n-2 for a two-group design), and n is the sample size. Using the given values for the Internet training group, we have
t = 2.83
n = 81
df = 79
So, r² = 2.83² / (2.83² + 79) = 0.073
Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.073, there is a small treatment effect.
For the job seekers who received training on interview skills, we can calculate Cohen's d and r² in a similar way
d = (M - M0) / SD = (8.1 - 7.4) / 0.8 = 0.88
t = 7.78
n = 81
df = 79
r² = 7.78² / (7.78² + 79) = 0.479
Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.88, there is a large treatment effect.
Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.479, there is a medium to large treatment effect.
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Answer:.317
.091
Small to med
Med
.875
.431
Large
Large
Step-by-step explanation:
A tram moved downward 12 meters in 4 seconds at a constant rate. What was the change in the tram's elevation each second?
Therefore , the solution of the given problem of unitary method comes out to be during the 4-second period, the tram's elevation changed by 3 metres every second.
What is an unitary method?To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.
Here,
By dividing the overall elevation change (12 metres) by the total time required (4 seconds),
it is possible to determine the change in the tram's elevation every second. We would then have the average rate of elevation change per second.
=> Elevation change equals 12 metres
=> Total duration: 4 seconds
=> 12 meters / 4 seconds
=> 3 meters/second
As a result, during the 4-second period, the tram's elevation changed by 3 metres every second.
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5. Select Yes or No to indicate whether each ordered pair is a point of intersection
between the line x - y = 6 and the circle y² - 26 = -x².
Ordered Pair
(1,-5)
(1,5)
(5,-1)
To determine if each ordered pair is a point of intersection between the line x - y = 6 and the circle y² - 26 = -x², we need to substitute the values of x and y in both equations and see if they are true for both.
Select Yes or No to indicate whether each ordered pair is a point of intersectionFor the ordered pair (1, -5):
x - y = 6 becomes 1 - (-5) = 6, which is true.
y² - 26 = -x² becomes (-5)² - 26 = -(1)², which is false.
Therefore, (1, -5) is not a point of intersection.
For the ordered pair (1, 5):
x - y = 6 becomes 1 - 5 = -4, which is false.
y² - 26 = -x² becomes (5)² - 26 = -(1)², which is true.
Therefore, (1, 5) is a point of intersection.
For the ordered pair (5, -1):
x - y = 6 becomes 5 - (-1) = 6, which is true.
y² - 26 = -x² becomes (-1)² - 26 = -(5)², which is false.
Therefore, (5, -1) is not a point of intersection.
So the answer is:
(1,-5) - No
(1,5) - Yes
(5,-1) - No
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A classmate of yours stated that a solid line is not a good representation of an arithmetic sequences. What logical assumption is your classmate using?
The classmate is not correct. A line is a good representation of an arithmetic sequence.
A line is a series of dots that represent each value of the sequence.
A line has the same slope as the common difference in the sequence.
An arithmetic sequence is a set of discrete values, whereas a line is a continuous set of values.
The logical assumption used is: An arithmetic sequence is a set of discrete values, whereas a line is a continuous set of values.
What is arithmetic sequence?An arithmetic sequence is a set of numbers where, with the exception of the first term, each term is obtained by adding a fixed constant to the term before it. Every pair of following terms in the sequence has the same fixed constant, which is known as the common difference. A1 stands for the first term in an arithmetic sequence, while an is used to represent the nth term.
A solid line symbolises continuous numbers, whereas the classmate's logical presumption is that an arithmetic series comprises of discrete values. This presumption is untrue, though, as a line can effectively represent an arithmetic series.
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Question:
The current (in amps) in a simple
electrical circuit varies inversely to
the resistance measured in ohms.
The current is 24 amps when the
resistance is 20 ohms. Find the
current (in amps) when the
resistance is 12 ohms.
The current in the circuit when the resistance is 12 ohms is 40 amps.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.
We can use the inverse proportionality formula to solve this problem, which states that:
current (in amps) x resistance (in ohms) = constant
Let's call this constant "k". We can use the information given in the problem to find k:
24 amps x 20 ohms = k
k = 480
Now we can use this constant to find the current when the resistance is 12 ohms:
current x 12 ohms = 480
current = 480 / 12
current = 40 amps
Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.
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Given that £1 = $1.62
a) How much is £650 in $?
b) How much is $405 in £?
Answer:
a 1053
b 250
multiply 650 by 1.62 for part a.
for part b divide by 1.62 since pound is less than dollar
hope this helps :)
Find the exact value of sin a, given that cos a=-5/9 and a is in quadrant 3
Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:
sin^2(a) + cos^2(a) = 1
sin^2(a) + (-5/9)^2 = 1
sin^2(a) = 1 - (-5/9)^2
sin^2(a) = 1 - 25/81
sin^2(a) = 56/81
Taking the square root of both sides:
sin(a) = ±sqrt(56/81)
Since a is in quadrant III, sin(a) is positive. Therefore:
sin(a) = sqrt(56/81) = (2/3)sqrt(14)
Label the net for the cylinder. Then find the surface area of the cylinder. Give your answer in terms of π and as a decimal number rounded to the nearest tenth.
The surface area of the cylinder is approximately 94.2 ft².
What is surface area?Surface area refers to the total area of the external or outer part of an object. It is the sum of the areas of all the individual surfaces or faces of the object. Surface area is typically measured in square units, such as square inches (in²), square feet (ft²), or square meters (m²), depending on the unit of measurement used.
According to the given information:
The surface area of a cylinder is the sum of the lateral surface area (the curved surface) and the area of the two circular bases.
The formula for the lateral surface area of a cylinder is given:
Lateral Surface Area = 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
Plugging in the given values for the radius (r = 3 ft) and height (h = 2 ft), we can calculate the lateral surface area:
Lateral Surface Area = 2π * 3 * 2 = 12π ft²
The formula for the area of a circle (which represents the bases of the cylinder) is given:
Circle Area = πr²
Plugging in the given value for the radius (r = 3 ft), we can calculate the area of each circular base:
Circle Area = π * 3² = 9π ft²
Since there are two bases in a cylinder, we multiply this by 2 to account for both bases:
2 * Circle Area = 2 * 9π = 18π ft²
Now, we can add the lateral surface area and the area of the two bases to find the total surface area of the cylinder:
Total Surface Area = Lateral Surface Area + 2 * Circle Area
= 12π + 18π
= 30π ft²
As a decimal rounded to the nearest tenth, the surface area of the cylinder is approximately 94.2 ft²
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what is the maximum number of consecutive odd positive integers that can be added together before the sum exceeds ?
The maximum number of consecutive odd positive integers that can be added together before the sum exceeds 401 is 11.
Let's assume the first odd integer is x. Then, the sum of the next n consecutive odd integers would be given by:
x + (x+2) + (x+4) + ... + (x+2n-2) = nx + 2(1+2+...+n-1) = nx + n(n-1)
We want to find the largest n such that the sum is less than or equal to 401:
nx + n(n-1) ≤ 401
Since the integers are positive and odd, we can start with x=1 and then try increasing values of n until we find the largest value that satisfies the inequality:
n + n(n-1) ≤ 401
n² - n - 401 ≤ 0
Using the quadratic formula, we find that the solutions are:
n = (1 ± √(1+1604))/2
n ≈ -31.77 or n ≈ 32.77
We discard the negative solution and round down to the nearest integer, giving us n = 11. Therefore, the maximum number of consecutive odd positive integers that can be added together before the sum exceeds 401 is 11.
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Complete Question:
what is the maximum number of consecutive odd positive integers that can be added together before the sum exceeds 401?
Please help me !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equivalent exponential expression for this problem is given as follows:
A. 4^15 x 5^10.
How to simplify the exponential expression?The exponential expression in the context of this problem is defined as follows:
[tex]\left(\frac{4^3}{5^{-2}}\right)^5[/tex]
To simplify the expression, we must first apply the power of power rule, which means that when one exponential expression is elevated to an exponent, we keep the base and multiply the exponents, hence:
4^(15)/5^(-10)
The negative exponent at the denominator means that the expression can be moved to the numerator with a positive exponent, hence the simplified expression is given as follows:
4^15 x 5^10.
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Jaxon made 5% of his free throws over the season. If he shot 220 free throws, how many did he make?
Answer:
Jaxon made 11 free throws over the season.
Step-by-step explanation:
If he made 5% of his free throws, we know that he will make 5% of the total number of free throws he took, which is 220:
We multiply 220 by 0.05, or 5% to find out how many free throws he made:
220*0.05 = 11
After that, we now know that Jaxon made 11 of his free throws out of 220 over the course of the season, or 5%.
All help is appreciated thank you.
Using the fact that the triangles are similar we can see that the value of x is 36
How to find the value of x?We can see that the triangles are similar due to the same interior angles, then ther is a scale factor k between them.
So we can write:
20*k = 48
k = 48/20 = 2.4
Then:
x = 15*2.4
x = 36
That is the value of x.
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Find the measure of the missing side.
1. 8.2
2. 9.9
3. 7.4
4. 10.9
Answer:
1
Step-by-step explanation:
First of all we use the "law of sines"
to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x
and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°
180°=70°+51°+ x
x = 180°-121°
=59°
Using law of sines:
(sides are represented by small letters/capital letters are the angles)
a/sinA= b/sinB= c/sinC
We have one given side which is "9"
so,
9/sin70= x/sin59
doing the criss-cross method,
9×sin59=sin70×x
9×sin59/sin70=x
x=8.2 (answer 1)
I hope this was helpful <3
ASAP I really need help doing a two column proof for this please.
The two column proof is written as follows
Statement Reason
MA = XR given (opposite sides of rectangle)
MK = AR given (opposite sides of rectangle)
arc MA = arc RK Equal chords have equal arcs
arc MK = arc AK Equal chords have equal arcs
Equal chords have equal arcsAn arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.
If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.
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The answers are in the picture. I need help ASAP!
The perimeter and the area of the regular polygon are 20 inches and 27.53 square inches.
How to calculate the area and the perimeter of a regular polygon
The figure representing a regular polygon with five sides of same length, whose perimeter and area is well described by following formulas:
Perimeter
p = n · l
Area
A = (n · l · a) / 2
Where:
A - Area of the polygon, in square inches. n - Number of sides.l - Side length, in inches. a - Apothema, in inches. p - Perimeter, in inches.Where the apothema is:
a = 0.5 · l / tan (180° / n)
If we know that l = 4 in and n = 5, then the perimeter and the area of the polygon are:
Perimeter
p = 5 · (4 in)
p = 20 in
Area
a = 0.5 · (4 in) / tan (180° / 5)
a = 0.5 · (4 in) / tan 36°
a = 2.753 in
A = [5 · (4 in) · (2.753 in)] / 2
A = 27.53 in²
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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 13 people took the trip. She was able to purchase coach tickets for $380
and first class tickets for $1200. She used her total budget for airfare for the trip, which was $9040. How many first class tickets did she buy? How many coach tickets did she buy?
number of first class tickets bought=
Answer: Sarah bought 5 first class tickets and (13-5) = 8 coach tickets.
Step-by-step explanation: The taken a toll of one to begin with lesson ticket is $1200 and the fetched of one coach ticket is $380.
So, the full taken a toll of first class tickets would be 1200x and the entire cost of coach tickets would be 380(13-x) = 4940 - 380x.
The overall fetched of the tickets is given as $9040, so we will set up the taking after condition:
1200x + 4940 - 380x = 9040
Streamlining and tackling for x, we get:
820x = 4100
x = 5
the rule T(-3,1) is applied to point 2,-7 in which part of the coordinate system is the translated point
the translated point is located in the third quadrant of the coordinate system, since both coordinates are negative.
What is Cartesian coordinate?
A coordinate system, also known as a Cartesian coordinate system, is a system used to describe the position of points in space. It is named after the French mathematician and philosopher René Descartes, who introduced the concept in the 17th century. In a coordinate system, each point is assigned a unique pair of numbers, called coordinates, that describe its position relative to two perpendicular lines, called axes. The horizontal axis is usually labeled x and the vertical axis is usually labeled y.
To apply the translation rule T(-3, 1) to the point (2, -7), we need to add the translation vector (-3, 1) to the coordinates of the point:
(2, -7) + (-3, 1) = (-1, -6)
The resulting point after the translation is (-1, -6).
Therefore, the translated point is located in the third quadrant of the coordinate system, since both coordinates are negative.
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A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these is true?
The correct statement about scale factor is the radius of the larger can will be 8 inches. (option c).
Let's first consider the dimensions of the small can of tomato paste. We are given that it has a radius of 2 inches and a height of 4 inches. Therefore, its volume can be calculated using the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we get:
V_small = π(2²)(4) = 16π cubic inches
Using these dimensions, we can calculate the volume of the larger can using the same formula:
V_large = π(6²)(12) = 432π cubic inches
Now, let's compare the volumes of the small and large cans. We have:
V_large = 432π cubic inches > 16π cubic inches = V_small
Therefore, we can conclude that the volume of the larger can is greater than the volume of the smaller can. But is it three times greater? Let's compare:
V_large = 432π cubic inches 3
V_small = 3(16π) cubic inches = 48π cubic inches
We see that 432π cubic inches is not equal to 48π cubic inches, so option b) is not correct.
Finally, let's consider the radius of the larger can. We found earlier that it is 6 inches, which is greater than the radius of the smaller can, but it is not 8 inches. Therefore, option c) is correct.
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Complete Question:
A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these true?
a) The radius of the larger can will be 5 inches.
b) The volume of the larger can will be 3 times the volume of the smaller can
c) The radius of the larger can will be 8 inches.
d) The volume of the larger can is 3 times the volume of smaller can
Evan takes 100 milligrams of medicine. The amount of medicine in his bloodstream decreases by 0.4 milligram each minute for a number of minutes, m, after that. He writes the expression 100 - 0.4m to find the amount of medicine in his bloodstream after m minutes. Which statement about his expression is true?
The statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
The expression 100 - 0.4m represents the amount of medicine in Evan's bloodstream after m minutes, where the amount of medicine decreases by 0.4 milligrams each minute.
The coefficient of the variable m (-0.4) represents the rate of change of the amount of medicine in Evan's bloodstream per minute. It tells us that for every one minute that passes, the amount of medicine in his bloodstream decreases by 0.4 milligrams.
The constant term (100) represents the initial amount of medicine in Evan's bloodstream before the medicine starts to decrease.
Therefore, the statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
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PLEASE HELP DUE TODAY!!!!!!!
Consider the functions g(x) = 2x + 1 and h(x) = 2x + 2 for the domain 0 < x < 5
a. Without evaluating or graphing the functions, how do the ranges compare?
b. graph the 2 functions and describe each range over the given interval
Answer:
see the images and explanation
Step-by-step explanation:
for the graph:
the domain 0 < x < 5
the range for each functions:
g(x) = 2x + 1
g(x) = y , 1 < y < 11
h(x) = 2x + 2 , 2 < y < 12
in a role playing game two special dice are rolled. one die has 4 faces numbered 1 through 4 and the other has 6 faces numbered 1 thorugh 6. what is the probabilty that the total shown on the two dice after they are rolled is greater than or equal to 8?
The probability that the total shown on the two dice after they are rolled is greater than or equal to 8 is 1/9.
Becca is construction triangle d e f using the following angles 50°, 65°, 65°,
what mistake did she make?
Becca made a mistake while constructing triangle DEF by using the angles 50°, 65°, and 65°. The mistake she made was violating the triangle inequality theorem.
According to the theorem, the sum of any two sides of a triangle must be greater than the third side. In other words, if we add the lengths of two sides of a triangle, it must be greater than the length of the third side.
Since Becca only used angles to construct the triangle, she did not consider the side lengths of the triangle. Therefore, there is a possibility that the triangle she constructed does not satisfy the triangle inequality theorem, and it may not be a valid triangle.
In order to ensure the triangle is valid, Becca needs to consider the side lengths while constructing the triangle. She could use trigonometric ratios or a ruler and protractor to measure the side lengths and angles accurately.
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