Assuming the exponential decay model applies, a similar calculator will cost $10.19 in the year 2023.
Question 2:
Part A:
The amount of caffiene that would still be in her system at bedtime is 28.36 mg
Part B:
The hours before she goes to sleep which she could drink a 16-oz coffee is 6.51 hours.
How do we determine the values?The average cost of a scientific calculator was $96.50 in 1970 and $22 in 2016. Using the exponential decay model, the cost of a similar calculator in 2023 would be $10.19.
Question 2:
Part A:
Reshanda was invited for coffee at 2:00 pm, and she normally goes to sleep at 10:00 pm. The half-life of caffeine is 5.5 hours. To determine how much caffeine would still be in her system at bedtime, we can use the formula:
C(t) = C0(1/2)^(t/T),
where C(t) is the amount of caffeine in her system at time t, C0 is the initial amount of caffeine (122 mg), t is the time in hours since she consumed the coffee, and T is the half-life of caffeine (5.5 hours).
At 10:00 pm, 8 hours after drinking the coffee, t = 8 hours. Plugging these values into the formula and solving for C(t), we get: C(8) = 122(1/2)^(8/5.5) = 28.36 mg
Part B:
Reshanda cannot sleep if she has 15 or more mg of caffeine in her system. We can use the formula from part A to solve for the time t when the caffeine level drops below 15 mg.
C(t) = 15, C0 = 122, T = 5.5
15 = 122(1/2)^(t/5.5)
then we can isolate t:
t = 5.5 * ln(122/15) = 6.51 hours
So, Reshanda could drink the coffee 6.51 hours before she goes to sleep.
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The ratio of the measures of the angles of a triangle is 5:7:9. How many degrees is the largest angle? Round answer to the nearest whole number.
50 POINTS FOR WHOEVER HELPS
Based on the ratio of the largest angle of the triangle with 180°, the degrees of the largest angle is 77°.
What is the ratio?The ratio is the proportion of one value to the whole.
Ratios compare the relative sizes of components.
Ratios are computed as the quotients resulting from division operations.
The ratio of the measures of the angels of a triangle = 5:7:9
The sum of ratios = 21
The ratio of the largest angle = 9/21
We know that the total angles of a triangle = 180°
The angle (degrees) of the largest angle = 77° (180° x 9/21)
Thus, the degree of the largest angle is 77°.
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At a given point 67.7ft at ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees find the height of the roof worker and the distance of the ø if someone is observing below.
The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.
The base will be calculated as:-
tan(38.6) = P / B
tan(38.6) = 67.7 / B
B = 67.7 / tan(38.6)
B = 54.8 ft
The height will be calculated as:-
Cos(42.4) = B / H
H = 84.8 / Cos(42.4)
H = 114.83 ft
Therefore, If someone were to look down from above, they would be 114.83 feet from the object and 84.8 feet away.
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True or False: In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.
In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it. This statement is False.
Hypothesis testing is an inferential procedure that uses data from a sample to draw a general conclusion about a population. It is a formal approach and a statistical method that uses sample data to evaluate hypotheses about a population. When interpreting a research question and statistical results, a natural question arises as to whether the finding could have occurred by chance. Hypothesis testing is a statistical procedure for testing whether chance (random events) is a reasonable explanation of an experimental finding.
In hypothesis testing, we will always set up a particular hypothesis that we want to demonstrate to be true. We then use probability to determine the likelihood of our hypothesis is correct. If it appears our original hypothesis was wrong, we reject it and accept the alternative hypothesis. The alternative hypothesis is usually the opposite of our original hypothesis. In Fisher’s case, his original hypothesis was that the lady was guessing. His alternative hypothesis was the lady was not guessing.
Generally speaking, the hypotheses that business researchers want to prove are stated in the alternative hypothesis.
Thus, the statement 'In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it' is False.
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In how may years ₹ 4,000 will amount to ₹ 14,400 at 10% p.a. Compounded interest payable quarterly ?
Answer:
P = ₹4,000
F = ₹14,400
r = 10% = 0.10
m = 4 (because interest is compounded quarterly)
So, we can plug in these values into the formula:
n = (log(14400 / 4000)) / (log(1 + 0.10 / 4))
n = (log(3.6)) / (log(1.025))
n = 2.59
Therefore, it will take approximately 2.59 years for the investment of ₹4,000 to grow to ₹14,400 at a 10% annual interest rate compounded quarterly.
Use the properties of exponents to generate an expression equivalent to each expression.
[tex](x^3y^7)^2[/tex]
[tex](144^3)^\frac{1}{6}[/tex]
[tex]2^(3t+4)[/tex]
x⁶y¹⁴ is the expression equivalent to (x³y⁷)², 12 is the equivalent expression of [tex](144^{3}) ^{\frac{1}{6} }[/tex] and 6t+8 is equivalent expression of 2(3t+4).
What is Expression?An expression is combination of variables, numbers and operators.
Equivalent expressions are expressions that work the same even though they look different.
The given expression is (x³y⁷)²
(x³)²(y⁷)²
x⁶y¹⁴
x⁶y¹⁴ is the expression equivalent to (x³y⁷)²
Expression is [tex](144^{3}) ^{\frac{1}{6} }[/tex]
[tex]144^{\frac{3}{6} }[/tex]
[tex]144^{\frac{1}{2} }[/tex]
√144
12
12 is the equivalent expression of [tex](144^{3}) ^{\frac{1}{6} }[/tex]
Expression is 2(3t+4)
Apply distributive property
6t+8
6t+8 is equivalent expression of 2(3t+4).
Hence, x⁶y¹⁴ is the expression equivalent to (x³y⁷)², 12 is the equivalent expression of [tex](144^{3}) ^{\frac{1}{6} }[/tex] and 6t+8 is equivalent expression of 2(3t+4).
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A card is drawn at random from a standard pack of playing cards.
Then a fair coin is flipped.
What is the probability of selecting a 9 and the coin landing on tails?
The probability of selecting a 9 and the coin landing on tails is 1/26.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Here,
The probability of selecting a card 9 is
Total number of outcomes =52
Number of favourable outcomes =4
Now, probability = 4/52
= 1/13
The probability of coin landing on tails is
1/2
Probability of an event = 1/13 × 1/2
= 1/26
Therefore, the probability of selecting a 9 and the coin landing on tails is 1/26.
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you are given a mc test where each question has four possible answers. the test is made up of 12 questions and you did not prepare for the test. the number of answers possible is
Since the MCQ test has twelve questions with each question having four possible answers, the number of ways in which the test can be answered are 16777216.
There are 12 questions in the given test. It has an MCQ test and every question in the test has 4 options, that is, 4 possible answers.
There are multiple possibilities by which the given test can be answered as we can select a different option every time while answer a question. To calculate the different amount of possibilities,
By the fundamental principle of counting,
The amount of possible ways to answer one question are
4¹ = 4
The amount of possible ways to answer 12 questions are
4¹² = 16777216
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Find the break-even point for the given cost and revenue equations. Round to the nearest whole unit.
C = 20n + 134,000
R = 160n
Answer:
in break-even point
C=R
20n+134000=160n
134000= 160n-20n
140n=134000
n=134000/140
n=957.14
n=957 ( nearest whole number)
C= 20(957.14) + 134000
= 153142.8
= 153143 (nearest whole number)
R= 160(957.14)
=153142.4
= 153142 (nearest whole number)
A couple ordered 50 ounces of pate for their engagement party of 36 people. The pate was such a hit that the couple has decided to serve it again at their wedding reception. How many ounces of pate should they order for 296 people?
The quantity of ounce of pate they should order for the 296 people which will be present for their wedding reception would be = 411.1 ounce.
How to calculate the quantity of ounce of pate?The quantity of ounce ordered for 36 people = 50 ounce.
Therefore the quantity of ounce that will be enough for 296 people = X ounce.
Make X ounce the subject of formula;
X ounce = 296 × 50 /36
= 14800/36
= 411.1 ounce.
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Which of the following describes dependent events?
✔
a.) Rufus spins a spinner and it randomly lands on the number
7. Rufus spins the spinner again, and it lands on the
number 7 again.
32°F
b.) Rudolph randomly picks names out of a hat. He chooses
"Mark" first. He puts Mark's name back in the hat and
chooses again. This time he chooses "Indira."
c.) Renata randomly chooses a chocolate chip cookie from a
cookie jar. She eats the cookie and chooses again. This
time she gets a sugar cookie.
d.) Rocky tosses a six-sided die that lands on the number 1.
Next, he picks a card from a standard deck of playing
The situation that can be described as dependent events is c.) Renata randomly chooses a chocolate chip cookie from a cookie jar. She eats the cookie and chooses again. This time she gets a sugar cookie.
What are dependent events ?Events that are dependent upon prior events are called dependent events. The results of earlier events have an impact on these current ones. For example, two or more occurrences that are interdependent are referred to as dependent events. An event generally qualifies as being reliant if it offers details about another event. If an event provides no information about other events, it is considered independent.
The dependent event would be Renata picking a sugar cookie the second time she chooses another cookie because she ate from the first cookie and so was able to avoid it the second time.
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If you divide a whole number greater than 10 by a fraction, the result is always larger than the original number.
Answer:
Yes
Step-by-step explanation:
This only works for positive integers. For example, 11/0.5 equals 22, but if you were to negate the 11 then the answer would be -22 which is less than negative 11 so the answer is yes it is true for whole positive integers.
how to Solve the following Systems of Linear Equations 4X + 3Y= 7
Answer:
4x−3y+4=0
⟹x=
4
−4+3y
Let, y=4, then x=
4
−4+3(4)
=2
Similarly, when y=0,x=−1
4x+3y−20=0
⟹x=
4
20−3y
Let, y=4, then x=
4
20−3(4)
=2
Similarly, when y=0,x=5
determine elements of set A
The items in A or the elements included in set A are A = 1, 2, 3, 4.
What is an element in a set?
In mathematics, any one of the unique things that make up a set is referred to as an element (or member). A distinct object belonging to a set is referred to as an element (or member) of a set.
The items in A and B, or the elements included in both sets, make up its constituent parts.
Example The elements of the set A B should be listed if A = 1, 2, 3, 4 and B = 2, 4, 6, 8.
A little letter, like x, y, or z, is typically used to represent a set element.
By listing all of a set's components inside braces, a set can be explained.
A = 2, 4, 6, 8 for instance, if Set A is composed of the integers 2, 4, 6, and 8.
Hence, The items in A, or the elements included in set A are A = 1, 2, 3, 4.
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An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.
P(high-quality oil)=0.45
p(medium-quality oil)=0.15
p(no oil)=0.40
a. What is the probability of finding oil (to 2 decimals)?
b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below.
p(soil | high-quality oil)=0.15
p(soil | medium-quality oil)= 0.75
P(soil | no oil)=0.15
Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals).
What is the new probability of finding oil (to 4 decimals)?
According to the revised probabilities, what is the quality of oil that is most likely to be found?
The total probability of filling oil is 0.60
a. P(oil) = 1 - P(no oil) = 1 - 0.40 = 0.60
b.P(soil ∩ high quality oil) = (0.45)(0.15) = 0.067
P(soil ∩ medium quality oil) = (0.15)(0.15) = 0.022
P(soil ∩ no oil) = (0.40)(0.40) = 0.16
New probabilities,
P(high quality oil | soil) = 0.067 / (0.067+0.022+0.16) = 0.067/0.269 = 0.269
P(medium quality oil | soil) = 0.022 / (0.067+0.022+0.16) = 0.022/0.269 = 0.088
P(no oil | soil) = 0.09 / (0.067+0.022+0.16) = 0.09/0.269 = 0.361
New probability of finding oil,
P(oil|soil)= 1 - P(no oil | soil) = 1 - 0.361 = 0.639
So the company has a lower chance of finding oil given that they find the particular soil.
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what is the correct ordering, from smallest to largest, of the following: $\dfrac{7}{6},$ $\dfrac{17}{15},$ $\dfrac{28}{25}\,?$
So, the correct ordering from smallest to largest is 17/15, 7/6, 28/25.
When comparing fractions, one way to determine which fraction is larger or smaller is by finding a common denominator and then comparing the numerators. A common denominator is a multiple of both denominators. The least common denominator (LCD) is the smallest common denominator.
In this case, the least common denominator for the fractions 7/6, 17/15, 28/25 is 30.
This is because 30 is the smallest multiple of 6 and 15 that is also a multiple of 25
So, 7/6 = 35/30, 17/15 = 17/15 and 28/25 = 84/75
The numerators of the fractions are 35, 17, and 84 respectively. Since 17 is the smallest numerator and 84 is the largest numerator, we can conclude that 17/15 is the smallest fraction and 84/75 is the largest fraction.
Therefore, the correct ordering from smallest to largest is 17/15, 7/6, 28/25.
In summary, to compare fractions, we can find a common denominator, then compare the numerators. In this case, we used the least common denominator 30, and then compared the numerators 35, 17, 84, which allowed us to order the fractions in an increasing order.
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In order to determine whether this horizontal position of the pumpkin trajectory represents a minimum or maximum, evaluate at Im. View Available Hint(s) dy a = -8.0 x 10-3m (negative, so this is a minimum) d=2a = –16 x 10-3 (negative, so this is a minimum) ay=2a = -16 x 10-4 (negative, so this is a maximum) = -8.0 x 10m (negative, so this is a maximum)
A projectile have a minimum speed at the highest point of its trajectory. This is because horizontal speed of the projectile remains constant.
Since the only force exerted on the projectile is gravity, which is
9.8 ms ^2 acting downwards and has no effects on the horizontal velocity.The maximum height the pumpkin reaches occurs at 62.5 horizontal meters from its launching spot.
The calculation is as follows;
The equation is y = -0.008x^2 +x
that corresponds to a curve presented by a parabola.
Now we can determine the maximum of this parabola with arms pointing down requesting the derivative slope of the tangent line to
the curve to be zero
So,= 62.5m
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The circumference of the inner circle is 64 ft. The distance between the inner circle and the outer circle is 2 ft. By how many feet is the circumference of outer circle greater than the circumference of the inner circle? Use 22/7 for pi.
The circumference of the outer circle, greater, 12.57 feet, than the circumference of the inner circle.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.
And the general formula of the circle,
(x – h)²+ (y - k)² = r²,
where (h, k) is the center and r is the radius of the circle.
Given:
The circumference of the inner circle is 64 feet.
The radius of the inner circle,
2πr = 64
r = 32 x 7/22
r = 112/11 feet.
The distance between the inner circle and the outer circle is 2 ft.
The radius of the outer circle,
= 112/11 + 2
= 134/11 feet.
The circumference of the outer circle,
= 2 x 22/7 x 134/11
= 76.57 feet.
Now, 76.57 - 64 = 12.57 feet.
Therefore, the circumference of the outer circle is greater than 12.57 feet.
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Please look at the picture for the problem
By performing a change of units, we will see that the cost is 161.36 US dollars.
How much was the cost in US dollars?Here we know that the cost of the dinner was 119 british pounds, and we want to change the units to US dollars.
We know that the exchange rates are:
Currency Dollar per foreign. Foreign per dollar.
British pound 1.356 0.7376
That means that each british pound is equal to 1.356 US dollars, then 119 british pounds is equivalent to:
119*(1.356 ) = 161.36 US dollars.
That is the cost in US dollars.
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Aiden asked a group of students to choose their favorite type of music from the choices of rock, hip-hop, and country. The results of the survey are shown in the graph.
Based on the graph, how many students in a class of 360 students would be expected to choose hip-hop or rock as their favorite type of music?
Number of students who are expected to choose hip hop or rock as their favorite type of music is 240.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Percentage is usually denoted by the symbol '%'.
From the graph,
Number of students who choose rock music = 20
Number of students who choose hip hop music = 40
Number of students who choose country music = 30
Total number of students = 20 + 40 + 30 = 90
Percentage of students who choose rock or hip hop = (20+ 40) / 90
= (60 / 90)
= 66.67%
Out of 360 students, 66.67% of students will chose hip hop or rock.
360 × (60/90) = 240
Hence 240 students choose either hip hop or rock as their favorite music.
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Oliver read for 450450450 minutes this month. His goal is to read for 10\%10%10, percent more minutes next month.
If Oliver meets his goal, how many minutes will he read in all during the two months?
Using percentages we know that he read for 945 minutes over two months, covering pages. If Oliver accomplishes his goal of reading for 19% more minutes next month.
What is the percentage?Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.
So, this month, Oliver read for 450 minutes.
He has promised to read for 10% extra minutes the following month.
Next month, he spent minutes reading pages:
450 + 10% * 450 = 450 + 45 = 945
He, therefore, read for pages at a time for two months = 450+495=945
Hence He read for 945 minutes over two months, covering pages.
Therefore, using percentages we know that he read for 945 minutes over two months, covering pages. If Oliver accomplishes his goal of reading for 19% more minutes next month.
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7) The perimeter of a triangle is 10z² +42-3. The sum of two of the sides is 82² +6x-7. What is the length of the missing side?
8/9
Length of missing side is 8/9x² - 5/9
What is the length of the missing side?The steps for this process are as follows
Step 1: Add the two equations together to form a new equation.
10z² + 42 - 3 + 82² + 6x - 7 = 8/9x² - 5/9
Step 2: Simplify the expression on the left side of the equation.
92² + 48x - 10 = 8/9x² - 5/9
Step 3: Subtract 8/9x² from both sides of the equation.
92² + 48x - 10 - 8/9x² = - 5/9
Step 4: Simplify the left side of the equation.
92² + 40x - 10 = -5/9
Step 5: Add 10 to both sides of the equation.
92² + 40x = 5/9
Step 6: Divide both sides of the equation by 40.
92²/40 + x = 5/9
Step 7: Simplify the left side of the equation.
x = 5/9 - 92²/40
Step 8: The length of the missing side is 8/9x² - 5/9 = 8/9 (5/9 - 92²/40) - 5/9.
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Using the given equation, Length of missing side is 8/9x² - 5/9
What is the length of the missing side of an equation?The steps for this process are as follows
Step 1: Add the two equations together to form a new equation.
10z² + 42 - 3 + 82² + 6x - 7 = 8/9x² - 5/9
Step 2: Simplify the expression on the left side of the equation.
92² + 48x - 10 = 8/9x² - 5/9
Step 3: Subtract 8/9x² from both sides of the equation.
92² + 48x - 10 - 8/9x² = - 5/9
Step 4: Simplify the left side of the equation.
92² + 40x - 10 = -5/9
Step 5: Add 10 to both sides of the equation.
92² + 40x = 5/9
Step 6: Divide both sides of the equation by 40.
92²/40 + x = 5/9
Step 7: Simplify the left side of the equation.
x = 5/9 - 92²/40
Step 8: The length of the missing side is 8/9x² - 5/9 = 8/9 (5/9 - 92²/40) - 5/9.
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The sum of ages of akua and yeboa is 23years akua is 3years older than yeboah fine , the age of yaboah, the product of their ages
Answer:
yaboah: 10product: 130Step-by-step explanation:
Given that akua is 3 years older than yaboah and the sum of their ages is 23, you want the age of yaboah and the product of their ages.
Sum and differenceLet 'a' and 'y' represent the ages of akua and yaboah, respectively. The given relations are ...
a + y = 23
a - y = 3
Adding these equations gives ...
2a = 26
a = 13
Using this in the second equation, we find ...
y = a -3 = 13 -3 = 10
ProductThe product of their ages is ...
a·y = 13·10 = 130
Yaboah is 10 and the product of their ages is 130.
a person weighs 156 pounds, convert their weight to kilograms
Answer:
70.824
Step-by-step explanation:
to solve, multiply the amount of pounds by 0.454.
EX:
156 * 0.454 = 70.824
what it actually equals:
70.7604 (answ on web)
vs
70.824 (answ with formula)
not bad eh?
hope this helps :)
Which of the following statements is true about the first quartile (Q1) value of a box and whisker plot?
Group of answer choices
One-quarter of the data lies below Q1 and three-quarters of the data lies above Q1.
Q1 means the same as Q3.
Half of the data lies below Q1 and half of the data lies above Q1.
Three-quarters of the data lies below Q1 and one-quarter of the data lies above Q1.
The correct option regarding the first quartile of a data-set is given as follows:
One-quarter of the data lies below Q1 and three-quarters of the data lies above Q1.
What is the first quartile of a data-set?The first quartile Q1 of a data-set is the 25th percentile, meaning that:
25% of the data lies below Q1.100 - 25 = 75% of the data lies above Q1.This means that the correct option is given by the first option.
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How did World War I affect fiction writing?
Answer:
Step-by-step explanation:
wwI effected fiction writing in many ways such as _________________.
Answer:
The First World War evoked a surge in literary output, which included poems, novels and drama. Whilst the poetry of Siegfried Sassoon, Rupert Brooke and Wilfred Owen immediately springs to mind, works by by Ivor Gurney, Edward Thomas, Charles Sorley, David Jones and Isaac Rosenberg are also widely anthologised.
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Nancy has to mark 1 1/2 and-1 1/2 on this number line. How many parts does she need between the integers 1 and 2, and between -1 and -2, to show1 1/2 and-1 1/2 on the number line?
Answer:
1
Step-by-step explanation:
according to hooke's law and Pythagorean theorem your answer is should be most definitely will be or is it honestly I don't know. but the answer should be too is in the number not the figure of speech.
Find the sum of 9x^2+5x+8 and 9x-7
Answer:
[tex]9x^2+14x+1[/tex]
Step-by-step explanation:
Hey there!
In order to find the answer to this problem, we must first form an equation; then we can solve/simplify it further
Our Equation:
----------------------------------------------------------------------------------------------------------
[tex](9x^2+5x+8)+(9x-7)[/tex]
1. Distribute the positive sign: positive and positive make positive, positive and negative make negative, negative and negative make positive
[tex]9x^2+5x+8+9x-7[/tex]
2. Combine like terms in each parenthesis: This means combining the x values and the constants.
[tex]9x^2+14x+1[/tex]
----------------------------------------------------------------------------------------------------------
This means that when you add the two given values, the answer you get is: [tex]9x^2+14x+1[/tex]
What way does f(x) shift for log (DWX) ?
Left, right, down, up?
The function f(x) can shift for log (w ± dx) in any of the four directions
How to determine the direction of shiftFrom the question, we have the following parameters that can be used in our computation:
log(DWX)
Express properly
log(w ± dx)
Where w and d are constants and x is the variable
The above function is a logarithmic function, and the parent function is
log(x)
The direction the function shifts is dependent on the values of w and d i.e.
w ± dx > 1 will shift the function right0 < w ± dx < 1 will shift the function leftAlso, the vertical shift depends on the w ± dxRead more about transformation at
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Sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (0,-2) is on the terminal side of θ. Then find the values of the six trignometric functions for the angle. Rationalize deniminators is applicable. Do not use a calculator.
Find sin θ, cos θ, tan θ, csc θ, sec θ, and cot θ.
If it is undefined, say undefined.
The values of the six trignometric functions for the angle are
Sinθ = Sin(3π/2) = -1Cosθ = Cos(3π/2) = 0tanθ = tan(3π/2) = undefined Cotθ = Cot(3π/2) = 0Cscθ = Csc(3π/2) = 1Secθ = Sec(3π/2) = undefinedThe above sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (0,-2) is on the terminal side of θ. We have to determine the value of six
triganomertric functions at angle θ. As we see at terminal side point (0,-2) the value of angle θ = 3π/2. The six trigonometric functions are sine, cosine , secant , cosecant , tangent , cotangent .
Now, Sinθ = Sin(3π/2) = Sin( π + π/2)= Sin ( 180° + π/2) = - sin(π/2) ( since, 180° + θ represents 3rd quadrant where sinθ is negative)
=> Sinθ = - 1
Cosθ = Cos(3π/2) = Cos( π + π/2)= Cos( 180° + π/2) = - Cos(π/2) ( since, 180° + θ represents 3rd quadrant where cosθ is negative)
=> Cosθ = Cos(π/2) = 0
tanθ = tan (3π/2) = tan( π + π/2)= tan( 180° + π/2) = - tan(π/2) ( since, 180° + θ represents 3rd quadrant where tanθ is positive)
=> tanθ = - sin(π/2)/cos(π/2) = 1/0
= undefined
Cscθ = Csc(3π/2) = Csc( π + π/2)= Csc( 180° + π/2) = - Csc(π/2) ( since, 180° + θ represents 3rd quadrant where cscθ is negative)
=> Cscθ = - Csc (π/2) = - 1/sin(π/2) = 1
Secθ = Sec(3π/2) = Se( π + π/2)= Sec( 180° + π/2) = - Sec(π/2) ( since, 180° + θ represents 3rd quadrant where secθ is negative)
=> Secθ = -Sec(π/2) = -1/cos(π/2) = - 1/0
= undefined
Cotθ = Cot(3π/2) = Cot( π + π/2)= Cot( 180° + π/2) = Cot(π/2) ( since, 180° + θ represents 3rd quadrant where cotθ is positive)
=> Cotθ = cot(π/2) = Cos(π/2)/sin(π/2) = 0
Hence, we determined all required triganomertric functions value for θ=3π/2.
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The six trignometric functions' values for the angle are
Tan = tan(3/2) = undefined, Sin = Sin(3/2) = -1, Cos = Cos(3/2) = 0, and vice versa.
Cot = Cot(3/2), Csc = Csc(3/2), and Sec = Sec(3/2), respectively.
The above drawing shows an angle in standard position with the point (0,-2) on the angle's terminal side and the smallest positive measure achievable. We must calculate the value of six.
Triganomertric operates at an angle. As can be seen, the angle's value is 3/2 at the terminal side point (0,-2). In trigonometry, there are six different functions: sine, cosine, secant, cosecant, tangent, and cotangent.
At this point, Sin = Sin(3/2) = Sin( + /2)
= Sin ( 180° + π/2) Since 180° + denotes the third quadrant, where sin is negative, the expression is equal to - sin(/2).
=> Sinθ = - 1
Cos is equal to Cos(3/2) = Cos(+/2)
because 180 degrees, = Cos(180° + /2) = - Cos(/2)
Since 180° + denotes the third quadrant, where cos is negative, the equation is Cos(180° + /2) = - Cos(/2).
Hence, Cos = Cos(/2) = 0.
Tan is equal to Tan (3/2) = Tan (+/2)
= tan( 180° + π/2) Since 180° + denotes the third quadrant, where tan is positive, the expression is = - tan(/2).
Consequently, tan = - sin(/2)/cos(/2) = 1/0
not defined
Csc is equal to Csc(3/2) = Csc(+/2)
Since 180° + represents the third quadrant, where csc is negative, Csc(180° + /2) = - Csc(/2)
=> 1/sin(/2) = 1 = Csc = - Csc (/2)
Se( + /2) = Se( = Sec(3/2)
Since 180° + represents the third quadrant, where sec is negative, sec(180° + /2) = - Sec(/2)
The formula is: Sec = -Sec(/2) = -1/cos(/2) = -1/0.
not defined
Cot = Cot(3/2), which equals Cot(+/2)
Since 180° + denotes the third quadrant, where cot is positive, the equation is Cot(180° + /2) = Cot(/2).
Consequently, Cot = Cot(2/2) = Cos(2/2)/sin(2/2) = 0
As a result, we calculated the values for all necessary triganomertric functions for 3/2.
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Use the following equation to derive a demand schedule and a demand curve. What types of products might exhibit this type of nonlinear demand curve?
The equation is as follows: Q = a - bP^2.Nonlinear demand curve like this can be found in luxury goods and Veblen goods. Where the luxury goods are the goods whose demand increases as the price increases and Veblen goods are the goods whose demand increases with an increase in the consumer's income.
The equation is as follows: Q = a - bP^2.
To derive a demand schedule, we can plug in different values of P (price) and solve for Q (quantity demanded). For example:
Q = a - bP^2
Q = a - (b * 10^2)
Q = a - 1000b
Q = a - (b * 9^2)
Q = a - 810b
Q = a - (b * 8^2)
Q = a - 640b
and so on.
To derive a demand curve, we can plot the different points from the demand schedule on a graph, with P on the x-axis and Q on the y-axis. The demand curve will be a downward-sloping parabola.
Nonlinear demand curve like this can be found in luxury goods and Veblen goods. Where the luxury goods are the goods whose demand increases as the price increases and Veblen goods are the goods whose demand increases with an increase in the consumer's income.
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