Which statements must be true? Check all that apply.
A'A = C'C
C'Q = QC
Line P T⊥ A'A
C'C ⊥ B'B
A'A || B'B
m∠TRB = 90°
Answers
The true statements based on the shape in the given image are:
C'Q = QCLine P T⊥ A'AA'A || B'Bm∠TRB = 90°What is the Reflection of Triangles?The result of flipping a triangle on a coordinate system based on a line of reflection is a figure known as a triangle reflection.
Let's say we wish to mirror the triangle A B C over the -axis or the line. The image that results from reflecting the triangle, if A B C is the pre-image, is A ′ B ′ C ′. When using triangle reflections, the final image will keep the triangle's shape.
With this explanation in mind and from the image provided, C'Q = QC because they are parallel to each other.
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Related Questions
13731 arks
a) Write the missing numbers.
10% of 140 =
5% of 140 =
1% of 140 =
b) Work out 16% of 140
You can use part (a) to help you.
000 0
Answers
.05 x 140 = 7
.01 x 140 = 1.4
Find the jacobian of the transformation. X = 6v + 6w2, y = 4w + 4u2, z = 9u + 9v2
Answers
To get the transformation's Jacobian, we must first compute the partial derivatives of each new variable with respect to each old variable: x/u = 0, x/v = 6 + 0 = 6, and x/w = 0 + 12w = 12w.
∂y/∂u = 8u ∂y/∂v = 0 ∂y/∂w = 8w + 0 = 8w z/u = 9 plus 0 = 9 z/v = 0 plus 18v = 18v z/w = 0 As a result, the transformation's Jacobian matrix is: [(x,y,z)/(u,v,w)] = J = \s[ 0 6 12w ] [ 8 0 8w ] [ 9 18v 0 ] A transformation's Jacobian is a matrix of partial derivatives that illustrates how changing the old variables impacts changing the new variables. We have three new variables x, y, and z in the provided transformation, which are functions of three old variables u, v, and w. To get the transformation's Jacobian, we must compute the partial derivatives of x, y, and z with respect to u, v, and w. We discover that x's partial derivative with respect to u is zero, x's partial derivative with respect to v is six, and x's partial derivative with respect to w is twelve. Likewise, y's partial derivative with regard to u.
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2x/5 - 2 = 5 (find value of x)
Answers
x = 17.5
Step by step explanation:
To solve for x in the equation:
2x/5 - 2 = 5
We need to isolate x on one side of the equation by performing inverse operations.
First, we'll add 2 to both sides of the equation:
2x/5 - 2 + 2 = 5 + 2
Simplifying the left side, we get:
2x/5 = 7
Next, we'll multiply both sides by 5 to eliminate the fraction:
2x/5 * 5 = 7 * 5
Simplifying the left side, we get:
2x = 35
Finally, we'll divide both sides by 2:
2x/2 = 35/2
Simplifying the left side, we get:
x = 17.5
Therefore, the value of x that satisfies the equation is 17.5.
The value of the of your quarters incense is a function of and the number of quarters. You have finally output when the input is 10
Answers
The value of the of your quarters incense is a function of and the number of quarters, then the output when input is 10 is 250.
Quarters:
In mathematical terms, quartering is the division of a whole into 4 equal parts, where 1 is the part referred to and 4 is the number of parts the whole is divided into.
Let the quarter be 25 cents then value(v) of quarter (cents) is functions of n then equation,
v = 25n
Putting input (n =10)
V = 25× 10
= 250
The independent value is: n
The dependent value is : v
The equation is: v = 25n
And, the output when input is 10 is 250.
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At a football game, a vender sold a combined total of 137 sodas and hot dogs. The number of sodas sold was 49 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold. Number of sodas sold: Number of hot dogs sold:
Answers
Answer:
From the problem, we know that:
s + h = 137 (the total number of sodas and hot dogs sold is 137)
s = h + 49 (the number of sodas sold is 49 more than the number of hot dogs sold)
Now we can substitute the second equation into the first equation:
(h + 49) + h = 137
Simplifying this equation:
2h + 49 = 137
Subtracting 49 from both sides:
2h = 88
Dividing both sides by 2:
h = 44
Now we know that 44 hot dogs were sold. We can use the second equation to find the number of sodas sold:
s = h + 49
s = 44 + 49
s = 93
Therefore, 93 sodas were sold.
Number of sodas sold: 93
Number of hot dogs sold: 44
Step-by-step explanation:
Answer: Let's use variables to represent the number of sodas and hot dogs sold.
Let x be the number of hot dogs sold.
According to the problem, the number of sodas sold was 49 more than the number of hot dogs sold, so the number of sodas sold is x + 49.
The problem also tells us that the combined total of sodas and hot dogs sold was 137. So we can set up an equation:
x + (x + 49) = 137
Simplifying the left side:
2x + 49 = 137
Subtracting 49 from both sides:
2x = 88
Dividing both sides by 2:
x = 44
So the number of hot dogs sold was 44.
To find the number of sodas sold, we can use the expression we set up earlier:
x + 49
Substituting in our value for x:
44 + 49 = 93
So the number of sodas sold was 93.
Answer: Number of sodas sold: 93, Number of hot dogs sold: 44.
Brainliest Appreciated
5 menos que el conciente de un número y 2.
Answers
The expression "5 less than the conscious number and 2" can be written mathematically as: n - 5 = 2
What is a Math Expression?A math expression is a combination of mathematical symbols, numbers, and variables that represents a mathematical statement or calculation. It can be as simple as a single number, such as 5, or as complex as a multi-term equation, such as 3x + 4y = 12.
Expressions can include arithmetic operations such as addition, subtraction, multiplication, and division, as well as other mathematical functions such as exponents, logarithms, and trigonometric functions.
How to solve the given expression?Where "n" represents the number in question. To find the value of "n", you can add 5 to both sides of the equation:
n - 5 + 5 = 2 + 5
This is the result:
n = 7
Therefore, the number in question is 7.
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The question in English is:
(What is) 5 less than the conscious of a number and 2
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is skewed
IQR, because Desert Landing is symmetric
Range, because Sunny Town is skewed
Range, because Desert Landing is symmetric
Answers
A. IQR or B. IQR is the correct response since Sunny Town is symmetrical or Sunny Town is asymmetrical.
How do distributions work?The pattern of data distribution across various values or intervals is referred to as a distribution. The form, centre, and dispersion of a set of data can be described and examined in this manner.
We need to measure the fluctuation of the temperature data in both locations in order to decide which place has the most stable temperature. The interquartile range (IQR), which quantifies the spread of the middle 50% of the data, is the ideal measure of variability for this application.
As a result, depending on how the distributions are shaped, the answer is either A. IQR because Sunny Town is symmetric or B. IQR because Sunny Town is skewed. The IQR would be a suitable tool to gauge the data's spread if Sunny Town's temperature data were symmetric. The IQR would also be useful to measure the spread of the data if Sunny Town's temperature data were skewed. Therefore, the range would not be a suitable indicator of variability if the temperature data from either location were not skewed.
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Write the equation of a circle with center at ( 3, -5 ), and a radius of 3.
A. (x - 3)² + (y + 5)² =9
B. 3 (x - 3)² + (y + 5)² =9
C. (x + 3)² + (y - 5)² =9
D. (x + 3)² + (y - 5)² =3
Answers
Answer:
The equation of a circle with center (h, k) and radius r is given by:
(x - h)² + (y - k)² = r²
So, substituting the values given in the question, we get:
(x - 3)² + (y + 5)² = 3²
Simplifying, we get:
(x - 3)² + (y + 5)² = 9
Therefore, the correct option is A) (x - 3)² + (y + 5)² = 9.
Step-by-step explanation:
Solve the equation.
5(y+2/5)=−13
y = ?
Answers
Answer:
-3
Step-by-step explanation:
5(y+2/5)=-13
5*y+5*2/5=-3
5y+2=-13
5y=-13-2
5y=-15
5y/5=-15/5
y=-3
Answer:
y = -3
Step-by-step explanation:
Now we have to,
→ Find the required value of y.
The equation is,
→ 5(y + (2/5)) = -13
Then the value of y will be,
→ 5(y + (2/5)) = -13
→ 5(y) + 5(2/5) = -13
→ 5y + (10/5) = -13
→ 5y + 2 = -13
→ 5y = -13 - 2
→ 5y = -15
→ y = (-15)/5
→ [ y = -3 ]
Hence, the value of y is -3.
Please help! What do I graph?
Answers
Answer:
look at image
Step-by-step explanation:
What is sinK? Triangle L M K. Angle L is 90 degrees. Hypotenuse K M is 13, adjacent K L is 5, opposite L M is 12. A. StartFraction 12 Over 13 EndFraction c. StartFraction 5 Over 13 EndFraction b. StartFraction 13 Over 12 EndFraction d. StartFraction 5 Over 12 EndFraction
Answers
According to the trigonometric functions, the answer is A. StartFraction 12 Over 13 EndFraction.
What are trigonometric functions?
Trigonometric functions are mathematical functions that relate the angles of a right triangle to the ratios of its sides. There are six primary trigonometric functions:
Sine (sin): the ratio of the opposite side to the hypotenuse of a right triangle.
Cosine (cos): the ratio of the adjacent side to the hypotenuse of a right triangle.
Tangent (tan): the ratio of the opposite side to the adjacent side of a right triangle.
Cosecant (csc): the reciprocal of the sine function, i.e. the ratio of the hypotenuse to the opposite side of a right triangle.
Secant (sec): the reciprocal of the cosine function, i.e. the ratio of the hypotenuse to the adjacent side of a right triangle.
Cotangent (cot): the reciprocal of the tangent function, i.e. the ratio of the adjacent side to the opposite side of a right triangle.
To find sin(K), we need to use the definition of sine which is the opposite side over the hypotenuse:
sin(K) = opposite / hypotenuse
In this case, the opposite side is LM and the hypotenuse is KM. We are given that KM = 13 and LM = 12, so we can plug these values into the formula:
sin(K) = 12/13
Therefore, the answer is A. StartFraction 12 Over 13 EndFraction.
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Evaluate the expression when m = -2
m^2 + 6m +9
Answers
m^2+6m+9
Substitute:
(-2)^2+6(-2)+9
Calculate:
4-12+9
Calculate:
1
Hope this helped!
Suppose that X is an event, and that P(X)=0.66 . What is P( X ˉ ) (i.e. the probability that X will not occur)? Answer = You have attempted this problem 0 times. You have unlimited attempts remaining.
Answers
The probability of X not occurring is 0.34.
What is Probability?
Probability is a branch of mathematics concerned with measuring the likelihood of events. It involves studying random phenomena, such as coin tosses, rolling dice, or weather patterns, and assigning numerical values to the likelihood of different outcomes .The formal definition of probability is based on the concept of equally likely outcomes, where the probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes
If P(X) = 0.66, then the probability of not X occurring (i.e., X complement or X bar) is:
P(X bar) = 1 - P(X)
P(X bar) = 1 - 0.66
P(X bar) = 0.34
Therefore, the probability of X not occurring is 0.34.
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The distribution of the ages of of all IRSC students is known to be normally distributed with a mean of 20.9
years and a standard deviation of 5.9 years. Use this information to determine the following probabilities.
Round solutions to four decimal places, if necessary.
Answers
The probability that a random sample of 55 students has a mean age of less than 19.2 age years is 0.3866 and the probability that a random sample of 55 students has a mean age between 18.8 and 23 years is 0.27808.
What is the probability that a random sample has a mean age of less than 19.2a. To find P(x < 19.2), we need to find the area under the normal distribution curve to the left of x = 19.2. We can use the formula for z-score to standardize the value of x:
z = (x - μ) / δ = (19.2 - 20.9) / 5.9 = -0.2881
Looking up the area to the left of z = -0.2881 in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.3869. So P(x < 19.2) is 0.3866.
b. To find P(18.8 < x < 23.0), we need to find the area under the normal distribution curve between x = 18.8 and x = 23.0. Again, we can standardize the values of x and use a standard normal distribution table or calculator:
z1 = (18.8 - 20.9) / 5.9 = -0.3559
z2 = (23.0 - 20.9) / 5.9 = 0.3559
Looking up the area between z1 = -0.3559 and z2 = 0.3559 in a standard normal distribution table or using a calculator, we find that the probability is approximately0.27808. So P(18.8 < x < 23.0) is 0.27808.
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The table gives the average number of days of rain in each month of the year. Find the mode of the given data. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Days of Rain 6 7 10 10 11 12 10 10 9 7 7 6 A. 7 B. 7 and 10 C. 9.5 D. 10
Answers
The mοde value fοr the table οf data given is οptiοn D. 10.
What is mοde?A mοde is described as the value in a grοup οf values that οccurs mοre frequently. The value that appears the mοst frequently is this οne.
The mοde is nοt necessarily unique tο a given discrete distributiοn, since the prοbability mass functiοn may take the same maximum value at several pοints x1, x2, etc. The mοst extreme case οccurs in unifοrm distributiοns, where all values οccur equally frequently.
The data is given fοr the average number οf days οf rain in each mοnth οf the year.
The mοde will the number οf days repeating itself mοre number οf times.
It can be seen that 10 is repeated 4 times amοng the data given.
Therefοre, the mοde value is 10.
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You are a real estate broker for Aurora Realty. One of your clients, Erica Heston, has agreed to purchase one of the homes your office has listed for sale for a negotiated price of $235,000. The down payment is 20%, and the balance will be financed with a 15-year fixed-rate mortgage at 8.75% and discount points. The annual property tax is $5,475, and the hazard insurance premium is $2,110. When Erica signed the original contract, she put down a deposit of $5,000, which will be credited to her down payment. In addition, at the time of closing, Erica must pay the following expenses:
Appraisal lee - $215
Credit report - $65
Roof inspection - $50
Mortgage insurance premium - 1/2% of amount financed
Title search - $125
Altorney's fees - $680
Escrow fee - $210
Prepaid interest - $630
Answers
The total monthly PITI of the mortgage loan, given the principal and the tax, would be $ 2, 512.08.
How to find the monthly PITI?To find the monthly PITI, you first need to find the principal and interest portion by the formula :
= Amount financed / 1, 000 x factor for 8.75%, 15 years
= 188, 000 / 1, 000 x 10
= $ 1, 880
The monthly tax and insurance portion would be:
= ( Estimated property tax + Annual insurance ) / 12
= ( 5, 475 + 2, 110 ) / 12
= $ 632.08
The monthly PITI on the mortgage loan is therefore :
= 1, 880 + 632.08
= $ 2, 512.08
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The question is:
What is the total monthly PITI of the mortgage loan?
The circumference of a circle is 6π ft. What is the area, in square feet? Express your answer in terms of
�
π.
Answers
Answer:
9π
Step-by-step explanation:
circumference=6ft
radius=3ft
radius squared=9ft
area=9ft ×π
area=9π
A 2-pound bag of corn costs $3.20. What is the price per ounce?
Answers
Answer:
$0.10
Step-by-step explanation:
2 pound = 32 ounces
32 ounces = $3.20
What is the price per ounce?
3.20 / 32 = $0.10
So, the price per ounce is $0.10
To promote his new business, Claudio made 300 tamales to give to pedestrians. The expression above describes the number of tamales remaining after passing out samples to p pedestrians. If Claudio passed out samples to 160 pedestrians, how many tamales would remain?
Answers
The answer is 140 tamales would remain.
What is an expression?An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, among others. It is a mathematical phrase that represents a value or a set of values when evaluated.
We are given that Claudio made 300 tamales to give to pedestrians. Let the number of tamales Claudio passed out to pedestrians be represented by p.
If we assume that Claudio passed out p tamales, then the number of tamales remaining would be:
300 - p
If Claudio passed out samples to 160 pedestrians, then the number of tamales remaining would be:
300 - 160 = 140
Therefore, 140 tamales would remain.
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2x + 3y = 8
-4x + 6y = 8
X-Z = -4
Nilai x+y+z adalah
Answers
Answer:
0
Step-by-step explanation:
Untuk menyelesaikan masalah ini, kita perlu menyelesaikan sistem persamaan linear dua variabel pertama dan sistem persamaan linear tiga variabel:
Sistem Persamaan Linear Dua Variabel:
2x + 3y = 8 ... (1)
-4x + 6y = 8 ... (2)
Untuk menyelesaikan sistem persamaan ini, kita dapat menggunakan metode eliminasi:
Langkah 1: Kalikan Persamaan (1) dengan 2 dan Persamaan (2) dengan 1. Kita memperoleh:
4x + 6y = 16 ... (3)
-4x + 6y = 8 ... (4)
Langkah 2: Tambahkan Persamaan (3) dan Persamaan (4). Kita memperoleh:
12y = 24
Langkah 3: Bagi kedua sisi dengan 12. Kita memperoleh:
y = 2
Langkah 4: Substitusikan y = 2 ke dalam Persamaan (1) atau (2). Kita memperoleh:
2x + 3(2) = 8
2x + 6 = 8
2x = 2
x = 1
Jadi, solusi dari sistem persamaan linear dua variabel adalah (x, y) = (1, 2).
Sistem Persamaan Linear Tiga Variabel:
x - z = -4 ... (5)
x + y + z = ?
2x + 3y = 8
Untuk menyelesaikan sistem persamaan ini, kita dapat menggunakan metode substitusi:
Langkah 1: Substitusikan x = 1 dan y = 2 dari sistem persamaan linear dua variabel ke dalam Persamaan (3). Kita memperoleh:
2(1) + 3(2) = 8
2 + 6 = 8
8 = 8
Langkah 2: Substitusikan x = 1 dari sistem persamaan linear dua variabel ke dalam Persamaan (5). Kita memperoleh:
1 - z = -4
z = 5
Langkah 3: Substitusikan x = 1 dan z = 5 ke dalam Persamaan (6). Kita memperoleh:
1 + y + 5 = ?
y = -6
Jadi, solusi dari sistem persamaan linear tiga variabel adalah (x, y, z) = (1, -6, 5).
Maka nilai x + y + z adalah:
x + y + z = 1 + (-6) + 5 = 0
Jadi, nilai x + y + z adalah 0
The triangle show below may not be congruent 
Answers
Answer:
Step-by-step explanation:
This is another question. It's not related to this question. Sorry.Wills mobile contract gives him 700 minutes of calls each month. Will made 113 minutes of calls during the first week how much call time does he have left during this month? give your answer in hours and minutes. How much total call time does wills phone have in the first 7 months. Give your answer in days hours and minutes
Answers
Will has 587 mins (9h 47m) of call time left for the month and used 791 mins (13h 11m) in the first 7 months. He has 4,909 mins (81h 49m) left for the remaining 5 months. His phone has 5,700 mins (95d 4h 20m) of call time in a year.
Will has 587 minutes of call time left for the rest of the month, which is 9 hours and 47 minutes (587/60). In the first 7 months, Will has used 791 minutes (113 minutes per month for 7 months), which is 13 hours and 11 minutes. He has 4,909 minutes (7 months x 700 minutes per month - 791 minutes used) or 81 hours and 49 minutes left for the remaining 5 months. In total, Will's phone has 5,700 minutes (12 months x 700 minutes per month) or 95 days, 4 hours and 20 minutes of call time in a year.
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At an ice cream shop, the cost of 4 milkshakes and 2 ice cream sundaes is $23.50. The cost of 8 milkshakes and 6 ice cream sundaes is $56.50.
Order the steps below for solving this system of linear equations using the elimination method.
Write the correct number, 1 for first through 4 for last, in front of each step listed.
Choices: Solve for y, Substitute the value for y into one of the equations to determine the value of x, Subtract from the other equation, and Multiply the equation 4x + 2y = 23.50 by 2.
Step 1:
Step 2:
Step 3:
Step 4:
Answers
x = 3.375 and y = 5 provide the system of equations' answer.
How Do You Solve an Equation System?The process of figuring out the unknown variables while keeping the equations balanced on both sides is known as the system of equations method. We solve an equation system by identifying the value of the variable that makes the condition of all the provided equations true. There are numerous methods for solving a system of equations.
Multiply the equation 4x+2y=23.50 by 2.
From the other equation, subtract.
Calculate y using a solution.
To find the value of x, substitute the value for y into one of the equations.
To eliminate one variable (either x or y) while utilising the elimination method, the equations are added or subtracted.
To start, we can multiply the first equation by 2 to get rid of the 2y term:
8x + 4y = 47
Next, we can subtract the second equation from this equation to eliminate the 8x term:
2y = 10
y = 5
Now that we have solved for y, we can substitute this value into one of the original equations (let's use the first one) to solve for x:
4x + 2(5) = 23.50
4x + 10 = 23.50
4x = 13.50
x = 3.375
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\Graph the following system of equations.
y = 3x + 9
6x + 2y = 6
What is the solution to the system?
There is no solution.
There is one unique solution (−1, 6).
There is one unique solution (0, 3).
There are infinitely many solutions. (not this one already checked)
Answers
The solution to the system of equations. is (x, y) = (-1, 6).
What is a System of Equations?Simplifying this equation, we get:
6x + 6x + 18 = 6
12x + 18 = 6
Subtracting 18 from both sides:
12x = -12
Dividing both sides by 12:
x = -1
Now that we know x = -1, we can substitute this value into either equation to find y. We'll use the first equation:
y = 3x + 9
y = 3(-1) + 9
y = 6
Therefore, the solution to the system is (x, y) = (-1, 6).
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Mr. Denson has a square shaped patio enclosed with a fence. The entire length of the fence around the perimeter of the patio is 72 meters. What is the area of his square-shaped patio?
Answers
The area of Mr. Denson's square-shaped patio that enclosed the fence is 324 m².
What is the area?The area is represented as the number of unit squares that cover the surface of an enclosed figure or object, measured in square units like cm² and m².
The area is the product of the two sides (length and breadth).
The perimeter of a square = 4a, where a is one length of the square.
If 4a = 72 meters, a = 18 meters (72/4).
The area of the square-shaped patio = 324 m² (18 x 18).
Thus, Mr. Denson should know that his square-shaped patio has an area of 324 m².
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find W (hypotenuse) if the angle is 15 degrees and the opposite side has a length of 7 cm
Answers
[tex]\sin(15^o )=\cfrac{\stackrel{opposite}{7}}{\underset{hypotenuse}{h}}\implies h=\cfrac{7}{\sin(15^o )}\implies h\approx 27.05[/tex]
Make sure your calculator is in Degree mode.
Answer: W ≈ 16.6
Step-by-step explanation:
The Pythagorean Theorem equation is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] =[tex]c^{2}[/tex]
First do [tex]15^{2} +7^{2} =w^{2}[/tex]
Which equals [tex]274=w^{2}[/tex]
Then do[tex]\sqrt{274} =w[/tex]
so w ≈ 16.6
It takes 3 people 4 hours to paint a wall. Assume that all people paint at the same rate. B) How long would it take 5 people to paint the same wall? Give your answer in hours and minutes
Answers
It would take 5 people to paint the same wall is 1 hour and 20 minutes or 1:20.
It is clear that workers twice as fast as people when painting the same surface. This means that John will always draw twice as much area as people at any given time if they are working at the same time. So if they plan well and finish painting the room at the same time, John will paint twice as much area as people.
There is only one possibility:
3 people = 4 hours
Divide by 3.
1 person = 4/3 or 1 1/3 hours
There are 60 minutes in 1 hour. Multiply 1/3 by 60.
(1/3)× 60 = 60/3 = 20
1/3 of an hour is 20 minutes.
It would take 1 person 1 hour and 20 minutes to paint the wall
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At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter
Answers
The initial fee per meter is $110.
Although the fundamentals of speed, time, and distance stay the same, the kind of problems posed in exams may vary.
Most of the time, applicants will be given 1-2 word problems based on Speed, Time, and Distance, but they should also be prepared for questions on data sufficiency and data interpretation based on the TDS (Time, Distance, and Speed) theme.
At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.
F(d) models the fee (in dollars) for climbing d meters.
F(d)=110+0.12d
To find the initial amount, substitute d=0 int the above function, and we get
F(0)=110+0.12(0)=110
Hence, the initial fee is $110.
The complete question is-
At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.F(d)models the fee (in dollars) for climbing d meters. F(d)=110+0.12d. What is the initial fee?
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Find the measure of each bolded arc. Round to the nearest hundredth.
Answers
The length of the shaded arc is 68.71 metres squared.
How to find the length of an arc?The arc of a circle is defined as the part or segment of the circumference of a circle. Therefore, the length of the bolded arc can be found as follows:
length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleTherefore,
r = 26 / 2 = 13 m
∅ = 360 - 57 = 303 degrees
length of an arc = 303 / 360 × 2 × 3.14 × 13
length of an arc = 24736.92 / 360
length of an arc = 68.7136666667
length of an arc = 68.71 metres squared
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Many families in California are using backyard structures for home offices, art studios, and hobby areas as well as for additional storage. Suppose that the mean price for a customized wooden, shingled backyard structure is $3100. Assume that the standard deviation is $1200.
a. What is the z-score for a backyard structure costing $2300?
b. What is the z-score for a backyard structure costing $4900?
c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.
d. If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier? Explain.
Answers
The z-score is a measure of how many standard deviations a data point is from the mean. It can be calculated using the formula
z = (x - μ) / σ,
where x is the data point, μ is the mean, and σ is the standard deviation.
a. The z-score for a backyard structure costing $2300 can be calculated as follows:
z = (2300 - 3100) / 1200 = -800 / 1200 = -0.67
b. The z-score for a backyard structure costing $4900 can be calculated as follows:
z = (4900 - 3100) / 1200 = 1800 / 1200 = 1.
c. The z-score in part (a) is -0.67, which means that the backyard structure costing $2300 is 0.67 standard deviations below the mean. The z-score in part (b) is 1.5, which means that the backyard structure costing $4900 is 1.5 standard deviations above the mean. Neither of these z-scores are extreme enough to be considered outliers, as they are both within 2 standard deviations of the mean.
d. The z-score for the backyard shed-office combination costing $13,000 can be calculated as follows:
z = (13000 - 3100) / 1200 = 9900 / 1200 = 8.25
This z-score is much larger than 2, which means that the structure costing $13,000 is more than 8 standard deviations above the mean. This is an extreme value and should be considered an outlier.
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