Answer:
1) choice B, they are equal in length
2) choice A, theyre equal in length
3) Choice D, (-3,0) (-3, -3) (-1, -3)
4) Choice A, Clockwise 90- degree rotation
Step-by-step explanation:
The statements which describe A'B' is:
A'B' and AB are equal in length ⇒ (B)
Step-by-step explanation:
Let us take about reflication:
⇒ Reflections are mirror images, means the shape or the size of
the figure does not affect by reflection, think of "folding" the
graph over the y-axis or the x-axis
⇒ On a grid, you used the formula (x, y) → (-x, y) for a reflection in
the y-axis and used the formula (x, y) → (x, -y) for a reflection in
the x-axis.
In our question segment AB, where A = (1, 3) and B = (5, 3) is
reflected about the y-axis
By using the rule above
∴ A' =(-1, 3)
∴ B' = (-5,3)
∵ Reflection does not change the shape or the size of the original figure
∴ Line segment A'B' has the same length of line segment AB
The correct answer is:
A'B' and AB are equal in length
You can check your answer by finding the lengths of AB and A'B'
∵ The length of AB = 5 - 1 = 4 units
∵ The length of A'B' = -1 - (-5) = -1 + 5 = 4 units
∴ AB = A'B'
Note:
If the y-coordinates of two points are equal, then the line joining them is horizontal and its length is the difference between the x-coordinates of the two points.
278÷3 in one decimal place
Answer:
92.6! Hope this helps.
Step-by-step explanation:
-lei
Sir Ronald Fisher's F-distribution is used in many statistical tests. Which one of the following uses the F-distribution for their test statistic?
a. To compare several population means simultaneously
b. Comparison of samples to see if they came from populations with the same proportions.
c. Test of two samples to see if they are from populations with the same median
The one which uses Sir Ronald Fisher's F-distribution for the test statistic is to compare several population means simultaneously.
What is the F-distribution?The F-distribution was developed by Sir Ronald Fisher to study the behavior of two variances from random samples taken from two independent normal populations. The F-distribution allows us to use a F statistic to compare two populations.
The F-distribution is also known as a right-skewed distribution used commonly in another statistical test called an Analysis of Variance (ANOVA). For ANOVA tests we can use the F-distribution to check whether the variance among the means of two populations significantly differ. The F-distribution can also be used in regression analysis to compare the fit of different models.
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Which inequality does this graph show? A. y > 0 B. y < 0 C. D.
Answer: The answer is B) y < 0
Answer: B
Step-by-step explanation:
what’s the area of this figure, rounded to the nearest tenth?
Answer:
198 in²
Step-by-step explanation:
triangle (A=1/2)bh [A=1/2(22×8)] b=22 H=8
rectangle (A=bh) [A= 22×5] B=22 H=5
triangle = 88
rectangle = 110
So, 88+110 = 198
The number of dogs Corey can wash varies directly with the amount of time he spends washing dogs. Corey can wash 12 dogs in 2 hours.
How many dogs can Corey wash in 8 hours?
Enter your answer in the box.
dogs
Answer:
corey can wash 48 dogs in 8 hours
Step-by-step explanation:
we know that he can wash 12 dogs in 2 hours. we need to know how many dogs he can wash in 1 hour, to do that we take the 12 dogs divided by 2 hours
12/2 = 6 dogs
he can wash 6 dogs in 1 hour
to find out how many dogs he can was in 8 hours you take number of dogs per hour times amount of time given.
6dogs * 8 hours= 48 dogs
b.The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank). c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time____ (mins) (enter the numbers only)
(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.
To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.
If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).
If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.
Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).
(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.
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Complete question:
The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.
(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).
c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)
If profits decrease by 13.8% when the degree of operating
leverage (DOL) is 3.8, then the decrease in sales is:
A) 0.28%
B) 0.52%
C) 3.63%
D) 10%
E) 52.44%
Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.
The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.
Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8
= -13.8% / x Thus, we have: x
= -13.8% / 3.8
= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage
= 13.8 / 3.8
= 3.63% The percentage decrease in sales is 3.63%.
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Determine wheter each regular polygon tessellates the plane. Explain. equilater triangle. a) yes; measure of interior angle = 60deegres. b) no; measure of interior angle = 60deegres. c) yes; measure of interior angle = 120deegres. d) no; measure of interior angle = 120deegres. please select the best answer from the choices provided
The correct answer is (a) yes; the equilateral triangle tessellates the plane.
A tessellation is a tiling of the plane using one or more geometric shapes without any gaps or overlaps. For a regular polygon to tessellate the plane, the sum of its interior angles must be a multiple of 360 degrees.
For an equilateral triangle, each angle measures 60 degrees, so the sum of the angles in a triangle is 180 degrees. Therefore, the sum of the interior angles in a tessellation of equilateral triangles must be a multiple of 180 degrees.
Since the measure of the interior angle of an equilateral triangle is 60 degrees, we can tile the plane with equilateral triangles meeting at each vertex. At each vertex, the sum of the interior angles of the three triangles is 180 degrees, so the tessellation meets the requirement that the sum of the interior angles is a multiple of 360 degrees.
Therefore, the answer is (a) yes; the equilateral triangle tessellates the plane.
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Filling swimming pools A hose can fill a swim-
ming pool in 6 hours. Another hose needs 3 more
hours to fill the pool than the two hoses combined.
How long would it take the second hose to fill the
pool
Answer:
I think it would take it 9 hours
Kylie works as a salesperson at an electronics store and sells phones and phone accessories. Kylie earns a $15 commission for every phone she sells and a $2 commission for every accessory she sells. On a given day, kylie made a total of $352 in commission and sold 6 more accessories than phones. Determine the number of phones sold and the number of accessories sold.
The number of phones sold would be 20
And, the number of accessories sold would be 26.
Used the concept of an equation that states,
An equation is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
Given that,
Kylie earns a $15 commission for every phone she sells and a $2 commission for every accessory she sells.
And, On a given day, Kylie made a total of $352 in commission and sold 6 more accessories than phones.
Let us assume that,
The number of phones sold = x
And, the number of accessories sold = y
Hence, the equation becomes,
15x + 2y = 352 .. (i)
And, y = x + 6 .. (ii)
Substitute the value of y in (i);
15x + 2y = 352
15x + 2 (x + 6) = 352
15x + 2x + 12 = 352
17x + 12 = 352
17x = 352 - 12
17x = 340
x = 340/17
x = 20
From (ii);
y = x + 6
y = 20 + 6
y = 26
Therefore, The number of phones sold = 20
And, the number of accessories sold = 26
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write each of the following numbers in words 7070 75
Answer:
7070- Seven thousand seventy/Seven thousand and seventy
75- Seventy five
Step-by-step explanation:
7070- Seven thousand seventy/Seven thousand and seventy
75- Seventy five
Y-3 = 5(X-2) in standard form
Answer:
5x-y=7
Step-by-step explanation:
y-3=5(x-2)
y-3=5x-10
y=5x-10+3
y=5x-7
5x-y=7
f(x)=5sinx+cosx then f ′
(x)=−5cosx−sinx Select one: True False
False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.
To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).
Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.
Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:
f'(x) = 5cos(x) - sin(x).
This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).
In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).
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What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
The area of the triangle is 48. 75 in²
How to determine the valueTo determine the value of the area, we need to know the following
The sum of the interior angles of a triangle is 180 degreesA triangle has three sidesIt has three anglesAlso, the formula for calculating the area of a triangle is expressed as;
A = 1/2bh
Such that the parameters are expressed as;
A is the area of the triangleb is the baseh is the heightSubstitute the values, we have;
Area = 1/2 × 13 × 7.5
Multiply the values, we get;
Area = 97.5/2
Divide
Area = 48. 75 in²
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Suppose f(x,y,z) = In(x + 2y2 + 3z"). Find the following partial derivatives. a. fx b. fz c.d2f/dzdx.
The partial derivatives are as follows :
(a) fx = 1 / (x + 2y^2 + 3z^3)
(b) fz = 3z^2 / (x + 2y^2 + 3z^3)
(c) d^2f/dzdx = -3z^2 / (x + 2y^2 + 3z^3)^2
To find the partial derivatives of the function f(x, y, z) = ln(x + 2y^2 + 3z^3), we differentiate with respect to each variable while treating the other variables as constants.
(a) Partial derivative with respect to x (fx):
To find fx, we differentiate the function f(x, y, z) with respect to x while treating y and z as constants. The derivative of ln(u) with respect to u is 1/u, so we have:
fx = d/dx ln(x + 2y^2 + 3z^3) = 1 / (x + 2y^2 + 3z^3)
(b) Partial derivative with respect to z (fz):
To find fz, we differentiate the function f(x, y, z) with respect to z while treating x and y as constants. Again, applying the derivative of ln(u), we get:
fz = d/dz ln(x + 2y^2 + 3z^3) = 3z^2 / (x + 2y^2 + 3z^3)
(c) Second partial derivative with respect to z and x (d^2f/dzdx):
To find d^2f/dzdx, we differentiate fz with respect to x while treating y and z as constants. We differentiate fx with respect to z while treating x and y as constants, and then take the derivative of the result with respect to z. It can be written as:
d^2f/dzdx = d/dx (d/dz ln(x + 2y^2 + 3z^3)) = d/dx (3z^2 / (x + 2y^2 + 3z^3))
= -3z^2 / (x + 2y^2 + 3z^3)^2
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If a pizza that is 12 inches in diameter provides three full meals, how many meals are provided by a pizza that is 20 inches in diameter?
Answer:
If 12 inches in diameter can provide 3 full meals then it's obvious that one meal is 4 inches in diameter. So 20 would give 5 full meals.
Step-by-step explanation:
Yeah
Last year there were 45 memebers of the tennis club at Marks Middle school. This year although the number of boys increeased by 20%, the number of girls decresed by 20%, the total numbers decresed by 1. Find how many boys anf girls are in the tennis club this year.
Answer:
24 boys & 20 girls
Step-by-step explanation:
Last year:
Number of boys = x
Total number = 45
Number of girls = 45 - x
An increase of 20% is the same as multiplying by 1.2
A decrease of 10% is the same as multiplying by 0.8
This year:
New number of boys: 1.2x
New number of girls: 0.8(45 - x)
New total number = 45 - 1 = 44
1.2x + 0.8(45 - x) = 44
1.2x + 36 - 0.8x = 44
0.4x + 36 = 44
0.4x = 8
x = 20
Last year there were 20 boys and 25 girls.
This year there are 20 * 1.2 = 24 boys
and 44 - 24 = 20 girls
Answer: 24 boys & 20 girls
What is the monthly repayment on the following hire-purchase agreement? A colour TV costs £640. The deposit was £200. The interest rate was 10% p.a. and it was paid off in two years.
The monthly repayment on the following hire-purchase agreement is £22.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a colour TV costs £640. The deposit was £200. The interest rate was 10% p.a. and it was paid off in two years.
The monthly repayment will be calculated as,
Total interest for two years = ( 640 - 200 ) x 1.2
Total interest for two years = ( 440 x 1.2 )
Total interest for two years = £528
The value of monthly repayment = 528 / 24 = £22
Therefore, the monthly repayment on the following hire-purchase agreement is £22.
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Find the Sine, cosine, tangent of - 120
Solution
Find the Sine, cosine, tangent of - 120
\(\sin (-120)\)\(\begin{gathered} \mathrm{Use\: the\: following\: property\colon}\: \sin \mleft(-x\mright)=-\sin \mleft(x\mright) \\ \sin \mleft(-120^{\circ\: }\mright)=-\sin \mleft(120^{\circ\: }\mright) \\ =-\sin \mleft(120^{\circ\: }\mright) \\ =-\frac{\sqrt{3}}{2} \end{gathered}\)\(\cos (-120)\)please help asap !! : (((((
Answer: it is 65%
Step-by-step explanation:
Find the value of the X, Triangle Similarity
Answer:
x = 22.5
Step-by-step explanation:
the segment from the vertex to the base is an angle bisector and divides the opposite side ( base) into segments that are proportional to the other two sides, that is
\(\frac{9}{x-9}\) = \(\frac{12}{18}\) = \(\frac{2}{3}\) ( cross- multiply )
2(x - 9) = 27
2x - 18 = 27 ( add 18 to both sides )
2x = 45 ( divide both sides by 2 )
x = 22.5
Given a number is a whole number, write an expression to describe the preceding whole number.
The expression which represents a whole number which is the preceding number to a whole number x is; x-1.
What are whole numbers?Whole numbers are a class of numbers which are otherwise termed, Integers. Furthermore, Integers number values include, 1, 5 and -3 among a host of other numbers.
Hence, if the actual number is; x, then it follows that the number which precedes x is such that it is less than x by 1 unit.
Ultimately, the required preceding number is; x-1.
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identify the constant that can be multiplied by both sides of the first equation to eliminate the variable x when the equations are added together.
The first equation can be multiplied by –12 and the second equation by 5 to eliminate x
According to the question,
The system of the equation is
5x + 13y = 232
12x + 7y = 218
We have to find the constant that can be multiplied by both sides of the first equation to eliminate the variable x when the equations are added together
So, to eliminate the x variable , the coefficient of x should be same
To make Same coefficient we have to multiple -12 to the equation one
and multiple 5 to equation 2
So , after multiplication
-60x -156y = -2784
60x + 35y = 1090
Adding now,
-60x -156y + 60x + 35y = 1090 - 2784
=> - 121y = -1694
=> y = 0.071
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A car requires 45 liters of petrol to travel a distance of 330 km.
1) the distance that the car can travel on 85 liters of petrol
2) the amount of petrol that the car owner has to pay to travel a distance of 990km if a liter of petrol costs $ 2.25.
Answer:
1) The car can travel 623.3 km with 85 liters of petrol.
2) The car owner has to pay $303.8.
Step-by-step explanation:
1) The distance traveled with 85 L of petrol can be found as follows:
\( d = \frac{330 km}{45 L}*85 L = 623.3 km \)
Hence, the car can travel around 623 km with 85 liters of petrol.
2) If the liter of petrol costs $2.25, then the amount of petrol that the car owner has to pay to travel a distance of 990 km is:
\(x = \frac{\$ 2.25}{1 L}*\frac{45 L}{330 km}*990 km = \$ 303.8\)
Therefore, the car owner has to pay $303.8.
I hope it helps you!
y^2+13y=-36
solve for x
please show work
Answer:
y = -9 or y = -4
Step-by-step explanation:
y^2 + 13y = -36
y^2 + 13y + 36 = 0
(y + 9)(y + 4)
y + 9 = 0
y = -9
y + 4 = 0
y = -4
Best of Luck!
Assignment Responses/submit/dep 29213268&tagswautosaved question4780406_8 Need Help Read it 9. [2/3 Points] DETAILS PREVIOUS ANSWERS SCALCETI 6.2.021. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, x = y; about y = 1 3 V 10" X Sketch the region. སུ་ e. X 2 2 - 1 -1
The volume V of the solid obtained by rotating the region bounded by the given curves about the specified line is π/243 cubic units.
To sketch the region, we first plot the curves y = x^2 and x = y. We can see that the region is bound by the curves y = x^2, x = y, and the x-axis between x = 0 and x = 1.
To rotate this region about y = 1/3, we need to translate the entire region up by 1/3 units. This gives us the following solid of rotation:
We can see that the resulting solid is a cone with its tip at the point (0, 1/3) and its base on the plane y = 4/9. To find the volume of this solid, we can use the formula for the volume of a cone:
V = (1/3)πr^2h
where r is the radius of the base and h is the height of the cone.
To find the radius, we need to find the distance between the point (0, 1/3) and the curve x = y. This gives us:
r = y - 1/3
To find the height, we need to find the distance between y = x^2 and the plane y = 4/9. This gives us:
h = 4/9 - x^2
We can express both r and h in terms of x, since x is the variable of integration:
r = y - 1/3 = x^2 - 1/3
h = 4/9 - x^2
Now we can substitute these into the formula for the volume:
V = ∫₀¹ (1/3)π(x^2 - 1/3)^2(4/9 - x^2) dx
Simplifying this integral is a bit messy, but doable with some algebraic manipulation. The final result is: V = π/243
Therefore, the volume of the solid obtained by rotating the region bounded by y = x^2, x = y, and the x-axis between x = 0 and x = 1 about y = 1/3 is π/243 cubic units.
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The population of the United States from 1790 to 1860 is given by the following formula, where t is years since 1790 and N is the population, in millions. N = 3.93 x 1.03 (a) What was the population in 1790? million 3.93 (b) Express the population in 1820 using functional notation. N 70 (c) Calculate the value of the population in 1820. (Round your answer to two decimal places.) x million 31.12
a. the population in 1790 was 3.93 million. b. the population in 1820 can be expressed as N = 3.93 x 1.03^t, where t is the number of years since 1790. c. the population of the United States in 1820 was approximately 31.12 million.
(a) To find the population in 1790, we plug in t = 0 into the given formula:
N = 3.93 x 1.03^0 = 3.93
Therefore, the population in 1790 was 3.93 million.
(b) To express the population in 1820 using functional notation, we plug in t = 30 into the given formula:
N = 3.93 x 1.03^30
Therefore, the population in 1820 can be expressed as N = 3.93 x 1.03^t, where t is the number of years since 1790.
(c) To calculate the value of the population in 1820, we plug in t = 30 into the formula and round to two decimal places:
N = 3.93 x 1.03^30 ≈ 31.12
Therefore, the population of the United States in 1820 was approximately 31.12 million.
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PQ= RQ and PS= RS a=?
The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.
What are interior angles?In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.
Given:
The length of the segment PQ is equal to the length of the segment RQ.The length of the segment PS is equal to the length of the segment RS.The following steps can be used in order to determine the measure of angle a:
Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.
Step 2 - Apply the sum of interior angle property on triangle PQR.
\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)
\(\angle\text{Q}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-60\)
\(\angle\text{R}=60^\circ\)
Step 3 - Now, apply the sum of interior angle property on triangle PSR.
\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)
\(\angle\text{S}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-90\)
\(\angle\text{R}=45^\circ\)
Step 4 - Now, the measure of angle a is calculated as:
\(\angle\text{a}=60-45\)
\(\angle\text{a}=15\)
The measure of angle a is 15 degrees.
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what is the distance along the unit circle between any two successive 8th roots of 1?
a. π/8
b. π/6
c. π/4
d. π/2
The distance along the unit circle between any two successive 8th roots of 1 is c) π/4.
To find the distance along the unit circle between any two successive 8th roots of 1, we can consider the concept of angular displacement.
Each 8th root of 1 represents a point on the unit circle that is evenly spaced by an angle of 2π/8 = π/4 radians.
Starting from the point corresponding to 1 on the unit circle, we can move π/4 radians to reach the first 8th root of 1. Moving π/4 radians further will bring us to the second 8th root of 1, and so on.
Since we are moving by π/4 radians for each successive 8th root of 1, the distance between any two successive 8th roots of 1 is π/4 radians.
Therefore, the correct answer is option c. π/4.
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can some one help me this please?
Answer:
x=-2
Step-by-step explanation: