On a coordinate plane, point b(–6, 1) is translated to b prime(–3, –2). indira uses these steps to find a rule to describe the translation. step 1 substitute the original coordinates and the translated coordinates into (x, y) right-arrow (x a, y b): b (negative 6, 1) right-arrow b prime (negative 6 a, 1 b) = b prime (negative 3, negative 2) step 2 write two equations: negative 6 a = negative 2. 1 b = negative 3. step 3 solve each equation: negative 6 a = negative 2. a = negative 2 6. a = 4. 1 b = 3. b = negative 3 minus 1. b = negative 4. step 4 write the translation rule: (x, y) right-arrow (x 4, y minus 4) which corrects indira’s first error? indira should have substituted b (negative 6, 1) right-arrow b prime (negative 3 a, negative 2 b) = b prime (negative 6, 1) in step 1. indira should have written the equations negative 6 a = negative 3 and 1 b = negative 2 in step 2. indira should have solved the equations to find that a = negative 8 and b = negative 2 in step 3. indira should have written the translation rule (x, y) right-arrow (x minus 4, y 4) in step 4.

Answers

Answer 1

Indira should have written the equation negative 6 + a = negative 3, and the equation 1 + b = negative 2 in step 2, as according to coordinate geometry.

For translation from point B(-6,1) to  point B'(-3,-2);

Step 1 : Substitute the original coordinates and the translated coordinates into (x,y) → (x+a,y+b) ; B (negative 6,1) → B prime (negative 6 + a, 1 + b) = B prime (negative 3, negative 2)

Step 2 ( Indira's mistake) : Two equations to be written, as in coordinate geometry; first one being negative 6 + a = negative 3 ; and the second one being 1 + b = negative 2

Step 3 : Solving the equations to get the values of a and b;

a = negative 3 + 6

a = 3, and

b = negative 2 minus 1

b = -3

Step 4 : By substitution method, using values of a and b we find B prime;

original coordinates of point B = (-6,1)

Translated coordinates of point B' = (-6 + a, 1 + b)

                                                          = ((-6) + 3 , 1 + (-3))            

                                                           = (-3,-2)

Thus, that is how, step-by-step using basic linear equation method, we solved for translated coordinates.

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Related Questions

The coefficient of x^7 in the expression (x^3+4/x^2)^4 is

Answers

The coefficient of x⁷ in the given expression is 16.

What are Expressions?

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given is the expression [x³ + (4 / x²)]⁴.

[x³ + (4 / x²)]⁴ =  (x³ + 4x⁻²)⁴

                      = (x³ + 4x⁻²)² (x³ + 4x⁻²)²

                      = (x⁶ + 8x + 16x⁻⁴) (x⁶ + 8x + 16x⁻⁴)  

                      = x¹² + 8x⁷ + 16x² + 8x⁷ + 64x² + 128x⁻³ + 16x² + 128x⁻³ +

                         256x⁻⁸

Rearranging with like terms, we get,

                      = x¹² + 16x⁷ + 96x² + 256x⁻³ + 256x⁻⁸

Hence the coefficient of x⁷ is 16.

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X, Y and Z form the vertices of a triangle, where

YXZ = 57°,

YZX = 47°, and XZ = 7.2cm.
Calculate the length of YZ rounded to 1 DP

Answers

Answer:

Step-by-step explanation:

Find the area of the following figure. Pictures are not drawn to scale. Round answers to the nearest tenth.

Answers

The area of the trapezium is 36.3 unit squared.

How to find area of a figure?

The figure above is a trapezium. Therefore, the area of a trapezium can be represented as follows:

Hence,

area of a trapezium = 1 / 2 (a + b)h

where

h = heighta and b are the top and base of the trapezium

Therefore,

area of a trapezium = 1 / 2 (a + b)h

where

a = 4b = 7 + 1.5 = 8.5

Using Pythagoras's theorem,

c² = a² + b²

where

a and b are the legsc is the hypotenuse

h² = 6² - 1.5²

h²= 36 - 2.25

h = √33.75

h = 5.80947501931

h = 5.81

Therefore,

area of the trapezium = 1 / 2 (4 + 8.5)5.8

area of the trapezium = 1 / 2 (12.5)5.8

area of the trapezium = 72.5 / 2

area of the trapezium = 36.3 units²

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What is 1800 * ? * 1 = 198

Answers

1800 * ? * 1 = 198

let x be the ?

By shifting 1800*1 into right hand side

x= 198/1800

x= 11/100= 0.11

Final answer = 0.11

Chris is buying a yard of material for a art project. two stores have the material she needs. compare prices to find which material is the better. explain how you know


artistic supplies- $1.25ft

craft center- $3 yards

Answers

craft center because she would spend $1 a yard whereas artistic supplies it would cost $3.75 for a yard

How do you prove theorem 8.9 Class 9?

Answers

In the triangle the line segment joining the midpoints 'S' and 'T' of the sides PQ and PR implies that ST || QR.

As given in the question,

Diagram is attached.

As per the attached diagram  we have,

Given : In triangle PQR with midpoints S and T of sides PQ and PR respectively.

To prove : ST is parallel to QR.

Proof : First construct a line through R parallel to PQ such that it meet the extended line of ST at point 'U'

In triangle PST and triangle RTU,

PQ|| RU and SU is the transversal

∠PST ≅ ∠RUT ( alternate angles )

∠PTS ≅ ∠RTU ( vertically opposite angles)

PT ≅TR ( 'T' is the midpoint of PR )

By AAS we have

ΔPST ≅ΔRTU

By congruent part of congruent triangle we have,

PS ≅ RU

⇒ SQ ≅ RU

In quadrilateral QSUR,

SQ ≅ RU

SQ || RU ( as PQ || RU by construction )

Quadrilateral with one pair of opposite side congruent and parallel implies it is a parallelogram.

Quadrilateral QSUR is a parallelogram.

⇒ SU || QR

S - T - U

⇒ ST is parallel to QR

Therefore, in the given triangle line segment formed by joining the midpoints of the other two sides is parallel to third side.

The above question is incomplete , the complete question is :

Prove theorem 8.9 : The line segment joining the midpoints of the two sides of the given triangle is parallel to the third side .

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A student used the sieve of eratosthenes to find all prime numbers less than 100. create a step-by-step set of directions to show how to complete it. use the word bank to help guide your thinking as you write the directions. some words may be used just once more than once or not at all.please help i am lost

Answers

Utilizing the Sieve of Eratosthenes method is simple. In order to encircle the remaining numbers, we must cancel all multiples of each prime number starting with 2 (including the number 1, which is neither a prime nor a composite).

What the sieve of Eratosthenes to find all prime numbers?

The Sieve of Eratosthenes can be used to locate all prime numbers that are less than 100, as seen in the example below. In ten rows, start by writing the numbers 1 through 100.

Therefore, based on the preceding table, we can conclude that the prime numbers 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 are. There are ten prime numbers between 50 and 100 in all. The required prime numbers are those that are surrounded.

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(02.05 HC)
The functions f(x) = -(x + 4)2+2 and g(x) = (x - 2)2-2 have been rewritten using the completing-the-square method. Apply your knowledge of
functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning
X544
ΩΣ

Answers

For a quadratic function [tex]y=ax^2+bx+c[/tex], we know the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].

It is easy to see that for a function of the form [tex]y=a(x-h)^2+k[/tex], the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].

Therefore, the vertex of the graph of [tex]f(x)[/tex] is a maximum, and the vertex of the graph of [tex]g(x)[/tex] is a minimum.

a disabled sailboat is drifting in a straight line at 4 miles per hour. a coast guard rescue craft is trailing it by 11 miles, moving along the same path at a rate of 29 miles per hour. how long will it be before the rescue craft reaches the sailboat?

Answers

It will take the rescue craft 0.44 hours or 26.4 minutes to reach the sailboat.

The time required for the rescue craft to reach the sailboat can be calculated by using the formula for relative velocity:

Relative Velocity = Velocity of the Rescue Craft - Velocity of the Sailboat

= 29 mph - 4 mph = 25 mph

Therefore, the time required for the rescue craft to reach the sailboat is given by:

time= Distance/Relative Velocity

= 11 miles/25 mph

= 0.44 hours

Therefore, it will take the rescue craft 0.44 hours or 26.4 minutes to reach the sailboat.

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What is the volume, in cubic inches, of the cone below?

Answers

Answer:

27π

Step-by-step explanation:

Volume = 1/3πr²h
=1/3*(3)²9π
=27π

ace pharmaceutical has developed a drug that it believes will help lower cholesterol and blood pressure at a significantly greater rate than fish oil. researchers wish to test the new drug and compare the results to those of fish oil and of a placebo. a total of 300 volunteers suffering from hypertension and high cholesterol will participate in the study. part a explain how you would carry out this test in a completely randomized experiment.

Answers

The subjects would be randomized at random to receive the new medication, fish oil, or a placebo. The effectiveness of the new variance medicine would next be evaluated by comparing the outcomes of the various therapies.

The test would be conducted using a completely randomized experiment. This means that the 300 volunteers would be randomly assigned to the three different treatments: the new drug, fish oil, or the placebo. This ensures that any differences between the groups can be attributed to the treatments, and not any other factor. The volunteers would be monitored for a period of time, and the results of the treatments would be compared to determine the effectiveness of the new drug. This could be done through measuring changes in cholesterol and blood pressure levels, as well as any side effects of the treatments. In addition, the volunteers’ health and dietary habits should be monitored to ensure that any differences between the treatments are not caused by any other factors.

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What is formula data type?

Answers

Formula data type is used to determine different values based on a variety of fields in the existing table.

It also helps to create a pattern that takes input from all the fields and gives you the final value. Other fields include constants or functions and by using formula data type, you can remove the need to repeatedly enter the same information again and again. It also eliminated the margin of error that could occur during manual entry in the entirety of your work. Formula data type is used to help solve a combination of different equations that have different fields and/or equations.

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In the diagram, four squares of side length 2 are placed in the corners of a square of side length 6. Each of the points $W$, $X$, $Y$, and $Z$ is a vertex of one of the small squares. Square $ABCD$ can be constructed with sides passing through $W$, $X$, $Y$, and $Z$. What is the maximum possible distance from $A$ to $P$

Answers

In this problem, you have a square with side length 6 and four smaller squares with side length 2 placed in the corners. The points W, X, Y, and Z are the vertices of the smaller squares. The goal is to find the maximum possible distance between points A and P.

[asy] size(200); pair A,B,C,D,P,W,X,Y,Z; A=(0,4); B=(4,4); C=(4,0); D=(0,0); P=(2,2); W=(0,6); X=(6,6); Y=(6,0); Z=(0,0); draw(A--B--C--D--cycle); draw(W--X--Y--Z--cycle); draw(A--P--C); label("A",A,NW); label("B",B,NE); label("C",C,SE); label("D",D,SW); label("P",P,S); label("W",W,N); label("X",X,NE); label("Y",Y,S); label("Z",Z,SW); [/asy]

The point A is located on the bottom-left corner of the square with side length 6, and the point P is the center of the square $ABCD$. To find the maximum distance from A to P, we need to find the longest diagonal of the square $ABCD$.

The longest diagonal of a square is the one that goes from one corner of the square to the opposite corner. In this case, the longest diagonal goes from point A to point C, which is a distance of 6 units. Therefore, the maximum possible distance from A to P is 6 units.

you are driving on a highway and are about 140 miles from a state border. you set your cruise control at 60 miles per hour and plan to turn it off within 30 miles of the border on either side. find the minimum and maximum numbers of hours you will have cruise control on.you will travel at least hour(s) and at most hour(s) with cruise control on.

Answers

The minimum number of hours you will have cruise control on is 1.83 hour(s) and the maximum is 2.83 hour(s).

To find the minimum and maximum numbers of hours you will have cruise control on, you need to calculate the distance you will travel with cruise control on and divide it by your speed.

The minimum distance you will travel with cruise control on is

140 miles - 30 miles = 110 miles.

The maximum distance you will travel with cruise control on is

140 miles + 30 miles = 170 miles.

To convert these distances into hours, you will divide them by your speed of 60 miles per hour.

Minimum hours: 110 miles / 60 mph = 1.83 hours

Maximum hours: 170 miles / 60 mph = 2.83 hours

Therefore, the minimum number of hours you will have cruise control on is 1.83 hour(s) and the maximum is 2.83 hour(s).

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This square-based oblique pyramid has a volume of 125\text{ m}^3125 m 3 125, start text, space, m, end text, cubed. 5\text{ m}5 m5\text{ m}5 m What is the height of the pyramid

Answers

If the volume of the square based Pyramid is 125 m³ and the base is of 5m then the height of the pyramid is 15 m .

The Volume of the Square based pyramid is = 125 m³ ;

the measure of the side of base of pyramid is = 5m ;

So , the Area of the base of pyramid is = [tex]5 \times 5[/tex] = 25 m² ;

We know that the formula for the Volume of the pyramid is = [tex]\frac{1}{3} \times Area\; Of \;Square \times Height[/tex] ;

Substituting the values  ;

we get ;

⇒ [tex]125= \frac{1}{3} \times 25 \times Height[/tex] ;

On solving further ,

we get ;

⇒ [tex]\frac{125\times 3}{25}[/tex]

⇒ 15 m .

Therefore , The Height of the Pyramid is 15 m.

The given question is incomplete , the complete question is

This square-based oblique pyramid has a volume of 125 m³ and the length of the side of the base is 5m . What is the height of the pyramid ?

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Need help 30 points....
in triangle abc, the measure of the largest angle is 32 less than 3 times the smallest angle. the measure of the middle angle is 8 more than half the measure of the largest angle. what is the measure of the middle angle? _______ degrees

Answers

The measure of the middle angle of  triangle abc is 52°

Let the largest angle of triangle be x, the smallest angle be z, and the third angle be y.

Given that the measure of the largest angle is 32 less than 3 times the smallest angle.

So, we get an equation,

x = 3z - 32              ............(1)

Also, the measure of the middle angle is 8 more than half the measure of the largest angle.

So, we get an equation,

y = 8 + (x/2)          .......(2)

From equation (1),

z = (x + 32)/3           ..........(3)

We know that the sum of all angles of triangle is 180 degrees.

x + y + z = 180

Substitute the values of y and z in above equation.

x + 8 + (x/2) + (x + 32)/3 = 180

6x + 48 + 3x + 2(x + 32) = 1080

9x + 48 + 2x + 64 = 1080

11x + 112 = 1080

11x = 1080 - 112

11x = 968

x = 88

Substituting above value of x in equation (2)

y =  8 + (88/2)

y = 8 + 44

y = 52 degrees

Therefore, the middle angle of triangle measures 52 degrees.

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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=88(0.977)^x

Answers

3% is the percentage rate of increase or decrease.

What does exponential decay mean?

A process known as exponential decay describes how a quantity depletes over time, with the rate of depletion become proportionately slower as the quantity shrinks. Finding the exponential drop—a rapid reduction over time—is made easier by the exponential decay formula.        

                                The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay. The formula for f(x) is f(x) = a (1 - r)x.

The formula for exponential decay is y=a(1-r)x.

r is the decay rate, expressed as a decimal.

In this case, r = .03 which represents 3%

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the backyard if a new home is shaped like a trapezoid with a height of 40 ft and bases of 73 ft and 111 ft. what is the cost of putting sod on the gard, if the landscaper charge 23 cent per square foot for sod

Answers

The cost of putting sod on the gard, given the area of the trapezoid backyard of the new home, is $ 864 . 40

How to find the area of a trapezoid ?

The backyard of the new home is said to be shaped like a trapezoid which means that the cost of putting sod on the gard can be found by checking for the area of the trapezoid.

The area of a trapezoid can be found by the formula :

= (( Base A + Base B ) x height ) / 2

= ( ( 73 + 111 ) x 40 ) / 2

= 3, 680 square feet

The cost of putting sod on the gard is therefore:

= Area of the backyard x cost per square foot of sod

= 3, 680 x 0. 23

= $ 864 . 40

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a triangular parcel of land has 114 meters of frontage, and the other boundaries have lengths of 70 meters and 95 meters. what angles does the frontage make with the two other boundaries? (round your answers to one decimal place.)

Answers

Use law of cosines to find angles A, B, and C. Angle A = X°, B = Y° and C = Z°.

What is triangle ?

A triangle is a polygon with three sides and three angles. The sum of the three angles in a triangle always equals 180 degrees. Triangles can be classified based on the length of their sides or the measure of their angles.

We can use the law of cosines to find the angles. The law of cosines states that for any triangle, the square of one side length is equal to the sum of the squares of the other two side lengths, minus twice the product of the other two side lengths multiplied by the cosine of the angle opposite the first side.

Let A, B, and C be the angles opposite the sides of length 114 meters, 70 meters, and 95 meters, respectively.

We can use the following equation to find angle A:

cos A = (70^2 + 95^2 - 114^2) / (2 * 70 * 95)

Once we have the value of cos A, we can use the inverse cosine function to find the angle A in degrees.

Similarly, we can use the same formula to find the angle B and C.

cos B = (114^2 + 95^2 - 70^2) / (2 * 114 * 95)

cos C = (114^2 + 70^2 - 95^2) / (2 * 114 * 70)

Use law of cosines to find angles A, B, and C. Angle A = X°, B = Y° and C = Z°.

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Find an equation for a line passing through (10,10) that is perpendicular to the line with equation 5x+8y=-9. Write your equation in

Answers

The equation of a line passing through (10,10) that is perpendicular to the line with equation 5x + 8y = -9 is y - 10 = (8/5)(x - 10) or y = (8/5)x - 6.

Get the slope of the line 5x + 8y = -9 by rewriting it in slope-intercept form. Subtract 5x from both sides and divide by 8.

y = (-5/8)x - (9/8)

The slope of this line is -5/8. The negative reciprocal of -5/8 is 8/5. Therefore, the slope of the line that is perpendicular to 5x + 8y = -9 is 8/5.

Using point-slope form, determine the equation of the line.

y - y₁ = m(x - x₁)

y - 10 = (8/5)(x - 10)

or using the slope-intercept form,

y = mx + b

y = (8/5)x + b

10 = (8/5)10 + b

b = -6

y = (8/5)x - 6

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1kg of apples costs £1.12 more than 1 kg of pears.
1kg of apples costs £2.35 less than 1 kg of bananas.
Jackson buys 3 kg of apples, 3 kg of pears and 2 kg of bananas. The total cost is £25.02
How much does 1 kg of apples cost?

Answers

Answer:

1 kg of apples cost £2.96

-----------------------------------------------

Let the cost of a 1 kg of apples be x.

Then pear costs x - 1.12 and banana costs x + 2.35.

The total cost is 25.02:

3x + 3(x - 1.12) + 2(x + 2.35) = 25.023x + 3x - 3.36 + 2x + 4.7 = 25.028x + 1.34 = 25.028x = 25.02 - 1.348x = 23.68x = 23.68/8x = 2.96

As a pot of tea cools, the temperature of the tea is modeled by a differentiable function H for Osts 10, where time t is measured in minutes and temperature H(t) is measured in degrees Celsius. Values of H(t) at selected values of time t are shown in the table. Use a trapezoidal sum with the four subintervals indicated by the table to estimate 1 10 Soº H

Answers

By using the Trapezoidal sum with the four subintervals indicated by the table the sum is 52.95.

What is Trapezoidal sum?

The trapezoidal rule is a method for roughly approximating the definite integral in calculus. The area of the region that roughly fits the shape of a trapezoid under the graph of the function f(x) is how the trapezoidal rule operates.

A Riemann sum is a technique for calculating the area under a curve by adding the areas of rectangles or trapezoids drawn along the curve. Triangular Riemann Sum: A trapezoidal Riemann sum determines the area under a curve by adding the areas of trapezoids.

Let,  [tex]\frac{1}{10}\int\limits^1_00 {H(t)} \, dt[/tex]  is the average temperature of the tea, in degree Celsius, over the 10 minutes.

[tex]\frac{1}{10}\int\limits^1_0_0 {H(t)} \, dt = \frac{1}{10}(2*\frac{66+60}{2}+ 3*\frac{60 + 52}{2}+4*\frac{52+44}{2}+1*\frac{44+43}{2} \\ \frac{1}{10}\int\limits^1_0_0 {H(t)} \, dt = 52.95[/tex]  

Hence, by using the Trapezoidal sum with the four subintervals indicated by the table the sum is 52.95.

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◄) A large square is composed of 16 smaller squares that are all the same size. Each of the small squares has an area of 4 square units. What is the side length of the large square?​

Answers

Answer:

8

Step-by-step explanation:

Each of the small squares has an area of 4 square units

so its length is 2 because 2*2 =4

so 4 small squares = 8 each side

How do I do this help me please

Answers

Answer: A. Yes

B. Yes

C. No

Step-by-step explanation:

A. 2z = 40 and z = 20, 20 is a solution of the equation because when you substitute z = 20 into the equation 2z = 40, the equation becomes true.

B. n + 5 = 20 and n = 15, 15 is a solution of the equation because when you substitute n = 15 into the equation n + 5 = 20, the equation becomes true.

C. v = 12 and v = 16, 12 is not a solution of the equation because v is assigned to 12 and 16 both, but the equation only has one solution, a variable can't be assigned to two different values.

In general, when solving equations, we check if the value of the variable makes the equation true. if it does it's a solution, if not it's not a solution.

I need help with division 3,340 divided by 8

Answers

Answer: 42.5

Step-by-step explanation:

8 multipled by 42.5 is 340. A strategy i use is multiply 8 by 5 or 10, for example 8 times 5 is 40, so i know that 8 times 50 is 400, that tells you the answer you need is just a little below 50

Which algebraic expression is equivalent to 9(4x + 8) - 4

Answers

Answer: 36x + 68

Step-by-step explanation:

Expanding it, you get:

36x + 72 - 4

= 36x + 68

what is the probability that the average electric service paid by the sample of electric service customers will exceed $170? show your work.

Answers

a) According to the central limit theorem, the mean is $142 and the standard deviation is $0.7488.

b) Nearly normal according to the central limit theorem.

c) 0.0901 = 9.01% probability that the average cable service paid by a sample of cable service customers exceeds $170 in the central limit theorem.

Normal probability distribution:

The normal probability distribution, discovered by Abraham De Moivre in 1733, approximates the binomial probability distribution when a particular experiment has a very large number of trials. In 1774 Laplace studied the mathematical properties of the normal probability distribution. By historical error, the discovery of the normal distribution was attributed to Gauss, first mentioned in his 1809 paper. In the 19th century, many scientists discovered that measurement errors in a particular experiment followed a pattern (usual error curve). ), which was very well approximated by this probability distribution.

Central Limit Theorem:

The central limit theorem is a statistical theory that for large sample sizes with finite variance, samples are normally distributed and the mean of the sample is approximately equal to the mean of the entire population.

According to the Question:

The average monthly charge is $142 with a standard deviation of $29.

This is μ = 142 and σ = 29

Part a:

The mean and standard deviation of the sampling distribution of x to show your research and support your argument:

1500 samples (over 30).

According to the Central Limit Theorem

The mean is 142 $

The standard deviation is s = [tex]\frac{29}{\sqrt{1500} }[/tex] = 0.7488

Part b:

Shape of sampling distribution of X.

Due to the large sample size, the shape of the sample distribution is almost normal. According to the central limit theorem, which states that the sampling distribution converges to the normal distribution as the sample size increases. Mean ~ N(142, 0.749²)

Part C:

The probability that the average cable service paid by a sample of cable service customers exceeds $170.

Therefore, by the central limit theorem, the p-value of Z when X= 170

                         Z =  x - μ/ σ

By the Central Limit Theorem:

   Z = 170 - 142 / 0.7488

      = 28/ 0.7488

      = 37.34 exceeds 0.9099

Using the Z probability calculator :

P(Z > 1.335) = 0.09093

Complete Question:

The amount people pay for cable service varies quite a bit but the mean monthly fee is $142 and the standard deviation is $29. the distribution is not normal many people pay about $76 for basic cable and about $160 for premium service but some pay much more. a sample survey is designed to ask a simple random sample of 1,500 cable service customers how much they pay. let x hat be the mean amount paid.

Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.

Part b: what is the shape of the sampling distribution of x hat justify your answer.

Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $170? show your work.

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this is a late assignment and I am really close to failing please help​

Answers

Answer: 14.825

Step-by-step explanation:

First , do 2 * 5.3 because it's 2a, you'll have to do 2 * a. This equals 10.6.

Second, you'll need to do 5.3 * 1.25. Why? Because in the problem you need to do a * b, which is that. It equals 6.62500.

Lastly, put it all together! 10.6 + 6.62500 - 2.4 equals 14.825.

two ice cream machines make a total of 320 gallons in a certain amount of time. working together for the same length of time, how many gallons of ice cream can each number of machines make? 3 ice cream machines

Answers

3 ice cream machines will make a total of 480 gallons for the same length of time and 4 ice cream machines will make a total of 640 gallons for the same length of time.

For the quantity 3 ice cream machines will make.

2 ice cream machines produce a total of 320 gallons in a certain amount of time.

If 2 ice cream machines can make a total of 320 gallons. Then,

3 ice cream machines will produce a total of x gallons in the same amount of time

x = (320 × 3)/2

x = 480 gallons

Hence, 3 ice cream machines will produce a total of 480 gallons.

For the quantity 4 ice cream machines will make.

If 2 ice cream machines can make a total of 320 gallons. Then,

4 ice cream machines will produce a total of y gallons in the same amount of time

y = (320 × 4)/2

y = 640 gallons

Hence, 4 ice cream machines will produce a total of 640 gallons.

--The given question is incomplete, the complete question is

"Two ice cream machines make a total of 320 gallons in a certain amount of time. Working together for the same length of time, how many gallons of ice cream can each number of machines make?

3 ice cream machines

4 ice cream machines"--

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In the figure, point $A$ is the center of the circle, the measure of angle $RAS$ is 74 degrees, and the measure of angle $RTB$ is 28 degrees. What is the measure of minor arc $BR$, in degrees

Answers

In circle A,  angle RAS is 74 degrees and  angle RTB is 28 degrees. The measure of minor arc BR is 81 degrees.

The figure is in the attached picture.

Notice that:

AS = AR = radii of the circle.

Hence, triangle SAR is an isosceles triangle, and ∠ASR = ∠ARS.

The sum of angles in a triangle is  180°.

Therefore,

∠ARS +  ∠ASR+ 74° =  180°

Since ∠ASR = ∠ARS,

2∠ARS + 74° =  180°

2∠ARS  = 106°

∠ARS  =  53°

and

∠ASR = ∠ARS = 53°

Angle in a straight line:

∠AST  + ∠ASR =  180°

∠AST   =  180° - ∠ASR =  180° - 53°  =  127°

Refer to triangle SAT:

∠SAT  =  180° - 28° - 127°  =  25°

The measure of minor arc BR = ∠RAB

∠RAB  =  180° - 74° - 25°  

∠RAB  =  81°

The picture in your question is missing, but most likely it was in the attached picture.

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