janice was given a piggy bank on her seventh birthday, and she put it to use immediately. each time she puts one or more coins into the piggy bank, she keeps track of the number of coins she has collected to date and the accumulated value of her collection. janice collects only nickels, dimes, and quarters. six months after her seventh birthday, janice looked at her record and ascertained that she had collected 540 coins, which were worth $60. janice counted 100 quarters in her savings. how many nickels and dimes are in her collection?

The Distance between line ℓ and the point j (-5,-1) is 8units.

The distance between a point PP and a line LL is the shortest distance between PP and LL; it is the minimum length required to move from point PP to a point on LL. In fact, this path of minimum length can be shown to be a line segment perpendicular to LL. The distance d can then be defined as the length of the line segment that has PP as an endpoint and is perpendicular to LL.

We know that the distance d between a point (x1,y1) and a line having equation in form of ax+by+c=0 can be expressed as,

[tex]d = \frac{|ax1+by1+c|}{\sqrt{(a^2+b^2)} }[/tex]

So, we have given that equation of line

y = 7

y-7=0

Point j = (-5,-1)

So, Distance between point j and line = d

d = [tex]\frac{|0(-5)+1(-1)-7|}{\sqrt{(0^2+1^2)} }[/tex]

d = [tex]\frac{8}{\sqrt{1} }[/tex]

d = 8 units

Therefore, The point j is at a distance of 8 units from the line ℓ.

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The transformation for Rectangle A which would result in Rectangle B is: A. reflection across the x-axis.

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Mathematics, a reflection over the x-axis would maintain the same x-coordinate (10 → 10) while the sign of the y-coordinate changes from positive to negative (4 → -4) . Therefore, a reflection over the x-axis is given by this rule:

(x, y) → (x, -y) = (10, 4) → (10, -4).

In conclusion, a reflection across the x-axis would transform Rectangle A to Rectangle B.

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Answer:

1 + 2 = 3

2 + 3 = 5

3 + 4 = 7

4 + 5 = 9

5 + 6 = 11

Step-by-step explanation:

 (-7,∞) &  (−∞, 1/2] are the interval notation.

What is interval notation in math?

8x-5>=6x-1 or 4+4x<=3x-3

8x-5 ≥6x-1

8x - 5 ≥ 6x - 1

8x - 6x ≥  5 - 1

 2x ≥  1

   x ≥  1/2

Therefore, x could be any number less than or equal to 1/2. In interval notation, this looks like

 (−∞, 1/2]

4+4x ≤ 3x-3

4 + 4x ≤  3x - 3

4x - 3x ≤  -3 - 4

   x ≤  -7

Therefore, x could be any number less than -7 , but x couldn't be -7, since that would make the two sides of the inequality equal. In interval notation, this looks like:

   (-7,∞)

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The given function y = x³ is not a linear function but a cubic function.

For the given function;

y = x.x.x

This, can be written, after adding the power of x as;

y = x³

Now, put x = 1; y = 1

Put x = 2; y = 8

Put x = 3; y = 27

This will not form a straight line but a cubical curve.

As, the function is not changing linearly but cubical.

Thus, the function is not linear function.

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Answer:

y = -3(x + 2)^2 + 10.

Step-by-step explanation:

y = –3x2 – 12x – 2

Divide first 2 terms by -3:

y = -3(x^2 + 4x) - 2            Now complete the square on x^2 + 4x:-

y = -3(x^2 + 4x + 4 - 4) - 2

y = -3[(x + 2)^2 - 4] - 2

y = -3(x + 2)^2 + 12 - 2

y = -3(x + 2)^2 + 10.

Answer:

x = 300°

Step-by-step explanation:

If m and n are parallel, then m∠4x is equal to 120, since they are congruent angles.

Solve for x:

4x = 1200

Divide both sides by four

x = 300

WS bisects angle BWV, m ∠BWS = 36° , then the measure of angle

m ∠BWV is equal to 72°.

As given in the question,

Measure of given angle :

m ∠BWS =36°   ____(1)

let 'x' be the measure of angle BWV

WS bisects angle BWV.

⇒ m ∠BWS= m ∠SWV

⇒ m ∠SWV=36° ____(2)

Also , m ∠BWV is equal to the sum of the measure of ∠ BWS and ∠SWV.

⇒ m ∠BWV =m ∠BWS + m ∠SWV

Substitute the value of m∠ BWS and m ∠SWV from (1) and (2),

⇒ m ∠BWV=36° + 36°

⇒m ∠BWV=72°

Therefore, WS bisects angle BWV, m ∠BWS=36° , then the measure of angle m ∠BWV is equal to 72°.

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Answer: 21 quarters and 2 nickels.

Step-by-step explanation: $0.25(one quarter) x 21 = $5.25. $0.05(one nickel) x 2 = $0.10. $5.25 + $0.10= $5.35.

Answer: The answer is C. You start off by first thinking about your slope equation, being y=Mx+b. Remember b equals your y- intercept. In this case one of your y-intercepts is positive 1 and the other is positive 2. Now you have the “b” part of the equation. Looking for slope or your “mx” part of the equation is next. All this is going to be is the rise over the run from your y intercept. How much did you rise and how much did you run to get to the next point. Both of these slopes are going up therefore both slopes will be positives. For the first one it rises 2 and runs 1 to get to the next point, however you do not need to write the one at the bottom of the 2 and can leave it as “2x+1”, because it is shaded below the red line the inequality will be less than or equal to

. The blue slope rises 1 and runs 2, it is written as

and because it is shaded above the blue one it will be greater than or equal to

.

Step-by-step explanation:

Considering the linear functions on the graph, the inequality that matches the situation is:

B. y ≥ x/2 + 2

   y ≤ 2x + 1

A linear function is modeled by:

y = mx + b, In which: m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

here, we have,

The lower bound of the interval is a linear function with

y-intercept of b = 2,

that also passes through (2,3), hence the slope is:

m = (3 - 2)/(2 - 0)

   = 1/2.

Hence the inequality is:

y ≥ x/2 + 2

The upper bound of the interval is a linear function with y-intercept of b = 1, that also passes through (2,5), hence the slope is:

m = (5 - 1)/(2 - 0) = 2.

Hence the inequality is:

y ≤ 2x + 1

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Answer:

use v for the value

Step-by-step explanation:

1800 lawns were mowed. 800 driveways were shoveled.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Given Data

Let mowed grass be x

Let shoveled snow be y

Last year you mowed grass and shoveled snow for 12 houses

x + y = 12

y = 12 -x

You earned $225 for each lawn you mowed and $200 for each house you shoveled for a total of $2600.

225x + 200y = 2600

Equating value of y

225x + 200(12-x) = 2600

225x + 2400 - 200x = 2600

225x - 200x = 2600 - 2400

25x = 200

x = 8

For value of y,

y= 12 -x

y = 12 - 8

y = 4

Lawn mowed = 225(8)

Lawn mowed = 1800

Shoveled snow = 200(4)

Shoveled snow = 800

1800 lawns were mowed. 800 driveways were shoveled.

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The scale of drawing of Bonnie's drawing is 5 inches : 6 yards.

She measured a city and made a scale drawing.

The neighbourhood park is 115 inches long in the drawing. The actual park is 138 yards long.

Therefore, the scale of the drawing can be calculated as follows:

Hence,

115 inches = 138 yards

5 inches = ?

cross multiply

scale of the drawing = 5 × 138 / 115

scale of the drawing = 690 / 115

Therefore,

scale of the drawing is 5 inches : 6 yards

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The correct answer to the task 0.80 divided by 50 given above is 0.016

When we are trying to find the number of times a number can be obtained in another number, we use the term "division" to describe the mathematical expression. The division can be represented as ÷

For instance, the division of 0.80 by 50 is represented and solved below:

0.80 ÷ 50 = 0.016

It can also be represented like this:

0.80 / 50 = 0.016.

Another example of division of numbers is:

8/4 = 2

10 ÷ 2 = 5

So therefore, from the explanation given above we can confirm that when 0.80 ÷ 50, the answer is 0.016.

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The mean number of people per day visiting in August will be equal to option (D) 180.

Mean number of students in July = 160

20 more people visited the people each day in the month of August.

As, there is a constant increase in the number of who are visiting the museum in August each day that is 20 people, the mean will also increase by the same number that is 20 and will be:

Mean number of people per day visiting in August = 160 + 20

Mean number of people per day visiting in August = 180

Therefore, we get that, the mean number of people per day visiting in August will be equal to option (D) 180.

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d. Using the Standard Form, identify the x - intercept of the graph and explain

how the x-intercept relates to the number of hot dogs and sodas sol

Maybe sorry if i got it wrong

Answer:

I'm guessing the whole question is: "A car drives 283.5 miles in 4.5 hours. Assuming that the distance traveled directly with the time traveled, how far will the car travel in 7 hours?"

Step-by-step explanation:

If so, here's the answer:

441 miles will be traveled in 7 hours

You could find the speed in mph

To do that, divide 283.5 by 4.5 which gives us 63

because [tex]\frac{283.5 miles}{4.5 hours}[/tex] divide to get the 4.5 hours into 1 hour so, [tex]\frac{283.5/4.5}{1}[/tex]

63 mph times 7 hours = 441

The expected number of points as a function of a and b is C = b+a.

In this questions what we are been asked is for the expected value C, to solve the problem we need to recognize the random variables and their respective probability.

x1 = roll a 1 -> P1 = 1/6

x2 = roll a 2 -> P2 = 1/6

x3 = roll a 6 -> P3 = 1/6

x4 = roll a 1, 4 or 5 -> P4 = 1/2

E = P1*x1 + P2*x2 + P3*x2 + P4*x4

x1 is equal to zero (no points and the game stop), x2 is equal to C+b (win a points, affecting the expected value), x3 is equal to C-a (win b points, affecting the expected value) and x4 is equal B (no points are lost and the game continues, therefore the expected value is not affected)

C = 1/6*0 + 1/6*(C+b) + 1/6*(C-a) + 1/2*(C)

1/6*C = 1/6*b + 1/6a

Solving for C

C = b+a

Conclusion: If you get a "2, 4 or 5, this means the game will be unaffected (in terms of points), you need to pay special attention to x1 and x2 (all with the same probability)  that are the results that are going to affect your game.  

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Probability when a student is selected at random to be the captain. Probability the captain has a blue shirt is unlikely. Probability the captain has a red shirt is impossible. Probability the captain has a blue or white shirt is likely certain.

The total number of students is 15.

4 students are wearing blue shirt.

11 students are wearing white shirt.

10 students are wearing yellow shirt.

Only any one student can be captain.

The total outcomes are 25.

Probability that the student has blue shirt B is,

Total favorable outcomes = 4

P(B) = 1/25.

Probability that the student has red shirt R is,

Total favorable outcomes = 0

P(B) = 0/25.

P(B) = 0

Probability that the student has blue or white shirt B and W is,

Total favorable outcomes = 15

P(B&W) = 15/25.

P(B&W) = 3/5.

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Answer:

x = -5/6

Step-by-step explanation:

First, set the equation (6x + 5) * 86 equal to 0. The equation is now (6x + 5) * 86 = 0. Next, simplify (6x + 5) * 86 by multplying 86 to 6x and 5. This will turn the equation into 516x + 430 = 0. Next, subtract 430 from both sides, cancelling out the 430 on the left side. After that, get the x value by itself by dividing 516 on both sides, cancelling out the 516 on the left side. Now, x = -430/516. From here, find the common factor of both the numerator and denominator; this turns out to be 86. Since 86 is the common factor, divide the numerator and denominator by 86 and you get x = -5/6.

The rule to describe the transformation, dilation by a scale factor of 4 with center of dilation at the  origin is (x,y)→(4x,4y) and the coordinates of rectangle Q'R'S'T' is are Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .

In the question ,

a rectangle QRST with coordinates Q(-8,5), R(-8,7), S(-5,7), and T(-5,5) is given ,

and to dilate the rectangle by a scale factor of 4 with center of dilation at the origin , we multiply coordinates of the original shape with the dilation factor

so the rule to describe the dilation will be

(x,y)→(4x,4y)

Using this rule to find the new coordinates of the rectangle Q'R'S'T' .

When Q = (-8,5)

Q' = (4*(-8),4*5)

Q' = (-32,20)

When R = (-8,7)

R' = (4*(-8),4*7)

R' = (-32,28)

When S = (-5,7)

S' = (4*(-5),4*7)

S' = (-20,28)

When T= (-5,5)

T'  = (4*(-5),4*5)

T' = (-20,20)

So the coordinates of the rectangle Q'R'S'T' is Q' = (-32,20) , R' = (-32,28) , S' = (-20,28) , T' = (-20,20) .

Therefore , the rule to describe the transformation, dilation by a sale factor of 4 with center of dilation at the origin is (x,y)→(4x,4y) and the coordinates of rectangle Q'R'S'T' are Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .

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Answer: True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The surface area of the sphere is 84453.44 yards².

We are given that:

the ride goes around the widest circle of the sphere whose circumference is =  514.96 yard.

The widest circle of the sphere is the plane contains the sphere's center

The circumference of the widest circle is:

C = 2 π r

where r is radius of the sphere.

The surface area of the sphere is defined as:

A = 4 π r²

where  r is radius of the sphere.

So, we get that:

514.96 =2 π r

514.96= 2 × 3.14 × r

r = 514.96 ÷ (2 × 3.14)

r = 514.96 ÷ 6.28

Surface Area A = 4 π r²

A = 4 × 3.14 × (514.96 ÷ 6.28) × (514.96÷ 6.28)

A = 84453.44 yards²

Therefore, we get that, the surface area of the sphere is 84453.44 yards².

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Answer:

Here are all 3 number combinations that you can multiply to get 300: 300 × 1 × 1 = 300 150 × 2 × 1 = 300 150 × 1 × 2 = 300 100 × 3 × 1 = 300:

Using the z-distribution, the 95% confidence interval for the proportion of unsatisfactory meals is given by:

(0.0553, 0.0647).

A confidence interval of proportions is given by the following rule:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The estimate and the sample size of the interval are given as follows:

[tex]\pi = \frac{600}{10000} = 0.06, n = 10000[/tex]

The lower bound of the interval is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.06 - 1.96\sqrt{\frac{0.06(0.94)}{10000}} = 0.0553[/tex]

The upper bound of the interval is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.06 + 1.96\sqrt{\frac{0.06(0.94)}{10000}} = 0.0647[/tex]

Hence the interval in (LCL, UCL) format is:

(0.0553, 0.0647).

The problems asks for the 95% confidence interval of unsatisfactory meals, considering that, out of 10000 meals, 600 were unsatisfactory.

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Answer:

19.5/3=6.5 centimeters

Step-by-step explanation:

The directed number suggested by the following will be:

A 14 degrees below zero = -14°

B altitude 200 metres = +200

It should be noted that the directed number simply means the numbers that had both size and direction. It should be noted that the direction can either be positive or negative.

A measurement of altitude or height is the distance between a location or item and a reference datum, typically in the vertical or "up" direction. Although the term "altitude" is frequently used to refer to a location's height above sea level, the term "elevation" is frequently preferred in the context of geography. The term "depth" often refers to vertical distance measurements taken in the "down" direction. Globally, the research team discovered that the pace of temperature change frequently quickens as altitude increases.

Therefore, the directed number suggested by 14 degrees below zero will be negative 14 and this will be -14°

Also, altitude 200 metres will be positive 200 and this will be +200

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The expression equivalent to (3x²z⁻³)² is 9x⁴z⁻⁶.

For the given question;

The expression is given as;

= (3x²z⁻³)²

Squaring each term individually.

= (3)²(x²)²(z⁻³)²

As the property of the index, the power will be multiplied.

= 9x⁴z⁻⁶.

Thus, the expression equivalent obtained for the given expression (3x²z⁻³)² is 9x⁴z⁻⁶.

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