a coin jar contains a combination of nickels and quarters. If there 60 total coins in the jar worth $7.20, how many nickels are there?

The trigonometric function for the values in the table is defined as follows:

y = 3sin(π/4(x - π/2)) + 3.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function has a maximum value of 6 and a minimum value of 0, for a difference of 6 units, hence the amplitude is obtained as follows:

2A = 6

A = 3.

Without vertical shift, a function with amplitude of 3 would oscillate between -3 and 3, while this one oscillates between 0 and 6, hence the vertical shift is given as follows:

D = 3.

The shortest distance between repetitions can be given by 8 - 0, hence the period is of 8 units and the coefficient B is given as follows:

2π/B = 8

B = 2π/8.

B = π/4.

The function is at's minimum value at x = 0, meaning that the sine function has a phase shift of π/2 units right, thus the coefficient C is given as follows:

C = π/2.

Then the function is defined as follows:

y = 3sin(π/4(x - π/2)) + 3.

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Answer: 10

Step-by-step explanation:

because

Probability that the event can happen = 1/2

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes

Given,

Total outcomes of event = 14

Outcomes, event can happen = 7

Probability

= Favorable Outcomes/Total Outcomes

= 7/14 = 1/2

Hence, 1/2 is Probability that the event occurs.

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The median of the data set is 12.

The mean is 11.29.

Increasing every piece of data by the same value increases the mean and median by the same amount.

The median of the data set is the middle value when the data is arranged in numerical order. To find the median of the data set, we need to arrange the data in increasing order: 9, 10, 11, 12, 12, 13, 34. The median of this data set is 12.

The mean of the data set is the average of all the values. To find the mean, we need to add up all the values and divide by the number of values: (9 + 10 + 11 + 12 + 12 + 13 + 34) / 7 = 11.29.

If every piece of data in the set is increased by 20 after treatment, the new values are 29, 30, 31, 32, 32, 33, 54. The new median is 32 and the new mean is 35.29.

When every piece of data is increased by the same value, the mean and median will increase by the same amount.

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The cost of printing x business cards can be represented by the linear function C(x) = 0.05x + 20.  The cost of printing 950 business cards is $67.50.

The cost of printing business cards is a linear function, C(x) = mx + b, where C(x) is the cost of printing x business cards, m is the rate at which the cost increases as the number of cards increases, and b is the constant term or the cost of printing zero business cards. In this case, m = 0.05 and b = 20.

The equation C(x) = 0.05x + 20 represents the cost of printing x business cards, where x is the number of cards printed. The term 0.05x represents the cost of printing x cards at a rate of $0.05 per card, and the term 20 represents a fixed cost of $20, regardless of the number of cards printed.

To find the cost of printing 950 business cards, we simply substitute x = 950 into the equation:

C(950) = 0.05 * 950 + 20

C(950) = 47.5 + 20

C(950) = 67.5

Therefore, the cost of printing 950 business cards is $67.50.

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Answer: Young gentleman. Here are some things you can use.

Step-by-step explanation: Calculator, Desmos (this was a website) ruler, protractor, math dictionary.

45.0 units is the required perimeter of triangle XYZ

Triangles are known to be similar if the ratio of the similar sides are equal to a constant. The perimeter is the sum of all the sides of the triangle.

From the given diagram , we need to solve for the value of x first as shown:

9/10 = 14/x

9x = 140

x = 140/9

x = 15.6

Find the required perimeter of XYZ
perimeter = ZY + XY + XZ

perimeter = 15.4 + 14 + 15.6

Perimeter = 45.0 units

Hence the perimeter of triangle XYZ is approximately 45.0 units

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Answer:

Step-by-step explanation:

this is a simultaneous  equation type. so there are only 2 solutions. one for X and one for Y

Answer:

y = -2.5x + 6.5

Step-by-step explanation:

The equation of the line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

With a slope of -2.5 and a point (2,1.5) on the line, we can use the point-slope formula to find the equation of the line:

y - 1.5 = -2.5 (x - 2)

Expanding the right-hand side, we get:

y - 1.5 = -2.5x + 5

Adding 1.5 to both sides, we get:

y = -2.5x + 6.5

So the equation of the line in slope-intercept form is y = -2.5x + 6.5.

Therefore , the solution of the given problem of ratio comes out to be

CD:DE = 1:2. and AB:BC = 2:1 .

Use the simple formula "a / b" to create a group of linked variables "a" and "b," where "b" may also be higher than zero. One ratio is created by combining two equation ratios. If there were only one man and three ladies, the ratio would be 1:1. There are 1/4 males and 3/4 girls in the group. A division between two or more objects, a number, or even a portion of a component's volume are all examples of parts.

Here,

Ratio 1: AB:BC = 2:1

Let's use the midpoint formula to find the coordinates of point C, which is the midpoint of line segment AB:

C = ((5+x)/2, (0+y)/2) = ((5+x)/2, y/2)

Since AB:BC = 2:1, we know that the distance from A to B is twice the distance from B to C. Using the distance formula, we can write:

2 * BC = AB

2 * √((x+1)² + y²) = √((x-5)^2 + y^2)

Simplifying this equation, we get:

4 * (x+1)² + 4y² = x² - 10x + 25 + y²

Simplifying further, we get:

3x²+ 8x - 16y² - 75 = 0

Ratio 2: CD:DE = 1:2

Let's use the midpoint formula to find the coordinates of point E, which is the midpoint of line segment CD:

E = ((p-1)/2, (q-4)/2)

Since CD:DE = 1:2.

Therefore , the solution of the given problem of ratio comes out to be

CD:DE = 1:2. and AB:BC = 2:1 .

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Answer:

(-4, 6) (-1, 0)

Source:

Took test. ✌

The values in the parallelogram figure are as follows

angle B = 74 degrees

x = 4

angle BCA = 49 degrees

Remembering that opposite angels of a parallelogram are equal will help us know that angel B is equal to angel D which is 74 degrees

The property that the two opposite sides of parallelogram is used to find x

4x = 16

x = 4

Applying alternate interior angles postulate, we can see that

angle BCA = angle DAC = 49 degrees

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A. X is a discrete random variable

B. The conditions are satisfied.

C. The expected value of X is 15.25

A. X is a discrete random variable because it can only take on specific values (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16) and not any value in an interval.

B. To show that the probability distribution is valid, we need to check if the following conditions are satisfied:

1. P(X=x) ≥ 0 for all x in the set of possible values of X

2. The sum of all probabilities equals 1

From the information given, it appears that these conditions are satisfied.

C. The expected value of X can be calculated as the weighted average of all possible values of X, where the weights are their corresponding probabilities.

E(X) = Σ[x * P(X=x)]

E(X) = (14*0.15) + (15*0.55) + (16*0.20) + (17*0.10) = 15.25

The expected value of X, which is 15.25, represents the mean or average number of credits taken by a randomly selected first-year student at the large state university.

D. The standard deviation measures the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the values are close to the mean (expected value), while a high standard deviation indicates that the values are spread out over a wider range. In this context, a standard deviation of 0.829 means that the number of credits taken by first-year students at the university is spread out over a range of approximately 0.829 units on average.

E. The event "taking at least 16 credits" can be expressed as X ≥ 16. To find its probability, we can sum up the probabilities of all the values that are greater than or equal to 16.

P(X ≥ 16) = ΣP(X = x)

P(X ≥ 16) = 0.20 + 0.10 = 0.30

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Answer:

x = 35°

Step-by-step explanation:

The triangle is an isosceles triangle since two sides are formed by the radii of the circle

Therefore m∠C = x°

The angle 70° is the exterior angle of the triangle

Exterior angle = sum of interior angles

70° = x + x = 2x

2x = 70

x = 35°

 Total volume of the salt shaker is 56.52+706.5=763.02 cm³

The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr²h.

Given here: The volume of a salt shaker  

The radius of the salt shaker which is 5 cm

Thus the volume of the cylinderical salt shaker is = π×3²×5²

                                                                                  =706.5 cm³

and the volume of the hemisphere at the top is=  (2/3)πr³

                                                                               =56.52 cm³

Hence, Total volume of the salt shaker is 56.52+706.5=763.02 cm³

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The complete question is Which is a better estimate for the volume of a salt shaker? where radius =3 cm and height =5 cm

The linear graph represents a proportional relationship, a graph of a line that passes through the points (0, 0) and (0.5, -3).

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the coordinates to find the  linear graph represents a proportional relationship,

we know the equation of a line given by,

y = mx + c

where m is the slope and c is the y-intercept,

to prove the graph the proportional value of the y-intercept should be zero, (0, 0)

when c = 0, y = mx

the equation will proportional,

When the line passes from the origin the equation will be proportional.

Hence option A is correct.

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Its A because if the line passes through the middle of the square is a proportional relationship.

The elevation gain from the base of the chairlift to the top is 835.2 m

Consider the following diagram.

The chairlift rises at a constant angle of 37°

i.e., the angle of elevation (∠ACB) = 37°

The length of the chairlift ride is 1,392 m

This means, for right triangle ABC, the length of hypotenuse AC = 1392 m

To find  the elevation gain from the base of the chairlift to the top i.e., the length of side AB.

Consider the sine of angle ∠ACB

sin(∠ACB) = AB/AC

sin(37°) = AB/1392

3/5 = AB/1392

AB = 835.2 m

Therefore, the elvation gain is 835.2 m

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The value of k that makes the probability distribution valid is given as follows:

k = 4.

To obtain the value of k, we must consider that the integral assumes a value of 1 over it's entire domain, that is:

[tex]\int_{-1}^{1} F(x) dx = 1[/tex]

The function F(x) is given as follows:

F(x) = (x + 2)/k.

Considering 1/k as a constant, the integral is given as follows:

1/k[0.5x² + 2x].

At x = 1, the integral is given as follows:

0.5 + 2 = 2.5.

At x = -1, the integral is given as follows:

0.5 - 2 = -1.5.

Applying the Fundamental Theorem of Calculus, the result of the integral is given as follows:

1/k[2.5 - (-1.5)] = 4/k.

As the result of the integral must be of one, the value of k is obtained as follows:

4/k = 1

k = 4.

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Answer:X[tex]x^{2} +2x-15[/tex]

Step-by-step explanation:   you do it by multiplying  out the brackets and then you  simplify the result expression by collecting the like terms.

Answer:

526.68

To find out how much the price went up, you first want to find what 32% of 399 is.

32% of 399 = 127.68

The price will go up $127.68.

Now, just add that to the original price:

127.68 + 399 = 526.68

The price of the game system will now be $526.68

Step-by-step explanation:

Hope it helps! =D

Since the abs. val. graph points down, there has to be a -1 outside the abs val symbol.

Since it's also going through (1,-3) and (-1,-3) instead of (1,-1) and (-1,-1), it's been stretched by a factor of 3.

So y = -3•|x| works.

let's say we have two points A(a , b) and B(c , d) partitioned by a point C, since we're dealing with the MidPoint, C is partitioning AB into two equal halves, so in the ratio of 1 : 1.

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(a,b)\qquad B(c,d)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:1} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{1}\implies \cfrac{A}{B} = \cfrac{1}{1}\implies 1A=1B \\\\\\ 1(a,b)=1(c,d) \implies (a~~,~~ b)=(c~~,~~ d) \\\\\\ C=\left( \cfrac{a+c}{1+1}~~,~~\cfrac{b+d}{1+1} \right)\implies \stackrel{ \textit{MidPoint Formula} }{C=\left( \cfrac{a+c}{2}~~,~~\cfrac{b+d}{2} \right)}[/tex]

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{ -2 }{ 1 } \implies - 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- 2}(x-\stackrel{x_1}{0})\implies {\Large \begin{array}{llll} y=-2x+3 \end{array}}[/tex]

Answer: 104

Step-by-step explanation:

To put it simply, let's say 100% is 160 dollars. When Christmas arrived, it was sold with a discount of 35%. This means we deduct 35% from 100% which is 65%. We then find 65% of 160 dollars, which is 104.

Hope that helps, if not, then please reply back :)

Pizza 4 has the area closest to 450 square inches.

What is an area?

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

To determine the pizza with the area closest to 450 square inches, Dante needs to calculate the area of each pizza. The formula for the area of a circle is A = πr², where r is the radius of the pizza.

Here are the areas of the four pizzas:

Pizza 1: A = π * 10² = 314 square inches

Pizza 2: A = π * 9² = 254.34 square inches

Pizza 3: A = π * 11² = 379.94 square inches

Pizza 4: A = π * 12²  = 452.16 square inches

Out of the four pizzas, Pizza 4 has the area closest to 450 square inches. The area of Pizza 4 is 452.16 square inches, which is only 2.16 square inches greater than 450.

So, Pizza 4 has the area closest to 450 square inches.

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The value has now surpassed $10,000, the car was worth more than $10,000 from year 3 until year 2, or 1 year.

Rounding to the nearest hundredth, the interval is 1 year.

Using the following formula, we can determine the car's value each year:

value = 20000 * [tex](1 - 0.15)^year[/tex]

We're looking for the years where the value exceeds $10,000.

Let's start by determining the car's value after 1 year:

value = 20000 * [tex](1 - 0.15)^1[/tex] = 20000 * 0.85 = 17000

We need to keep lowering the value since it will eventually exceed $10,000 because the value after one year is less than $10,000.

After 2 years:

value = 20000 * (1 - 0.15)² = 20000 * 0.85² = 14525

Still less than $10,000.

After 3 years:

value = 20000 * (1 - 0.15)³ = 20000 * 0.85³ = 12318.75

Since the value has now surpassed $10,000, the car was worth more than $10,000 from year 3 until year 2, or 1 year.

Rounding to the nearest hundredth, the interval is 1 year.

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Answer: $252 for 120 ft

Step-by-step explanation: Divide the money by the feet value in order to find dollars per foot. Since 252/120 = 2.1 $/ft and 285/150 = 1.9 $/ft, it would be better value to go with the 1.9 $/ft option.

Answer:

Below

Step-by-step explanation:

You multiplied the  '4' by 10 to get 40   .....multiply the '1' by 10 the get the second number = 10     this will keep the ratio correct

Answer:

[tex]width = \dfrac{75*(5-\sqrt{2}}{23}[/tex]

Step-by-step explanation:

To find the width of the rectangle, divide the area by the length.

      [tex]Width = \dfrac{area}{length}[/tex]

                 [tex]=\dfrac{75}{\sqrt{2}+5}\\\\\\\text{To rationalize, multiply the denominator and the numerator by } \ \sqrt{2}-5[/tex]

              [tex]=\dfrac{75* (5 - \sqrt{2})}{(5+\sqrt{2})(5-\sqrt{2})}\\\\\\=\dfrac{75*(5-\sqrt{2})}{5^2 - (\sqrt{2})^2}\\\\\\=\dfrac{75(5-\sqrt{2})}{25-2}\\\\\\=\dfrac{75*(5-\sqrt{2})}{23}[/tex]

Answer:

Let the width of the rectangle be w. Then we have:

[tex]lw = 75[/tex]

[tex]w(\sqrt{2} + 5) = 75[/tex]

[tex]w = \frac{75}{\sqrt{2} + 5}[/tex]

Multiplying both the numerator and denominator by [tex]\sqrt{2} - 5[/tex], we get:

[tex]w = \frac{75(\sqrt{2} - 5)}{(\sqrt{2} + 5)(\sqrt{2} - 5)}[/tex]

Simplifying the denominator, we get:

[tex]w = \frac{75(\sqrt{2} - 5)}{-1}[/tex]

[tex]w = -75\sqrt{2} + 375[/tex]

Therefore, the width of the rectangle is approximately 264.1 cm.