A vending​ machine's coin box contains​ nickels, dimes, and quarters. The total number of coins in the box is 252 . The number of dimes is three times the number of nickels and quarters together. If the box contains dollars 24 and ​cents 85, find the number of​ nickels, dimes and quarters that it contains.

here are ​nickels,
​dimes,
quarters in the coin box.

Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

Answer:

it is called an irrational number

Step-by-step explanation:

I think that this is a fact answer, so I don't know how to explain it

The values of the variables are;

x = 7

y = -9

From the information given, we have that;

5x−y=44

−3x−y=−12

Using the elimination method of solving simultaneous equations

Subtract equation (2) from equation (1), we get;

5x - y - (-3x - y) = 44 - (-12)

Now, expand the bracket

5x - y+ 3x + y = 56

collect the like terms

5x + 3x = 56

add the terms

8x = 56

Make 'x' the subject of formula

x= 7

Now, substitute the value of x in equation (2)

-3x - y = -12

-3(7) - y = -12

expand the bracket

-21 - y= - 12

collect like terms

-y = 9

y = -9

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Answer:

\(c = \frac{2}{0.42} \)

Step-by-step explanation:

AB = c

\( \frac{a}{sin \: A} = \frac{c}{sin \: C} \\ \frac{2}{sin \: 25} = \frac{c}{sin \: 90} \\ \frac{2}{0.42} = \frac{c}{1} \\ 0.42 \: c = 2 \\ c = \frac{2}{0.42} \)

Answer:

4.73

Step-by-step explanation:

​

​

Answer:

48,236.7

Step-by-step explanation:

40,000 + 8,000 + 200 + 30 + 6 + 7/10

7/10 can also be written .7

The graph of the inequality t < 20 is given by the image presented at the end of the answer.

The four inequality symbols, along with their meaning, are presented as follows:

A temperature below 20 ºC means that the temperature was less than 20ºC, hence the inequality is:

t < 20.

The graph is composed by the numbers to the left of t = 20, with an open interval at t = 20.

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Answer: \(I = Pe^r^t\)

Step-by-step explanation:

For continuously compounded interest, the above formula is used. The meaning of the variables are as follows:

I: final amount

P: principal amount (what you start off with)

r: interest rate (usually a percent or decimal less than 1)

t: time

Hai drink 11/24 gallons of water in all day

Two or more expressions with an Equal sign is called as Equation.

Given,

Hai has 1 gallon jug of water.

Drinks 1/8 gallons of water before lunch

2/3 gallons of water after lunch.

We need to find how much water did Hai drink all day.

Now we have to add the water he drink.

1/8+2/3

LCM of 8 and 3

3+8/24

11/24

Hence, he drink 11/24 gallons of water in all day.

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Answer:

0.0097 = 0.97% probability that it is defective

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Product is shipped.

Event B: It is defective.

Probability of the product being shipped:

100 - 10 = 90% of 85%(not defective).

5% of 100 - 85 = 15%(defective). So

\(P(A) = 0.9*0.85 + 0.05*0.15 = 0.7725\)

Probability of being shipped and being defective:

5% of 15%. So

\(P(A \cap B) = 0.05*0.15 = 0.0075\)

What is the probability that it is defective?

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0075}{0.7725} = 0.0097\)

0.0097 = 0.97% probability that it is defective

Answer:

y=-1/3x+1

Step-by-step explanation:

The slope of this line is negative, and is equal to rise over run.

To find slope, count the number of spaces it has moved down or up, and then the number of spaces it has moved left or right.

The y intercept is represented by +1, and is where the line crosses the y axis.

Hope this helps!

Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

The recursive formula for this problem is given as follows:

\(P_n = 1.05 \times P_{n - 1}\)

The explicit formula for this problem is given as follows:

\(P_n = 150(1.05)^n\)

The number of tickets in 2026 is given as follows:

297 tickets.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number which is defined as the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n}\)

In which \(a_1\) is the first term.

The parameter values for this problem are given as follows:

\(a_1 = 150, q = 1.05\)

Hence the function is given as follows:

\(P_n = 150(1.05)^n\)

2026 is 14 years after 2012, hence the number of tickets is given as follows:

\(P_{14} = 150(1.05)^{14} = 297\)

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Answer : 8$

you have 1$ left

Answer:

i think it is 3 8 19.

Step-by-step explanation:

Answer:108

Step-by-step explanation:

Answer:

\( \frac{6}{7} \)

Step-by-step explanation:

\( \frac{5}{7} - ( - \frac{1}{7} )\)

\( \frac{5}{7} + \frac{1}{7} \)

\( = \frac{6}{7} \)

Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

The ending inventory at May 31 using FIFO is $312.

The ending inventory at May 31 using LIFO is $260.

The ending inventory at May 31 using average cost is $287.30.

Ending inventory = total purchases - total goods sold

100 - 74 = 26

The first in, first out (FIFO) method assumes that the earliest purchased inventories are the first to be sold to consumers. This means that the 26 units in the ending inventory would be made up of the inventories purchased on May 24.

Ending inventory = (26x 12) = $312

The last-in, first-out (LIFO) method assumes that the latest purchased inventories are the first to be sold to consumers.   This means that the 26 units in the ending inventory would be made up of the May 1 inventories.

Ending inventory = 26 x $10 = $260

The average cost method using the weighted average cost to determine the value of goods sold

Weighted average = total cost of goods / number of goods bought

$1105 / 100 = $11.05

Ending inventory = 26 x $11.05 = $287.30

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The number of cell phones sold in 2015 is (0.29)(1.28x)

The correct answer is A) (0.29)(1.28x).

What is a linear equation?

A linear equation is an equation in which the highest power of the variable is 1. Linear equations can be written in the form ax + b = 0, where a and b are constants and x is the variable. Linear equations are called "linear" because they represent a straight line when plotted on a graph.

We are told that the number of cell phones Hongbo sold in 2014 was 128% greater than in 2013, which means that he sold 128/100 = 1.28 times as many cell phones in 2014 as he did in 2013. This can be represented by the equation x * 1.28 = number of cell phones sold in 2014.

We are also told that the number of cell phones Hongbo sold in 2015 was 29% greater than in 2014, which means that he sold 29/100 = 0.29 times as many cell phones in 2015 as he did in 2014. This can be represented by the equation (number of cell phones sold in 2014) * 0.29 = number of cell phones sold in 2015.

Substituting the first equation into the second equation, we get:

(x * 1.28) * 0.29 = number of cell phones sold in 2015

This simplifies to:

(0.29)(1.28x) = number of cell phones sold in 2015

Hence, the number of cell phones sold in 2015 is (0.29)(1.28x)

the correct answer is A) (0.29)(1.28x).

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7. B <1.4,6,7,8} is NOT a subset of {1,3,5,6,7,8,9,12}.

8. C (2,8,9,12,18} is NOT a subset of all the even integers.

9. C

10. True

11. True

12. True

13. C

14. The sets A = {x I x < 8} and B = {x I x < 12} are subsets of each other.

15. C

16. C

17. C

A subset is a group of objects, elements, or values taken from a larger set. Subsets are typically used to define specific characteristics or qualities of the larger set. For example, a subset of numbers might include only the even numbers from 1 to 10.

7. B <1.4,6,7,8} is NOT a subset of {1,3,5,6,7,8,9,12}.

A subset is a collection of elements that are part of a larger set. In this case, the larger set is {1,3,5,6,7,8,9,12}. B <1.4,6,7,8} is not a subset of this larger set because it includes an element, 1.4, that is not found in the larger set.

8. C (2,8,9,12,18} is NOT a subset of all the even integers.

A subset is a collection of elements that are part of a larger set. In this case, the larger set is all the even integers. C (2,8,9,12,18} is not a subset of all the even integers because it includes an element, 9, that is not even.

9. C

The sets {3,4,8} and {1,2,3,4,5,6} are not subsets of each other. The set {3,4,8} is not a subset of {1,2,3,4,5,6} because it includes an element, 8, that is not found in the larger set.

10. True

The set {1,3,5,7} is a subset of all positive integers. A subset is a collection of elements that are part of a larger set. In this case, the larger set is all positive integers. The set {1,3,5,7} is a subset of this larger set because all of its elements, 1, 3, 5, and 7, are found in the larger set.

11. True

The counting numbers is a subset of the whole numbers. A subset is a collection of elements that are part of a larger set. In this case, the larger set is the whole numbers. The counting numbers is a subset of this larger set because all of its elements, 1, 2, 3, 4, and so on, are found in the larger set.

12. True

The set of all whole numbers is a subset of the natural numbers. A subset is a collection of elements that are part of a larger set. In this case, the larger set is the natural numbers. The set of all whole numbers is a subset of this larger set because all of its elements, 0, 1, 2, 3, 4, and so on, are found in the larger set.

13. C

The sets {-2,0,1,3,8} and all whole numbers are not subsets of each other. The set {-2,0,1,3,8} is not a subset of all whole numbers because it includes an element, -2, that is not found in the larger set.

14. The sets A = {x I x < 8} and B = {x I x < 12} are subsets of each other. The set A is a subset of B because all of its elements, x < 8, are found in the larger set. One element of A that is not found in B is 7.

15. C

The sets A = {x I -2 3} and B are not subsets of each other. The set A is not a subset of B because it includes an element, -2, that is not found in the larger set.

16. C

The sets A = (xIx12 and B = (xIx>1} are not subsets of each other. The set A is not a subset of B because it includes an element, 12, that is not found in the larger set.

17. C

The sets A = {x | 3x + 6 < 0} and B = {x I x < 0} are not subsets of each other. The set A is not a subset of B because it includes an element, -2, that is not found in the larger set.

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Answer:

This is true every triangle has to have 1 acute angle.

Step-by-step explanation:

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

C.

Step-by-step explanation:

This is because the area of the rectangle is 24 square feet and the area of the triangle is 12 square feet. This option is the only one that gives this answer.

I hope it's correct!

This is a transformation of the parent square root function, and it can be written as:

f(x) = √(-x + 4) - 2

It is ratter easy to identify the shape of the general square root function:

f(x) = √x

The only difference is that now it opens to the left, and it starts at the point (4, -2)

Then:

The sign of the x must be negative.

And with the known vertex we can write the equation:

f(x) = √(-x + 4) - 2

That is the graphed function.

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Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

Answer:

50.04

Step-by-step explanation:

Answer: 3.11

Step-by-step explanation:

khan academy hint.

Check the picture below, so the parabola looks more or less like so, the "p" distance is negative, because the horizontal parabola is opening to the left-hand-side, so

\(\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-2\\ k=5\\ p=-5 \end{cases}\implies 4(-5)( ~~ x-(-2) ~~ )=(y-5)^2 \implies -20(x+2)=(y-5)^2 \\\\\\ x+2=-\cfrac{1}{20}(y-5)^2\implies {\Large \begin{array}{llll} x=-\cfrac{1}{20}(y-5)^2-2 \end{array}}\)

Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

The trend line that best fits the data in this problem is given by the following option:

Option D.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

Hence the graph of the line of best fit should have the smallest possible residual values, meaning that the points on the scatter plot are the closest possible to the line.

As option D has the points the closest to the line, it is the correct option in the context of this problem.

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Answer:

the answer world be b) y=x+15

Step-by-step explanation:

no need it's right