The store sells two types of toys, dolls, and cars. The dolls cost $15 each and the cars cost $10 each. If a customer buys a total of 10 toys and spends 120, how many dolls and cars did the customer buy?

Write given world problem as equations

a) The exponential equation is h = h₀ * \(r^{x}\).

b) The multiplier represents the ratio between the height of the ball after each bounce.

c) We cannot determine the height.

a. To model the given situation, we can use an exponential equation of the form:

h = h₀ * \(r^{x}\)

where:

h represents the height of the ball after x bounces,

h₀ represents the initial height of the ball,

r represents the multiplier that determines the ratio between consecutive bounces,

x represents the number of bounces.

In this case, the initial height of the ball is 200 inches, and after the third bounce, the height is 12.8 inches. Therefore, we can write the exponential equation as:

12.8 = 200 * \(r^{3}\)

b. The multiplier (r) in this context represents the ratio between the height of the ball after each bounce. Since the ball is dropping and bouncing, the multiplier should be between -1 and 1 to account for the decreasing height with each bounce. A multiplier greater than 1 would result in an increasing height with each bounce, which is not applicable in this scenario.

c. To find the height the ball rose to after the second bounce, we can substitute x = 2 into the exponential equation. Using the given information, we have:

h = 200 * \(r^{2}\)

To find the value of r, we need additional information or assumptions about the bouncing behavior of the ball. Without that information, we cannot determine the exact height the ball rose to after the second bounce.

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Answer:

24%

Step-by-step explanation:

we subtract to see how much it increased

62-50=12

Now divide 12 by 50 to get percent

12/50

0.24

0.24x100

24%

Hopes this helps please mark brainliest

Answer:

SAS

Step-by-step explanation: every triangle contains a total of 180 degrees if you substract 180 by 60+70(which is 130) you would get 50 degrees which is the exact degree missing in the first triangle, so after confirming that both triangles have an equal degrees on each side the answer would be SAS (which stands for Side-Angle-Side), SAS is the answer you would give to triangles that are congruent(equal)

The change over 24 seconds is 984 feet means It’s increased 984 feet. Therefore, the correct option is B.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

The equation to find the altitude at x seconds as;

41x = y

Where X is the seconds and y being the total altitude.

41 ft =1 sec

For about 24 sec, just have to replace x with 24 , since we’re looking for the change over 24 seconds.

41 x 24 = 984

Hence, The change over 24 seconds is 984 feet means It’s increased 984 feet.

Therefore, the correct option is B.

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The distance between the two given points is 13 units.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The Pythagorean theorem is given by the following formula:

h² = a² + b²

Where h is the hypotenuse and a and b are the legs of the right triangle.

In the given image, when you construct a right triangle with the line of the two points as a hypotenuse, you have for a and b:

a = 5

b = 12

Replace the previous values of a and b in the formula for h:

h² = (5)² + (12)²

h² = 25 + 144

h² = 169

h = √169

h = 13

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Answer:

Use the Pythagorean Theorem to find the diagonal:

\(5^{2} +l^{2} =(\sqrt{125})^{2}\\ 5^{2} +l^{2} =125\)

They function by balancing their budgets through a combination of these revenue streams, along with careful budgeting and expenditure management.

Comparing a state without an income tax to one with an income tax, the key differences lie in the tax burden placed on residents and businesses. In the absence of an income tax, individuals in the state without income tax enjoy the benefit of not having a portion of their businesses may find it more attractive to operate in such states due to lower tax obligations. However, these states often compensate for the lack of income tax by imposing higher sales or property taxes.

States without a state income tax, such as Texas, Florida, and Nevada, function by generating revenue from various alternative sources. Sales tax is a major contributor, with higher rates or broader coverage compared to states with an income tax.

Property taxes also play a significant role, as these states tend to rely on this form of taxation to fund local services and public education. Additionally, fees on specific services, licenses, or permits can contribute to the state's revenue stream.

Comparing such a state to one with an income tax, the key differences lie in the tax structure and the burden placed on residents and businesses. In states without an income tax, individuals benefit from not having a portion of their earnings withheld, resulting in potentially higher take-home pay. This can be appealing for professionals and high-income earners. For businesses, the absence of an income tax can make the state a more attractive location for investment and expansion.

However, the lack of an income tax in these states often means higher reliance on sales or property taxes, which can impact residents differently. Sales tax tends to be regressive, affecting lower-income individuals more significantly. Property taxes may be higher to compensate for the revenue lost from the absence of an income tax.

Additionally, the absence of an income tax can result in a greater dependence on other revenue sources, making the state's budget more susceptible to fluctuations in the economy.

Overall, states without a state income tax employ alternative revenue sources and careful budgeting to function. While they offer certain advantages, such as higher take-home pay and potential business incentives, they also impose higher sales or property taxes, potentially impacting residents differently and requiring careful management of their budgetary needs.

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9514 1404 393

Answer:

  A, B, C, D, F . . . as written

Step-by-step explanation:

Any mixed number, fraction, or finite or repeating decimal is rational. The only one in your list that is irrational is E, which appears to be a non-repeating, non-terminating decimal.

__

Your B selection appears to be 11² = 121, an integer and a rational number.

If your B selection is supposed to be √11, then that number is irrational, as it is not the root of a perfect square.

E is irrational; B is rational as written, but irrational if it should be √11. All the others are rational.

An undefined equation can be one where the denominator is 0.

SO here in the option d,

This expression is undefined. All the other expressions can be solved.

Answer:

a

Step-by-step explanation:

it has a negative number which causes the parabola to be a maximum as opposed to a minimum

Using parabola concepts, it is found that the graph that represents \(f(x) = -2x^2\) is given by option A.

In this problem, we have \(f(x) = -2x^2\), which has a negative leading coefficient, thus it is a concave down parabola, which is represented by option A.

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Answer:

1

Step-by-step explanation:

The problem is basically asking us to find the value on the graph corresponding to the x value of 1. We can draw a line with the equation x = 1(or just trace your finger up) to see that when x = 1, the output of the function is at the value 1 as well(the y value).

The geometric cumulative distribution function should be used.

The geometric cumulative distribution is a discrete likelihood conveyance where the random variable demonstrates the quantity of the Bernoulli trial expected to get the primary achievement. A Bernoulli trial is an experiment that can have just two potential results, ie., achievement or disappointment. All in all, in a mathematical dispersion, a Bernoulli trial is rehashed until a triumph is gotten and afterward halted. Here we are interested in the first success in the three chances, which is completely specified with the distribution function of a geometric distribution, and because the question asked for the probability of having a hand with five cards in the same suit in one of the first three hands. Hence the correct option is the cumulative distribution function.

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To find the magnitudes of the velocity (v) and acceleration (a) and the angles they make with the x-axis at t = 4.1 s, we need to differentiate the given equations for x and y with respect to time (t).

Given:

x = 1.3t^2 - 6.6t

y = 2.8t^2 - (t^3)/4.0

Velocity (v):

The velocity is the rate of change of position with respect to time. It can be calculated by taking the derivatives of x and y with respect to t:

vx = dx/dt = d/dt(1.3t^2 - 6.6t)

vy = dy/dt = d/dt(2.8t^2 - (t^3)/4.0)

Calculate vx and vy by differentiating the expressions:

vx = 2.6t - 6.6

vy = 5.6t - (3t^2)/4.0

At t = 4.1 s, substitute t = 4.1 into vx and vy to find the components of the velocity vector at that time.

Acceleration (a):

The acceleration is the rate of change of velocity with respect to time. We can calculate it by taking the derivatives of vx and vy with respect to t:

ax = d(vx)/dt = d/dt(2.6t - 6.6)

ay = d(vy)/dt = d/dt(5.6t - (3t^2)/4.0)

Calculate ax and ay by differentiating the expressions:

ax = 2.6

ay = 5.6 - (3t)/2.0

Again, substitute t = 4.1 s into ax and ay to find the components of the acceleration vector at that time.

Angles with the x-axis (θx):

To find the angles that the velocity and acceleration vectors make with the x-axis, we can use the inverse tangent function:

θx = arctan(vy / vx)

Calculate θx using the values of vx and vy at t = 4.1 s.

Substitute the values of v, a, and θx into the answers to complete the solution.

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x = 120

Too long to exaplin.

Just trust me

Depending on the accounting method used, the expense shown on the income and expense statement for the year would either be $150 or $500.

When purchasing a $500 stereo on an installment plan, the expense recorded on the income and expense statement for the year will depend on the accounting method used.

1. Cash Basis Accounting:

Under cash premise bookkeeping, costs are recorded when money is paid. In this case, since you made two payments of $75 each during the year, the expense recorded would be the total amount of cash paid, which is $75 x 2 = $150.

2. Accrual Basis Accounting:

Under accrual basis accounting, expenses are recorded when they are incurred, regardless of when the cash is paid. In this case, the expense recorded would be the total cost of the stereo, which is $500. The payments made during the year would be recorded as a reduction in the accounts payable liability associated with the stereo purchase.

Therefore, depending on the accounting method used, the expense shown on the income and expense statement for the year would either be $150 (cash basis accounting) or $500 (accrual basis accounting). It's important to note that the chosen accounting method should align with the accounting principles and regulations applicable to your situation.

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Answer:

The asnwer is a. 4.5%

Step-by-step explanation:

.05 * 25000 + $275 = 4.5

Answer:

Yes ur right

Step-by-step explanation:

Answer:

1) b. at vertex ( 0,20) P = 5(20) = 100 at vertex ( 4,4) P = 3(4) + 5(4) = 32 at vertex (20,0) P = 3(20) = 60 c. x = 4 , y = 4 2) x-intercepts x 1 = 1.66667, ...

Step-by-step explanation:

Sarah scored 82 points on her first test of the year. On the second test,

82%

On the Second Test, She scored 77 points

77%

82

-77

=5

The Percent of Change is 5%

or -5% Because The second test Is lower than her first test

Answer:

5%

Step-by-step explanation:

82% - 77%=5%

82%

77%

so there fore the answer is 5%

1a)The values of l range from 0 to (n-1), so for n = 3, l can have the values 0, 1, and 2.

b) The values of m can be -2, -1, 0, +1, and +2

c) There are a total of 9 orbitals

The qualities and traits of quantum systems, like the electrons in atoms, are described by a set of numbers known as quantum numbers. They offer knowledge on the system's energy, angular momentum, orientation, and spin, among other characteristics.

Using the formula, number of electrons = \(n^2\)

Number of electrons =\(3^2 = 9\)

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Answer:

x-intercept is (-16,0) and y-intercept is (0,2)

Step-by-step explanation:

To find the x-intercept of the equation 1/2x = -4y - 8, we need to set y to 0 and solve for x.

1/2x = -4(0) - 8

1/2x = -8

x = -8*2

x = -16

So the x-intercept of the equation is (-16,0)

To find the y-intercept of the equation 1/2x = -4y - 8, we need to set x to 0 and solve for y.

1/2(0) = -4y - 8

-8 = -4y

y = 8/4

y = 2

So the y-intercept of the equation is (0,2)

Answer:

the x-intercept of the equation is (-16, 0).
the y-intercept of the equation is (0, 2).

Step-by-step explanation:

To find the x-intercept and y-intercept of the equation 1/2x = -4y - 8, we can set one of the variables to zero and solve for the other variable.

For the x-intercept, we set y = 0 and solve for x:

1/2x = -4(0) - 8

1/2x = -8

x = -8 * 2

x = -16

So the x-intercept of the equation is (-16, 0).

For the y-intercept, we set x = 0 and solve for y:

1/2(0) = -4y - 8

-4y = -8

y = 2

So the y-intercept of the equation is (0, 2).

Answer:

c=8

Step-by-step explanation:

The value of c that makes z = -5/4 an extraneous solution is c = 24/5.

A linear equation is defined as an equation in which the highest power of the variable is always one.

The equation is given as:

√{4z + 9} = cz + 8

An extraneous solution is a solution that is not a valid solution to the original equation, but it is obtained during the process of solving the equation. In this case, the extraneous solution is z = -5/4.

To determine the value of c that makes z = -5/4 an extraneous solution, we can substitute -5/4 for z in the original equation. This gives us the following:

√{4 × -5/4 + 9} = -5/4 × c + 8

√{-5 + 9} = -5/4 × c + 8

√4 = -5/4 × c + 8

2 = -5/4 × c + 8

5/4 × c =  8 - 2

5/4 × c = 6

c = 6 × 4/5

c = 24/5

Therefore, the value of c that makes z = -5/4 an extraneous solution is c = 24/5.

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a) The actual distance between towns K and L is: 100 km

b) As shown in the attached file

c) The bearing of town L from town K is 117 degrees.

The scale of the map is given as:

1 cm to represent 50 km

Now, when we measure the distance between K and L on the map, we see that it gives us a distance of 2 cm.

Using the scale of 1 cm: 50 km, we can say that:

Actual distance between towns K and L = (2 * 50)/1 = 100 km

b) Using a compass and it’s 3cm aiming down {South} as seen in the attached photo. Then a line was drawn aiming {South} with a ruler. On the end of the line the (x) point was put there to get the mark.

c) Measuring the angle gives the bearing of town L from town K which is 117 degrees.

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To find the values of x at the points where y = 4x - x² intersects y = 0, we can set 4x - x² equal to 0 and solve for x.

4x - x² = 0

Factor out x:

x(4 - x) = 0

Therefore, either x = 0 or 4 - x = 0.

If x = 0, then the point where the two curves intersect is (0,0).

If 4 - x = 0, then x = 4 and the point where the two curves intersect is (4,0).

So the values of x at the points where the two curves intersect y = 0 are x = 0 and x = 4.

The probability of winning $100 by matching exactly three of the first five and the sixth numbers is 0.0018. The probability of winning $100 by matching four of the first five numbers but not the sixth number is 0.0003.

To calculate the probability of winning $100 by matching exactly three of the first five and the sixth numbers, we first need to determine the total number of possible combinations for the first five numbers. Since each of the five numbers can be any number between 1 and 69, there are 69 choose 5 (written as 69C5) possible combinations, which is equal to 11,238,513. Out of these 11,238,513 possible combinations, we need to choose three numbers that will match the drawn numbers and two numbers that will not match. The probability of matching three numbers is calculated as 5C3/69C5, which is equal to 0.0018. The probability of not matching the remaining two numbers is 64C2/64C2, which is equal to 1.

Therefore, the probability of winning $100 by matching exactly three of the first five and the sixth numbers is 0.0018 x 1, which is equal to 0.0018. To calculate the probability of winning $100 by matching four of the first five numbers but not the sixth number, we need to determine the total number of possible combinations for four of the first five numbers. Since each of the four numbers can be any number between 1 and 69, there are 69 choose 4 (written as 69C4) possible combinations, which is equal to 4,782,487.

Out of these 4,782,487 possible combinations, we need to choose four numbers that will match with the drawn numbers and one number that will not match. The probability of matching four numbers is calculated as 5C4/69C4, which is equal to 0.0003. The probability of not matching the remaining number is 64/64, which is equal to 1. Therefore, the probability of winning $100 by matching four of the first five numbers but not the sixth number is 0.0003 x 1, which is equal to 0.0003.

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In the given diagram, the value of x is 15

From the question, we are to determine the value of x

From one of the circle theorems, we have that

Opposite angles of a cyclic quadrilateral are supplementary.

Thus, in the diagram

5x + 7x = 180°

12x = 180°

x = 180°/12

x = 15

Hence, the value of x is 15

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Explanation

Step 1

let x represents the number so

a) 2/9 of a number is 8

so, the numer is 36

Step 2

b) 3/11 of a number is 12​

so, the number is 44