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

Answer:

2.78

Step-by-step explanation:

you could have used a calculator

Answer:

23.2 times 0.14 is 3.248

The term used to describe events that have no outcomes in common is called "Mutually Exclusive."

Probability is a measure of how likely an event is to occur. The probability of an event ranges from 0 to 1, where 0 means that an event will not occur, and 1 means that an event will certainly occur.

In Mutually Exclusive events, the probability of both events happening at the same time is 0, which means that the outcome of one event completely eliminates the possibility of the outcome of the other event. The probability of getting heads and tails at the same time is 0, as it is impossible for the coin to show both heads and tails at the same time.

In mathematical terms, Mutually Exclusive events are represented by

=> P(A) + P(B) = P(A or B),

where P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A or B) represents the probability of either event A or B occurring.

To summarize, Mutually Exclusive events are events that have no outcomes in common and have a probability of 0 of occurring simultaneously.

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Answer:

89 meters

Step-by-step explanation:

We know it's 9 + "the height of the triangle".

Fortunately, the height of the triangle (let's call it y) can be computed from:

y^2 + 18^2 = 82^2 (Pythagoras theorem).

y^2 = 82^2 - 18^2 = 6724 - 324 = 6400

y = 80 (or y = -80 but it doesn't make sense in geometry).

so x = y + 9 = 89;

Answer:

The approximate value of 36/π is 11.4591559026

Step-by-step explanation:

Answer:

Step-by-step explanation:

So we need to divide the volume of the cylindrical glasses by the cylindrical jugs to see how many we can fill.

The equation to find the volume of a cylinder is Height*Area of Circle

To find the area of a circle is: \(\pi r^{2}\)

In this senario "r" (radius) is 3 (d/2)

Volume for cylindrical glass:

hx\(\pi r^{2}\)

= 10x 3.14x 3^2

= 10x3.14x 9

= 282.6\(cm^{3}\)

Now for the cylindrical jug:  r= 5 and h=18

hx\(\pi r^{2}\)

= 18x3.14x5^2

= 18x3.14x25

= 1413\(cm^{3}\)

Now finally we divide them:

1413/282.6

= 5

So they can fill 5 cylindrical glasses :)

Answer:

Should be 65%

Step-by-step explanation:

adding up all the numbers from the table and then dividing by the number of students in just sports gives you 65%.

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Answer:

neither they are the same value of ratio

Step-by-step explanation:

18:10 - jacks class

54:30- micheal’s class

18:10

x3 x3

54:30

Meaning the ratio is the exact same value

Hopes this helps please mark brainliest

Answer: The index of refraction for the unknown wavelength is approximately 1.355.

Step-by-step explanation:

We can use Snell's law to relate the incident angle and refracted angle to the indices of refraction:

n1 sinθ1 = n2 sinθ2

where n1 and θ1 are the index of refraction and incident angle of the light in air, and n2 and θ2 are the index of refraction and refracted angle of the light in glass. Since the incident angle is 45.00 degrees, we have:

sinθ1 = sin(45.00) = √2/2

Since we know the index of refraction for the 450.0 nm light is 1.482, we can solve for the refracted angle θ2:

1.000 * √2/2 = 1.482 * sinθ2

sinθ2 = 1.000 * √2/2 / 1.482 = 0.4951

θ2 = sin^(-1)(0.4951) = 29.07 degrees

Now, we can use Snell's law again to relate the index of refraction to the refracted angle for the unknown wavelength:

n1 sinθ1 = n3 sinθ3

where n3 is the index of refraction for the unknown wavelength, and θ3 is the refracted angle for the unknown wavelength. We know that θ3 is 0.8000 degrees greater than θ2:

θ3 = θ2 + 0.8000 = 29.87 degrees

Substituting all the known values into Snell's law, we get:

1.000 * √2/2 = n3 * sin(29.87)

n3 = 1.000 * √2/2 / sin(29.87) = 1.355

Therefore, the index of refraction for the unknown wavelength is approximately 1.355.

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Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Answer:

861.56 km2

Step-by-step explanation:

the formula for the area of a trapazoid is

a= (a+b/2) + h

Answer:

kinder

Step-by-step explanation:

1. 8

2. 2

The time that it will take for them to complete the work is given as follows:

2 and 17/20 days.

To obtain the remaining time, we use the together rate, which is the sum of each of the separate rates.

The rates for this problem are given as follows:

Hence the together rate is obtained as follows:

1/x = 1/8 + 1/12

1/x = 5/24

5x = 24

x = 3.8 days.

Ann worked two days, meaning that only 6/8 = 75% of the document has to be completed, hence the time is of:

0.75 x 3.8 = 2.85 days = 2 and 17/20 days.

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To price the derivative using the two-period binomial model, we need to calculate the expected payoff of the derivative using the risk-neutral probabilities.

The possible outcomes for the two-period binomial model are H and T,  there are four possible states of the world: HH, HT, TH, and TT.

To calculate the expected payoff we need to calculate the probability of each state occurring. The probability of HH occurring is pp=0.60.6=0.36, the probability of HT and TH occurring is pq+qp=0.60.4+0.40.6=0.48, and the probability of TT occurring is qq=0.40.4=0.16.

Next, we can calculate the expected payoff in HH and TT states, the derivative pays off 1, and in the HT and TH states, the derivative pays off 0. The expected payoff of the derivative in the HH and TT states is 10.36=0.36, and the expected payoff in the HT and TH states is 00.48=0.

We need to discount the expected payoffs back to time 0 using the risk-neutral probabilities.

The probability of that state occurring multiplied by the discount factor, which is 1/(1+r), where r is the risk-free interest rate.

Since this is a risk-neutral model, the risk-free interest rate is equal to 1. Therefore, the risk-neutral probability of each state occurring is

HH: 0.36/(1+1) = 0.18

HT/TH: 0.48/(1+1) = 0.24

TT: 0.16/(1+1) = 0.08

Finally, we can calculate the price of the derivative

Price = 0.181 + 0.240 + 0.240 + 0.081 = 0.26

Therefore, the price of the derivative is 0.26.

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the equation of the tangent line is y = -46x + 166.

To find the slope of the tangent line to the graph of the function at the given value of x, we need to take the derivative of the function and evaluate it at x = 1.

Differentiate the function f(x) = x^4 - 25x^2 + 144 with respect to x:

f'(x) = 4x^3 - 50x

Evaluate the derivative at x = 1:

f'(1) = 4(1)^3 - 50(1) = 4 - 50 = -46

So, the slope of the tangent line is -46.

To find the equation of the tangent line, we can use the point-slope form of a linear equation. We have the point (1, f(1)) on the tangent line, and we know the slope is -46.

Find the value of f(1):

f(1) = (1)^4 - 25(1)^2 + 144 = 1 - 25 + 144 = 120

Use the point-slope form with the point (1, 120) and slope -46:

y - y1 = m(x - x1)

y - 120 = -46(x - 1)

y - 120 = -46x + 46

y = -46x + 166

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Answer:d

Step-by-step explanation:

Answer:

d is the answer to your question

Answer:

The answer is D!!!

Step-by-step explanation:

x=-7/5,=8/5 or (x=-1 2/5,y= 1 3/5) D one -7/5 = 1 2/5. 8/5 = 1 3/5

D IS THE CORRECT ANSWER

The graph of the sine function f(x) = sin(400πx) is given by the image at the end of the answer.

The sine function in this problem is defined as follows:

f(x) = sin (y × 2πx).

In which the relevant variable for the graph is the variable y, which is the number of cycles in a single second of the wave.

In this problem, it is states that the note has a frequency of 440 Hz, meaning that it has 440 cycles in one second, thus the equation is:

f(x) = sin (440 × 2πx).

f(x) = sin (880πx).

The function is not multiplied by any value, hence the amplitude is of 1, meaning that the function oscillates between 0 and 1, and also there is not any phase shift or vertical shift, meaning that it oscillates between -1 and 1 starting at the origin.

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Answer:

p = 5t

Step-by-step explanation:

We'll check by plugging in t = 3 and p has to equal 15

p = 5t     ✅

p = 5(3)

p = 15

3t = 15p ❌

3(3) = 15p

9 = 15p

p = 15/9 = 5/3

p/t = 15 ❌

p/3 = 15

p = 45

p = 1/5t ❌

p = 1/5(3)

p = 3/5

f(x)Δx = 0.090. the exact answer for f(x)Δx in problem 14 has only one decimal place, so we did not need to round it. Similarly, the exact answer for f(x)Δx in problem 16 has two decimal places, so we rounded to three decimal places. In both problems, we are given a function and values for x and Δx. We need to find Δy and f(x)Δx.

To find Δy, we can use the formula Δy = f(x + Δx) - f(x). For problem 14, we have f(x) = -2/x, x = 2, and Δx = 0.2. Plugging these values in, we get:

f(x + Δx) = -2/(2 + 0.2) = -2/2.2
Δy = f(x + Δx) - f(x) = (-2/2.2) - (-2/2) = -0.1818...
Rounding to three decimal places, we get Δy = -0.182.

To find f(x)Δx, we can use the formula f(x)Δx = f(x) * Δx. Plugging in the values from problem 14, we get:

f(x)Δx = (-2/2) * 0.2 = -0.2
Rounding to three decimal places, we get f(x)Δx = -0.200.

We follow a similar process for problem 16. We have f(x) = 3/x^2, x = 1, and Δx = 0.03. Plugging these values into the formula for Δy, we get:

f(x + Δx) = 3/(1 + 0.03)^2 = 2.768...
Δy = f(x + Δx) - f(x) = 2.768... - 3 = -0.231...
Rounding to three decimal places, we get Δy = -0.231.

To find f(x)Δx, we use the formula f(x)Δx = f(x) * Δx. Plugging in the values from problem 16, we get:

f(x)Δx = (3/1^2) * 0.03 = 0.09
Rounding to three decimal places, we get f(x)Δx = 0.090.

Note that we were asked to round to three decimal places unless the exact answer has less decimal places. In both problems, the exact answer for Δy has more decimal places than three, so we rounded to three decimal places. However, the exact answer for f(x)Δx in problem 14 has only one decimal place, so we did not need to round it. Similarly, the exact answer for f(x)Δx in problem 16 has two decimal places, so we rounded to three decimal places.

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The gas station serves 16 vehicles per hour, and 72 vehicles arrive in 4 hours. The vehicles will spend 4.50 hours at the gas station.



To find the total time the vehicles will spend at the gas station, we need to calculate the total number of vehicles that arrive and then divide it by the rate at which the gas station serves vehicles.

Given:

Arrival rate: 18 vehicles per hour

Service rate: 16 vehicles per hour

Time: 4 hours

First, let's calculate the total number of vehicles that arrive during the 4-hour period:

Total number of vehicles = Arrival rate * Time

                      = 18 vehicles/hour * 4 hours

                      = 72 vehicles

Since the gas station can serve 16 vehicles per hour, we can determine the time it takes to serve all the vehicles:

Time to serve all vehicles = Total number of vehicles / Service rate

                         = 72 vehicles / 16 vehicles/hour

                         = 4.5 hours

Therefore, the vehicles will spend 4.5 hours at the gas station. Rounded to 2 decimal places, the answer is 4.50 hours.

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This is actually pretty simple, so i think you should catch on fast, so basically, the opposite of 59 is -59. so basically, just add a negative on there and your all set. If its negative, switch it to positive. Hope it helped!

Answer:

(8.6)(-2)+(8.6)(-0.5)

Step-by-step explanation

Since -2+-0.5= -2.5, we need to use a plus sign. Also, since we multiply both by 8.6, that is the answer.

15.6 - (-22.2)

15.6 + 22.2

37.8

Answer:

5

Step-by-step explanation:

angles A and D are congruent, 10 times 5 = 50

Answer:

\(33 units^{2}\)

I counted the squares.

Answer:

12.10on zas

Step-by-step explanation:

Esun as uma

Answer:

0.417

*I rounded

Or fraction form, 5/12

Answer:

5/12

Step-by-step explanation:

or in decimal form its 0.416 with the 6 repeating

The limit of (7x - ln(x)) as x approaches infinity is infinity.

To see why, note that the natural logarithm function ln(x) grows very slowly compared to any polynomial function of x. Specifically, ln(x) grows much more slowly than 7x as x becomes large. Therefore, as x approaches infinity, the 7x term in the expression 7x - ln(x) dominates, and the overall value of the expression approaches infinity. Alternatively, we could apply L'Hopital's rule to the expression by taking the derivative of the numerator and denominator with respect to x. The derivative of 7x is 7, and the derivative of ln(x) is 1/x. Therefore, the limit of the expression is equivalent to the limit of (7 - 1/x) as x approaches infinity. As x approaches infinity, 1/x approaches zero, so the limit of (7 - 1/x) is 7. However, this method requires more work than simply recognizing that the 7x term dominates as x approaches infinity.

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The Pythagorean identities are a set of trigonometric identities that relate the three basic trigonometric functions: sine, cosine, and tangent.

"TIDBIT" During my exploration of the identities and techniques over the past weeks, I came across an interesting tidbit related to the Pythagorean identities. The Pythagorean identities are a set of trigonometric identities that relate the three basic trigonometric functions: sine, cosine, and tangent. One of the Pythagorean identities states that for any angle θ, the square of the sine of θ plus the square of the cosine of θ is always equal to 1.

sin²θ + cos²θ = 1

This identity has a fascinating geometric interpretation. Consider a right-angled triangle where one of the acute angles is θ. The sine of θ represents the ratio of the length of the side opposite θ to the length of the hypotenuse, while the cosine of θ represents the ratio of the length of the side adjacent to θ to the length of the hypotenuse. The identity essentially states that the squares of these ratios sum up to 1, which means that the sum of the squares of the lengths of the two sides (opposite and adjacent) is equal to the square of the hypotenuse's length. This result is a fundamental property of right-angled triangles and is known as the Pythagorean theorem.

The connection between the Pythagorean theorem and the Pythagorean identities is intriguing. It demonstrates that the trigonometric functions and the geometric properties of right triangles are deeply intertwined. It also highlights the usefulness of trigonometry in solving problems involving triangles and angles. Understanding this connection can provide a deeper appreciation for the Pythagorean identities and their applications in various mathematical contexts.

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