A car travels 76km in
47 minutes. What is
Its average speed in
km/h? Give your answer
rounded to 1 decimal
place

We have the following function given:

We want to apply a dilation with a scale factor k centered at the origin

Assuming that the scale factor is k, then we just need to do the following :

And with this we preserve the condition of centered at the origin and with the dilation factor

Ninety-five percent of people have IQs between 70 and 130.99.7 percent of people have IQ scores between 55 and 145.With IQ scores between 55 and 145, only 0.3% of the population falls outside this range.

How likely is it that a student chosen at random will have an IQ of 115 or higher?

Since half should be over the normal of 100 (by evenness), this implies 50 - 34.13 = 15.87 (%) has an intelligence level score over 115.

Which level of understudies might have scored either higher than 90 or lower than 70?

That always prompts the same response: 95%!Since we are aware that one standard deviation equals five points, two standard deviations equal two x 5.As a result, 95% of scores fall between 70 and 90, which is 10 points above the mean of 80.

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Using a proportional relationship, it is found that her speed is of 35 meters per minute.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

The line goes through point (40, 1400), hence the constant is:

k = 1400/40 = 35.

Thus her speed is of 35 meters per minute.

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Answer:

b

Step-by-step explanation:

f(x)=y

this question tell us that f(0)=1 and f(4)=3

try b, b option matches those given.

The number of hours Meghan volunteered is 14 hours.

According to the question,

We have the following information:

Aani volunteered for four more than three times the number of hours that Meghan did. Altogether, they volunteered for 60 hours.

Now, let's take the number of hours for Meghan to be x.

So, we have:

Aani's number of hours = (3x+4)

Now, we have the following expression:

3x+4+x = 60

4x+4 = 60

Moving 4 from the left hand side to the right hand side will result in the change of the sign from plus to minus:

4x = 60-4

4x = 56

x = 56/4

x = 14 hours

Hence, the correct option is A (the first one).

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Answer:

The probability that a Dutch male is between 173.5 and 191.5 cm is 0.616

or 61.6%

Step-by-step explanation:

Mean = M = 182.5

Standard Deviation = S = 10.3,

We need to find the z values and then calculate the probabilities,

Probability of being lower than 173.5,

P(X < 173.5),

Finding the z value,

z = (x - M)/S

z = (173.5 - 182.5)/10.3

z = -0.87

Then the corresponding value for the area and hence the probability is,

P(X<173.5) = P(z = -0.87) = 0.1922

P(X < 173.5) = 0.1922

Probability of being lower than 191.5,

P(X<191.5)

Finding the z value,

z =(x-M)/S

z = (191.5 - 182.5)/10.3

z = 0.87

Then the corresponding value for the probability is,

P(X < 191.5) = 0.8078

The probability that a Dutch male is between 173.5 and 191.5 cm is,

P(173.5 < X < 191.5) = P(X < 191.5) - P(X < 173.5)

P(173.5 < X < 191.5) = 0.8078 - 0.1922

P(173.5 < X < 191.5) = 0.6156

To 3 decimal places,

P(173.5 < X < 191.5) = 0.616

P(173.5 < X < 191.5) = 61.6%

Answer: 59.58 ft

Step-by-step explanation:

Given

The area of the neighbor's fence is  \(A=887.5\ ft^2\)

Suppose the length of the fence is L and the shape of the fenced area is square

So, we can write

\(\Rightarrow L^2=887.5\\\Rightarrow L=\sqrt{887.5}=29.79\ ft\)

According to the question, Cody's fence length must be twice of neighbor's

The length of Cody's fence is \(=2L=2\times 29.79=59.58\ ft\)

If P(t) is the size of a population at time t , the differential equation describes linear growth in the size of the population is \(\frac{dP}{dt}=200\)

The differential equation is is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point.

dy/dx = f(x)

Here “x” is an independent variable and “y” is a dependent variable

According to the question,

Size of population at t time = P(t)

Also given ,The differential equations have a linear growth in the size of the population.

So, The degree of the variable must be one. And the equation of the population will be quadratic.

Therefore , dP/dt = 200 tells us the rate change of population with respect to time.

A derivative of linear function is constant .

Hence , option B is correct.

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Answer:

-4

Step-by-step explanation:

first remove the parentheses

5-4-7+2

then calculate the sum or difference

-4

The experimental probability of an event is the ratio of the number of successful outcomes to the number of trials performed. In this case, the experimental probability of the spinner landing on red is given as 1/8, which means that for every 8 spins, it should land on red 1 time.

Option D : The experimental probability of the spinner landing on red is given as 1/8. If it landed on red 6 times, then the number of trials is

8 * 6 = 48.

The experimental probability of an event is the ratio of the number of successful outcomes to the number of trials performed. In this case, the experimental probability of the spinner landing on red is given as 1/8, which means that for every 8 spins, it should land on red 1 time.

To determine the number of trials that were performed, we need to know how many times the spinner landed on red. In this case, it landed on red 6 times.

Using the experimental probability,

Trials = Red spins * (1 / Experimental probability)

= 6 * (1 / 1/8)

= 6 * 8

= 48

Therefore, the number of trials performed is 48.

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The percentage increase per year in the winner's check over the given period. If the winner's prize increases at the same rate, it will be $1,454,735,139.69 in 2040.

To calculate the percentage increase per year in the winner's check over the period from 1895 to 2007, we can use the following formula:

Percentage Increase = (Final Value - Initial Value) / Initial Value * 100

a. Calculating the percentage increase:

Initial Value = $140

Final Value = $1,171,000

Percentage Increase = (1,171,000 - 140) / 140 * 100 ≈ 835,714.29%

b. To estimate the winner's prize in 2040, we can assume the same annual percentage increase will continue. We need to calculate the number of years from 2007 to 2040 and apply the percentage increase to the 2007 prize.

Number of years = 2040 - 2007 = 33 years

Estimated prize in 2040 = 1,171,000 * (1 + (Percentage Increase / 100))^33

Estimated prize in 2040 = 1,171,000 * (1 + (835,714.29 / 100))^33 ≈ $1,454,735,139.69

Therefore, if the winner's prize increases at the same rate, it is estimated to be approximately $1,454,735,139.69 in 2040.

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The solutions to the questions are given below

a)

sample(n) word length sample mean

1                    5,4,4,2    3.75

2                    3,2,3,6     3.5

3                         5,6,3,3    4.25

b)R =0.75

c)

The table below shows sample means in the table.

sample(n) word length sample mean

1                    5,4,4,2    3.75

2                    3,2,3,6     3.5

3                         5,6,3,3    4.25

b)

Generally, the equation for is  mathematically given as

variation in the sample means

R =maximum -minimum

R=4.25-3.5

R =0.75

c)

In conclusion, In most cases, the mean of many samples will provide a more accurate estimate than the mean of a single sample.

They may have a higher level of confidence in their estimate if the range of the sample means is closer to 0 than it is now.

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Answer:

P = 37.4 m

Step-by-step explanation:

let the third side of the triangle be x

using Pythagoras' identity in the right triangle.

x² + 7² = 16²

x² + 49 = 256 ( subtract 49 from both sides )

x² = 207 ( take square root of both sides )

x = \(\sqrt{207}\) ≈ 14.4 m ( to 1 decimal place )

the perimeter (P) is then the sum of the 3 sides

P = 7 + 16 + 14.4 = 37.4 m

Answer:

The slope is:

Step-by-step explanation:

Given the table

Pounds, x        3        4        5       6

Cost, y             6        8        10     12

Taking any two points let say (3, 6) and (4, 8)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(3,\:6\right),\:\left(x_2,\:y_2\right)=\left(4,\:8\right)\)

\(m=\frac{8-6}{4-3}\)

Refine

\(m=\frac{2}{1}\)

\(m = 2\)

Therefore, the slope is:

Answer:

Given,

Distance traveled = 20 km

Speed = 60 km/h

So, timetaken=DistanceSpeed=2060=13h

For the next journey

Distance traveled = 20 km

Speed = 80 km/h

So, timetaken=DistanceSpeed=2080=14h

Now,

Total distance traveled = 20 + 20 = 40 km

Total time taken = 13+14=712

We know,

Averagespeed=TotaldistancetraveledTotaltimetaken=40712=68.5 km/h

Hence the average speed of the train is 68.5 km/h

Answer:

c. x=3

Step-by-step explanation:

Given:

7x < 21

Divide both sides by 7

7x / 7 < 21 / 7

x < 21/7

x < 3

x = 3

Check:

7x < 21

7(3) < 21

21 = 21

Answer:

Approximately \(50\; \rm m \cdot s^{-2}\), assuming that air resistance is negligible and that the rock was released with zero initial velocity.

Step-by-step explanation:

Let \(g\) denote the gravitational acceleration on this planet.

Let \(x\) denote the displacement of this rock during this fall. Let \(t\) denote the duration of this fall. Assume that the rock was released with an initial velocity \(v_{0} = 0\; \rm m \cdot s^{-1}\).

Assume that the air resistance is negligible (such that gravity is the only force on this rock). The acceleration \(a\) of the rock during the fall would be constantly equal to the gravitational acceleration \(g\).  

Since the acceleration of the rock during the fall was constantly \(a = g\), the following SUVAT equation would apply:

\(\displaystyle x = \frac{1}{2}\, a \, t^{2} + v_{0}\, t\).

Rearrange this equation to find an expression for acceleration \(a\):

\(\begin{aligned}a &= \frac{x - v_{0}\, t}{t^{2} / 2}\end{aligned}\).

Convert the height and duration of this fall to standard units:

\(\begin{aligned}h &= 89\; \rm km \times \frac{10^{3}\; \rm m}{1\; \rm km} \\ &= 8.9\times 10^{4}\; \rm m\end{aligned}\).

\(\begin{aligned}t &= 0.99\; \rm min \times \frac{60\; \rm s}{1\; \rm min} \\ &= 59.4\; \rm s\end{aligned}\).

Substitute in the values to find the value of acceleration \(a\):

\(\begin{aligned}a &= \frac{x - v_{0}\, t}{t^{2} / 2} \\ &= \frac{89000\; \rm m}{(59.4\; \rm s)^{2} / 2} && (\text{Note that $v_{0} = 0\; \rm m\cdot s^{-1}$.}) \\ &\approx 50\; \rm m\cdot s^{-2} \end{aligned}\).

By the assumptions above, the acceleration of this rock during this fall would be equal to the gravitational acceleration on this planet. Thus, \(g \approx 50\; \rm m\cdot s^{-2}\) on this planet.

Answer:

Step-by-step explanation:

For the length of AC

cosθ = 14/17

θ = arcCos 14/17

θ = 34.56

Let x = opposite

cot34.56  = 14/x

1.45=14/x

x1.45 = 14

x = 9.66

therefore, the length of AC is 9.66

For angle B is 34.56  

For angle C is 55.44

For Angle C :

90 + c + 34.56   = 180

c = 180 - 124.56

c = 55.44

The area of the kite is 40 square meters, calculated by using the area of a kite formula.

To calculate the area of a kite, you need to know the lengths of both the diagonals. Once you have those values, you can use the following formula to find the area:

Area = (d1 x d2) / 2

where d1 and d2 are the lengths of the diagonals.

Here is an example of how to use this formula:

Let's say you have a kite with diagonals of 8 meters and 10 meters. To find the area, you would use the formula:

Area = (8 x 10) / 2

Area = 40 square meters

So the area of the kite is 40 square meters.

There are also many online calculators available that can help you find the area of a kite if you enter the values of the diagonals.

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Answer:

integers is -15+253-36sumn

The value of cos a and sin a are 0.5, 0.28 respectively.

From the figure,

We have the following information from the question:

The coordinates of c are (0. 96, 0. 28).

and, To find the value of cos a and sin a

Now, According to the question:

We have the square and inscribed a triangle .

From using the triangle to find the value of cos a and sin a.

Now, We know that:

Cos a = base/ hypotenuse

Sin a = Altitude/ base

Now, put the value in above formula :

Cos a= 0.5/1 = 1/2 = 0.5

Sin a= 0.28/1 = 0.28

Hence, The value of cos a and sin a are 0.5, 0.28 respectively.

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Answer:

Slope = 3/1 or 3

Y intercept = (0, -5) or 5

Step-by-step explanation:

The slope intercept form : y = mx+b shows that the m represents the place of the slope and the b represents the place of the y intercept.

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Uncle Ben has to pay a total of \(\( \mathrm{P} 12,800 \)\) at the end of the fifth year to pay off his loan.

To calculate the amount Uncle Ben needs to pay at the end of the fifth year, we first need to determine the total amount he has paid over the last four years. He paid \(\( \mathrm{P} 2,000 \)\) per annum for four years, so the total amount paid is \(\( \mathrm{P} 2,000 \times 4 = \mathrm{P} 8,000 \)\).

Next, we need to calculate the interest on the principal amount borrowed. The principal amount is \(\( \mathrm{P} 10,000 \)\), and the interest rate is \(\( 12\% \)\) per annum. Using the formula for simple interest, we can calculate the interest for five years as follows:

\(\[\text{{Interest}} = \frac{{\text{{Principal}} \times \text{{Rate}} \times \text{{Time}}}}{100} = \frac{{\mathrm{P} 10,000 \times 12 \times 5}}{100} = \mathrm{P} 6,000\]\)

Now, we add the total amount paid over four years \((\( \mathrm{P} 8,000 \))\) to the interest accrued \((\( \mathrm{P} 6,000 \))\) to find the total amount that Uncle Ben needs to pay at the end of the fifth year:

\(\[\text{{Total amount}} = \text{{Amount paid over four years}} + \text{{Interest accrued}} = \mathrm{P} 8,000 + \mathrm{P} 6,000 = \mathrm{P} 12,000\]\)

Therefore, Uncle Ben has to pay \(\( \mathrm{P} 12,800 \)\) at the end of the fifth year to pay off his loan.

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Answer:

-1,209.85

Step-by-step explanation:

Answer:

the first and last one they are the answers

Step-by-step explanation:

multiplied exponents are added.

like x² × x³ = x⁵

so, up there we have

(-2x³y⁴)(-3x⁴y⁴).

as all operations (except for the exponents) are simms multiplications, this results in one longer expression.

(-2)x³y⁴(-3)x⁴y⁴.

we can unite terms of the same base unit.

-2 × -3 = 6

x³x⁴ = x⁷

y⁴y⁴ = y⁸

so, we get

6x⁷y⁸

9514 1404 393

Explanation:

The proof has two more steps:

2. AC ≅ AC . . . . reflexive property of congruence

3. ΔABC ≅ ∆CDA . . . . SSS congruence postulate

Answer:

circumference = 25.43 in

Step-by-step explanation:

circumference = πd

circumference = (3.14)(8.1) = 25.43 in

The thickness of the film of oil is approximately 1.0315 cubic miles.

Given the total oil spilled is 250 gallons and the area covered by oil is 1.20 square miles, we need to find the thickness of oil film. We can use the formula for this, which is Thickness of oil film = Volume of oil spilled / Area covered by oil.

To find the volume of oil spilled, we first need to convert gallons to cubic miles, which is 1 gallon = 0.00495113 cubic miles. So, 250 gallons of oil is equal to 0.00495113 x 250 = 1.2377825 cubic miles. Now, we can substitute the values in the formula to find the thickness of the oil film.

Therefore, the thickness of the film of oil is approximately 1.0315 cubic miles.

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