Find the product.
(x-3)(x+5)

(a)  The cheetah's average acceleration during the short sprint is approximately 5.78 \(m/s^2.\)

(b) At t = 3.0 s, the cheetah's displacement is approximately 8.22 meters.

(a) Determine the cheetah's average acceleration during the short sprint.

Initial velocity (u) = 0 km/h = 0 m/s

Final velocity (v) = 84 km/h = 23.33 m/s

Distance (s) = 47 m

Using equation 3, we can find the acceleration (a):

\(v^2 = u^2 + 2as\)

\((23.33 m/s)^2 = (0 m/s)^2 + 2a(47 m)\)

\(542.7689 m^2/s^2 = 94a m\)

a ≈ \(5.78 m/s^2\)

Therefore, the cheetah's average acceleration during the short sprint is approximately 5.78 m/s^2.

(b) Find its displacement at t = 3.0 s.

Initial velocity (u) = 0 m/s

Acceleration (a) = 5.78 m/s^2

Time (t) = 3.0 s

Using equation 2, we can find the displacement (s):

\(s = ut + (1/2)at^2\)

\(s = 0 m/s * 3.0 s + (1/2)(5.78 m/s^2)(3.0 s)^2\)

s ≈ 8.22 m

Therefore, at t = 3.0 s, the cheetah's displacement is approximately 8.22 meters.

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Answer:

y = 4.5x + 8.5

Step-by-step explanation:

this is true

Question

Answer

\(→ \frac{3 \times - 12}{5 \times - 20} \\ \)

\( \sf \: solution→ \sf \: factor \: the \: expression \: \frac{7(a + b)}{ {a}^{2} - b } \\ \)

\( \sf \red{ answer \: is→ \frac{9}{a - b}} \\ \)

Answer:

The area of the parallelogram is 630.4 square units, to the nearest tenth.

Step-by-step explanation:

The formula to find the area of a parallelogram is:

\(A=bh\)

where b is the base and h is the height.

For the given parallelogram ABCD, BC and AD are the bases and h is the height. Therefore, we need to calculate the height, h, before we can calculate the area of the parallelogram.

The height of the parallelogram is also the side opposite angle 62° in the right triangle of the given diagram. As we also know the hypotenuse of this triangle, we can use the sine trigonometric ratio to find "h".

\(\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

Given:

Therefore, the expression for h is:

\(\implies \sin 62^{\circ}=\dfrac{h}{21}\)

\(\implies h=21\sin 62^{\circ}\)

Given the base of the parallelogram is 34 units, substitute b = 34 and the expression for h into the formula for the area:

\(\begin{aligned}\implies \textsf{Area}&=34 \cdot 21\sin 62^{\circ}\\&=630.424581...\\&=630.4\; \sf square\;units\;(nearest\;tenth) \end{aligned}\)

Therefore, the area of the parallelogram is 630.4 square units, to the nearest tenth.

Answer: $59.88

Step-by-step explanation:

1): Multiply

    $4,99 x 12 = $59.88

The Percentage error is 40%. This means that the recorded value is 40% lower than the true value. In other words, the recorded value is only 60% of the true value.

To find the percentage error, we need to calculate the difference between the recorded value and the true value, then divide that difference by the true value and multiply by 100 to get a percentage.

True value = 1,500

Recorded value = 900

Difference = True value - Recorded value

Difference = 1,500 - 900

Difference = 600

Percentage error = (Difference / True value) x 100

Percentage error = (600 / 1,500) x 100

Percentage error = 40

Therefore, the percentage error is 40%. This means that the recorded value is 40% lower than the true value. In other words, the recorded value is only 60% of the true value.

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Answer:

i think it is, the second one and the fourth one

Step-by-step explanation:

Answer:

53 cupcakes

Step-by-step explanation:

Take the amount of frosting and divide by the amount needed per cupcake

431/8

53.875

We round down since we cannot frost part of a cupcake

53 cupcakes

Answer:

53 cupcakes

Step-by-step explanation:

He has a total of 431 ounces and each cupcake needs 8 ounces of frosting. Therefore can divide the total amount of frosting (431 ounces) by the amount per cupcake (8 ounces)

total amount/ amount per cupcake

431 ounces/8 ounces

431/8

53.875

0.875, or a fraction/part of a cupcake can’t be frosted, so we should round down to the nearest whole number.

53

He can frost 53 cupcakes.

The town's population is currently 23,000 and is growing by 2.3% each year. If this growth rate continues, it will take approximately 20 years for the town's population to reach 58,000.

To calculate the number of years required for the town's population to reach 58,000, we can use the compound interest formula. The formula for compound interest is A = P(1 + r)^n, where A is the final amount, P is the initial amount, r is the growth rate as a decimal, and n is the number of years. In this case, P is 23,000, r is 2.3% or 0.023, and A is 58,000.

We can rearrange the formula to solve for n: n = log(A/P) / log(1 + r). Plugging in the values, we get n = log(58,000/23,000) / log(1 + 0.023) ≈ 19.6. Therefore, it will take approximately 20 years for the town's population to reach 58,000 if the growth rate remains constant at 2.3% per year.

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The most appropriate statement is that C. The shaded area represent both 2/3 and 6/9 of the whole shape.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Given a square.

This square is divided in to 9 equal sized squares, with 3 rows and 3 columns.

Out of the 9 equal sized squares, 6 squares are shaded.

We can write the fraction of shaded squares to total number of squares as 6/9.

In the same way, we have in the question that, 6 squares which are shaded is the squares in the first two columns, where each column has three squares.

So we can say that, out of 3 equal sized columns, two columns are shaded.

Fraction of shaded columns to total columns is 2/3.

So 2/3 = 6/9.

Hence shaded area represent both 2/3 and 6/9 of the whole shape.

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Answer:

x = 25

Step-by-step explanation:

\( \triangle DGH\sim\triangle DEF... (given) \)

\( \frac{DG}{DE} =\frac{GH}{EF} \)

\( \frac{52}{91} =\frac{x+3}{2x-1} \)

\( \frac{4}{7} =\frac{x+3}{2x-1} \)

4(2x - 1) = 7(x + 3)

8x - 4 = 7x + 21

8x - 7x = 21 + 4

x = 25

a. To solve the initial value problem (IVP) y'' - y - 6y = 0 with the initial condition y(0) = 11, we can use the Laplace transform.

Taking the Laplace transform of the differential equation, we have:

s²Y(s) - sy(0) - y'(0) - Y(s) + Y(s) - Y(0) - 6Y(s) = 0

Substituting the initial condition y(0) = 11, we have:

s²Y(s) - 11s - y'(0) - Y(s) + Y(s) - Y(0) - 6Y(s) = 0

Now, rearranging the equation to solve for Y(s), we get:

Y(s) = (11s + y'(0) - Y(0)) / (s² - 1 - 6)

Simplifying further, we have:

Y(s) = (11s + y'(0) - Y(0)) / (s² - 7)

Taking the inverse Laplace transform of Y(s), we obtain the solution y(t).

b. To solve the IVP y'' - 4y + 4y = 0 with the initial conditions y(0) = 8.1 and y'(0) = 28, we can use the Laplace transform.

Taking the Laplace transform of the differential equation, we have:

s²Y(s) - sy(0) - y'(0) - 4Y(s) + 4y(0) = 0

Substituting the initial conditions y(0) = 8.1 and y'(0) = 28, we have:

s²Y(s) - 8.1s - 28 - 4Y(s) + 4(8.1) = 0

Now, rearranging the equation to solve for Y(s), we get:

Y(s) = (8.1s + 28 - 32.4) / (s² - 4)

Simplifying further, we have:

Y(s) = (8.1s - 4.4) / (s² - 4)

Taking the inverse Laplace transform of Y(s), we obtain the solution y(t).

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The percentage of alcohol in a handy is 3%. 3/5 * 5% = 3% , Since beer is 5% alcohol, then 3/5 of the handy is 5% alcohol.

The ratio of beer to lemonade in a handy is 3:2, which means that 3 parts of the handy is beer and 2 parts of the handy is lemonade. To express it in terms of fractions, 3/5 of the handy is beer and 2/5 of the handy is lemonade. Since beer is 5% alcohol, then 3/5 of the handy is 5% alcohol. Therefore, if you take the proportion of the beer in the handy and multiply it by the alcohol percentage of the beer, you will get the percentage of alcohol in the handy. In this case, 3/5 * 5% = 3%. This means that the percentage of alcohol in a handy is 3%. It's important to note that this assumes that the beer and lemonade are mixed together evenly and there's no spillage or evaporation. Also, it's important to consider the fact that the alcohol percentage of the beer can vary depending on the brand and type of beer.

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Answer:

Step-by-step explanation:

3

Answer:

The best stems would be: 1, 2, and 3

Step-by-step explanation:

When you are making the stem and leaf plots, you are using the diget in the tens place as the stem

Answer:

Step-by-step explanation:

The statement

Twice the difference of a number and 8 is written as

2( b - 8)

The expression is greater than - 21 so we represent it by the > sign

So we have

2( b - 8) > - 21

Expand

2b - 16 > - 21

2b > - 21 + 16

2b > - 5

Divide both sides by 2

Hope this helps you

Answer:

x)45

y)45

z)135

Step-by-step explanation:

There is a one-to-one correspondence between the even and odd divisors, we can conclude that an even integer k, not divisible by 4, has the same number of even and odd divisors.

To prove that an even integer k, not divisible by 4, has the same number of even and odd divisors, we can establish a bijection between them.

Let's consider an even integer k. Since k is even, it can be expressed as k = 2n, where n is an integer.

First, let's consider the even divisors of k. An even divisor of k is of the form 2m, where m is an integer. Since k = 2n, we can write the even divisor as 2m = 2n. Simplifying this equation, we get m = n.

Now, let's consider the odd divisors of k. An odd divisor of k is of the form 2m + 1, where m is an integer. Again, we can write this odd divisor as 2m + 1 = 2n. Simplifying this equation, we get m = n - 1/2.

Now, let's establish a bijection between the even and odd divisors. For every even divisor 2m, we can find a corresponding odd divisor 2m + 1, and vice versa. The correspondence is given by the equation m = n for even divisors and m = n - 1/2 for odd divisors.

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The correct answer is option c A stem plot of the data would be skewed right.

A median that is larger than the mean in a set of exam scores suggests that the data is skewed to the right (or positively skewed), meaning that there are more scores at the high end of the distribution. This results in a longer tail on the right side of the distribution, which is often seen in data that contains outliers or extreme values. In this case, a stem plot of the data would be skewed to the right, showing a long tail on the right side of the plot.

Option a (a stem plot of the data would be symmetric) is incorrect because a symmetric distribution would have a median and mean that are equal, which is not the case here.

Option b (a stem plot of the data would be skewed left) is incorrect because a skewed left distribution would have a median that is smaller than the mean, which is not the case here.

Option d (the data set must be so large that it would be better to draw a histogram rather than a stem plot) is incorrect because the size of the data set does not affect the skewness of the data or the choice of a plot to use.

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The answer is c. Statistic because the value is a numerical measurement describing a characteristic of a sample.

A statistic is a value that summarizes a characteristic of a sample. In this case, the percentage of employees in the sample who own a television (45%) is a statistic because it summarizes a characteristic of the sample of employees that was selected. A parameter, on the other hand, is a value that summarizes a characteristic of a population. For example, if we were to consider the percentage of all employees in the company who own a television, then the mean or median percentage of television ownership would be a parameter because it would describe a characteristic of the entire population of employees. In summary, statistics are values that describe a characteristic of a sample, while parameters are values that describe a characteristic of a population.

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Answer:

13

Step-by-step explanation:

it will be B because it find the missing side you need to do the pythagorean theorem

Answer:

40%

Step-by-step explanation:

15/100 +25/100 = 40/100 or 40%

Answer:

The answer is 4186. 67

Step-by-step explanation:

\(v = \frac{4}{3} \times 3.14 \times {(10)}^{3} \\ v = 4186.66666 \\ v = 4186.67\)

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Answer:

The discriminant is 0

There is 1 real solution

Step-by-step explanation:

Use the discriminant formula, D = b² - 4ac

In the equation y = x² - 4x + 4, a is 1, b is -4, and c is 4.

Plug in these values into the formula:

D = b² - 4ac

D = (-4)² - 4(1)(4)

D = 16 - 4(4)

D = 16 - 16

D = 0

So, the discriminant is 0.

With a discriminant of zero, there is one real solution.

So, the number of real solutions is 1.

Answer:

Step-by-step explanation:

This equation has infinitely many solutions as for any value of x we have same result

Answer:

Infinitely many

Step-by-step explanation:

this answer is wrong

Answer:

7

Step-by-step explanation:

the left side is 9+18=27

so the right side is 20+x=27

and 27-20=7

Volume is the amount of space in an object. The fraction occupied by the cube is: \(\frac{r\sqrt2}{\pi(r + 2)}\)

First, we calculate the volume of the cube.

\(Volume = Length^3\)

From the figure, we have:

\(Length = r\sqrt 2\)

So:

\(V_1 = (r\sqrt2)^3\)

\(V_1 = (2\sqrt2)r^3\)

Next, the volume of the cylinder

\(Volume=\pi r^2h\)

So, we have:

\(V_2 = \pi r^2 (2r + 4)\)

The fraction (n) occupied by the cube is:

\(n = \frac{V_1}{V_2}\)

So, we have:

\(n = \frac{(2\sqrt2)r^3}{\pi r^2(2r + 4)}\)

Factor out 2 in the denominator

\(n = \frac{(2\sqrt2)r^3}{2\pi r^2(r + 2)}\)

Cancel out common terms

\(n = \frac{r\sqrt2}{\pi(r + 2)}\)

Hence, the fraction occupied by the cube is: \(\frac{r\sqrt2}{\pi(r + 2)}\)

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The option b "The area under the curve is 1." and the option d "It is symmetrical" are true about the probability function for a t distribution.

When the sample size is small and the population standard deviation is unknown, the t-distribution is used in statistics.

Option b confirms that the total area under the t-distribution curve is 1, indicating that the sum of probabilities for all possible outcomes is also equal to 1.

Option d confirms the symmetry of the t-distribution, implying that the curve is balanced on both sides of the mean. The mean, median, and mode of a symmetrical distribution are all equal.

To summarize, the t-distribution is a useful tool in statistics when working with small sample sizes because it accounts for the uncertainty in the population standard deviation.

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The Mean of the dispersion of z-scores will be 0, and the standard deviation will be 1. 

On the off chance that all of the scores within the populace are changed into z-scores, at that point the coming about the conveyance of z-scores will have a cruel (mean) of and a standard deviation of 1.

Usually, since the change of a crude score x to a z-score is given by:

z = (x - μ) / σ

where μ is the populace Mean.

and σ is the populace standard deviation.

When all scores within the populace are changed to z-scores, the Mean of the coming about dispersion of z-scores will be:

( Mean of z-scores)

= [(Mean  of crude scores) - μ] / σ

= (μ - μ) / σ =

So also, the standard deviation of the dissemination of z-scores will be:

(standard deviation of z-scores) = (standard deviation of crude scores) / σ = σ / σ = 1

In this manner,

The cruel of the dispersion of z-scores will be 0, and the standard deviation will be 1. 

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If all of the scores in the population are transformed into z-scores, the values for the mean and standard deviation for the complete set of z-scores will be a mean of 0 and a standard deviation of 1.

This is because the process of transforming scores into z-scores involves subtracting the mean of the population and dividing by the standard deviation, which effectively standardizes the data to have a mean of 0 and a standard deviation of 1. When all the scores in a population are transformed into z-scores, the mean of the complete set of z-scores will be 0 and the standard deviation will be 1. This is because z-scores represent the number of standard deviations a value is from the mean, and the transformation standardizes the distribution.

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