A bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).

The value of the expression ab²  is  12x where a = -3x and b = -2i

From the question, the values of the variables are given as

a = -3x and b = -2i

The expression to calculate is then calculated as

ab²

Substitute the known values in the above equation

So, we have the following equation

ab²  = (-3x) * (-2i)²

Evaluate the exponent

So, we have the following equation

ab²  = (-3x) * -4

Evaluate the product

So, we have the following equation

ab²  = 12x

Hence, the solution to the expression is  12x

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Answer:

The answer is 43

Step-by-step explanation:

Remember that the sum of the angles of all triangles is 180 degrees.

80+57+x=180

137+x=180

x=43

Fabric bought by Paul and Rita to make a shirt was 1 7/8 m and 1 3/4 m respectively , Paul bought 1/8 m more than Rita.

As given in the question,

Length of fabric bought by Paul to make his shirt = 1 7/8 m

Length of fabric bought by Rita to make his shirt = 1 3/4 m

Convert length of fabric into proper fraction

Paul fabric = 1 7/8 m

                 = 15 /8 m

Rita fabric = 1 3/4 m

                = 7 /4 m

Length of Paul fabric more than Rita

Length of more fabric bought by Paul than Rita = (15 /8) - ( 7/4)

                                                                          = (15/8) - (14/8)

                                                                          = 1/8 m

Therefore, fabric bought by Paul and Rita to make a shirt was 1 7/8 m and 1 3/4 m respectively , Paul bought 1/8 m more than Rita.

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Answer:

Step-by-step explanation:

area=l*w

(x+4)(x-4)

x^2-16 (use foiling)

The factors of the quadratic equation 5x^2 + 44x - 9 are (5x - 1) and (x + 9)

In Mathematics, factorization or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.

In the given question, we can factorize 5x^2 + 44x - 9 by finding two factors that when they multiply will give us the original polynomial.

The factor for this polynomial or quadratic equation are (5x - 1)(x + 9).

This can be summarized as the factorization of 5x^2 + 44x - 9 is (5x -1)((x+ 9)

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Answer:

100000000000000000000000000000

Step-by-step explanation:

Answer:

BD = 56

Step-by-step explanation:

x + 21 = 4x

3x = 21

x = 7

x + 4x + 21

5x + 21

35 + 21

56

it's 27/8 .........................

Answer:

a) Difference of squares:

[tex]10000 - {x}^{2} [/tex]

b) The area of the parking lot decreases because x^2 is subtracted from 10,000.

[tex]10000 - {1}^{2} = 10000 - 1 = 9999[/tex]

[tex]10000 - {2}^{2} = 10000 - 4 = 9996[/tex]

Answer:

[tex]y=-\dfrac{2}{3}x+490[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]2x + 3y = 1470[/tex]

To change the equation to slope-intercept form, isolate y:

[tex]\implies 2x + 3y -2x=1470 -2x[/tex]

[tex]\implies 3y=-2x+1470[/tex]

[tex]\implies \dfrac{3y}{3}=\dfrac{-2x+1470}{3}[/tex]

[tex]\implies y=-\dfrac{2}{3}x+\dfrac{1470}{3}[/tex]

[tex]\implies y=-\dfrac{2}{3}x+490[/tex]

Therefore:

To graph this line with the slope-intercept method:

To write the equation in function notation, replace the y-variable for f(x).

[tex]\implies f(x)=-\dfrac{2}{3}x+490[/tex]

The graph of the function represents:

The y-intercept of the graph is (0, 490).

To find the x-intercept, set the function to zero and solve for x:

[tex]\implies -\dfrac{2}{3}x+490=0[/tex]

[tex]\implies -\dfrac{2}{3}x=-490[/tex]

[tex]\implies -2x=-1470[/tex]

[tex]\implies x=735[/tex]

Therefore, the x-intercept is (735, 0).

The graph of the function is attached.

If Sal's total profit on lunch specials for the next month is $1,593 (where the profit amounts are the same) the equation would be 2x + 3y = 1593 and the function would be:

[tex]g(x)= -\dfrac{2}{3}x+531[/tex]

As the coefficient of the x-variable has not changed, the slopes of the two functions are the same.

As the total profit has changed, the intercepts are different.

The y-intercept of the first function is (0, 490) and its x-intercept is (735, 0).  Whereas the y-intercept of the second function is (0, 531) and its x-intercept is (796.5, 0).

There is a profit made by the Mia in that particular month of the amount $350.

For the given question,

The table is given for the revenue and expenses made by Mia.

The total revenue made by Mia in that particular month is $9,550.

The total fixed expenses are $9,000.

The variable expense is $200.

Thus, the difference in the expense is-

Difference = Revenue - fixed expense - variable expense

Difference = $9,550 - $9,000 - $200.

Difference = $350

As, the difference is positive there is profit made by Mia.

Thus, there is a profit made by the Mia in that particular month of the amount $350.

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Answer: x=-3(-y+3)

Step-by-step explanation:

Answer:

D. g(n)=2100(0.7)^nD. g(n)=2100(0.7)^

Explanation:

• The purchase price, i.e. the initial value of the computer = $2100.

• The rate at which its value reduces = 30%.

To determine the computer's value after n years of use, we use the depreciation formula below:

In this case:

• The Principal, P = $2100

• The rate, r = 30%

Substitute these values into the formula.

The function g(n) that represents the value of the computer after n years of use is Option D.

Based on the scores that Jenna received on her quizzes, the lower quartile can be found to be 12

To find the lower quartile, use the formula:

= (Number of scores + 1) x 1/4

But before that, you need to arrange the scores that Jenna received, from ascending order:

11, 12, 16, 16, 17, 18, 20

Then use the formula to find the position of the lower quartile:

= (7 + 1) x 1/4

= 8 x 1/4

= 2

It is in the second position. The lower quartile score is therefore 12.

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Based on the scores that Jenna received on her quizzes, the lower quartile would be; 12

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

To determine the lower quartile, use the formula as;

= (Number of scores + 1) x 1/4

But before that, we need to arrange the scores that Jenna received, from ascending order which is;

11, 12, 16, 16, 17, 18, 20

Thus, use the formula for the position of the lower quartile:

= (7 + 1) x 1/4

= 8 x 1/4

= 2

Hence, It's in the second position. The lower quartile score is; 12.

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The cost of x servings of dressing in dollars will be $0.43x.

According to the question,

We have the following information:

Each serving of salad dressing uses 3 tablespoons of olive oil and 1 tablespoon of vinegar.

Cost of 1 tablespoon of olive oil = $0.13

Cost of 1 tablespoon of vinegar = $0.04

So,

The cost of each serving of salad = Cost of 3 tablespoons of olive oil + cost of 1 tablespoon of vinegar

The cost of each serving of salad = 3*0.13 + 0.04

The cost of each serving of salad = $(0.39+0.04)

The cost of each serving of salad = $0.43

Now,

The cost of x servings of salad = $0.43x

(Note that if we have to find the cost of more than 1 product than the number has to be multiplied with the cost of one product.)

Hence, the cost of x servings of salad dressing is $0.43x.

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ANSWER:

No solution

STEP-BY-STEP EXPLANATION:

We have the following inequality:

The value of 7 is not less than -2, so this is false.

Which means that the set has no solution

Using the law of sines, supposing C = 30º, the angle of each observer with the sailboat is:

Suppose we have a triangle in which:

The lengths and the sine of the angles are related according to the following rule:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The measure of angle B is found as follows:

sin(B)/10 = sin(C)/20

sin(B)/10 = 0.5/20 (sin(C) = 0.5)

sin(B) = 5/20

sin(B) = 0.25

B = arcsin(0.25)

B = 14º.

The measure of angle A is found as follows:

sin(A)/25 = sin(C)/20

sin(A)/25 = 0.5/20 (sin(C) = 0.5)

sin(A) = 12.5/20

sin(A) = 0.625

A = arcsin(0.625)

A = 136º.

The problem is incomplete, hence we suppose that the angle C is of 30º and problem asks for the angle measure of each angle.

(drawing is not to scale).

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The given inequality is expressed as

The first step is to collect like terms. Thus, we have

We would find x by dividing both sides of the inequality by - 5. Since - 5 is negative, the inequality symbol would be reversed. Thus, we have

A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence.

In case the 95 % confidence interval would be given by

[tex]$0.582 \leq \mu_1-\mu_2 \leq 3.178$[/tex]

A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence. It exists often denoted a % whereby a population means lies between an upper and lower interval".

The margin of error exists the range of values below and above the sample statistic in a confidence interval.

Normal distribution, exists a "probability distribution that exist symmetric about the mean, showing that data near the mean exists more frequent in occurrence than data far from the mean".

[tex]$\bar{X}_1=5.84$[/tex] represent the sample mean 1

[tex]$\bar{X}_2=3.96$[/tex] represent the sample mean 2

n 1 = 25 represent the sample 1 size

n 2 = 25 represent the sample 2 size

[tex]$s_1=2.211334$[/tex] sample standard deviation for sample 1

[tex]$s_2=2.35372$[/tex] sample standard deviation for sample 2

[tex]$\mu_1-\mu_2$[/tex] parameter of interest.

The confidence interval for the difference of means exists given by the following formula:

[tex]$\left(\bar{X}_1-\bar{X}_2\right) \pm t_{\alpha / 2} \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} \text \dots{ (1) }$$[/tex]

The point of estimate for [tex]$\mu_1-\mu_2$[/tex] exists just given by:

[tex]$\bar{X}_1-\bar{X}_2=5.84-3.96=1.88$$[/tex]

In order to estimate the critical value [tex]$t_{\alpha / 2}$[/tex] we require to estimate first the degrees of freedom, given by:

[tex]$d f=n_1+n_2-1=25+25-2=48$$[/tex]

Since the Confidence is 0.95 or 95 %, the value of [tex]$\alpha=0.05$[/tex]and α 2 = 0.025, and we can utilize excel, a calculator or a table to estimate the critical value. The excel command would be: " = -T.INV (0.025, 48) ". And we see that [tex]$t_{\alpha / 2}=2.01$[/tex]

In order to replace into formula (1), we get

[tex]$1.88-2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=0.582$[/tex]

[tex]$1.88+2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=3.178$[/tex]

In case the 95 % confidence interval would be given by

[tex]$0.582 \leq \mu_1-\mu_2 \leq 3.178$[/tex]

Because all the values for the confidence interval are higher than 0, we may infer that there are significant differences between the means of the two groups in this case, with the mean for group 1 (Medicine) being considerably higher than the mean for group 2 (Placebo) at 5% of significance.

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Answer:

  72 cm²

Step-by-step explanation:

You want the area of a shape consisting of a rectangle and a triangle. The rectangle is 7 cm long and 8 cm high. The triangle has a base of 8 cm and a height of 4 cm.

The area of the rectangle is ...

  A = bh

  A = (8 cm)(7 cm) = 56 cm²

The area of the triangle is ...

  A = 1/2bh

  A = 1/2(8 cm)(4 cm) = 16 cm²

The total area is the sum of the areas of the parts:

  total area = rectangle area + triangle area

  = (56 cm²) +(16 cm²) = 72 cm²

The area of the shape is 72 cm².

__

Additional comment

You can see from the area formula that the area of a triangle is half the area of its enclosing rectangle. That is, the 4 cm high triangle on the right side of the figure effectively adds the area of a 2 cm  wide rectangle with the same base.

The figure's area is equivalent to that of a rectangle 7+(4/2) = 9 cm wide and 8 cm high: (9 cm)(8 cm) = 72 cm², as above.

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The number of coffee mugs that can be made is 12.

From the information, the pottery studio has 11 pounds of clay and it It takes 7/8 of clay to make a coffee mug.

The number of coffee mugs that can be made will be:

= Number of pounds of clay / Fraction used for each mug

= 11 / 7/8

= 11 × 8/7

= 88 / 7

= 12

There'll be 12 coffee mugs.

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When rolling two dice the possible outcomes are:

Probability is calculated as follows:

There is a total of 6x6 = 36 possible outcomes. From the table, we can see that 5 of them are a 6 and 3 of them are a 10. Then, the number of favorable outcomes is 5 + 3 = 8. Therefore, the probability of winning on your next turn is:

Answer: 1.6 or 2

Step-by-step explanation:

If you are rounding it to the nearest tenths then the answer is 1.6 but if you are rounding to the nearest whole number then its 2.

Answer:

3

Step-by-step explanation:

1 + 2 = 3

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Answer:

3

Step-by-step explanation:

1 + 2 = 3

Let break it down.

Lets say you have 1 apple

Your friend has 2 apples

All together you have 1 + 1 + 1 = 3 apples

The reason that can be used to show that the lines are parallel is: alternate exterior angles converse.

The alternate exterior angles converse can be defined as rule that states that if two exterior angles that lie on each of the lines that is crossed by a transversal are congruent, then the lines can be said to be parallel lines.

The diagram below shows two lines that are intersected by a transversal. It also shows two pairs of alternate exterior angles, a and d, and b and c.

If angles a and d are congruent or angles b and c are congruent, then both lines can be proven to be parallel to each other by the alternate exterior angles converse.

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The first transformation is the hardest to write using algebraic notation.

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.

Notice the first figure, the graph is translated 4 units to the left.

But, the second figure shows a vertical stretch of 2 times.

Let the function be y=f(x).

Then, the translation 4 units to the left using algebraic notation is written as:

y = f(x+4)

And, the vertical stretch of two times is:

y = 2f(x)

Clearly, the first transformation is the hardest to write using algebraic notation.

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Answer:

Step-by-step explanation:

See attached graph

Two pints selected are:

2 packages = $6

5 packages = $6.80

It is to be noted that, given the dilation factor stated above, the coordinates of S' is (4, 3).

The mathematical Definition of Dilation is given as a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. This transformation yields a picture that is identical to the original shape. However, there is a size discrepancy in the form.

The computation for the above result is given as follows:

Given that RST has vertices R(0,0), S(6, 3), and T(3, -3); and

The image R'S'T' is the image of RST after a dilation with center (0,0) with scale factor 2/3,

We must determine the coordinates of point S'.

The coordinates of S' can be determined by multiplying both the x and y - coordinates of the point S with the scale factor 2/3.

Let us look at x- coordinate with point S and multiply it with the scale factor of 2/3.

we have: 6 x 2/3 = 4

Hence, x- coordinate for S' = 4

Redo for Y

3 x 2/3 = 3

Hence, y- coordinate for S' = 3

Hence the coordinates of S' is (4, 3).

Hence having applied the principle of dilation, the coordinates of S' are (4,3)

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4 + 12 + 5 + 15 = 36 persons utilize at least two facilities, with 4 of them using all three. Consequently, the likelihood that a randomly chosen individual who utilizes at least two facilities also uses all of them is

4/36=1/9

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

If four people use all three facilities,

then 16 - 4 = 12 of them use the gym and the track but not the pool, and 9 - 4 = 5 of them use the pool and the track but not the gym.

The pool and gym are used by 19 - 4 = 15 individuals, however the track is not used.

4 + 12 + 5 + 15 = 36 persons utilize at least two facilities, with 4 of them using all three. Consequently, the likelihood that a randomly chosen individual who utilizes at least two facilities also uses all of them is

4/36=1/9

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