A ball is thrown from an initial height of 5 feet with an initial upward velocity of 31 ft/s. The ball's height (in feet) after t seconds is given by the following.
h=5+31t-16t^2

Find all values of t for which the ball's height is 19 feet.
t= _ seconds
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

Using the formula for the distance between two points, it is found that:

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In this problem, we use the formula to find the lengths for each side of the triangle.

For example, side AB has length given by the distance between (-6,3) and (3,5), hence:

[tex]AB = \sqrt{(-6 - 3)^2 + (3 - 5)^2} = 9.22[/tex]

Side AC has length given by:

[tex]AC = \sqrt{(-6 - 1)^2 + (3 - (-4))^2} = 9.9[/tex]

Side BC has length given by:

[tex]BC = \sqrt{(3 - 1)^2 + (5 - (-4))^2} = 9.22[/tex]

Since sides AB and BC have the same length, which is different of side AC, the triangle is an isosceles triangle.

The area of a triangle is given by half the length of the base multiplied by the height.

The midpoint of side BC, of length of 9.22 units, is of (2,0.5). The height is the distance of this point from point A, hence:

[tex]d = \sqrt{(-6 - 2)^2 + (3 - 0.5)^2} = 8.38[/tex]

Hence the area is:

A = 0.5 x 9.22 x 8.38 = 38.63 units squared.

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1. The z-scores corresponding to Kathy's starting salary is -1.5

2. The z-scores corresponding to Linda's starting salary is -2

z = (x - μ) / σ

Where

z = (x - μ) / σ

z = (31500 - 42000) / 7000

z-score for Kathy's starting salary = -1.5

z = (x - μ) / σ

z = (33000 - 45000) / 6000

z-score for Linda's starting salary = -2

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The estimated value of 5,016 exists 1 / 264 ≈ 0.00379.

Fractions describe the regions of a complete or group of objects. A fraction contains two regions. The number on the top of the line exists named the numerator. It describes how many equivalent regions of the real or group stand accepted. The number below the line exists named the denominator. It exhibits the total number of equivalent regions the whole exists divided into or the total number of the exact objects in a group.

The value of 5,016 can be simplified by using a fraction

Consider a denominator 19, then

19 divided by 5,016, then we get

19 and 5016 have a common divisor of 19.

then, we get

19 / 5016 = 1 / 264

Now, you need to divide.

1 / 264 ≈ 0.00379

Therefore, the estimated value of 5,016 exists 1 / 264 ≈ 0.00379.

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Answer:

4.13

Step-by-step explanation:

Using sine ratio where it states that sine of a measurement is equal to ratio of opposite of measurement to hypotenuse (slant side/side with slope)

From the question, our opposite is x, hypotenuse is given as 15 units and the measurement is 16°. Apply the formula:

[tex]\displaystyle{\sin 16^{\circ} = \dfrac{x}{15}}[/tex]

Move 15 to multiply sin(16°):

[tex]\displaystyle{15\sin 16^{\circ} = x}[/tex]

Go ahead and input the value in a calculator since it's not a special triangle - a measurement that can be found using hand method - after you find the value, round it to 2 decimal places:

[tex]\displaystyle{x = 4.13456033...}[/tex]

Therefore, after rounding to 2 decimal places, the answer is:

[tex]\displaystyle{x=4.13}[/tex]

Therefore, the value of x is 4.13 units.

Answer:

refer to the attachment

The complete factorization of the equation 81x² - 100 is; (9x - 10)(9x + 10)

We are given the quadratic equation;

81x² - 100

Now, according to quadratic identities, we know that;

(a + b) * (a - b) = a² - b²

Now, our equation can also be expressed as;

81x² - 100 = 9²x² - 10²

Thus, applying the quadratic identity gives us;

(9x + 10)(9x - 10)

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Answer:

x = 7.43

Step-by-step explanation:

X - 2.13 = 5.3

add -2.13 to both sides

x -2.13+2.13 = 5.3 + 2.13

-2.13 + 2.13 cancel out and 5.3 +2.13 equals 7.43

therefore x =7.43

check your work by substituting 7.43 for x

7.43 - 2.13 = 5.3

Answer:

yes it's true no problem sir

Work Shown:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.2 + 0.8 - 0.07

P(A or B) = 0.93

An expression which shows the length of this rope is: 10/cos35 ≈ 12.2 feet.

In order to determine the length of this rope, we would apply the law of cosine because both the rope and apple formed an angle that are adjacent in a right triangle:

cos(θ) = Adj/Hyp

Where:

Substituting the given parameters into the formula, we have;

cos(35) = 10/Hyp

Hyp = 10/cos35

Hyp = 12.2 feet.

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The transcribe expression is the expression of the equation in words.

The expression can be transcribe as follows;

1. st  = s multiply by t

2. 6 / t - 4 = 6 divided by t minus 4

3. 20 + t² = 20 plus t squared.

4. 50 - x = 50 minus x

5. x - y² = x minus y squared.

6. 24 / 12 + 12 = 24 divided by 12 plus 12

7. xy - 16 = x multiply by y minus 16

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The value of the expression is 972

The expression is given as:

27(36)

Express 36 as 18 + 18

27(18+ 18)

Expand

486+ 486

Evaluate the sum

972

Hence, the value of the expression is 972

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Answer: THE ANSWER IS A) $860

Step-by-step explanation: I GOT A 100 ON THE TEST

samples confidence intervals needed is Option C 136.

According to the Empirical rule, if data exists normally distributed then about 68% of the population lies within one standard deviation from the mean.

We assume that the mean of a normally distributed population exists at 300, and 200 simple random samples exist drawn from the population.

Number of simple random samples, n= 200

By Empirical rule, approximately 68% of 200 samples’ confidence intervals we would expect to have the population mean.

Required number of samples = 68% of 200

= 0.68 x 200 = 136

The required number of samples = 136

Therefore, the correct answer is option C) 136.

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Considering that the data is only noted and not changed, this is an example of an observational study.

In this problem, the data, which is the number of miles traveled, is only analyzed, no interventions are made, hence this is an example of an observational study.

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The volume of the cylinder is 602.88 ft³.

The surface area of the cylinder is  301.44 ft²

volume of a cylinder = πr²h

volume of a cylinder = 3.14 × 4² × 12

volume of a cylinder = 3.14 × 16 × 12

volume of a cylinder = 602.88 ft³

Surface are of a cylinder = 2πr(r + h)

Surface are of a cylinder = 2 × 3.14 × 4(4 + 8)

Surface are of a cylinder =  25.12(12)

Surface are of a cylinder = 301.44 ft²

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Answer:

  HM = 3   or   HM = 15

Step-by-step explanation:

The product of segment lengths is the same for both chords.

  FM·EM = GM·HM

  GM +HM = 18

Substituting for GM, we have ...

  FM·EM = (18 -HM)·HM

  5·9 = (18 -HM)·HM

Effectively, we want two factors of 45 that have a total of 18. Looking at the factors of 45, we have ...

  45 = 1·45 = 3·15 = 5·9

The totals of these pairs are 46, 18, 14. The factor pair we're looking for is 3·15.

Either of these factors could be HM. The other will be GM.

There is nothing in the problem description that suggests the length of HM relative to other lengths on the diagram. (We know the diagram is not to scale.) So, there are two possible solutions:

  HM = 3   or   HM = 15

Due to length restrictions, we kindly invite to read the explanation of this question for further details about the table and graph of the function.

In this problem we must plot the graph of a function on a Cartesian plane. The procedure is summarized below:

After following the procedure, we have the following result:

Input, x             x + 4                Output, y             (x, y)

   - 2               - 2 + 4                     2                    (- 2, 2)

     0                 0 + 4                     4                     (0, 4)

     2                 2 + 4                     6                     (2, 6)

     4                 4 + 4                     8                      (4, 8)

     6                 6 + 4                    10                      (6, 10)

     8                 8 + 4                    12                      (8, 12)

Lastly, we plot the graph of the linear function.

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[tex]f(x) = kx + m \\ f(x - 1) = k(x - 1) + m[/tex]

[tex]f(x - 1) - f(x) = 2 \\ k(x - 1) + m - kx - m = 2 \\ kx - k + m - kx - m = 2 \\ - k = 2 \\ k = 2[/tex]

[tex]f( - 2) = k( - 2) + m = 1 - m \\ k( - 2) + m = 1 - m \\ ( - 2)( - 2) + m = 1 - m \\ 4 + m = 1 - m \\ 2m = - 3 \\ m = \frac{ - 3}{2} [/tex]

[tex]f(x) = - 2x - \frac{3}{2} [/tex]

The annual breakeven point is $550157

Given that the Sales price is $ 31.00, Per-unit variable costs: Invoice cost is 17.05, Sales commissions is 4.05, Total per-unit variable costs is $ 21.10, Total annual fixed costs: Advertising is $ 23,100, Rent is 28,200, Salaries is 124,200 and Total fixed costs is $ 175,500.

The break-even point is your total fixed cost divided by the difference between the unit price and the variable cost per unit.

The sales price is $31 and the total variable cost is $21.10.

Now, we will find the Contribution margin by subtracting the Total variable cost from the sales price, we get

Contribution margin= Sales price-Total sales price

Contribution margin=31-21.10

Contribution margin=9.9

Further, we will find the contribution margin ratio by dividing the contribution margin by Sales price, we get

contribution margin ratio=contribution margin/Sales price

contribution margin ratio=9.9/31

contribution margin ratio=0.319

contribution margin ratio=31.9%

Furthermore, we will find the break-even point, we get

Break-even point=Fixed cost/contribution margin

Break-even point=175500/9.9

Break-even point=17727.27

Now, we will find the break-even sales in dollars, we get

Break-even sales=Fixed cost/contribution margin ratio

Break-even sales=(175500/31.9)×100

Break-even sales=550157

Hence, the annual breakeven point in unit sales is calculated to be $550157.

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The the anticipated return after financing cost with the most aggressive asset financing mix is $200000.

Most aggressive

Low liquidity = $2,500,000 *18%

Low liquidity = $450,000

Short-term financing = -$2,500,000*10%

Short-term financing = -$250,000

Anticipated return = $450,000 + (-$250,000)

Anticipated return = $200,000

Most conservative

High liquidity = $2,500,000 *14%

High liquidity = $350,000

Long-term financing = –$2,500,000 * 12%

Long-term financing = -$300,000

Anticipated return = $350,000 + (-$300,000)

Anticipated return = $50,000

Moderate approach

Low liquidity = $2,500,000 *18%

Low liquidity = $450,000

Long-term financing =–$2,500,000 * 12%

Long-term financing = -$300,000

Anticipated return = $450,000 + (-$300,000)

Anticipated return = $150,000

Moderate approach

High liquidity = $2,500,000 *14%

High liquidity = $350,000

Short-term financing = -$2,500,000*10%

Short-term financing = -$250,000

Anticipated return = $350,000 + (-$250,000)

Anticipated return = $100,000

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Complete question:

a. Compute the anticipated return after financing cost with the most aggressive asset financing mix.

b. Compute the anticipated return after financing cost with the most conservative asset financing mix.

c. Compute the anticipated return after financing cost with the two moderate approaches to the asset financing mix.

See the graph in the attached image.

Answer:

314402 steps

Step-by-step explanation:

10142 x 31

The conditional relative frequency for female students who prefer playing sports is 34%.

The table of values is given as:

                        Sports   Dancing Row totals

Male students      18             16        34

Female students  18             35       53

Column totals       36            51         87

Mason's calculation is given as:

P = 21%

This is gotten by

18/87 = 21%

The above represents the joint relative frequency of female students who prefer playing sports.

To calculate the conditional relative frequency, he should divide 18 by the row total.

So, we have

18/53 = 34%

Hence, the conditional relative frequency for female students who prefer playing sports is 34%.

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Answer:

Step-by-step explanation:

hello : here is a solution

The amount after 1 year is $7280 and the amount after two year is $8153.

Given that $6500 is placed in an account that pays 12% interest compounded each year.

Compounding is the addition of interest to the principal of a loan or deposit, or in other words, interest on principal plus interest.

Compounded interest=12%

Principal amount=$6500

Time period = 1 year

[tex]A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]

where P is Principle amount, r is annual interest, n is number of times the interest compounded monthly, t is number of years

Here P=6500, r=12%, n=1, t=1

Substitute these values in the formula, we get

A=6500(1+(0.12/1))¹⁽¹⁾

A=6500(1+0.12)¹

A=6500×1.12

A=7280

Now we have to calculate for two years.

That is if n=2 , then

A=6500(1+(0.12/1))¹⁽²⁾

A=6500(1+0.12)

A=6500×1.2544

A=8153.6

Hence, the amount for one year and two year when $6500 is placed in an account that pays 12% interest compounded is $7280 and $8153.60.

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The tax that will be withheld is D. $16.48.

From the information, it was stated that Tim Worker is checking his earnings statement and that his weekly earnings are $520.00.

The tax that will be withheld will be:

= 3.16% × $520

= $16.48

In conclusion, the correct option is D.

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Answer:

B=37

H=66

Step-by-step explanation:

Use algebra and find the answer.

The maximum value of the objective function is 26 and the minimum is -10

The objective function is given as:

z=−3x+5y

The constraints are

x+y≥−2

3x−y≤2

x−y≥−4

Start by plotting the constraints on a graph (see attachment)

From the attached graph, the vertices of the feasible region are

(3, 7), (0, -2), (-3, 1)

Substitute these values in the objective function

So, we have

z= −3 * 3 + 5 * 7 = 26

z= −3 * 0 + 5 * -2 = -10

z= −3 * -3 + 5 * 1 =14

Using the above values, we have:

The maximum value of the objective function is 26 and the minimum is -10

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Using the binomial distribution, the probabilities are given as follows:

a) 0.37 = 37%.

b) 0.5065 = 50.65%.

c) 0.3260 = 32.60%.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the fixed parameter is:

p = 0.37.

Item a:

The probability is P(X = 1) when n = 1, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{1,1}.(0.37)^{1}.(0.63)^{0} = 0.37[/tex]

Item b:

The probability is P(X = 3) when n = 3, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{3,3}.(0.37)^{3}.(0.63)^{0} = 0.5065[/tex]

Item c:

The probability is P(X = 2) when n = 4, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{4,2}.(0.37)^{2}.(0.63)^{2} = 0.3260[/tex]

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