A box falls off a warehouse shelf from a height of 16 feet. The function h=−16x2+16 gives the height h (in feet) of the box after x seconds. When does it hit the floor?

Answer:

sales tax is  31 dollars and 53 cents

Step-by-step explanation:

You want the sales tax in dollars and cents.

so

Sales tax = 6% * $525.50 = 0.06* $525.5 =  $31.53

Answer:

For the first one it would be 84

Second: 45

Step-by-step explanation:

First one: 7 times 12.

Second: add 30 and 30 together which is 60. Then divide 30 in half which is 15. Then add 15 to 30.

Answer:

3. 84 inches

4. 75 miles

Step-by-step explanation:

3.

Scale = 1/12 × actuall

7 = 1/12 × actual

actual = 7 × 12 = 84 inches

4.

Map : actual

1 in : 30 miles

2.5 in : X miles

X/2.5 = 30/1

X = 2.5×30 = 75 miles

Answer:

23. Length = 21 feet, Width = 3 feet

24. Larger Angle = 162 degrees, Smaller Angle = 18 degrees

Step-by-step explanation:

23.

Let us say:                                                                                                      l ⇒ length of the rectangular pool, w ⇒ width of the rectangular pool

According to the problem we could formulate two equations as such:

2l + 2w = 48,

l = 15 + 2w

Now let us solve for the dimensions;

First convert the two equations to standard form:

2l + 2w = 48,

l - 2w = 15

Using process of elimination:

  2l + 2w = 48

+   l  - 2w = 15

Simplify:

3l = 63,

length = 21 feet

Substitute this value of length into the second equation.....:

21 - 2w = 15

.......And simplify:

-2w = -6,

width = 3 feet

24.

Let us say:                                                                                                      L ⇒ larger angle, S ⇒ smaller angle,

According to the problem we could formulate two equations as such:

L + S = 180,

L = 9S

Now let us solve for the angles;

Let us here use substitution:

(9S) + S = 180

Simplify:

10S = 180,

Smaller Angle = 18 degrees

Substitute this value of the smaller angle into the second equation.....:

L = 9(18)

.......And simplify:

Larger Angle = 162 degrees

Answer:

The answer to this question is maximum

Answer:

Maximum

A downward parabola will have the highest point at the very top, so it will have a maximum.

Answer: Infinite solutions.

x could be equal to anything, and you can't solve for x since there is no equation on the other side of an equal sign for you to solve it. Hope that helps.

The answer is A on USA test prep

Step-by-step explanation:

Answer:

[tex]P(90<X<110)=P(\frac{90-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{110-\mu}{\sigma})=P(\frac{90-100}{15}<Z<\frac{110-100}{15})=P(-0.67<z<0.67)[/tex]

[tex]P(-0.67<z<0.67)=P(z<0.67)-P(z<-0.67)[/tex]

[tex]P(-0.67<z<0.67)=P(z<0.67)-P(z<0.67)=0.749-0.251=0.498[/tex]

Step-by-step explanation:

Let X the random variable that represent the IQ scores, and for this case we know the distribution for X is given by:

[tex]X \sim N(100,15)[/tex]  

Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]

We want to find this probability

[tex]P(90<X<110)[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(90<X<110)=P(\frac{90-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{110-\mu}{\sigma})=P(\frac{90-100}{15}<Z<\frac{110-100}{15})=P(-0.67<z<0.67)[/tex]

And we can find this probability with this difference:

[tex]P(-0.67<z<0.67)=P(z<0.67)-P(z<-0.67)[/tex]

And in order to find these probabilities we can use the normal standard table or excel and we got.  

[tex]P(-0.67<z<0.67)=P(z<0.67)-P(z<0.67)=0.749-0.251=0.498[/tex]

Answer:

(a + 8) (a + 8)

Step-by-step explanation:

a² + 16a + 64

a² + 8a + 8a + 64

a(a + 8) + 8(a + 8)

(a + 8) (a + 8)

The answer would be M= 23/2 or 11.5.

Answer:

113.1

there u go

Answer:

Solving the expression, it is equal to 48. But it you want and expression equal to 48:

4 x 12 can be the answer.

Step-by-step explanation:

[tex]$4\cdot \left[\left(12\:+\:4\right)\:-\:\left(\frac{12}{3}\right)\right]$[/tex]

[tex]4\left(12+4-4\right)[/tex]

[tex]4 \cdot 12\\48[/tex]

Answer:

C

Step-by-step explanation:

The solution is: quadratic; y = 2.5x^2, this function best models the data.

Option (1)

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

x               -2              -1                 0                    1                   2

y               10            2.5                0                  2.5                3.0

Ist difference,

d_1 = -7.5  

d_2= -2.5

d_3 = 2.5

d_4 = 7.5

2nd difference,

x_1  = 5

x_2 = 5

x_3 = 5

Since 2nd difference is common, given table represents a quadratic equation.

Let the equation is,

y = ax²+ bx + c

For a point (0, 0) passing through the quadratic equation,

0 = c

Therefore, quadratic equation is y = ax² + bx

Since ordered pair (-1, 2.5) passes through the graph of the function,

2.5 = a(-1)² + b(-1)

a - b = 2.5 ------(1)

For another point (1, 2.5)

2.5 = a(1)² + b(1)

a + b = 2.5 ------(2)

By adding equations (1) and (2),

2a = 5

a = 2.5

and from equation (2)→ y = 0

Therefore, equation of the quadratic function given in the table is y = 2.5x²

Option (1) is the answer.

Hence, The solution is: quadratic; y = 2.5x^2, this function best models the data. i.e. Option (1)

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Complete question:

Graph the data in the table. Which kind of function best models the data? Write an equation to model the data. quadratic; y = 2.5x2 linear; y = 2.5x quadratic; y = –2.5x2 exponential; y = 2.5x

Answer:

31.5789%

Step-by-step explanation:

Answer:

24%

Step-by-step explanation:

If you use the "is over of" form.

"19 is what percent of 25"

You'd set it up like this:

[tex]\frac{19}{25}[/tex]=[tex]\frac{x}{100}[/tex]

Then cross multiply:

19 times 100 = 1900

25 times x = 25x

Divide 25 into 1900 and get 76.

That is the percent (%) of what 19 is of 25.

BUT we want the space in between the numbers.

To get that, we subtract 100 - 76.

(100 is the whole 100%)

This gives you 24%

Answer: 34

Step-by-step explanation:

(x+22) + x = 90

Given that angles A and B are complementary. Angle A is (x + 22) degrees. Angle B is x degrees. The value of x is 34°.

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

(x + 22) + x = 90

2x + 22 = 90

2x = 68

x = 34

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Answer:

a) [tex] df =n_1 +n_2 -2 =15 +17-2 =30[/tex]

And then since we want to conduct a two tailed test we need to llok in the t distribution with 30 degrees of freedom a value who accumulate 0.05 of the area and we got:

[tex] t_{\alpha/2} =\pm 1.697[/tex]

b)[tex]S^2_p =\frac{(15-1)(12)^2 +(17 -1)(15)^2}{15 +17 -2}=187.2[/tex]

[tex]S_p=13.682[/tex]

c) [tex]t=\frac{(350 -342)-(0)}{13.682\sqrt{\frac{1}{15}+\frac{1}{17}}}=1.65[/tex]

d) For this case the statistic calculated is lower than the critical value so then we FAIL to reject the null hypothesis at the significance level given.

e) The p value for this case would be given by:

[tex]p_v =2*P(t_{30}>1.65) =0.1094[/tex]

Step-by-step explanation:

We are assuming that the two population deviations are equal:

[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]

And the statistic is given by this formula:

[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}[/tex]

Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:

[tex]\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]

Part a

For this case we need to find the degrees of freedom given by:

[tex] df =n_1 +n_2 -2 =15 +17-2 =30[/tex]

And then since we want to conduct a two tailed test we need to llok in the t distribution with 30 degrees of freedom a value who accumulate 0.05 of the area and we got:

[tex] t_{\alpha/2} =\pm 1.697[/tex]

Part b

The pooled deviation can be founded with this formula:

[tex]S^2_p =\frac{(15-1)(12)^2 +(17 -1)(15)^2}{15 +17 -2}=187.2[/tex]

And the deviation would be:

[tex]S_p=13.682[/tex]

Part c

The system of hypothesis on this case are:

Null hypothesis: [tex]\mu_1 = \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]

Replacing the info given we got:

[tex]t=\frac{(350 -342)-(0)}{13.682\sqrt{\frac{1}{15}+\frac{1}{17}}}=1.65[/tex]

Part d

For this case the statistic calculated is lower than the critical value so then we FAIL to reject the null hypothesis at the significance level given.

Part e

The p value for this case would be given by:

[tex]p_v =2*P(t_{30}>1.65) =0.1094[/tex]

The question refers to hypothesis testing for difference in population means. The null hypothesis is rejected both by using the critical value approach and the p-value approach, indicating a significant difference in population means at the 0.10 significance level.

This question deals with hypothesis testing for difference in population means with a given significance level.

(a) The decision rule for this two-tailed test is: Reject the null hypothesis if the absolute value of the test statistic is greater than the critical value at the 0.10 significance level, or if the p-value is less than the significance level.

(b) The pooled estimate of the population variance is calculated using the formula: [(n1-1)s1^2 + (n2-1)s2^2] / (n1+n2-2) = [(15-1)*12^2 + (17-1)*15^2] / (15+17-2) = 196.77.

(c) The test statistic is calculated as: (x1 - x2) / sqrt[(pooled variance)*(1/n1 + 1/n2)] = (350 - 342) / sqrt[(196.77)*(1/15 + 1/17)] = 1.87.

(d) With degrees of freedom of (15+17-2)=30, the critical values for a two-tailed test at the 0.10 significance level are approximately ±1.697. As our test statistic is greater than the critical value, we reject the null hypothesis.

(e) The p-value associated with the test statistic of 1.87 is approximately 0.07, which is less than the significance level of 0.10. Hence, we again reject the null hypothesis. Therefore, we conclude that there is a significant difference in the population means at the 0.10 significance level.

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Answer:

f(x)=1200(1.04)^n

Step-by-step explanation:

We have been a right triangle. We are asked to find the missing length of the given triangle.

We can see that our given triangle is 30-60-90 triangle.

We know that the lengths of the sides of a 30-60-90 triangle are in the ratio [tex]1:\sqrt{3}:2[/tex].

If the side opposite to 30 degree is [tex]n[/tex], then the side opposite to 60 degree angle will be [tex]\sqrt{3}n[/tex] and side opposite to hypotenuse will be [tex]2n[/tex].

We can see that side corresponding to hypotenuse is 6 that is [tex]2n=6[/tex].

Let us solve for n.

[tex]\frac{2n}{2}=\frac{6}{2}[/tex]

[tex]n=3[/tex]

The side corresponding to 30 degree angle will be half of 6 that is 3. Therefore, the value of y is 3.

The value of x will be [tex]3\sqrt{3}[/tex] as it is side corresponding to 60 degree angle.

Answer:

1,055.58 in^3

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h

We need the radius

r = d/2 = 12/2 =6

V = 1/3 (pi) (6)^2 *28

Using the pi button on the calculator

   =1055.575132

Rounding to 2 decimal places

 1,055.58 in^3

Answer:

380 different ways

Step-by-step explanation:

We can solve this problem using a permutation formula, as the order in a group of two students matter.

So, for this problem, we have 20 students and want to form groups of 2, so we have a permutation of 20 choose 2:

P(20,2) = 20! / (20-2)! = 20! / 18! = 20 * 19 = 380 different ways

Another way to solve this problem is:

For the first student being chose, we have 20 students available, and for the second student, we have just 19, as one was already chose, so the number of ways to choose these two students is 20 * 19 = 380

Answer:

y intercept (0,-32)

x intercept (3.2,0)

Step-by-step explanation:

To find the y intercept set x = 0 and solve for y

y = 10x -32

y = 0-32

y = -32

(0,-32)

To find the x intercept set y = 0 and solve for x

y = 10x -32

0 = 10x -32

Add 32 to each side

32 = 10x

Divide by 10

32/10 = x

(3.2,0)

Answer:

[tex]y-intercept(0,-32)\\\\x-intercept(\frac{16}{5},0)[/tex]

Step-by-step explanation:

The y-intercept happens where x is 0, and the x-intercept if where y is 0. You can use this knowledge to find the intercepts.

This equation is written in slope-intercept form:

[tex]y=mx+b[/tex]

where b is the y-intercept, so the y-intercept is -32.

To find the x intercept, insert 0 as the value of y:

[tex]0=10x-32[/tex]

Solve for x. Add 32 to both sides:

[tex]0+32=10x-32+32\\\\32=10x[/tex]

Divide both sides by 10:

[tex]\frac{32}{10}=\frac{10x}{10} \\\\x=\frac{32}{10} =\frac{16}{5}[/tex]

The x-intercept is at [tex]\frac{16}{5}[/tex] or [tex]3.2[/tex] .

Find the points:

[tex]y-intercept(0,-32)\\x-intercept(\frac{16}{5},0)[/tex]

Finito.

Answer:

Answer choice A

Step-by-step explanation:

For the first letter, there are 26 options, as there are for the second and third letter. For each of the three numbers, there are 10 digits to choose from. Therefore, 26*26*26*10*10*10=17,576,000, or answer choice A. Hope this helps!

Option (A) the number of different ways of license plate arrangements are 17,576,000 is the correct answer.

A permutation is an arrangement of objects in a definite order. It is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

For the given situation,

A state license plate consists of three letters followed by three digits.

There are 26 letters from a to z and 10 digits from 0 to 9.

The license plate consists of three letters and three digits so the possibility of arrangements are

⇒ [tex](26)(26)(26)(10)(10)(10)[/tex]

⇒ [tex]17576000[/tex]

Hence we can conclude that option (A) the number of different ways of license plate arrangements are 17,576,000 is the correct answer.

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Answer:is yes

Step-by-step explanation:

no

Answer:

A= 8.182

B= 8

Step-by-step explanation:

Answer:

subtract 3 each term

Step-by-step explanation:

Answer:

  -$500

Step-by-step explanation:

The expected value of a payment from the policy is ...

  $500,000 × 0.002 = $1000

Since the business pays $1500 for the policy, the expected value to the business is ...

  $1000 - 1500 = -$500 . . . per year

_____

Of course, the expected value to the insurance company is $500 per year.

_____

We have computed on the basis of 1 claim per year. If we consider the possibility of multiple independent claims, then the expected payment from the insurance goes up by a factor of 1/(1 -0.002) ≈ 1.002004008016.... This has the effect of increasing the expected value by $2.00 per year to -$498.

Answer: 3.708 * 10^4

Step-by-step explanation:

Answer:

i think thats d sorry if incorrect

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Trust me

Answer:

2 + 2 = 4

Step-by-step explanation:

Are you sure?  Is this a trick?  Or is the "+"  a different kind of plus?

Answer:

11 pens weigh 53.43 grams.

2 pens weigh X grams.

We have:

11/53.43 = 2/X

=> X = 2 x 53.43/11 = 9.72 grams

Hope this helps!

:)

Answer: A the member can tolerate a temp of 173 fahrenheit for 0 minutes

The true statement is (a) The member can tolerate a temperature of 173∘ Fahrenheit for 0 minutes.

The equation of the line of best fit for the data is given as:

y = -1.5x + 173

Set x to 0, to calculate the y-intercept

y = -1.5 * 0 + 173

Evaluate the product

y = 0 + 173

Evaluate the sum

y = 173

This means that initial temperature is 173

Hence, the true statement is (a) The member can tolerate a temperature of 173∘ Fahrenheit for 0 minutes.

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m=-2-4/3-4=-6/-1=6

y-4=6(x-4)

y=6x-20