A rock is projected directly upward from ground level. After t seconds, its height
is given by: f(t) = -16t? + 64t + 80.
a
a)
After how many seconds will it reach a height of 144 ft?
b)
When will the rock return to the ground?

The calculated area of the minor sector is 90π square cm

From the question, we have the following parameters that can be used in our computation:

The circle (see attachment)

Where, we have

The area of the minor sector is then calculated as

Area = θ/360 * πr²

Substitute the known values in the above equation, so, we have the following representation

Area = 36/360 * π * 30²

Evaluate

Area = 90π

Hence, the area is 90π

Read more about sector area at

https://brainly.com/question/31752704

#SPJ1

Here is a Venn diagram illustrating the relationship between the sets a, b, and c, where a is a subset of b and b is a subset of c:

     _______________

    |       c       |

    |               |

    |      _________

    |     |         |

    |     |    b    |

    |     |         |

    |     |______   |

    |            |  |

    |       a    |__|

    |_______________|

In this diagram, the set c is represented by the outer rectangle, the set b is the area inside the rectangle but outside the inner circle, and the set a is the area inside both the rectangle and the inner circle.

Since a is a subset of b, every element in a is also in b, and therefore the inner circle is entirely contained within the area representing b.

Similarly, since b is a subset of c, every element in b is also in c, and therefore the area representing b is entirely contained within the outer rectangle representing c.

This diagram shows that if a is a subset of b and b is a subset of c, then a is also a subset of c.

To know more about Venn diagram refer here:

https://brainly.com/question/20795347#

#SPJ11

Answer: 123 IS

Step-by-step explanation:

Answer: 123

Step-by-step explanation:

Don’t know how to do it with out a calculator, but you press 75 the the green 2nd button a then the number 2. Then multiply by 164.

The regression analysis provides important insights into the relationship between single-parent households and student math performance.

To begin our analysis, we will run a simple linear regression of math4 on pctsgle. This will help us understand the relationship between the percentage of single-parent households in a school's ZIP code and the math performance of the students in that school.

Mathematically, the simple linear regression model can be written as:

math4 = β₀ + β₁pctsgle + ε

where math4 represents the average math score for a given school, pctsgle represents the percentage of single-parent households in the school's ZIP code, β₀ and β₁ are the intercept and slope coefficients respectively, and ε represents the error term.

After running the regression, we will obtain the following results:

math4 = 63.91 - 0.52pctsgle

Interpreting the results, we can see that for every one percent increase in the percentage of single-parent households in a school's ZIP code, the average math score of the students in that school decreases by 0.52 points.

The effect of single parenthood may seem small based on the slope coefficient of -0.52. However, it is important to note that this is just one variable and there may be other factors that could be contributing to the decrease in math performance.

Therefore, further analysis may be needed to fully understand the impact of single-parent households on student math performance.

To know more about regression here.

https://brainly.com/question/14184702

#SPJ4

Complete Question:

Use the data in MEAPSINGLE to study the effects of single-parent households on student math performance. These data are for a subset of schools in southeast Michigan for the year 2000. The socioeconomic variables are obtained at the ZIP code level (where ZIP code is assigned to schools based on their mailing addresses).

Run the simple regression of math4 on pctsgle and report the results in the usual format. Interpret the slope coefficient. Does the effect of single parenthood seem large or small?

The correct order of the steps in a hypothesis test are as follows:

Determine the null and alternative hypotheses.

Select a sample and compute the z-score for the sample mean.

Determine the probability at which you will conclude that the sample outcome is very unlikely.

Draw a conclusion about the unknown population using what is known about the sample.

First, you need to define the null and alternative hypotheses. The null hypothesis is the assumption that there is no significant difference between the sample and the population mean, while the alternative hypothesis is the opposite. Then, you need to select a random sample from the population and calculate the z-score for the sample mean. This involves finding the difference between the sample mean and the population mean, divided by the standard deviation of the sample mean.

Next, you need to determine the probability, known as the alpha level, at which you will conclude that the sample outcome is very unlikely, assuming that the null hypothesis is true. This is often set to 0.05 or 0.01. If the probability of obtaining the observed sample mean under the null hypothesis is lower than the alpha level, then the null hypothesis is rejected in favor of the alternative hypothesis.

Finally, you can draw a conclusion about the unknown population using what is known about the sample. If the null hypothesis is rejected, it suggests that there is a significant difference between the sample and the population mean, and the alternative hypothesis may be accepted.

Therefore, the correct order of the steps in a hypothesis test is to first determine the null and alternative hypotheses, then select a sample and calculate the z-score, determine the probability, and finally draw a conclusion based on the observed results.

To learn more about hypothesis test here:

brainly.com/question/30588452#

#SPJ11

SOLUTIONS

For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.

(a) Event A: A tail on the first toss or the second toss (or both)

(b) Event B: A head on each of the first two tosses

(c) Event C: Two or more tails

Answer:

Around 22200 dollars

Step-by-step explanation:

Firstly, it was depreciating 20% per year for 17 years. So, if we were to go back in time, it would be appreciating by 25%. Therefore, after doing the plugging in, it is 500 * 1.25^17. The initial value is around 22200. It is around 22204, to be exact.

The independent variable in this study is the place of residence, specifically whether the participants live in Florida or Pennsylvania.

The researcher is interested in examining the relationship between the location of residence and the amount of money spent on clothes. By selecting participants from both Florida and Pennsylvania, the researcher can compare the spending habits of individuals from these two locations and determine if there is a significant difference. Thus, the independent variable is the categorical variable that defines the groups being compared, which in this case is the place of residence.

Know more about place of residence here:

https://brainly.com/question/32383705

#SPJ11

Answer:

x₂ = - 3

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to \(\frac{5}{6}\)

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (9, 9) and (x₂, y₂ ) = (x₂, - 1)

m = \(\frac{-1-9}{x_{2}-9 }\) , that is

\(\frac{-10}{x_{2}-9 }\) = \(\frac{5}{6}\) ( cross- multiply )

5(x₂ - 9) = - 60 ( divide both sides by 5 )

x₂ - 9 = - 12 ( add 9 to both sides )

x₂ = - 3

Answer:

\(\large\fbox{\green{\underline{Cylinder P :- \blue{ 794.0275 in ³}}}}\)

\(\large\fbox{\green{\underline{Cylinder Q :- \blue{1,307.81 in³}}}}\)

Step-by-step explanation:

Volume of cylinder = π × ( radius ) ² × h

1.) Here, radius = 4.25 in and height = 14 in.

Volume of cylinder = π × ( radius ) ² × height

substitute the values

Volume of cylinder P = 3.14 × ( 4.25 in ) ²×14 in.

now, simplify

= 3.14 × 18.0625 in²× 14 in.

= 3.14 × 252.875 in³

multiplying the value

= 794.0275 in³

\( \small \: \: \sf \: \fbox{ cirumference \: of \: cylinder \: P \: = {794.0275 in³}}\)

2.) Here, radius = 7 in. and height = 8.5 in.

Volume of cylinder Q = π × ( radius ) ² × height

substitute the values

Volume of cylinder Q = 3.14 × ( 7 in )² × 8.5 in.

Simplify

= 3.14 × 49 in² × 8.5 in.

multiply the values

= 3.14 × 416.5 in³

\( \small \sf \fbox{Volume of cylinder Q = 1,307.81 in ³}\)

The p-value is less than 0.1, so there is evidence at the 0.1 level that the doors are either too long or too short.

To determine if there is evidence that the doors are either too long or too short, we can conduct a hypothesis test.

Let's assume the null hypothesis (H0) is that the mean height of the doors is equal to 2058 millimeters, and the alternative hypothesis (Ha) is that the mean height of the doors is not equal to 2058 millimeters.

We can use a t-test to compare the sample mean of 2072 millimeters to the population mean of 2058 millimeters, given the sample size of 18 and the standard deviation of 33.

Calculating the test statistic using the formula:
t = (sample mean - population mean) / (standard deviation / sqrt(sample size))

Substituting the values:
t = (2072 - 2058) / (33 / sqrt(18))

Calculating the p-value associated with this test statistic, we find that it is less than 0.1.

Since the p-value is less than the significance level of 0.1, we reject the null hypothesis and conclude that there is evidence at the 0.1 level that the doors are either too long or too short.

Know more about p-value here:

https://brainly.com/question/33325466

#SPJ11

Answer:

the answer is 180°

Step-by-step explanation:

x+45°+55°+80°=360°

x+180=360°

x=360°-180°

x=180°

Answer:

6x-y=4 is the answer.........

Using the law of cosines, it is found that the measure of angle Y is of 64º.

The problem is incomplete, hence we research it on a search engine, and we have that we have a triangle in which:

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 12, b = 17, c = 16, C = Y.

Hence:

c² = a² + b² - 2abcos(Y)

16² = 12² + 17² - 2(12)(17)cos(Y)

408cos(Y) = 177

cos(Y) = 177/408

Y = arccos(177/408)

Y = 64º.

The measure of angle Y is of 64º.

More can be learned about the law of cosines at https://brainly.com/question/4372174

#SPJ1

Answer:

y = 5

Step-by-step explanation:

2(40 - 5y) : 80 - 10y

10y + 5(1 + y) : 5y + 5

80 - 10y = 5y +5

-10y = 5y -75

-10y - 5y = 5y - 75 - 5y

-15y/-15 = -75/-15

-15y/-15 : y

-75/-15 : 5

Hence, The answer should be 5

Answer:

b+\(c{2}\) = 19 + \(5^{2}\)

b-3c = 19 - 15

The solution is Option C.

The total distance skated by the ice skater is 126 meters

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the centre for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

Given data ,

Let the distance traveled by the skater be = D

Let the diameter of the circle A be = 20m

Let the diameter of the circle B be = 20m

So , the radius of circle A = 10 m

The radius of circle B = 10 m

Now , the value of π = 3.14

So , the distance traveled by the skater = perimeter of circle A + perimeter of circle B

Perimeter of Circle A = 2πr

Substituting the values in the equation , we get

Perimeter of Circle A = 2 x 3.14 x 10

Perimeter of Circle A = 62.8 m

And ,

Perimeter of Circle B = 2πr

Perimeter of Circle B = 2 x 3.14 x 10

Perimeter of Circle B = 62.8 m

Therefore , the distance traveled by the skater = Perimeter of Circle A + Perimeter of Circle B

Substituting the values in the equation , we get

The distance traveled by the skater = 2 x 62.8

The distance traveled by the skater = 125.6 meters

The distance traveled by the skater = 126 meters

Therefore , the value of D is 126 meters

Hence , The total distance skated by the ice skater is 126 meters

To learn more about circle click :

https://brainly.com/question/28391204

#SPJ2

The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

Learn more about expressions here:

https://brainly.com/question/1859113

#SPJ1                      

Noncollinear points are points that do not lie on the same line as defined terms.

What do you mean by defined terms?

Defined terms are words that are given a specific definition in a contract. The term's definition applies in the context of the particular contract and the definitions are usually only applicable to that contract.

If you see a capitalized word in a contract, the chances are its definition is somewhere in the document.

Defined terms give clarity and a sense of definitiveness to a contract.

They also remove ambiguity and make contracts easier to understand.

Collinear points are two or more straight-line points, whereas non-collinear points are points that do not lie on a single straight line.

Learn more about defined terms here:

https://brainly.com/question/4258163

#SPJ1

The number of batteries expected to last between three years and one month and three years and seven months, is 12,500 batteries.

Given that the mean shelf life of the flashlight batteries is three years and four months and the standard deviation is three months.

To find the number of batteries that can be expected to last between three years and one month (3.08 years) and three years and seven months (3.58 years), we need to calculate the probability within this range.

First, we convert the given time intervals to years:

Three years and one month = 3.08 years

Three years and seven months = 3.58 years

Next, we calculate the z-scores for these values using the formula:

z = (x - μ) / σ

For 3.08 years:

z1 = (3.08 - 3.33) / 0.25 = -1

For 3.58 years:

z2 = (3.58 - 3.33) / 0.25 = 1

Now, we can use the standard normal distribution table or a calculator to find the probabilities corresponding to these z-scores.

The probability of a value falling between -1 and 1 is the difference between the two probabilities.

Let's assume that the distribution is symmetric, so half of the batteries would fall within this range.

Therefore, the number of batteries that can be expected to last between three years and one month and three years and seven months is approximately:

Number of batteries = 0.5 × Total number of batteries = 0.5 × 25,000 = 12,500 batteries.

Learn more about Standard Deviation here:

https://brainly.com/question/475676

#SPJ11

Answer:

  u = -2.34  or  u = 18.34

Step-by-step explanation:

You want to solve u² -16u = 43 by completing the square.

To complete the square, add the square of half the coefficient of the linear term to both sides.

  u² -16u +(-16/2)² = 43 +(-16/2)²

  u² -16u +64 = 107 . . . . . . . simplify

  (u -8)² = 107 . . . . . . . . . write as a square

  u -8 = ±√107 . . . . . . square root

  u = 8 ± √107  . . . add 8

  u = -2.34  or  u = 18.34 . . . . . find the decimal values

<95141404393>

Answer:

Step-by-step explanation:

First table:(left)

(1, 15) (2, 30)

(30 - 15)/(2 - 1) = 15/1 = 15

y - 15 = 15(x - 1)

y - 15 = 15x - 15

y = 15x

Second table:(right)

(0, 10)  (1, 25)

(25 - 10)/(1 - 0)= 15/1= 15

y - 10 = 15(x - 0)

y - 10 = 15x - 0

y = 15x + 10

Answer:

Step-by-step explanation:

if we wouldnt have the semicircle, all would be easy...

Area , A=10*30=300 ft^2

the semicircle has a diameter d=12 ft, than r=6

Area of the circle is Ac=3.14*r^2=113.10 ft^2

we need half of that

113.10/2=56.55

the area of the cover would be

300-56.55=243.45 ft^2

Answer:

-3

Step-by-step explanation:

     Let x = the number

Then 3x = its triple, and the condition is:

x - 8 < 3x

Subtract x from each side

-8 < 2x

Divide each side by 2

-4 < x

Reverse the inequality

x > -4

The smallest integer greater than -4 is -3.

Check:

-3 - 8 < 3(-3)

-11 < -9

It checks.

Answer:

100mi

Step-by-step explanation:

There are 176,851 ways to assign the 100 pages to the four printers.

Since there are no restrictions on how many pages a printer can print, we can think of this problem as distributing 100 identical pages among 4 distinct printers. This is an example of a "balls and urns" problem, which can be solved using the stars and bars formula.

The stars and bars formula states that the number of ways to distribute k identical objects among n distinct containers is:

C(k+n-1, n-1)

where C represents the combination function. In this case, we have k = 100 identical pages and n = 4 distinct printers. Therefore, the number of ways to assign the pages to the printers is:

C(100+4-1, 4-1) = C(103, 3) = 176,851

So there are 176,851 ways to assign the 100 pages to the four printers.

To learn more about statistics  here

https://brainly.com/question/15525560

#SPJ4

The table formed using equivalent ratios.

16 : 128

5 : 40.

3 sticks of butter -----> 24 cookies.

Let the number of cookies made for other stick of butter be 'y'.

Then, number cookies for the 16  sticks of butter

3/24 = 16/ y

y = 16*24 / 3

y = 128 cookies.

Again, number cookies for the 5 sticks of butter

3/24 = 5/ y

y = 5*24 / 3

y = 40 cookies.

Thus, number of cookies made by 5 sticks of buter are 40.

To know more about the equivalent ratios, here

https://brainly.com/question/2914376

#SPJ4

Answer:

22.7 miles

Step-by-step explanation:

The hikers start walking 15 miles due east and then they turn north and walk 17 miles to a large pond.

The shape of their journey can be represented as a right angled triangle, shown below.

To find the distance between the pond and the base camp, we need to find the hypotenuse of the triangle.

We can do this by using Pythagoras theorem:

\(hyp^2 = a^2 + b^2\)

where a and b are the other two sides of the triangle. Therefore:

\(hyp^2 = 15^2 + 17^2\\\\hyp^2 = 514\\\\hyp = \sqrt{5`4} \\\\hyp = 22.7 miles\)

The pond is 22.7 miles far from the base camp.

To find each answer, we just have to solve for t. It is important to use the important angles in trigonometry to provide an exact answer.

The first answer is t = 225°.

The second answer is 30°.

The third answer is t = 150°.