The simplified expressions for the area and perimeter of the rectangle are 16x and 4x, respectively.
To simplify the expressions for the area and perimeter of the rectangle, we can extract common factors:
Area: [tex]\(8(x + x) = 8 \times 2x = 16x\)[/tex]
Perimeter: [tex]\(2(x + x) = 2 \times 2x = 4x\)[/tex]
Therefore, the simplified expressions are:
Area: 16x
Perimeter: 4x
Mitchel climbs 8 feet up the vertical ladder of a slide and zips down the 17-foot slide. How far is the bottom of the ladder from the bottom of the slide
Answer:
the bottom of the ladder from the bottom of the slide is 15 feet far from
the bottom of the slide
Step-by-step explanation:
Given that Mitchel climbs 8 feet up the vertical ladder of a slide and zips down the 17-foot slide.
The slide the vertical ladder and the floor together form a right triangle if we can vizualise.
The hypotenuse would be the slide , and one leg is ladder and other the bottom of the ladder from the bottom of the slide
We have hypotenuse = 17 feet and one leg = 8 feet
So use Pythagorean theorem to find other leg
Other leg = [tex]\sqrt{17^2-8^2} \\=\sqrt{(17+8)(17-8)} \\= 15[/tex]
the bottom of the ladder from the bottom of the slide is 15 feet far from
the bottom of the slide
Sociologists want to test whether the number of homeless people in a particular urban area is increasing. In 2010, the average number of homeless people per day who sought shelter was 42.3 (σ = 6.2). Data from the current year reveal that the mean number of people seeking shelter per day is 45.3. Compute the test statistic using an alpha = .01 and n = 1000.
Answer:
The test statistic value is 15.3.
Step-by-step explanation:
The hypothesis for this test is:
H₀: The average number of homeless people is not increasing, i.e. μ = 42.3.
Hₐ: The average number of homeless people is increasing, i.e. μ > 42.3.
Given:
[tex]\bar x=45.3\\\sigma=6.2\\n=1000[/tex]
As the population standard deviation is provided use a single mean z-test for the hypothesis testing.
The test statistic is:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{45.3-42.3}{6.2/\sqrt{1000}}=15.3[/tex]
Thus, the test statistic value is 15.3.
Using the z-distribution, it is found that the test statistic is of z = 15.3.
At the null hypothesis, it is tested if the mean number has not increased, that is, it still is of 42.3, hence:
[tex]H_0: \mu = 42.3[/tex]
At the alternative hypothesis, it is tested if it has increased, that is, the mean is greater than 42.3, hence:
[tex]H_1: \mu > 42.3[/tex]
We have the standard deviation for the population, hence, the z-distribution is used.
The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are:
[tex]\overline{x} = 45.3, \mu = 42.3, \sigma = 6.2, n = 1000[/tex]
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{45.3 - 42.3}{\frac{6.2}{\sqrt{1000}}}[/tex]
[tex]z = 15.3[/tex]
The test statistic is of z = 15.3.
To learn more about the z-distribution, you can take a look at https://brainly.com/question/16313918
A professor grades students on four tests, a term paper, and a final examination. Each test counts as 15% of the course grade. The term paper counts as 20% of the course grade. The final examination counts as 20% of the course grade. Alan has test scores of 79, 95, 89, and 81. Alan received an 81 on his term paper. His final examination score was 85. Use the weighted mean formula to find Alan's average for the course.
Answer:
The Alan's average for course is 72.65.
Step-by-step explanation:
Given that,
Each test counts as 15% of the course grade. 20% of course grade is counted term test paper. Alan has test scores of 79, 95, 89, and 81. Alan got 81 score on his term paper . Alan's final examination score = 85.
[tex]\sum w=1[/tex]
Let n number x₁,x₂,.......,[tex]x_n[/tex] with respect to assigned weight[tex]w_1[/tex],[tex]w_2[/tex],.......,[tex]w_n[/tex] is
[tex]{\textrm{weighted mean}}= \frac{\sum w.x}{\sum w}[/tex]
Where [tex]\sum w.x[/tex] is the sum of the products the number with the relevant weight.
weighted mean [tex]=\frac{79\times 15\%+95 \times 15\%+89\times 15\%+81\times 20\%+85\times20\%}{1}[/tex]
=72.65
The Alan's average for course is 72.65.
Factor completely. If the polynomial is not factorable, write prime.
5.) 3x^3y+x^2y^2+x^2y
6.) 8r^3-64s^6
Step-by-step explanation:
5)
3x³y + x²y² + x²y
x²y (3x + y + 1)
6)
8r³ − 64s⁶
8 (r³ − 8s⁶)
8 (r − 2s²) (r² + 2rs² + 4s⁴)
Math-The park department wants to have new tree planted. They agreed that 1/10 of the tree will be oak,3/10 will be pine, and 2/10 will be willow. They are undecided about the rest. What fraction of trees will be oak, or pine?
On a river you must release any fish that you catch ifvit measures less than 12 inches. Define a variable and then write an algebraic inequality for each senario. can you keep a fish that is 11.99 inches?
Let f = fish
If f < 12, let the fish go.
We cannot catch a fish measuring 11.99 inches.
If f = fish, then f < 11.99. It must be released.
Students were divided into two groups. Students in one group were ignored when they talked without raising their hands. Students in the other group were attended to in the teacher's usual manner. The independent variable in this experiment was _____.
Answer:
The independent variable in this experiment was the attention students gets from the teacher
Step-by-step explanation:
An independent variables are variables in maths, statistics and experimental sciences that stands alone and isn't affected by the other variables you are trying to measure.
Final answer:
The independent variable was the teacher's response to the student behavior of either ignoring or attending to students when they talked without raising their hands.
Explanation:
The independent variable in this experiment was the strategy used by the teacher regarding whether or not to ignore the students when they talked without raising their hands.
In experimental design, the independent variable is the condition that is manipulated by the researcher to observe its effects on the dependent variable.
In this case, students in one group were ignored when they spoke without raising their hands, making them the experimental group.
The other group, which the teacher attended to in their usual manner, acted as the control group.
Since the independent variable is the only factor that is intentionally changed to test its impact on outcomes, observing changes in the students' behavior helped determine the effects of this teaching strategy.
Triangle ABC is reflected across the line y = x. What are the coordinates of the vertex B' of the resulting triangle A'B'C'?
A. (2, -5)
B. (-2, 5)
C. (5, -2)
D. (-5, -2)
please help
As x increases by 1 unit, what is the exponential growth factor?
Answer: The answer is 3, I just finished doing the assignment.
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Look at the system of equations below.
{y = − 2 x + 3
4 x − 3y = 11
What is the solution to the system? Show your work.
Answer:
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=2,\:y=-1[/tex]
Step-by-step explanation:
Considering the system of the equation
[tex]\begin{bmatrix}y=-2x+3\\ 4x-3y=11\end{bmatrix}[/tex]
[tex]\mathrm{Subsititute\:}y=-2x+3[/tex]
[tex]\begin{bmatrix}4x-3\left(-2x+3\right)=11\end{bmatrix}[/tex]
[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:4x-3\left(-2x+3\right)=11[/tex]
[tex]4x-3\left(-2x+3\right)=11[/tex]
[tex]4x+6x-9=11[/tex]
[tex]10x-9=11[/tex]
[tex]10x-9+9=11+9[/tex]
[tex]10x=20[/tex]
[tex]x=2[/tex]
[tex]\mathrm{For\:}y=-2x+3[/tex]
[tex]\mathrm{Subsititute\:}x=2[/tex]
[tex]y=-2\cdot \:2+3[/tex]
[tex]y=-1[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=2,\:y=-1[/tex]
A deck of 52 cards has only one queen of diamonds. The deck is well-shuffled and you draw the first and last card (without replacement). What is the chance that the first card is a queen of diamonds or the last card is a queen of diamonds
Answer:
3.8% chance
Step-by-step explanation:
Someone has 240$ for a road trip this is 2/5of the coast of the trip how much dose the trip coat
Answer:
$600
Step-by-step explanation:
Divide 240 by 2/5
Chloé had 100 math problems to complete over the 3-day weekend. She recorded the number of problems in her math journal. She completed 39/100 of the problems on Friday,5/10 of the problems on Saturday,and another 15 problems on Sunday. Did chloe fill out her math journal correctly ?
The answer is no, Chloe did not fill out her math journal correctly.
To determine if Chloe completed all 100 math problems correctly, we need to calculate the total number of problems she completed over the weekend.
On Friday, Chloe completed [tex]\( \frac{39}{100} \)[/tex] of the problems. This fraction represents the portion of the total problems she completed on Friday. To find out how many problems this corresponds to, we multiply the total number of problems by this fraction:
[tex]\[ \text{Problems on Friday} = \frac{39}{100} \times 100 = 39 \text{ problems} \][/tex]
On Saturday, Chloe completed [tex]\( \frac{5}{10} \)[/tex] of the problems. Again, we multiply the total number of problems by this fraction to find out the number of problems completed on Saturday:
[tex]\[ \text{Problems on Saturday} = \frac{5}{10} \times 100 = 50 \text{ problems} \][/tex]
On Sunday, Chloe completed another 15 problems.
Now, we add up the problems completed each day to find the total number of problems completed over the weekend:
[tex]\[ \text{Total problems completed} = \text{Problems on Friday} + \text{Problems on Saturday} + \text{Problems on Sunday} \][/tex]
[tex]\[ \text{Total problems completed} = 39 + 50 + 15 \][/tex]
[tex]\[ \text{Total problems completed} = 104 \][/tex]
Chloe completed a total of 104 problems, which is more than the 100 problems she was supposed to complete. Therefore, she did not fill out her math journal correctly, as she recorded more problems than were assigned.
Chloé's math journal is not filled out correctly.
Let's calculate how many problems Chloé completed each day:
Friday: She completed [tex]\frac{39}{100}[/tex] of 100 problems, which equals 39 problems.Saturday: She completed [tex]\frac{5}{10}[/tex] (or 50%) of 100 problems, which equals 50 problems.Sunday: She completed 15 problems.Adding these up: 39 (Friday) + 50 (Saturday) + 15 (Sunday) = 104 problems.
This must be incorrect since she only had 100 problems to start with. Therefore, Chloé's math journal is not filled out correctly.
If a member variable is declared , all objects of that class share that variable. A(n) function is not a member of a class, but has access to the private members of the class. A(n) tells the compiler that a specific class will be declared later in the program. When the operator is overloaded, its function must have a dummy parameter. The class Stuff has both a copy constructor and an overloaded = operator. Assume that blob and clump are both instances of the Stuff class. For each of the statements, indicate whether the copy constructor or the overloaded = operator will be called: Staff blob = clump ; clump = blob ; blob.operator =(clump) ; showValues(blob) ; // blob is passed by value Consider the following class declaration: class Thing { private: int x ; int y ; static int z ; public: Thing() { x = y = z ; } static void putThing(int a) { z = a ; } } ; int Thing:: z = 0 ; Assume a program containing the class declaration defines three Thing objects with the following statement: Thing one, two, three ; How many separate instances of the x member exist? How many separate instances of the y member exist ? How many separate instances of the z member exist? What value will be stored in the x and y members of each object? Write a statement that will call the putThing member function before the Thing objects are defined. Explain why the parameter of a copy constructor must be a reference.
Answer:
a shs s s s ss bsbsbsbs s s s s s s s s s s s s s
A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 54 .
What is the volume of the dilated prism?
Enter your answer, as a decimal, in the box.
cm³
Answer:
New base area = 8 x 25/16 = 25/2 = 12•5 cm²
New height = 7•5 cm²
V = 7•5 x 12•5 cm³
V = 93•75 cm³
Step-by-step explanation:
Brynn ate 4/10 funnel cakes and 37/100 of the food was cotton candy. The rest of the food was popcorn. What fraction of the food brynn are was funnel cakes or cotton candy?
Answer:
?
Step-by-step explanation:
Convert 4/10 into 40/100(so you can have same denominator as other fraction) and then add 40/100 and 37/100 and you will get the answer!
The cost, in dollars, of producing x belts is given by Upper C (x )equals 751 plus 12 x minus 0.067 x squared. Find the rate at which average cost is changing when 256 belts have been produced.
Answer:
-$0.07846 per belt
Step-by-step explanation:
The average cost per belt is ...
[tex]c(x)=\dfrac{C(x)}{x}=\dfrac{751+12x-0.067x^2}{x}=751x^{-1}+12-0.067x[/tex]
Then the rate of change of average cost is ...
[tex]c'(x)=-751x^{-2}-0.134\\\\c'(256)=\dfrac{-751}{256^2}-0.067\approx -0.07846[/tex]
The rate at which average cost is changing is about -0.078 dollars per belt.
_____
Note that the cost of producing 256 belts is -$567.91, so their average cost is about -$2.22 per belt.
The student is asked to calculate the rate of change of average cost for producing belts when 256 belts are produced, by finding and evaluating the derivative of the average cost function.
Explanation:The question asks about the rate at which the average cost is changing for the production of belts given a certain cost function C(x) = 751 + 12x - 0.067x2. To find this rate when 256 belts are produced, we need to first calculate the average cost, which is C(x) divided by x, and then take the derivative of the average cost to find its rate of change. The derivative of the average cost function gives us the rate at which the average cost is changing with respect to the number of belts produced. We evaluate this derivative at x = 256 to find the specific rate of change at the production of 256 belts.
Flip a coin 25 times and keep track of the results. What is the experimental probability of landing on tails? What is the theoretical probability of landing on heads or tails?
Answer:
you must flip a coin 25 times and record it on a table for experimental. Theoretical would be 50% chance ( showing working)
The theoretical probability of landing on heads or tails is always 0.5 or 50%. The experimental probability of landing on tails is determined by dividing the number of times you land tails by the total number of flips. Over the long term, thanks to the Law of Large Numbers, these values tend to converge.
Explanation:The subject of the question is the probability of landing on heads or tails when flipping a coin 25 times. The experimental probability of landing on tails can only be determined empirically by actually performing the experiment. After flipping the coin 25 times, you would calculate the experimental probability of landing on tails by dividing the number of times you landed on tails by the total number of flips (25).
On the other hand, the theoretical probability of landing on heads or tails on a single flip of a fair coin is always 0.5, or 50%, due to the nature of the coin having two equally likely outcomes. This is known as the Law of Large Numbers, which states that as the number of trials of a random experiment increases, the experimental probability approaches the theoretical probability.
For example, if we talk about Karl Pearson's experiment, after flipping a coin 24,000 times, he obtained heads 12,012 times. The relative frequency of heads is 12,012/24,000 = 0.5005, which is very close to the theoretical probability (0.5).
Learn more about Probability here:https://brainly.com/question/32117953
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Find the volume of a right circular cone that has a height of 8.8 cm and a base with a diameter of 18.6 cm. Round your answer to the nearest tenth of a cubic centimeter.
Final answer:
The volume of the cone is approximately 860.6 cm³.
Explanation:
To find the volume of a right circular cone, we can use the formula V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone. In this case, the diameter of the base is 18.6 cm, so the radius is half of that, which is 9.3 cm. The height of the cone is 8.8 cm. Plugging these values into the formula, we get V = (1/3)π(9.3 cm)²(8.8 cm). Calculating this, we find that the volume of the cone is approximately 860.6 cm³.
1) Bronson is an action and horror movie junkie. He started a movie review vlog and needs to keep
up with his movie viewing at a high pace. It has been a total of 50 weeks since he has stated his
vlog and he has watched 1250 movies. He has watched twice as many horror movies as action
movies. Write two equations that can model this situation.
two equations which can model this situation is : [tex]y=2x[/tex] and [tex]x+y=1250[/tex]
Step-by-step explanation:
Here we have , Bronson is an action and horror movie junkie. He started a movie review vlog and needs to keep up with his movie viewing at a high pace. It has been a total of 50 weeks since he has stated his vlog and he has watched 1250 movies. He has watched twice as many horror movies a action movies. We need to Write two equations that can model this situation. Let's find out:
Let Bronson watched x action movies and y horror movies , than according to question horror movies he watched is twice that of action movies i.e.
⇒ [tex]y=2x[/tex] ........(1)
Now , he has watched 1250 movies i.e.
⇒ [tex]x+y=1250[/tex] .......(2)
⇒ [tex]x+2x=1250[/tex]
⇒ [tex]3x=1250[/tex]
Therefore , two equations which can model this situation is : [tex]y=2x[/tex] and [tex]x+y=1250[/tex] .
Dustin bought 9 pencils. Some of the pencils were green and cost $0.90 each. The remainder of the pencils were purple and cost $0.65 each. If Dustin paid $7.10 for all of the pencils, how many green pencils did he buy?
Answer: he bought 5 green pencils
Step-by-step explanation:
Let x represent the number of green pencils that Dustin bought.
Dustin bought 9 pencils. The remainder of the pencils were purple. This means that the number of purple pencils that he bought is 9 - x
Some of the pencils were green and cost $0.90 each. The remainder of the pencils were purple and cost $0.65 each. If Dustin paid $7.10 for all of the pencils, it means that
0.9x + 0.65(9 - x) = 7.1
0.9x + 5.85 - 0.65x = 7.1
0.9x - 0.65x = 7.1 - 5.85
0.25x = 1.25
x = 1.25/0.25
x = 5
Please help!!! ASAP someone please
Answer:
0.31 yr
Step-by-step explanation:
The formula for interest compounded continuously is
[tex]FV = PVe^{rt}[/tex]
FV = future value, and
PV = present value
If FV is twice the PV, we can calculate the doubling time, t
[tex]\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}[/tex]
1. Brianna's doubling time
[tex]\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.065}\\\\& = & \textbf{10.663 yr}\\\end{array}[/tex]
2. Adam's doubling time
The formula for interest compounded periodically is
[tex]FV = PV\left (1 + \dfrac{r}{n} \right )^{nt}[/tex]
where
n = the number of payments per year
If FV is twice the PV, we can calculate the doubling time.
[tex]\begin{array}{rcl}2 & = & \left (1 + \dfrac{0.0675}{4} \right )^{4t}\\\\&= & (1 + 0.016875 )^{4t}\\& = & 1.016875^{4t}\\\ln 2& = & 4 (\ln 1.01688)\times t \\& = & 0.066937t\\t& = & \dfrac{\ln 2}{0.066937}\\\\& = & \textbf{10.355 yr}\\\end{array}[/tex]
3. Brianna's doubling time vs Adam's
10.663 - 10.355 = 0.31 yr
It would take 0.31 yr longer for Brianna's money to double than Adam's.
In the following set, the mode is the most effective measure of central tendency if you want to emphasize how small the values are. 32, 21, 68, 21 True False
Answer:
FALSE
Step-by-step explanation:
The mode is a measure of the number with the highest frequency in a group of data. In the set of values (32, 21, 68, 21), the number that appears most is 21 and this is the mode.
If a set of data has two modes, it is bi-modal. If it has several modes, it is multi-modal
Consider the set of data below
2,2,3,3,5,7,8
The numbers 2 and 3 appears with the same frequency, therefore this set of data is bi-modal.
Factor the expression. 16j2 + 24j + 9
(4j – 3)Factor the expression. 16j2 + 24j + 9
(4j – 3)2
(4j + 3)(4j – 3)
(4j + 3)^2
(4j – 9)(4j + 1)^2
(4j + 3)(4j – 3)
(4j + 3)^2
(4j – 9)(4j + 1)
Option C: [tex](4 j+3)^{2}[/tex] is the correct answer.
Explanation:
The given expression is [tex]16 j^{2}+24 j+9[/tex]
We need to factor the expression.
Let us rewrite the expression as
[tex](4j)^{2}+24 j+(3)^2[/tex]
Also, we can rewrite the term [tex]24j[/tex] as [tex]2(4)(3)j[/tex]
Thus, we have,
[tex](4j)^{2}+2(4j)(3)+(3)^2[/tex]
Hence, the equation is of the form,
[tex](a+b)^{2}=a^{2}+2 a b+b^{2}[/tex]
where [tex]a=4 j[/tex] and [tex]b=3[/tex]
Hence, the factor of the expression can be written as [tex](4 j+3)^{2}[/tex]
Thus, the factored expression is [tex](4 j+3)^{2}[/tex]
Therefore, Option C is the correct answer.
Final answer:
The factored form of the expression 16j^2 + 24j + 9 is (4j + 3)².
Explanation:
To factor the expression 16j2 + 24j + 9, we look for two binomials ((aj + b)(cj + d)) that when multiplied together, give us the original quadratic expression. The factors of 16j2 are 4j imes 4j, and the factors of 9 are 3 imes 3. Our binomial factors will have the format (4j + 3).
Expanding the binomial (4j + 3)², we have:
(4j + 3) imes (4j + 3)
= 16j2 + 12j + 12j + 9
= 16j2 + 24j + 9
This matches the original expression exactly, so the factored form of the expression is (4j + 3)².
DONT SKIP PLZ
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-3, -1) and point (-2, -4) rounded to the nearest tenth?
3.2 units
2.9 units
3.4 units
4.1 units
Answer:
The first one: 3.2 units
Answer: 3.2 units
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the graph given,
x2 = -2
x1 = - 3
y2 = - 4
y1 = - 1
Therefore,
Distance = √(- 2 - - 3)² + (-4 - - 1)²
Distance = √1² + - 3² = √1 + 9 = √10
Distance = 3.2
HELP PLEASEEEEEEE
can you help me find the period of the function from this table?
Answer: It’s either 6, or 2, though the answer is most likely 6, because of the way the table is created.
Step-by-step explanation:
Period is 12.
We can see the pattern 50, 33, 50, 67 that keeps repeating every m=12 points.
a + b = 10
a - b = 2
Solve the system of equations.
Answer:
a=6 b=4
Step-by-step explanation:
they can't both equal 5 so you need to find 2 numbers that add up to equal 10 but when you subtract one from the other it equals 2
walnuts cost $3.60 per pound and peanuts cost $2.70 per pound. For a fundraiser, the softball team will be selling bags of mixed nuts. How many punds of walnuts and how many pounds of peanuts should the team buy in order to make a 60 pound . ixture that will sell for $3.00 per pound?
Answer: 20 pounds of walnuts should be mixed with 40 pounds of peanuts.
Step-by-step explanation:
Let x represent the number of pounds of walnuts that should be in the mixture.
Let y represent the number of pounds of peanuts that should be in the mixture.
The number of pounds of the mixture to be made is 60. This means that
x + y = 60
Walnuts cost $3.60 per pound and peanuts cost $2.70 per pound. The mixture will sell for $3.00 per pound. It means that the total cost of the mixture is 3 × 60 = $180. The expression would be
3.6x + 2.7y = 180- - - - - - - - - - - - -1
Substituting x = 60 - y into equation 1, it becomes
3.6(60 - y) + 2.7y = 180
216 - 3.6y + 2.7y = 180
- 3.6y + 2.7y = 180 - 216
- 0.9y = - 36
y = - 36/ - 0.9
y = 40
x = 60 - y = 60 - 40
x = 20
A trampolinist steps off from 15 feet above ground to a trampoline 13 feet below. The function h (t) = -16 t 2 + 15, where t represents the time in seconds, gives the height h, in feet, of the trampolinist above the ground as he falls. When will the trampolinist land on the trampoline?
Answer:
Trampolinist will land on the trampoline after 0.9 seconds.
Step-by-step explanation:
The function h(t) = -16t² + 15 represents the relation between height 'h' above the ground and the time 't' of the trampolinist.
We have to find the time when trampolinist lands on the ground.
That means we have to find the value of 't' when h(t) = 15 - 13 = 2
[Since trampoline is 2 feet above the ground]
When we plug in the value h(t) = 2
2 = -16t² + 15
2 + 16t² = -16t² + 16t² + 15
16t² + 2 = 15
16t² + 2 - 2 = 15 - 2
16t² = 13
[tex]\frac{16t^{2}}{16}=\frac{13}{16}[/tex]
[tex]t^{2}=\frac{13}{16}[/tex]
t = [tex]\sqrt{\frac{13}{16}}[/tex]
t ≈ 0.9 seconds
Therefore, trampolinist will land on the trampoline at 0.9 seconds.
We would like to construct a 66% confidence interval for the proportion of voters that support building a new prison. What is the appropriate multiplier (z) that would be used in this situation?
Answer:
The appropriate z multiplier for 66% confidence interval is 0.95
Step-by-step explanation:
We are given the following in the question:
Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
We have to make a 66% confidence interval for the proportion of voters.
Confidence level = 66%
Significance level =
[tex]\alpha = 1 - 0.66 = 0.34[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.34} = \pm 0.95[/tex]
Thus, the appropriate z multiplier for 66% confidence interval is 0.95