In what country of United states of heightlandia, the height measurements of ten year old children are approximately normally distributed with a mean of 53.2 inches and standard deviation of 6.7 inches?
Step-by-step explanation:
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The probability that a certain movie will win an award for acting is 0.15, the probability that it will win an award for direcing is 0.23, and the probability that it will win both is 0.09. Find the probabilities of the following.
a. The movie wins an award for acting, given that it wins both awards.
b. The movie wins an award for acting, given that it wins exactly one award.
c. The movie wins an award for acting, given that it wins at least one award.
Answer:
a) 0.15 / 0.09
b) 0.15 / 1
c) 0.15 / 0.23
Exam grades: Scores on a statistics final in a large class were normally distributed with a mean of 75 and a standard deviation of 9. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals. (a) Find the 41st percentile of the scores. (b) Find the 74th percentile of the scores. (c) The instructor wants to give an A to the students whose scores were in the top 8% of the class. What is the minimum score needed to get an A
Solution :
Using the TI-84 PLUS calculator
a). Area : 0.41
μ = 75
σ = 9
InvNorm(0.41,75,9)
= 72.95209525
Therefore, the 41st percentile of the scores is 72.95209525
b). Area : 0.74
μ = 75
σ = 9
InvNorm(0.74,75,9)
= 80.79010862
Therefore, the 74st percentile of the scores is 80.79010862
c). 8%
So, Area : 0.92
μ = 75
σ = 9
InvNorm(0.92,75,9)
= 87.64564405
Therefore, X = 80.79010862
can anyone help me and explain
Answer:
cf
=41
5 f-46
Step-by-step explanation:
thiis is the answer
Answer:
To find the inverse, switch the y(F(C)) and the x(C) variables.
So this function:
[tex]y=\frac{9}{5}x+32 \\[/tex]
Will become this function:
[tex]x=\frac{9}{5}y+32 \\[/tex]
You will then solve for y:
[tex]x=\frac{9}{5}y+32 \\x-32=\frac{9}{5}y\\5(x-32)=5(\frac{9}{5}y)\\5x-160=9y\\y=\frac{5x-160}{9}\\y=\frac{5x}{9}-\frac{160}{9}[/tex]
Substitute in the variables of this problem:
[tex]C(F)=\frac{5C}{9}-\frac{160}{9}[/tex]
The following data was collected to explore how the average number of hours a student studies per night and the student's GPA affect their ACT score. The dependent variable is the ACT score, the first independent variable (x1)is the number of hours spent studying, and the second independent variable (x2) is the student's GPA
Effects on ACT Scores
Study Hours GPA ACT Score
5 4 27
5 2 18
5 3 18
1 3 20
2 4 21
Step 1 of 2: Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.
Step 2 of 2: Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.01 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.
Answer:
Pvalue = 0.1505
y = 0.550x1 + 3.600x2 + 7.300
Step-by-step explanation:
Given the data :
Study Hours GPA ACT Score
5 4 27
5 2 18
5 3 18
1 3 20
2 4 21
Using technology, the Pvalue obtained using the Fratio :
F = MSregression / MSresidual = 30.228571/ 8.190476 = 3.69
The Pvalue for the regression equation is:
Using the Pvalue from Fratio calculator :
F(1, 3), 3.69 = 0.1505
Using the Pvalue approach :
At α = 0.01
Pvalue > α ; Hence, we fail to reject H0 and conclude that ; There is not enough evidence to show that the relationship is statistically significant.
The regression equation :
y = A1x1 + A2x2 +... AnXn
y = 0.550x1 + 3.600x2 + 7.300
x1 and x2 are the predictor variables ;
y = predicted variable
Think of 5 positive integers that have a mode of 5 and 6, a median of 6 and a mean of 7.
Answer:
5,5,6,6,13
Step-by-step explanation:
Mode means most often. The 5 numbers has 2 modes 5 and 6
This means that 4 of the numbers must be 5,5,6,6
Median means the middle number must be 6
5,5,6,6,x is the only way to to get the middle number to be 6
We need to average to 7
(5+5+6+6+x) /5 = 7
(5+5+6+6+x) /5 *5= 7*5
(5+5+6+6+x) =35
22+x = 35
x = 35-22
x = 13
The other number is 13
Which figure can be formed from the net?
pls answer fast for brainiest !
Answer:
It should be the top right one
(with 6ft as the height)
Step-by-step explanation:
Answer:
It must be the lower to the left choice.
Step-by-step explanation:
As you can see, the net we have is composed of only triangles.
So we should be choosing a figure with a triangular base.
Our answers are narrowed down into the top right and lower left choices because both figures have triangular bases.
The other person down there chose the top right choice and was incorrect, so the answer should be the lower to the left figure.
Also, its the lower left figure because look at the triangular base, it is an isosceles meaning that two sides have the same length.
If the net says that the long side measures 9 ft, then the other two sides should be the same length and shorter than 9 ft. So the answer is the lower left figure.
Hope this helps
Ms. Weaver plans to decorate the bulletin board in her classroom. She purchased 30 sheets of construction paper for $0.30 per sheet, 5 boxes of thumbtacks for $0.70 per box, and 4 framed pictures for $6.00 per picture. How much money did Ms. Weaver spend for the items?
Answer:
$36.5 money ms.weaver spent for the items
Jill has 32 crayons. She loses 4 of the crayons. How many are left?
Answer:
the answer here is d
the answer is d
Answer:
28
Step-by-step explanation:
Total number of crayons = 32
Number of crayons lost = 4
Therefore, number of crayons she is left with is : 32 - 4 = 28
Working :
[tex]32\\04 - \\\overline{28}[/tex]
Pls could someone help me with this
Answer:
- Bar Gaps should be the same
Y-axis up in units of 5 would help out
Step-by-step explanation:
for the equation (x+3)(x+1)=1 explain why the solutions are not -3 and -1
Answer:
Step-by-step explanation:
(x+3)(x+1)=1
x²+3x+x+3=1
x²+4x+2=0
x²+4x+4=-2+4
(x+2)²=2
x+2=±√2
x=2+√2
and x=2-√2
so x≠-3
and x≠-1
Help please somebody ASAP
Answer:
[tex]\frac{-2x+11}{(x-4)(x+1)}[/tex]
Step-by-step explanation:
I don't think we can factor this so we'll have to multiply to make the denominators the same
[tex]\frac{3(x+1)}{(x^2-3x-4)(x+1)}-\frac{2(x^2-3x-4)}{(x+1)(x^2-3x-4)}\\\\\frac{3x+3-(2x^2-6x-8)}{(x^2-3x-4)(x+1)}=\frac{-2x^2+9x+11}{(x^2-3x-4)(x+1)}\\-2x^2+9x+11=(x+1)(-2x+11)\\\\x^2-3x-4=(x+1)(x-4)\\\frac{(x+1)(-2x+11)}{(x+1)(x-4)(x+1)}=\frac{-2x+11}{(x-4)(x+1)}[/tex]
The population of watesville decreases at a rate of 1.6% each year if the population was 62,500 in 2015 what will it be in 2021
Answer:
Step-by-step explanation:
We need to first find the model for this particular situation, knowing that this is an exponential decay problem. The main equation for exponential growth/decay (as far as population goes for our problem) is
[tex]y=a(b)^x[/tex] where a is the initial population, b is the rate of decrease in the population which can also be written as (1 - r), y is the population after a certain amount of time, x, goes by. We will let year 2015 = 0 so year 2021 can = 6. This keeps our numbers lower and doesn't change the answer!
Our initial population in the year x = 0 is 62500. Our rate of decay is
(1 - .016) so our b value is .984
Filling in to find our model:
[tex]y=62500(.984)^x[/tex]
Now we can use that model and sub in a 6 for x to find the population in the year 2021:
[tex]y=62500(.984)^6[/tex] and
y = 62500(.9077590568) so
y = 56734.9 or, rounded to the nearest person, 56735
The light from a lamp creates a shadow on a wall with a hyperbolic border. Find the equation of the border if the distance between the vertices is inches and the foci are inches from the vertices. Assume the center of the hyperbola is at the origin.
The equation of the hyperbola is,
(x/12)² - 4y²/(527) = 1
The standard equation of the hyperbola is
(x/a)² - (y/b)² = 1
Here (a, 0) and (-a, 0) are vertices and asymptotes y = ± √(b/a)x
Foci are (c, 0) & (-c, 0)
Then a² + b² = c²
Here we have to give that.,
2a = 24
a = 12
And 2c = 7
c = 7/2
Therefore a = 12 and c = 3.5
Substituting a and c in Pythagorean identity;
b² = 527/4
Then, the equation of the hyperbola is
(x/12)² - 4y²/(527) = 1
For further information regarding hyperbolas, kindly refer
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We have b = 0, which implies that the foci coincide with the vertices, making the hyperbola a degenerate case. In this scenario, the equation of the border would be a vertical line passing through the vertices/foci, given by the equation x = ±a.
To find the equation of the hyperbolic border created by the shadow on the wall, we can start by understanding the properties of a hyperbola. A hyperbola is defined as the set of all points such that the difference of the distances from any point on the hyperbola to two fixed points, called the foci, is constant.
Let's label the vertices of the hyperbola as A and B, and the foci as F1 and F2. The distance between the vertices is given as 2a inches, and the foci are located at a distance c inches from the vertices.
Using the given information, we can find the value of a and c. Since the center of the hyperbola is at the origin, the coordinates of the vertices are (±a, 0), and the coordinates of the foci are (±c, 0).
The distance between the foci is given by the equation:
c = √(a^2 + b^2)
We know that the distance between the foci is given as 2c inches, so:
2c = 2√(a^2 + b^2)
Since c is given as a distance from the vertices, we can substitute c = a - b to simplify the equation:
2(a - b) = 2√(a^2 + b^2)
Squaring both sides to eliminate the square root:
4(a - b)^2 = 4(a^2 + b^2)
Expanding the equation:
4(a^2 - 2ab + b^2) = 4a^2 + 4b^2
Simplifying the equation:
4a^2 - 8ab + 4b^2 = 4a^2 + 4b^2
Canceling out the common terms:
-8ab = 0
Dividing by -8:
ab = 0
This implies that either a = 0 or b = 0. However, since a represents the distance between the vertices and b represents the distance between the foci and vertices, we can rule out a = 0 as it would result in a degenerate hyperbola.
for such more question on hyperbola
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Four times a number is 88 less than 6 times the number. Find the number.
Answer:
44
Step-by-step explanation:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
The number is 44.
To find the number.
What is arithmetic?science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers. Arithmetic is the basics of the abstract science of numbers and operations on them. The formula for any arithmetic sequence is this: an = a1 + d (n - 1).
Given that:
Let x represent the number.
Create an equation, and solve for x:
4x = 6x - 88
-2x = -88
x = 44
So, the number is 44.
Learn more about arithmetic here:
https://brainly.com/question/24163536
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Is a linear model or a quadratic model a better fit? Quadratic model graph quadratic model linear model
The level of significance is the a. same as the p-value. b. maximum allowable probability of Type I error. c. same as the confidence coefficient. d. maximum allowable probability of Type II error.
Answer:
The level of significance is the
b. maximum allowable probability of Type I error.
Step-by-step explanation:
The significance level provides the maximum probability of rejecting the null hypothesis when it is true. It is the same as a type I error (also known as false-positive). This error occurs when a researcher or investigator rejects a true null hypothesis that is supposed to be accepted. It is the opposite of a type II error (false-negative), which occurs when the researcher fails to reject a false null hypothesis.
Please help
Find the value of x,
m∠5 = x-6, m∠4 = 2x+4, m∠2 = 2x-26
9514 1404 393
Answer:
x = 30 2/3
Step-by-step explanation:
Angles 4 and 5 are complementary, so we have ...
m∠4 +m∠5 = 90°
(2x +4) +(x -6) = 90
3x -2 = 90 . . . . . . . . . collect terms
3x = 92 . . . . . . . . . . add 2; next, divide by 3
x = 92/3 = 30 2/3
The salaries of 235 nurses were recorded and analyzed. The analyst later found that the highest salary was incorrectly recorded as 10 times the actual amount. After the error was corrected, the report showed that the corrected value was still higher than any other salary. Which sample statistic must have changed after the correction was made?
The sample statistic that must have changed after the correction was made is mean. Because mean is based on all the observation in the data. So changing any value in the data will impact mean.
Changing the highest salary in the data will have no impact on median because median lies at the center of data.
Changing the highest salary in the data will have no impact on mode because mode is the most frequently occurring value in the data.
Changing the highest salary in the data will have no impact on minimum because minimum is the smallest value in the data.
Hence the only statistic which will change is mean.
Answer: A-Mean
Step-by-step explanation:
A.) Mean
B.) Median
C.) Mode
D.) Minimum
A cyclist completes a journey of 500 m in 22 seconds, part of the way at 10 m/s and the remainder at 50 m/s. How far does she travel at each speed. solve by forming simultaneous equation
Answer:
150 m at 10 m/s
350 m at 50 m/s
Step-by-step explanation:
x + y = 500
x/10 + y/50 = 22
~~~~~~~~~~~~~~~~~
x + y = 500
5x + y = 1100
~~~~~~~~~~~~~~~~
x + y = 500
-5x - y = -1100
-4x = -600
x = 150
y = 350
4
On a plan with a scale of 1:50, the floor of a rectangular cupboard is
shown with dimensions 25 cm by 3.6 cm. What are the actual dimensions
of the floor? Give your answers in metres.
Anyone know the answer ?
Answer:
The actual dimensions of the floor are 12,5m by 1,8m.
Step-by-step explanation:
Scale problems are solved by proportions, using a rule of three.
Scale of 1:50
This means that each cm on the cupboard has a real dimension of 50 cm
25 cm on the cupboard:
So the real dimension is:
25*50 = 1250 cm = 12,5m
3.6 cm
The real dimension is:
3.6*50 = 160 cm = 1,8 m
The actual dimensions of the floor are 12,5m by 1,8m.
Exactly how many planes contain points J, K, and N?
a - 0
b - 1
c - 2
d - 3
∠A and \angle B∠B are vertical angles. If m\angle A=(5x-9)^{\circ}∠A=(5x−9) ∘ and m\angle B=(8x-30)^{\circ}∠B=(8x−30) ∘ , then find the value of x
9514 1404 393
Answer:
x = 7
Step-by-step explanation:
Vertical angles have the same measure, so ...
m∠A = m∠B
(5x -9)° = (8x -30)°
21 = 3x . . . . . . . . . divide by °, add 30-5x
7 = x . . . . . . . . . . divide by 3
In the diagram, WZ=StartRoot 26 EndRoot.
On a coordinate plane, parallelogram W X Y Z is shown. Point W is at (negative 2, 4), point X is at (2, 4), point Y is at (1, negative 1), and point Z is at (negative 3, negative 1).
What is the perimeter of parallelogram WXYZ?
units
units
units
units
Answer:
[tex]P = 8 + 2\sqrt{26}[/tex]
Step-by-step explanation:
Given
[tex]W = (-2, 4)[/tex]
[tex]X = (2, 4)[/tex]
[tex]Y = (1, -1)[/tex]
[tex]Z = (-3,-1)[/tex]
Required
The perimeter
First, calculate the distance between each point using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 -y_2)^2[/tex]
So, we have:
[tex]WX = \sqrt{(-2- 2)^2 + (4-4)^2 } =4[/tex]
[tex]XY = \sqrt{(2- 1)^2 + (4--1)^2 } =\sqrt{26}[/tex]
[tex]YZ = \sqrt{(1- -3)^2 + (-1--1)^2 } =4[/tex]
[tex]ZW = \sqrt{(-3--2)^2 + (-1-4)^2 } =\sqrt{26}[/tex]
So, the perimeter (P) is:
[tex]P = 4 + \sqrt{26} + 4 + \sqrt{26}[/tex]
[tex]P = 8 + 2\sqrt{26}[/tex]
Answer:
its D.
Step-by-step explanation:
took test
A small radio transmitter broadcasts in a 69 mile radius. If you drive along a straight line from a city 93 miles north of the transmitter to a second city 78 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Answer:
See Explanation
Step-by-step explanation:
According to the Question,
We have A small radio transmitter that broadcasts in a 69-mile radius. If you drive along a straight line from a city 93 miles north of the transmitter to a second city 78 miles east of the transmitter.Thus,
The distance that you get reception is the length of the chord created by the intersection of the circle defining the edge of transmission and the line defining the car trip.
x2 + y2 = 69² this is the circleAnd,
The Transmitter at the origin
City to the north at (0,93) & City to the east at (78,0)
the Slope is M=(-93/78)
Intercept is B= y - mx ⇒ 93 - (-93/78)(0) = 93
The equation of the line between the cities is y = (-93/78)x + 93
y = -93x/78 + 93 this is the lineNow, Solve the above two Equations
The intersection is gotten from the picture or solving:
x^2 + [(-93/78)*x + 93]^2 = 69^2
on solving we get, the points approximately are: (67.952,11.98 ) and (23.6277, 64.82)Now,
From the Pythagorean theorem the total distance of the trip is:
d1 = √(93^2 + 78^2) ≈ 121.37miles
And the distance when the signal is picked up is:
d2 =√ [(67.952-23.627)^2 + (64.82 - 11.98)^2] ≈ 68.96 miles
You will pick up a signal from the transmitter in (d2/d1)*100 = 56% of the drive.
Please help ASAP !!! Thank you !
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.06. If 235 are sampled, what is the probability that the sample proportion will differ from the population proportion by greater than 0.04
Answer:
0.0098 = 0.98% probability that the sample proportion will differ from the population proportion by greater than 0.04
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose the true proportion is 0.06.
This means that [tex]p = 0.06[/tex]
235 are sampled
This means that [tex]n = 235[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.06[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.06*0.94}{235}} = 0.0155[/tex]
What is the probability that the sample proportion will differ from the population proportion by greater than 0.04?
Proportion below 0.06 - 0.04 = 0.02 or above 0.06 + 0.04 = 0.1. Since the normal distribution is symmetric, these probabilities are equal, which means that we can find one of them and multiply by 2.
Probability the proportion is below 0.02.
p-value of Z when X = 0.02. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.02 - 0.06}{0.0155}[/tex]
[tex]Z = -2.58[/tex]
[tex]Z = -2.58[/tex] has a p-value of 0.0049.
2*0.0049 = 0.0098
0.0098 = 0.98% probability that the sample proportion will differ from the population proportion by greater than 0.04
J. Aitchison collected expenditures data for 20 randomly selected single men and 20 randomly selected single women. He uses the data to conduct a hypothesis test to determine if the mean percent of expenditures that goes toward housing (including fuel and light) is different for men and women. What is the correct alternative hypothesis?
a. Md = 0
b. μα = 0
c. ud > 0
d. Opmen — Вwomen
e. Himen > Mwomen
f. Mmen Mwomen
Answer:
The alternative hypothesis is [tex]H_1: \mu_M - \mu_W \neq 0[/tex], considering M for men and W for women.
Step-by-step explanation:
He uses the data to conduct a hypothesis test to determine if the mean percent of expenditures that goes toward housing (including fuel and light) is different for men and women.
At the null hypothesis, we test if there is not difference, that is, the difference of the mean is 0, so:
[tex]H_0: \mu_M - \mu_W = 0[/tex]
At the alternative hypothesis, we test if there is a difference, that is, the difference of the means is different of 0, so:
[tex]H_1: \mu_M - \mu_W \neq 0[/tex]
Carlos has an aquarium which is 45 cm long, 32 cm wide, and 35 cm high. How much water can the aquarium hold?
Answer:
volume =l×b×h
45cm×32cm×35cm=48,960cm³
Complete the information for that object by making estimates using appropriate units of measurement of the dimensions and by getting the actual measurements using an appropriate measuring instrument.
Answer:
hlo how are u?whats ur day is going