Answer:
1) As the P-value (0.097) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the women's claim that female employees were passed over for management training in favor of their male colleagues.
2) The 95% confidence interval for the population proportion is (0.173, 0.427).
The populations proportion (π=0.4) is included in this confidence interval, so the claim has no enough evidence to be supported.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that female employees were passed over for management training in favor of their male colleagues.
We use the women's part for sample and population proportions.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.4\\\\H_a:\pi<0.4[/tex]
The significance level is 0.05.
The sample has a size n=50 persons.
The sample proportion is p=0.3.
[tex]p=X/n=15/50=0.3[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.4*0.6}{50}}\\\\\\ \sigma_p=\sqrt{0.0048}=0.069[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.3-0.4+0.5/50}{0.069}=\dfrac{-0.09}{0.069}=-1.299[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.299)=0.097[/tex]
As the P-value (0.097) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that female employees were passed over for management training in favor of their male colleagues.
b) We have to calculate a 95% confidence interval for the proportion.
The sample proportion is p=0.3.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.3*0.7}{50}}\\\\\\ \sigma_p=\sqrt{0.0042}=0.0648[/tex]
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0648=0.127[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.3-0.127=0.173\\\\UL=p+z \cdot \sigma_p = 0.3+0.127=0.427[/tex]
The 95% confidence interval for the population proportion is (0.173, 0.427).
The populations proportion (π=0.4) is included in this confidence interval, so the claim has no enough evidence to be supported.
Which of the following choices describes volume?
a
The amount of juice a carton can hold.
b
The weight of a bowling ball.
c
How tightly the molecules in a glass of water are packed together.
d
The temperature that must be reached for ice to melt.
Answer:
C. How tightly the molecules in a glass of water are packed together
Step-by-step explanation:
Volume of a substance is different according to the state of the matter.
So for a water molecule, the volume of the the water is definite and can be measured by the container which is the glass cup
So volume can be the measure of how tight the molecule of that substance ate together.
similarity statements between triangles
Answer:
Two triangles are said to be similar if any two corresponding sets of angles are equal and the corresponding sides are in the same ratio.
5b + 1 is at most 51
Step-by-step explanation:
5(10)+1
50+1
51
10 could be one possible answer
You are paid $10.65/hr. Your deductions are FICA (7.65%), federal tax withholding (9.9%), and state tax withholding (7.35%). Your housing and fixed expenses are $493.68/month. How many hours per month must you work to be sure those expenses are paid?
62 hours
64 hours
68 hours
66 hours
Answer:
The first option; You must work about 62 hours.
Step-by-step explanation:
The total percent that you pay in taxes is 24.9%.
That means that you keep 75.1% of the money that you earn. We can write the following equation to determine the number of hours, h, that it will take to earn 493.68.
0.751(10.65)h = 493.68
Just divide by 0.751 and 10.65 and you will get the number of hours needed.
Answer:
A.) 62 hours
Step-by-step explanation:
I took the consumer math test :)
Write a 3×3 matrix A which A^2 is diagonal while A is not diagonal ?
Consider the matrix
[tex]A=\begin{bmatrix}0&1&0\\1&0&0\\0&0&1\end{bmatrix}[/tex]
Multiplying A by itself has the effect of swapping the first and second rows:
[tex]A^2=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}[/tex]
which is diagonal, while A itself is not.
Please answer this correctly
In asking all 349 second graders in a school district, it is found that on average, these second graders have 2.5 pets. Is this number a parameter or a statistic and why?
Answer:
Parameter
Step-by-step explanation:
A statistic describes a sample. A parameter describes a population. Since the entire population of second graders in the district is surveyed, this is a parameter.
Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50 a plus 3.75 b equals 2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?
Answer:
168 adult tickets were sold
Step-by-step explanation:
Multiply the amount of students by the cost of the student ticket (82 times 3.75) which equals 307.5 . Subtract that from the total amount earned (2071.5) and you get 1764. Divide that by the cost of an adult ticket (10.50), and you'll get the amount of adults who attended, which is 168.
Answer:
168 Adult tickets were sold
Step-by-step explanation:
Vote me brainliest
An automobile battery manufacturer offers a 31/54 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated-credit period. Under this warranty, if a battery fails within 31 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 31 months but within 54 months, the manufacturer provides a prorated credit toward the purchase of a new battery. The manufacturer assumes that X, the lifetime of its auto batteries, is normally distributed with a mean of 45 months and a standard deviation of 5.6 months.
1. If the manufacturer's assumptions are correct, it would reed to replace _______ of its batteries free.2. The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect. A standard deviation of ____ results in a 1.07% replacement rate.3. Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?
Answer:
1) If the manufacturer's assumptions are correct, it would reed to replace 0.621% of its batteries free
2) The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect. A standard deviation of 6.084 results in a 1.07% replacement rate
3) Using the revised standard deviation for battery life, the percentage of the manufacturer's batteries that don't qualify for free replacement but do qualify for the prorated credit = 92%
Step-by-step explanation:
This is a normal distribution problem with
Mean = μ = 45 months
Standard deviation = σ = 5.6 months.
Batteries that fail within the first 31 months get a free replacement and batteries that fail after 31 months but within 54 months get a prorated credit toward the purchase of a new battery.
1) Percentage of batteries that'll qualify for a replacement are the batteries that fail within 31 months. That is, P(X ≤ 31)
To obtain this, we first normalize or standardize 31 months.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (31 - 45)/5.6 = - 2.50
The required probability
P(X ≤ 31) = P(z ≤ -2.50)
We'll use data from the normal probability table for these probabilities
P(X ≤ 31) = P(z ≤ -2.50) = 0.00621 = 0.621%
2) The company finds that the percentage of free batteries replaced is actually 1.07%
P(X ≤ 31) = 1.07% = 0.0107
Let the z value of 31 months under this new normal distribution be z'
P(X ≤ 31) = P(z ≤ z') = 0.0107
From the normal distribution table,
z' = -2.301
z' = (x - μ)/σ
-2.301 = (31 - 45)/σ
σ = (-14) ÷ (-2.301) = 6.084 months
3) Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?
That is, P(31 < X ≤ 54)
We first normalize 31 and 54 using the revised standard deviation
For 31
z = (x - μ)/σ = (31 - 45)/6.084 = - 2.30
For 54
z = (x - μ)/σ = (54 - 45)/6.084 = 1.48
The required probability = P(31 < X ≤ 54)
= P(-2.30 < z ≤ 1.48)
Using the normal distribution tables
P(31 < X ≤ 54) = P(-2.30 < z ≤ 1.48)
= P(z ≤ 1.48) - P(z < -2.30)
= 0.93056 - 0.0107
= 0.91986 = 91.986% = 92% to nearest whole number.
Hope this Helps!!!!
Use angles shown to make other angles
Answer:
angle ABC and angle KLM
Step-by-step explanation:
Angle ABC equals to 35 degrees and KLM equals to 95 degrees. Their sum equals 135 degrees.
Answer:
The answer is B and C.
Step-by-step explanation:
When these 2 angles are added together, they form 130° :
∠ABC + ∠KLM = 35° + 95°
= 130°
show work 1/4 ÷ 3/8 simplest form
Answer:
2/3
Step-by-step explanation:
1/4 ÷ 3/8 = 1/4 x 8/3 = 8/12 = 2/3
Answer:
2/3
Step-by-step explanation:
to divide make sure to use the reciprocal of the 3/8 which is
1/4*8/3
reduce the numbers with the greatest common factor divisor of 4
8/4=2 then 1*3 equals 3 which is 2/3
so it is 2/3
James invests $100 at the beginning of each quarter in stock ABC. According to the table below, how many shares of ABC will James own at the end of the year?
A.
44 shares
B.
37 shares
C.
38 shares
D.
41 shares
Answer:
ABC | Stock price
Q1 | $10.50
Q2 | $11.50
Q3 | $9.00
Q4 | $10.50
Step-by-step explanation:
Answer is 37 shares on AP3X
Anna and Lionel share $675 in the ratio 4 : 5 Lionel gives 3/5 of his share of the money to his mother. How much money does Lionel give to his mother?
Answer:
$225
Step-by-step explanation:
Total share ratio = 4+5 = 9
Lionel's ratio = 5
Lionel's share = (5/9) × 675
= $375
Lionel's mum = (3/5) x 375
= $225
slope of the line with points (4,-2) and (24,-17)
Answer:
-3/4
Step-by-step explanation:
y2-y1/x2-x1
-17+2 divided by 24-4
-15/20
-3/4
Answer:
-3/4
Step-by-step explanation:
The slope of a line is given by
m = (y2-y1)/(x2-x1)
= (-17- -2)/(24-4)
= (-17+2)/(20)
= -15/20
=-3/4
Let A, P, and D by n x n matrices. Mark each statement true or false. Justify each answer.
a. A is diagonalizable if A = PDP^-1 for some matrix D and some invertible matrix P. Choose the correct answer below.
O The statement is true because the columns of P are the n linearly independent eigenvectors of A.
O The statement is false because A must have n distinct eigenvalues for the matrix D and P to exist.
O The statement is true because if A = PDP^-1, then A is diagonalizable by definition.
O The statement is false because the symbol D does not automatically denote a diagonal matrix.
Answer:
Correct answer is the 4th answer.
Step-by-step explanation:
By definition, a matrix is called diagonalizable if there exists some invertible matrix P and a diagonal matrix D such that AP = PD, which is equivalent to having A = PDP^-1.
We are not told that D is a diagonal matrix, hence, it could be any matrix. If A=PDP^-1 for some matrix D that is not diagonal, it doesn't imply that A is diagonalizable. Consider the following case: Let us take A a non diagonalizable matrix. Take D = A and P = identity matrix of size n. Then, this equation holds, but A is still not diagonalizable.
there are 7 row of 9 people how many people in all
Answer:
63
Step-by-step explanation:
You simply just multiply the 7 and 9.
A shop has the following offers. Fig rolls (125g packet) Normal price £1.08. Buy one, get 2nd half price
Step-by-step explanation:
Fig rolls = 1.08
Half price = 1.08 ÷ 2 = 0.54
Total price = 1.08 + 0.54 = 1.62
Answer:
£8.52
Step-by-step explanation:
Fig rolls: £1.08+£1.08=£2.16
Crisps: £1.59+£1.59=£3.18 £3.18x2=£6.36
Total price= £2.16+£6.36=£8.52
Find the mean and median of these data: 3, 4, 10, 12, 18, 20.
Answer:
the median is 10 and 12
the mean is 11.17
Step-by-step explanation:
Mean=11.16
Median=11
look at the attached picture
Hope it will help you...
Good luck on your assignment..
~pragya
How are the functions f (x) = 16 Superscript x and g (x) = 16 Superscript one-half x related
Answer:
g(x) is f(x) expanded horizontally by a factor of 2
Step-by-step explanation:
Given:
f(x) = 16^x
g(x) = 16^(x/2)
__
Replacing x in a function with x/k expands the graph horizontally by a factor of k. Here, it seems we have ...
g(x) = f(x/2)
so g(x) is a horizontal expansion of f(x) by a factor of 2.
Answer:
c). The output values of g(x) are the square root of the output values of f(x) for the same value of x.
Step-by-step explanation:
Find an equation of the tangent line to the graph of
y = g(x) at x = 4 if g(4) = −3 and g'(4) = 2.
(Enter your answer as an equation in terms of y and x.)
Answer:
[tex] y- y_o = m(x-x_o) [/tex]
For this case m represent the slope and is given by [tex]m= g'(4) = 2[/tex] and from the other condition given we know that [tex] x_o = 4, y_o =-3[/tex]. And replacing we got:
[tex] y -(-3) = 2 (x-4)[/tex]
And if we reorganize the terms we have:
[tex] y+3 = 2x -8[/tex]
And subtracting 3 in both sides we got:
[tex] y = 2x -11[/tex]
Step-by-step explanation:
For this case we have the following function y=g(x) and we want to find the tangent line to this function using the conditions: [tex] g(4) =-3, g'(4)=2[/tex]
So we need a function like this one:
[tex] y- y_o = m(x-x_o) [/tex]
For this case m represent the slope and is given by [tex]m= g'(4) = 2[/tex] and from the other condition given we know that [tex] x_o = 4, y_o =-3[/tex]. And replacing we got:
[tex] y -(-3)=2(x-4)[/tex]
And if we reorganize the terms we have:
[tex] y+3 = 2x -8[/tex]
And subtracting 3 in both sides we got:
[tex] y = 2x -11[/tex]
The equation of a circle is given below.
9
x^2+ (y - 7.5)^2 =9/49
What is its center?
Answer:
(0, 7.5)
Step-by-step explanation:
Compare the equation to the standard-form equation of a circle:
(x -h)^2 +(y -k)^2 = r^2 . . . . . . . center at (h, k); radius r
You will notice that ...
h = 0
k = 7.5
The center is (h, k) = (0, 7.5).
Lisa is packing a set of cubic inch blocks into the box shown below How many blocks will fit in the box8 in.5 in.3 in.A.16B. 32C. 120D. 180
Answer:
120 Blocks or letter C
Step-by-step explanation:
I did 8x5x3, because lxwxh so i got 120
how do you change the equation 10q−5r=30 so that r is the independent variable?
Answer:
r=2q-6
Step-by-step explanation:
10q-5r=30
Subtract 10q from both sides:
-5r=30-10q
Divide both sides by -5:
r=2q-6
Hope this helps!
if X/4 = x+1/5, then x =
Answer:
as written, -4/15with parentheses, 4Step-by-step explanation:
As the problem is written, you have ...
[tex]\dfrac{x}{4} =x+\dfrac{1}{5}\\\\5x=20x+4\qquad\text{multiply by 20}\\\\-15x=4\\\\x=-\dfrac{4}{15}[/tex]
__
If you add parentheses to include x in the numerator, then you have ...
x/4 = (x +1)/5
[tex]5x=4(x+1)\qquad\text{multiply by 20}\\\\5x -4x = 4\qquad\text{eliminate parentheses, subtract 4x}\\\\x=4[/tex]
__
Additional comment
We include the second working because it is a fairly common mistake to neglect to put parentheses around a numerator or denominator. The solutions to such problems are not often fractions, so we suspect you intend the latter form.
una mulita está atada a un aranjo la mulita aburrida ha dado vueltas y vueltas alrededor del árbol manteniendo estirada la cuerda sin que ésta Se enrolle si la distancia que hay de la mulita al centro del árbol es de 5 metros qué distancia habrá recorrido después de dar 150 vueltas
Answer:
[tex]\Delta s_{T} = 4712.4\,m[/tex]
Step-by-step explanation:
(This exercise is written in Spanish and for this reason the response will be presented in such language).
La distancia recorrida por la mulita tras una vuelta es:
[tex]\Delta s = 2\pi\cdot (5\,m)[/tex]
[tex]\Delta s \approx 31.416\,m[/tex]
Ahora, la distancia recorrida total es directamente proporcional a la cantidad de vueltas invertidas. Este indicador se determina por regla de tres simple:
[tex]\Delta s_{T} = \frac{150}{1}\times (31.416\,m)[/tex]
[tex]\Delta s_{T} = 4712.4\,m[/tex]
10^xy=1000, where x and y are positive integers and x > y, what is one possible value of x?
Answer:
hey
Step-by-step explanation:
The function F(c)=log0.5x is decreasing true or false
Answer:
true
Step-by-step explanation:
We assume you intend your function to be ...
[tex]F(x)=\log_{0.5}x[/tex]
A logarithm with a base less than 1 is a decreasing curve. Here, the base appears to be 0.5, a value less than 1. Hence the curve is decreasing.
In a certain Algebra 2 class of 23 students, 11 of them play basketball and 13 of them play baseball. There are 8 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answer:
9/23
Step-by-step explanation:
Of the 23 students, 9 play both baseball and basketball. The probability of choosing one of those is 9/23.
___
Let A represent basketball, and B represent baseball. Then ...
P(A or B) = P(A) +P(B) -P(A and B)
Since 8 students play neither sport, we have ...
1 -8/23 = 11/23 +13/23 -P(A and B)
15/23 = 24/23 -P(A and B)
P(A and B) = (24 -15)/23
P(A and B) = 9/23
What is the domain of the given function?
{(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
Solve the system of equations by elimination.
2x + 2y = -2
3x - 2y = 12
5x = 10
x = 2
2(2) + 2y = -2
4 + 2y = -2
2y = -6
y = -3