Answer:
a)
Answer : d)
Null hypothesis:-H₀ : p =0.8
Alternative Hypothesis :H₁: p < 0.8
b)
Answer : c)0.77
point estimate of the population proportion= 0.77
c)
Answer : e) -0.863
Step-by-step explanation:
step(i):-
Given Population proportion 'p' =80% = 0.80
Given a sample of 120 housing loan applications, the group found that 92 were settled within 7 working days.
Sample proportion or point estimation
[tex]p^{-} = \frac{x}{n} = \frac{92}{120} =0.766[/tex]
Null hypothesis:-H₀ : p =0.8
Alternative Hypothesis :H₁: p < 0.8
Step(ii):-
Test statistic
[tex]Z = \frac{p^{-} -p}{\sqrt{\frac{p q}{n} } }[/tex]
population proportion p =0.8
q = 1-p = 1-0.8 =0.2
[tex]Z = \frac{0.77 -0.80}{\sqrt{\frac{0.80 x 0.20}{120} } }[/tex]
Z = -0.863
|Z| = | -0.863| = 0.863 < 1.96 at 0.05 level of significance
Null hypothesis is accepted
. A customer group believes that all housing loans applied to this corporation that are settled within 7 working days is equal to the 80% of all housing loans.
a tree needs to be stake with four wires, each wire is attached to the trunk 6 feet above the ground, and then anchored to the ground 8 feet from the base of the tree. How many feet of the wire is needed for 5 trees???
Answer:
89
Step-by-step explanation:
12 m 20 m 16 m 6m 10m x find the length represented by x for each pair of similar triangles
Answer:
x = 8mStep-by-step explanation:
Let the two triangles be represented as A and B.
Given two triangles with sides 12m 20m 16m and 6m 10m x.
Lengths of sides of triangle A = 12m, 20m, 16m
Lengths of sides of triangle B = 6m, 10m, x
It can be seen that each length of triangle A are twice that of B i.e triangle B dilated by a factor of 1/2.
A = 2B
Considering the 16m length in triangle A and comparing it with the 'x'm length in triangle B, we can get the unknown length x as shown;
16 = 2x
x = 16/2
x = 8m
Find the difference between points P (4,6) and Q (8,9)
[tex]distance = \sqrt{x2 - x1 + y2 - y1} \\ here \\ \: \: \: \: x1 = 4 \\ \: \: \: \: x2 = 8 \\ \: \: \: \: y1 = 6 \\ \: \: \: \: y2 = 9 \\ now \: we \: have \: to \: substitute \: the \: given \: values \: in \: the \: above \: formula \\ we \: get \\ \: \: \: \: \: \: = \sqrt{8 - 4 + 9 - 6} \\ \: \: \: \: \: \: = \sqrt{4 + 3} \\ \: \: \: \: \: \: = \sqrt{7} \\ \\ hope \: it \: helped[/tex]
Lisa reads 46 pages and Sunday 15 pages on Monday and 19 pages on Tuesday which of the following is the closest to the mean number of the pages she read over the three dayperiod
Answer:
80
Step-by-step explanation:
46+15+19 which should give you a total answer of 80
Please answer this correctly
Answer:
1-5: Make it 1 unit tall
6-10: Make it 4 units tall
11-15: Make it 1 unit tall
16-20: Make it 0 units tall (Change nothing)
21-25: Make it 5 units tall
Step-by-step explanation:
1-5: 1 (1 number)
6-10: 7, 9, 9, 10 (4 numbers)
11-15: 13 (1 number)
16-20: (0 numbers)
21-25: 21, 23, 23, 25, 25 (5 numbers)
what is the equation of the line that passe through the points (-3,-3) and (3,1)
Answer:
work is shown and pictured
Can someone help me with this?
Answer:
Step-by-step explanation:
These are mostly calculator problems. The only trick is the last one. Your calculator will have either a y^x button or ^ button. They both do the same thing.
So for the last one, you must do it as
64 y/x (1÷6)= and you will get 2. Perhaps all of them should be done that way.
If your calculator uses ^ then you would do it
64^(1÷6)= which is the same thing.
Answers
a 4
b 10
c 5
d 2
Suppose a student carrying a flu virus returns to an isolated college campus of 7000 students. Determine a differential equation governing the number of students x(t) who have contracted the flu if the rate at which the disease spreads is proportional to the number of interactions between students with the flu and students who have not yet contracted it. (Use k > 0 for the constant of proportionality and x for x(t).)
Answer:
The differential equation is [tex]\frac{dx(t)}{dt} = k x(t) [7000 - x(t)][/tex]
Step-by-step explanation:
From the question we are told that
The number of students are [tex]n = 7000[/tex]
The number of student that have contracted the flu is x(t)
The number of student that don't have the flu is mathematically represented as
[tex]z = 7000 - x(t)[/tex]
The rate at which the disease spread is proportional to the number of interactions between students with the flu and students who have not yet contracted it, which can be mathematically represented as
[tex]\frac{dx(t)}{dt} \ \ \ \alpha\ \ \ x(t) [7000 - x(t)][/tex]
=> [tex]\frac{dx(t)}{dt} = k x(t) [7000 - x(t)][/tex]
G(x) =19.60 + 1.75x what is the value of g (30) ?
Answer:
72.1
Step-by-step explanation:
G(x) =19.60 + 1.75x
Let x = 30
G(30) =19.60 + 1.75*30
=19.60 +52.5
72.1
What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?
Who failed to support civil rights for freed slaves? (wrong category by mistake, not mathematics)
Answer:
The Supreme Court.
Step-by-step explanation:
After the end of the Civil War and the enactment of the Thirteenth Amendment in 1865, slavery was officially abolished in the United States. Thus, the millions of African American slaves that inhabited the southern states of the country won their freedom and equality before the law against whites.
Now this situation began to dismember in 1877, when federal troops left the southern states and Reconstruction officially came to an end. From then on, Democratic governors and legislators began to sanction the Black Codes and Jim Crow Laws, aimed at curtailing the civil and political rights of African-Americans.
This situation was tested before the Supreme Court in 1896 in the case Plessy v. Ferguson. But in the ruling of said case, the Supreme Court established that racial segregation was constitutional and therefore neglected African Americans and their rights.
Find the factorization of the polynomial below.
81x2 - 18x + 1
Answer:
(9x - 1)²
Step-by-step explanation:
If you can tell, the square root of 81 is 9. This should be a clue that the polynomial could be one binomial squared. If you tried factoring starting out with 9x in both parenthesis, you could see that you would get (9x - 1)² as your answer.
Answer:
(9x-1)²
Step-by-step explanation:
81x² - 18x + 1= (9x)²- 2*9x+1²= (9x-1)²
The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is
unknown
What is the smallest possible perimeter of the triangle, rounded to the nearest tenth?
41.0 in
512 in
724 in
81.2 in
Answer:
(C)72.4 in
Step-by-step explanation:
Given an acute triangle in which the longest side measures 30 inches; and the other two sides are congruent.
Consider the attached diagram
AB=BC=x
However to be able to solve for x, we form a right triangle with endpoints A and C.
Since the hypotenuse is always the longest side in a right triangle
Hypotenuse, AC=30 Inches
Using Pythagoras Theorem
[tex]30^2=x^2+x^2\\900=2x^2\\x^2=450\\x=\sqrt{450}\\x=21.21$ inches[/tex]
Therefore, the smallest possible perimeter of the triangle
Perimeter=2x+30
=2(21.21)+30
=42.42+30
=72.4 Inches (rounded to the nearest tenth)
A country commits to decreasing spending for infrastructure in various ways at a rate of 30% per year. At the time of the announcement, the country is spending $12 billion per year. Which graph models the amount of infrastructure spending for future years?
Answer:
You want the curve to be decreasing from left to right since they are decreasing the amount spent so we can eliminate options 2 and 3. The initial amount (when x = 0) has to be 12 so the answer is the last option.
What is the value of a3 - b2 for a=3 and b = 1/2
Answer:
Answer = 26.75
Answer = 27
Step-by-step explanation:
[tex]a^{3} -b^{2} \\a =3\\b =\frac{1}{2} \\3^{3} -(\frac{1}{2} )^{2} \\27 -\frac{1}{4} \\\\\\Answer = 26.75\\Answer = 27[/tex]
Answer:
26 3/4 God bless!
Step-by-step explanation:
the correct
9. 5(x - 2) = 15
a. 10
b. 5
c. 1
Answer:
the answer is 5
Step-by-step explanation:
Answer:
x=5
Step-by-step explanation:
5x-10=15
5x=25
x=5
Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Alissa got a score of 68.568.5; this version has a mean of 60.460.4 and a standard deviation of 99. Morgan got a score of 252.5252.5; this version has a mean of 227227 and a standard deviation of 1717. Norma got a score of 7.967.96; this version has a mean of 6.76.7 and a standard deviation of 0.70.7. If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Answer:
Due to the higher Z-score, Norma should be offered the job
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Whoever has the higher z-score should be offered the job.
Alissa:
[tex]X = 68.5, \mu = 60.4, \sigma = 9[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{68.5 - 60.4}{9}[/tex]
[tex]Z = 0.9[/tex]
Morgan:
[tex]X = 252.5, \mu = 227, \sigma = 17[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{252.5 - 227}{17}[/tex]
[tex]Z = 1.5[/tex]
Norma:
[tex]X = 7.96, \mu = 6.7, \sigma = 0.7[tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.96 - 6.7}{0.7}[/tex]
[tex]Z = 1.8[/tex]
Due to the higher Z-score, Norma should be offered the job
Point A on a coordinate grid is at (3, 4). What are the coordinates of R y=x (A)?
Answer:
A'(4, 3)
Step-by-step explanation:
When a point is reflected across the line y = x, the transformation is ...
(x, y) ⇒ (y, x)
A(3, 4) ⇒ A'(4, 3)
The reflected point is (4, 3).
One week 72 people got a speeding ticket the next week only 36 people get a speeding ticket what is the percentage of change in the speeding tickets
Answer:
The answer would be 50%
Step-by-step explanation:
You Would get this by dviding 36/72 which would give you .5 and then you convert that to a percentage
Answer:
50%
Step-by-step explanation:
A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 51 months and a standard deviation of 11 months. Using the Empirical Rule rule, what is the approximate percentage of cars that remain in service between 73 and 84 months
Answer:
The approximate percentage of cars that remain in service between 73 and 84 months
P( 73 < x < 84 ) = 0.02145 = 2.1 %
Step-by-step explanation:
Explanation:-
Given mean of the Population 'μ ' = 51 months
Standard deviation of the Population 'σ' = 11 months
Let 'X' be the random variable of Normal distribution
Let 'X' = 73
[tex]Z = \frac{x-mean}{S.D} = \frac{73-51}{11} = 2[/tex]
Let 'X' = 84
[tex]Z = \frac{84-51}{11} = 3[/tex]
The approximate percentage of cars that remain in service between 73 and 84 months
P( 73 < x < 84 ) = P( 2 < Z < 3)
= P( Z<3) - P( Z <2)
= 0.5 + A(3) - ( 0.5 + A(2))
= A(3) - A( 2)
= 0.49865 - 0.4772 ( From Normal table)
= 0.02145
P( 73 < x < 84 ) = 0.02145
The approximate percentage of cars that remain in service between 73 and 84 months
P( 73 < x < 84 ) = 0.02145 = 2.1 %
A publisher reports that 41% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually less than the reported percentage. A random sample of 320 found that 36% of the readers owned a laptop. Is there sufficient evidence at the 0.05 level to support the executive's claim? Find the value of the test statistic. Round your answer to two decimal places. Specify if the test is one-tailed or two-tailed. Determine the decision rule for rejecting the null hypothesis, H0. Make the decision to reject or fail to reject the null hypothesis. State the conclusion of the hypothesis test.
Step 1 of 6: State the null and alternative hypotheses.
Answer:
Step-by-step explanation:
Hello!
The objective is to test the claim that less than 41% of the publisher's readers own a laptop.
To do so, a sample of 320 readers was taken and the proportion of readers that own a laptop resulted in 36%
Be X: number of readers that own a laptop.
X~Bi(n;p)
n=320
Sample proportion p'= 0.36
The hypotheses are:
H₀: p ≥ 0.41
H₁: p < 0.41
α: 0.05
[tex]Z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]≈N(0;1)
[tex]Z_{H_0}=\frac{0.36-0.41}{\sqrt{\frac{0.41(1-0.41)}{320} } }= -1.82[/tex]
This test is one-tailed to the left, meaning, that you'll reject the null hypothesis to small values of Z, there is only one critical value that defined the rejection region:
[tex]Z_{\alpha }= Z_{0.05}= -1.645[/tex]
The decision rule is:
If [tex]Z_{H_0}[/tex] ≤ -1.645, reject the null hypothesis.
If [tex]Z_{H_0}[/tex] > -1.645, do not reject the null hypothesis.
The calculated value is less than the critical value, then the decision is to reject the null hypothesis.
So at a 5% significance level, the test is significant. You can conclude that the population proportion of the publisher's readers that own a laptop is less than 41%.
I hope this helps!
The orthocenter of a triangle may lie outside the triangle because an altitude does not necessarily intersect the____
of the triangle
A. Median
B. Angles
C. Sides
D. Vertices
Answer: sides
Step-by-step explanation:
The orthocenter of the triangle will be the intersection of the three altitudes of a triangle. The orthocenter has several vital properties with other parts of a triangle, including the area ,incenter circumcenter and more. Typically, the orthocenter is represented by letter H.
The altitude of a triangle is a line that passes through the vertex of a triangle and it is also perpendicular to the opposite side. The orthocenter of a triangle can lie outside the triangle because an altitude may not necessarily intersect the side.
The line whose equation is 3x - 5y = 4 is dilated by a scale factor of 3
centered at the origin. Which statement is correct? *
Answer:
Answer 1.
Step-by-step explanation:
The complete question is:
The line whose equation is 3x - 5y = 4 is dilated by a scale factor of 3 centered at the origin. Which statement is correct?
1. The image of the line has the same slope as the pre-image but a different y-intercept.
2. The image of the line has the same y-intercept as the pre-image but a different slope.
3. The image of the line has the same slope and the same y-intercept as the pre-image.
4. The image of the line has a different slope and a different y-intercept from the pre-image.
Recall that a dilation by a scale factor r centered at the origin takes a point (x,y) and maps it to the point (r*x,r*y).
Consider also a line of equation [tex]ax+by=c[/tex]. From this equation, the slope of the line is given by the number [tex]\frac{-a}{b}[/tex] and the y-intercept is given by [tex]\frac{c}{b}[/tex].
Consider the given equation 3x-5y =4. If we replace (x,y) with (3x,3y), we get
[tex]3(3x)-5(3y) = 4 = 3 (3x-5y) = 4 [/tex]
which is equivalent to
[tex] 3x-5y = \frac{4}{3}[/tex]
Note that comparing the equations 3x-5y=4 and [tex]3x-5y=\frac{4}{3}[/tex] the values of a and b are equal but the value of c is different. This means that they have the same slope but a different y-intercept.
plsss help meeeeeee I would really appreciate it I would be really happy if u help meeee
[tex]the \: answer \: is \: 22.4 \: cm \\ please \: see \: the \: attached \: picture \\ for \: full \: solution \\ hope \: it \: helps[/tex]
The length of AE is 22.4cm rounded to one decimal place.
SOMEONE PLEASE HELP ME !! ASAP!!
Answer:
A
Step-by-step explanation:
RT=12
TU=5
RU=12+5=17
RS=17+7=24
SU=√(RS²-RU²)=√(24²-17²)=√(24-17)(24+17)=√(7×41)=√287
area=1/2×12×√287=6×√287≈101.6 unit²
Two lines intersect and two of the vertical angles measure 37°. What is the measure of the other two vertical angles?
Answer:
286 degrees and 143 degrees
Step-by-step explanation:
When line intersect the two vertical angle adds up to 180 degrees
To find the other vertical angle:
180 -37=143 degrees
So for two vertical angles
we take (180*2)-(37*2)=286 degrees
DAN Summer 2020
English
Determining an unknown Angle measure
m26 is (2x - 5)' and m 28 is (x + 5)
What is m 23?
1 2
3 4
5 6
78
Dona
Answer:
m∠3 = 115°
Step-by-step explanation:
Since measure of angle 6 = (2x - 5)°
And measure of angle 8 = (x + 5)°
Since ∠6 and ∠8 are the supplementary angles,
m∠6 + m∠8 = 180°
(2x - 5)° + (x + 5)° = 180°
3x = 180°
x = 60°
Therefore, m∠6 = (2x - 5) = (120 - 5) = 115°
and m∠8 = (x + 5) = 65°
Since angle 6 and angle 3 are interior alternate angles,
Therefore, m∠6 = m∠3 = 115° will be the answer.
A poster of area 3840 cm? has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the sides. Find the
dimensions that maximize the printed area.
(Use decimal notation. Give your answers as whole or exact numbers.)
width:
cm
height:
cm
Answer:
Dear user,
Answer to your query is provided below
The dimensions to maximise the printed area to 2160 is length = 100cm and width = 60cm
Step-by-step explanation:
Explanation for the answer is attached in the image
Put this equation into slope-
intercept form.
3x – 2y = 4
Answer:
y= 3/2x -2
Step-by-step explanation:
make y be on one side by itself ( -2y = -3x + 4 )
divide by negative 2 in order to get y by itself ( -2y/-2 = -3/-2 + 4/-2 )
two negatives make a positive ( y = 3/2 + -2 )
Jack and Rebecca Pearson just had triplets. They want to have enough money for their
children's college fund. So they decide to deposit $100 at the end of each quarter for 20
years into an account paying 4.2% annual interest compounded quarterly.
a) How much is in the account at the end of 20 years?
b) How much did the Pearsons actually contribute to the college fund account?
c) How much interest did the account earn in those 20 years?
Answer:
a) $12,440.43
b) $8,000.00
c) $4,440.43
Step-by-step explanation:
the question is a bit ambiguous, I calculated from zero initial Deposit to $100 per quarter. If they deposited $100 initially and then $100 quarterly for 20 years then the numbers are as follows.
a) $12,671.05
b) $8,100
c) $4,571.05
a) $12,440.43
b) $8,000.00
c) $4,440.43
Step-by-step explanation:
the question is a bit ambiguous, I calculated from zero initial Deposit to $100 per quarter. If they deposited $100 initially and then $100 quarterly for 20 years then the numbers are as follows.
a) $12,671.05
b) $8,100
c) $4,571.05