Using the z-distribution, as we are working with a proportion, it is found that there is evidence that the proportion has decreased.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is still the same, of 27/100 = 0.27, hence:
[tex]H_0: p = 0.27[/tex]
At the alternative hypothesis, it is tested if the proportion has decreased, hence:
[tex]H_1: p < 0.27[/tex].
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In this problem, the parameters are as follows:
[tex]n = 175, \overline{p} = \frac{30}{175} = 0.1714[/tex]
Hence, the value of the test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.1714 - 0.27}{\sqrt{\frac{0.27(0.73)}{175}}}[/tex]
z = -2.94.
What is the decision?Considering a left-tailed test, as we are testing if the propoortion is less than a value, the critical value is of [tex]z^{\ast} = -1.645[/tex].
Since the test statistic is less than the critical value for the left-tailed test, it is found that there is evidence that the proportion has decreased.
More can be learned about the z-distribution at https://brainly.com/question/26454209
Emily practices piano for 2/3 of an hour on Monday and 1/2 hour on Wednesdays. How many hours does Emily spend practicing piano in one week?
Answer:
50 minutes
Step-by-step explanation:
Given:
[tex]\bullet \ \ \text{Monday:} \ \dfrac{2}{3} \times \text{Hour}\\\\\bullet \ \text{Wednesday:} \ \dfrac{1}{2} \times \text{Hour}[/tex]
Since Emily only practiced on Monday and Wednesday, the sum of time on both days is the time Emily practiced on the piano for a week.
[tex]\implies \text{Monday + Wednesday = Total time practiced on piano for a week}[/tex]
Substitute the times in the equation
[tex]\implies (\dfrac{2}{3} \times \text{Hour}) + (\dfrac{1}{2} \times \text{Hour}) = \text{Total time practiced on piano for a week}[/tex]
Simplify the equation
[tex]\implies (\dfrac{2}{3} \times 60 \ \text{minutes}) + (\dfrac{1}{2} \times 60 \ \text{minutes}) = \text{Total time practiced on piano for a week}[/tex]
[tex]\implies (20 \ \text{minutes}) + (30 \ \text{minutes}) = \text{Total time practiced on piano for a week}[/tex]
[tex]\implies \boxed{50 \ \text{minutes} = \text{Total time practiced on piano for a week}}[/tex]
73 in.
55 in.
b
What is the length of the missing leg? If necessary, round to the nearest tenth.
b =
inches
Answer:
48 (rounded to 10).....
The population of bulgaria has been decreasing at an annual rate of 0.89%. if the population of bulgaria was about 7,450,349 people in the year 2005, predict its population in the year 2015.
Answer:
i have uploaded an answer i have found from the internet hope this helps :)
Step-by-step explanation:
Can anyone help me with this one to
Find the missing angle using the diagram below. The figure is a parallelogram.
(5x + 5)°
135
28
180
90
145
Answer:
145°
Step-by-step explanation:
35+(5x+5)° = 180° (opposite angles sum up to 180°)
35+5x+5 = 180
40+5x = 180
5x= 180- 40
5x = 140
x = 28
therefore, the missing angle = (5x+5)°
= (5×28+5)= 140+5= 145°
there are 20 students in mr.clarks fourth grade class there are 5 times as as many students in the entire fourth grade class as there are in mr.clacks. which equation can be used to determine the number of students,n, in the entire fourth grade?
Answer:
there are 20 students in mr.clarks fourth grade class there are 5 times as as many students in the entire fourth grade class as there are in mr.clacks. which equation can be used to determine the number of students,n, in the entire fourth grade?
n= 20(5)
100 kids in the fourth grade
or
there are 140 kids in the 4 th grade
Step-by-step explanation:
the equation is n=20(5)
because 20(5) is the same as 20×5 so that 8s the equation
A group of friends were working on a student film. They spent all their budget on
equipment and props. They spent $369 on equipment, and 55% of the total budget on
props. What was the total budget for their student film?
Answer:
$820
Step-by-step explanation:
Total = Equipment + Props
T = 369 + 0.55T
0.45T = 369
T = 820
I hope this helps!
The height of a cuboid is 5 cm and its length is 2cm more than the breadth. If its volume is 240cm, find its length and breadth.
Answer:
Final answer -
[tex]length = 6 \: cm \\ breadth = 6 + 2 = 8 \: cm[/tex]
hope helpful :D
EASY! PLEASE HELP, I AM STUCK
Answer:
A. 16 seconds.
Step-by-step explanation:
Well, it would take him 4 seconds to get 4/16 of the way, or 1/4. So just multply that by 4 and boom, 16 seconds. (yes ik my technique is weird)
if angle 6 is 25 degrees how much is 7
Given:
Angle 6 = 25 degrees
To Find:
The value of Angle 7
Solution:
We know that,
the value of Angle 6 is equal to 25 Degrees
Since Angle 6 and Angle 7 together comprise of a Straight Line, this means that they are Supplementary Angles.
Therefore,
Angle 6 + Angle 7 = 180 degrees
This implies that,
25 degrees + Angle 7 = 180 degrees. (since Angle 6 = 25 Degrees)
Angle 7 = (180-25) degrees
Thus ,
Angle 7 = 155 degrees
Hence, Angle 7 is 155 degrees (Option 1)
The figure shows a person estimating the height of a tree by looking at the top of the tree with a mirrow. Assuming that both the person and the tree form right angles with the ground, which of the following proportions can be use to estimate the height of the tree
In a recent survey, 2\3 of the students
said they rode the bus to school.
There were 24 students who took
the survey. How many said that they
rode the bus to school?
Answer:
16
Step-by-step explanation:
2/3 of 24 students
2/3 * 24 = 16
Lamont designs a survey of town residents in an attempt to predict who will be elected mayor. he chooses his sample of 500 people from the town’s 40,000 residents by asking his question to every person leaving the public library on a saturday. which suggestion would most improve lamont’s random sample? lamont should sample only adults. lamont should sample only registered voters. lamont should decrease the sample size. lamont should ask every fifth person.
Lamont should sample only registered voters to predict who will be elected mayor
What is a survey?A survey is a research method used for collecting data from a predefined group of respondents to gain information and insights into various topics
Since Lamont is trying to predict who will be elected, surveying people that are not registered to vote will not give him an accurate prediction. If someone is not registered to vote, they cannot vote for any candidate.
To get more accurate results, Lamont should only sample people that are registered voters.
To know more about the survey follow
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Answer:
b
Step-by-step explanation:
edge test
Select the graph that represents h = -16t^2+ 80.
Answer:
Attach the graph options so i can help...
Step-by-step explanation:
Mary put $2225.50 into an investment at 1.2% for eight years. What will the balance be at the end of eight years? ( what is the total amount of the investment plus interest after 8 years?) round to the nearest hundreth.
interest: $_____
+$2,225.50
=$____(total)
Answer: $2400
Step-by-step explanation:
$2225.50 x 1.2% = $26.71 + $2225.50 = $2252.21 - Year 1
$2252.21 x 1.2% = $27.03 + $2252.21 = $2279.23 - Year 2
$2279.23 x 1.2% = $27.35 + $2279.23 = $2306.58 - Year 3
$2306.58 x 1.2% = $27.68 + $2334.26 = $2334.26 - Year 4
$2334.26 x 1.2% = $28.01 + $2362.27 = $2362.27 - Year 5
$2362.27 x 1.2% = $28.35 + $2362.27 = $2390.62 - Year 6
$2390.62 x 1.2% = $28.69 + $2390.62 = $2419.31 - Year 7
$2419.31 x 1.2% = $29.03 + $2419.31 = $2448.34 - Year 8
Rounded to the nearest 100th = $2400
The population standard deviation for the price of the Big Mac is six cents. If
we want to be 82% confident that the sample mean price is within three cents
of the true population mean price, how many randomly selected stores must
be analyzed?
Round your answer up to the whole number, i. E. , 4. 02 stores will be rounded
to 5 stores.
Using the z-distribution, as we have the standard deviation for the population, it is found that 8 stores must be analyzed.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The margin of error is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have an 82% confidence level, hence[tex]\alpha = 0.82[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.82}{2} = 0.91[/tex], so the critical value is z = 1.34.
The standard deviation for the population is of [tex]\sigma = 0.06[/tex], and we want a margin of error of M = 0.03, hence we solve for n to find the sample size needed.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.03 = 1.34\frac{0.06}{\sqrt{n}}[/tex]
[tex]0.03\sqrt{n} = 1.34 \times 0.06[/tex]
Simplifying by 0.03:
[tex]\sqrt{n} = 1.34 \times 2[/tex]
[tex](\sqrt{n})^2 = (1.34 \times 2)^2[/tex]
[tex]n = 7.2[/tex]
Rounding up, 8 stores must be analyzed.
More can be learned about the z-distribution at https://brainly.com/question/25890103
What is the product? startfraction 2 y over y minus 3 endfraction divided by startfraction 4 y minus 12 over 2 y 6 endfraction two-thirds ten-ninths startfraction 4 y over y minus 3 endfraction startfraction 4 y over y 3 endfraction
The product of the expression [tex]\rm \dfrac{\dfrac{2y}{y-3} }{\dfrac{4y-12}{2y+6}}\\\\\\[/tex] is [tex]\rm \dfrac{(y^2+3y)}{(y^2-6y+9)}\\[/tex].
What is the product?In mathematics, the term 'product' refers to the answer to a multiplication problem.
The product of the given expression is determined in the following steps given below.
[tex]\rm =\dfrac{\dfrac{2y}{y-3} }{\dfrac{4y-12}{2y+6}}\\\\\\=\dfrac{2y}{y-3}\times \dfrac{2y+6}{4y-12}\\\\= \dfrac{2y \times 2y + 2y \times 6}{y(4y-12)-3(4y-12)}\\\\=\dfrac{4y^2+12y}{4y^2-12y-12y+36}\\\\=\dfrac{4y^2+12y}{4y^2-24y+36}\\\\=\dfrac{4(y^2+3y)}{4(y^2-6y+9)}\\\\ =\dfrac{(y^2+3y)}{(y^2-6y+9)}\\[/tex]
Hence, the product of the expression [tex]\rm \dfrac{\dfrac{2y}{y-3} }{\dfrac{4y-12}{2y+6}}\\\\\\[/tex] is [tex]\rm \dfrac{(y^2+3y)}{(y^2-6y+9)}\\[/tex].
To know more about the product click the link given below.
https://brainly.com/question/15029466
Answer:
3
Step-by-step explanation:
D on edge 2022
Consider f(x) = bx. which statement(s) are true for 0 < b < 1? check all that apply. the domain is all real numbers. the domain is x > 0. the range is all real numbers. the range is y > 0. the graph has x-intercept 1. the graph has a y-intercept of 1. the function is always increasing. the function is always decreasing.
The true statement for f(x)=b^x is the function is always decreasing function.
We have given,
f(x)=b^x where 0<b<1
What is the domain?Domain is all possible values of x for which any function is defined
We can select any values of x for which function
It will be defined for all real x
So, the domain is [tex](-\infty,\infty)[/tex]
The range is all possible values of y for which x is defined
we are given that b is positive
The value of the function will always be positive
So, the range is [tex](0,\infty)[/tex]
y>0
The x-intercept:
Set f(x)=0 and then we can solve for x
f(x)=b^x=0
x is undefined
The x-intercept does not exist
Increasing or decreasing:
Since, 0<b<1
The b is a positive value less than 1
As we increase the value of, [tex]b^x[/tex] will keep decreasing
This is decreasing function
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Find the perimeter of this semi-circle with radius, r = 42cm. Give your answer as an expression in terms of π .
Answer:
C≈263.89 cm
Step-by-step explanation:
The anwser is down below
Answer:
B) 2/9
Step-by-step explanation:
2 + 3 + 5 = 10 marbles altogether
One blue is taken out, so it's now 2 and 9 (10-1).
A student usually saves $20 a month. He would like to reach a goal of saving $350 in 12 months. The student writes the equation 350 = 12(x+20) to represent this situation. Solve the equation for x.
Write your answer as a sentence that describes what the variable x represents.
Enter your answers and your work or explanation in the box provided.
Answer:
The student would need to save $9.17 more per month
Step-by-step explanation:
350 = 12(x+20)
350 = 12x + 240
12x = 110
x = 110/12
x = $9.17
What is the length of the cylinder's height? Please help
Answer:
Height = 9 cm which means Option C is the answerStep-by-step explanation:
In the question we are given ,
Volume of cylinder = 225π cm³Radius of cylinder = 5 cmAnd , we have to find the height of cylinder .
We know that ,
[tex]
\longrightarrow \pink{ \boxed{Volume \: of \: Cylinder = \pi r {}^{2}h }} \longleftarrow[/tex]
Our solution starts from here :
[tex] \longmapsto \: \pi \: r {}^{2} h = 225\pi[/tex]
Step 1 : Cancelling π with π :
[tex] \longmapsto \: \cancel{\pi} \: r {}^{2} h = 225 \cancel{\pi}[/tex]
Step 2 : Substituting value of radius which is 5 cm in the formula :
[tex] \longmapsto \: (5) {}^{2} \times h = 225[/tex]
[tex] \longmapsto \: 25h = 225[/tex]
Step 3 : Transposing 25 to right hand side :
[tex] \longmapsto \: h = \frac{225}{25} [/tex]
Step 4 : Cancelling 225 by 25 :
[tex] \longmapsto \: \red{\boxed{h = 9 \: cm}}[/tex]
Henceforth , height of cylinder is 9 cm#Keep LearningI need help, please.
Answer:
2.5
Step-by-step explanation:
you take 15 and divide it by 6 and that gives you 2.5
Answer: is it D). 2.5 hours?
Step-by-step explanation:
if x cubed = -8, what does x equal
Let's start the sum as follows:
x³ = 8
X × X × X = 8
This means there are 3 number which after Multiplication gives answer 8.
If 2 is multtiplied 3 times it will give you 8
Thus the answer of x is 2
x = 2.
x^3 = -8
The cube root of 8 is 2 = 2 x 2 x 2 is 8.
But, the answer is negative, which means that the cube root of -8 must be -2.
-2 x -2 x -2 = -8
x = -2
Hope this helps!
the radius of a circle is 10.8ft the length of a chord is 12ft what is the approximate distance of the chord from the center of the circle
Answer:
9.0 ft (nearest tenth)
Step-by-step explanation:
The chord is the base of an isosceles triangle with sides of the radius.
To calculate the approximate distance of the chord from the center of the circle, we need to find the height of this triangle.
[tex]\sf height=\sqrt{s^2-(\frac{b}{2})^2}[/tex]
(where s is the side length and b is the base length of an isosceles triangle)
Given:
s = radius = 10.8 ftb = chord = 12 ft[tex]\begin{aligned}\implies \sf height & =\sqrt{10.8^2-\left(\frac{12}{2}\right)^2}\\ & = \sqrt{116.64-36}\\ & = \sqrt{80.64}\\ & = 8.979977728...\\ & = 9.0\: \sf ft\:(nearest\:tenth) \end{aligned}[/tex]
Perpendicular=P=?
Apply Pythagorean theorem
P²=H²-B²P²=10.8²-6²P²=80.64P=8.97P≈9ftplease help me !!!!!!!!!!
[tex]y = - x - 1[/tex]
[tex]y = - 5x - 13[/tex]
Multiply the lower equation by -1:[tex]y = - x - 1[/tex]
[tex] - y = 5x + 13[/tex]
Add the systems:[tex]0 = 4x + 12[/tex]
[tex]4x = - 12[/tex]
[tex]x = \frac{ - 12}{4} = - 3[/tex]
Substitute x=3 in any equation:
[tex]y = - x - 1[/tex]
[tex]y = - ( - 3) - 1[/tex]
[tex]y = 3 - 1 = 2[/tex]
SoLuTiOn PaiR:( -3 , 2 )(WILL MARK BRAINLIST)
Use the function f(x) = x2 – 2x + 8 and the graph of g(x) to determine the difference between the maximum value of g(x) and the minimum value of f(
2.
Answer:
3 or 4, I am confused
Step-by-step explanation:
I'll assume that f(x) = x2 – 2x + 8 is meant to be f(x) = x^2 – 2x + 8
Find the value of f(x) for x = 2:
f(x) = x^2 – 2x + 8
f(2) = (2)^2 – 2*(2) + 8
f(2) = 4 - 4 + 8
f(2) = 8
=============
From the graph, we can find that g(2) = 11
The differece between g(2) and f(2) is thus:
11 - 8 = 3
3 is not an option, so I wonder if the question is asking for the difference between the absolute maximum of g(x) and f(2). If so, the maximum for g(x) is 12, at x = 3.
This would lead to a difference of 12 - 8, or 4. This is still not an option, so I'm confused. Perhaps you can find my error and find the ciorrect answer, or at least one that appears in the options.
Find the slant height?
35
43
45
47
Answer:
45
Step-by-step explanation:
Slant height = √(altitude)² - (1/2 base)²
Sh = √53² - 28²Sh = √2809 - 784Sh = √2025Sh = 45Apologies as my previous response was incorrect.
Use the triangle to answer the question.
ul
diagram not drawn to scale
4
What is the length of the side labeled x?
Ο Α. V11
OB. V21
Oc 11. D.21
The length of the side labeled x is Option B. [tex]\sqrt{21}[/tex].
Pythagorean theorem.Pythagorean theorem is a basic principle to be applied when determining the unknown side of a given right triangle when the values of two sides are given. The theorem states that;
/Hyp/^2 = /Adj/^2 + /Opp/^2
From the triangle given, we have;
/Hyp/^2 = /Adj/^2 + /Opp/^2
x^2 = 4^2 + ((5)^1/2)^2
= 16 + 5
= 21
x = 21^1/2
= [tex]\sqrt{21}[/tex]
The length of the side labeled x is [tex]\sqrt{21}[/tex]. Option B.
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The figure shows a line graph and two shaded triangles that are similar: A line is shown on a coordinate grid. The x axis values are from negative 15 to positive 15 in increments of 3 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 12, negative 4, and 0, 0, and 12, 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled O to negative 6, negative 2 labeled A, one leg is from 0, 0 to 0, negative 2, and the second leg is from 0, negative 2 to negative 6, negative 2. Another shaded right triangle is formed with the hypotenuse from negative 6, negative 2 to negative 9, negative 3 labeled B, one leg is from negative 6, negative 2 to negative 6, negative 3, and the second leg is from negative 9, negative 3 to negative 6, negative 3. Which statement about the slope of the line is true? It is 3 throughout the line. It is fraction 1 over 3 throughout the line. The slope from point O to point A is fraction 1 over 3 time the slope of the line from point A to point B. The slope from point O to point A is three times the slope of the line from point A to point B.
hope this helps
The figure below shows a line graph and two shaded triangles that are similar:
A line is shown on a coordinate grid. The x axis values are from negative 20 to positive 20 in increments of 4 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 16, 4, and 0, 0, and 16, negative 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled as O to negative 8, 2 labeled as A, one leg is from 0, 0 to negative 8, 0, and the second leg is from negative 8, 0 to negative 8, 2. Another shaded right triangle is formed with the hypotenuse from negative 8, 2 to negative 12, 3 labeled as B, one leg is from negative 8, 2 to negative 12, 2, and the second leg is from negative 12, 2 to negative 12, 3.
Which statement about the slope of the line is true?
The slope from point O to point A is fraction 1 over 4 times the slope of the line from point A to point B.
The slope from point O to point A is 4 times the slope of the line from point A to point B.
It is fraction negative 1 over 4 throughout the line.
It is −4 throughout the line
Step-by-step explanation:
not my answer found it on a different page but it should help.