Using the z-distribution, it is found that the sample is enough evidence that the proportion is below 51%.
What are the hypotheses tested?At the null hypotheses, it is tested if the proportion is of 51%, that is:
[tex]H_0: p = 0.51[/tex]
At the alternative hypotheses, it is tested if the proportion is less than 51%, hence:
[tex]H_1: p < 0.51[/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 given as follows:
[tex]p = 0.51, n = 250, \overline{p} = \frac{109}{250} = 0.436[/tex]
Hence, the test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.436 - 0.51}{\sqrt{\frac{0.51(0.49)}{250}}}[/tex]
z = -2.34.
What is the decision?Considering a left-tailed test, as we are testing if the proportion is less than a value, with a standard significance level of 0.05, 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, we reject the null hypothesis, and find that the sample is enough evidence that the proportion is below 51%.
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HELP PLEASE! Chords NO and PQ are congruent. Arc NO measures 4x + 10 and Arc PQ measures 2x + 20. What is each of their measures?
The measure of each arc is 30.
What is the arc of a circle?The arc of a circle is defined as the part or segment of the circumference of a circle.
Given that, a circle, Chords NO and PQ are congruent. Arc NO measures 4x + 10 and Arc PQ measures 2x + 20.
We know that,
Chord Arcs Theorem :-
If two chords in a circle are congruent, then their intercepted arcs are congruent.
2x+20 = 4x+10
2x = 10
x = 5
Therefore,
2(5) + 20 = 30
Hence, the measure of each arc is 30.
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Manuel labore earns $19. 50/hr. And works an average of 38 hours a week. He is considering renting a house for $1,700/ month. His real estate friend recommends he spend no more than 28% of his monthly income on housing.
Answer:
Given:
Wage = $19.50 per hourWeekly hours worked = 38⇒ Weekly income = 38 × $19.50 = $741
⇒ Monthly income = ($741 × 52.14) ÷ 12 = $3219.65
28% of monthly income
= 0.28 × $3219.65 = $901.50
As $1700 > $901.50 Manuel should not rent the house for $1700 per month since it is more than 28% of his income.
The cost of rent at $1700 per month is actually 52.8% of his monthly income:
(1700 / 3219.65) x 100 = 52.8%
12x + 3y = 9 solve for y
Answer:
[tex]\Longrightarrow: \boxed{\sf{y=3-4x}}[/tex]
Step-by-step explanation:
To solve for y, you have to isolate it on one side of the equation.
12x+3y=9First, you have to subtract by 12x from both sides.
[tex]\Longrightarrow:\sf{12x+3y-12x=9-12x}[/tex]
Solve.
[tex]\Longrightarrow:\sf{3y=9-12x}[/tex]
Then, you divide by 3 from both sides.
[tex]\Longrightarrow:\sf{\dfrac{3y}{3}=\dfrac{9}{3}-\dfrac{12x}{3}}[/tex]
Solve.
[tex]\sf{\dfrac{9}{3}-\dfrac{12x}{3}}[/tex]
[tex]\sf{\dfrac{9-12x}{3}}[/tex]
Use the distributive property.
[tex]\underline{\text{DISTRIBUTIVE PROPERTY:}}[/tex]
⇒A(B+C)=AB+AC9-12x=3(3-4x)
[tex]\sf{\dfrac{3\left(3-4x\right)}{3}}[/tex]
Divide the numbers from left to right.
3/3=1
3-4x
Then, rewrite the problem down.
[tex]\Longrightarrow: \boxed{\sf{y=3-4x}}[/tex]
Therefore, the correct answer is y=3-4x.I hope this helps! Let me know if you have any questions.
Answer:
y = (3) - (4x)
Step-by-step explanation:
Note: Since there is only one equation given, the value of "y" will not be a fixed value.
Given equation:
12x + 3y = 9Our main goal to solve for "y" is to have the y-variable on one side, and a specific value or variable on the other side (e.g., y = 3 or y = 4x) . Start out by subtracting both sides by 12x. This will isolate the y-variable and it's cooeficient (3).
⇒ 12x + 3y = 9⇒ 12x + 3y - 12x = 9 - 12x⇒ 3y = 9 - 12xOnce the y-variable and the cooeificent of the variable have been isolated, we can divide both sides by the cooeficient to isolate the variable.
⇒ 3y/3 = (9 - 12x)/3⇒ y = (9 - 12x)/3⇒ y = (9 ÷ 3) - (12x ÷ 3)⇒ y = (3) - (4x)Therefore, the value of "y" is 3 - 4x.
3x−4/5=−1/2
What is the value of x?
A technology company is going to issue new ID codes to its employees. Each code will have two letters, followed by one digit, followed by one letter. The letters D ,Z G , and and the digit 8 will not be used. So, there are 23 letters and digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?
The number of times employee ID codes can be generated is that have two letters, followed by one digit, followed by one letter is 109503.
What is arrangement?Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.
The number of possible ways to arrange is the n!.Here, n is the number of objects.
A technology company is going to issue new ID codes to its employees. Each code will have two letters, followed by one digit, followed by one letter.
The letters D ,Z, G and Z and the digit 8 will not be used. So, there are 23 letters and 9 digits that will be used. The letters can be repeated.[tex]\text{Each code=Two latter + One digit}[/tex]
The first letter is chosen from the 23 letters in 23 number of ways. As letters can be repeated, thus second letter chosen from 23 letters in 23 ways.
One digit can be chosen from the 9 digits in 9 different ways. The last letter can also be chosen in 23 ways. Thus, the number of times employee ID codes can be generated is,
[tex]n=23\times23\times9\times23\\n=109503[/tex]
Thus, the number of times employee ID codes can be generated is that have two letters, followed by one digit, followed by one letter is 109503.
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Find the length of the missing side please help
Step-by-step explanation:
7. Since they are similar triangles we have:
[tex] \frac{10}{8} = \frac{x}{12} \\ \\ x = 15[/tex]
So DF is 15
8. They are also similar. So:
[tex] \frac{14}{7} = \frac{x}{5} \\ x = 10[/tex]
So PR is 10
What is the most important question jamir needs to consider before he agrees to a lease? will he enjoy driving his new car? will he be able to stay under the 15,000 miles per year limit? will he be able to afford his $432 payment? will he be able to come up with the $2,500 down payment?
Answer:
Answer is B. Will he be able to stay under the 15,000 miles per year limit?
Step-by-step explanation:
Just took the tes
Answer:
B. Will he be able to stay under the 15,000 miles per year limit?
Step-by-step explanation:
Colleen is attending a carnival. The price of admission to the carnival is shown. It costs $3 to play a game. Colleen has $35.
A Ferris wheel is shown. Carnival admission is eight dollars.
What is the greatest number of games she can play?
Answer:
9
Step-by-step explanation:
Reduce the admission fee. Then divide the rest with cost per game
35 - 8 = 27
=> 27/3 = 9
I need help like a lot
i just want the points but if i do some math based off of the question i think its C
Which is an equation for the line that contains the points (-2, 3) and (2, -1)?
Answer:
J
Step 1. Find slope
(-1 - 3)/(2 + 2)
-4/4
m = -1
Step 2. Write equation
y - 3 = -1 (x + 2)
y = -x -2 + 3
y = -x + 1
Answer:
Step-by-step explanation:
First find the slope:
[tex]\frac{-4}{4} =-1[/tex]
This immediately rules out all answers but J.
this picture represents 1-4 of the distance from maria house to the park which represents the whole distance?
(Pls need help ASAP) Willing to give 10 points for 1 question)
Answer:
D. {(1,2) , (2,3) , (3,4) , (4,5)}
Step-by-step explanation:
Functions are relations with one output for any unique input. Relations that pass the vertical line test have one output for each input. In this case, D was the only set that met the criteria.
A dog is leashed to a point in the center of a large yard. If the leash is 18.8 feet long, what is the total area of the region the dog is able to explore? Round to the nearest tenth.
Worth 25 points!! pls hurry I have a test
Answer:
1109.8 square feet
Step-by-step explanation:
In this case, assume the leash to be the radius of the circular yard.
Area
πr²3.14 x (18.8)²3.14 x 353.441109.8 square feetWhat is the base of a parallelogram with an area of 36 square centimeters, if its height is 3 centimeters?
15 cm
33 cm
9 cm
12 cm
PLS HELP ASAP
Answer:
12 cmStep-by-step explanation:
Formula_____________
Area of a parallelogram = base × height
==================================
Area of the parallelogram = base × height
⇔
36 = base × 3
⇔
base = 36/3
= 12
Determine the total annual fica tax for an annual salary of $38,480. a. $294.37 b. $717.96 c. $2,385.76 d. $2,943.72
The total annual fica tax for an annual salary of $38,480 is: d. $2,943.72.
Total annual FICA taxFICA tax comprises of:
Social security= 6.2%
Medicare=1.45%
Hence:
Social Security=$38,480 x 0.062
Social security =$2,385.76
Medicare= $38,480 x 0.0145
Medicare=$557.96
FICA tax=$2,385.76+$557.96
FICA tax=$2,943.72
Therefore the total annual fica tax for an annual salary of $38,480 is: d. $2,943.72.
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Answer:
D
Step-by-step explanation:
When building a house, the number of days required to build varies inversely with with the number of workers. One house was built in 136 days by 7 workers. How many days would it take to build a similar house with 34 workers
Answer:
it would take them 4 days to build the house
WILL GIVE BRAINLIEST
Write 2/7x(1.4x^2-3.5y) as a polynomial
The expression (2/7)x (1.4x² - 3.5y) can be written in the form of a polynomial as 0.4x³ - xy.
What is polynomial?Polynomial is an algebraic expression that consists of variables and coefficients. Variables are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
The expression is given below
[tex]\rm \dfrac{2x}{7} \times (1.4x^2-3.5y)[/tex]
The expression can be written in the form of the polynomial
[tex]\rightarrow \rm \dfrac{2x}{7} \times (1.4x^2-3.5y)\\\\\\\rightarrow \rm \dfrac{2x \times 1.4x^2}{7} - \dfrac{3.5y\times 2x}{7 }\\\\\\\rightarrow \dfrac{2.8x^3}{7} - \dfrac{7xy}{7 }\\\\\\\rightarrow 0.4x^3 - xy[/tex]
The expression in the form of a polynomial is given as
[tex]\rm \rightarrow 0.4x^3 - xy[/tex]
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all possible 4 digit patterns with 2,4,5,6,7,8,9
Answer:
7^4 = 2401
Step-by-step explanation:
___, ___, ___, ___
all blank spaces can be filled with all 7 numbers each.. so 7*7*7*7 is total number of paterns you can get if repititions is allowed
Please help!! A red block and a block are on a scale right. The red block weighs 9 ounces. The total weight of both blocks is 16 ounces. Which inequality best represents b, the possible weight of the blue block in ounces?
Answer:
b ≤ 7
Step-by-step explanation:
Given that:
A red block and a blue block are on a scale. The red block weights 9 ounces. The total weight of both blocks is 16 ounces.
To Find:
Which inequality best represents b, the possible weight of the blue block in ounces?
Knowing that;
< ⇒ less than
> ⇒ Greater than
≤ ⇒ less than or equal to
≥ ⇒ greater than or equal to
Solve:
Since the total blocks is 16 ounces that means it can't be pass 16 also known as can't be greater than. As well as, it given us that the red block weight 9 ounces that means
16 - 9 = 7
which given us that it must be equal to 7 or less than 7 to make it true.
Thus,
b ≤ 7
Kavinsky
if a+ b = 5 ( a and b positive), find the maximum value of a² + b²
Answer:
2 for A, 1 for B
The tiny floating two means multiply the number by itself, so;
[tex]2 * 2 = 4[/tex]
[tex]1 * 1 = 1[/tex]
Add the two together.
[tex]4 + 1 = 5[/tex]
hey please i need this really quick
Answer:
the answer of that question is 45
Good people I critically need an assistance with great pleasure!!
Answer:
(y + 3)² - 8
Step-by-step explanation:
y² + 6y +1
Step 1: Divide the co efficient of y by 2
6 ÷2 = 3
Step2: Now find the square of 3
3² = 9
Step3: Add and subtract 9
y² + 6y + 9 - 9 + 1 = y² +6y + 9 - 8
= y² + 2*y*3 + 3² - 8
Compare y² +2 * y*3 + 3² with a² +2ab + b²
= (y + 3)² - 8
State the center and radius of each circle. then write the equation of the circle in standard form.
See attached:
Answer:
Step-by-step explanation:
Center: (h, k) (the coordinate of the middle point)r(radius): d(diameter)/2 (can be found by counting the number of units vertically or horizontally)Standard form of a circle: (x - h)² + (y - k)² = r²1.
Center: (-2, 3)
Radius: 10/2 = 5
Standard form/ equation: (x + 2)² + (y - 3)² = 25
Standard form:
(x - (-2))² + (y - 3)² = 5²
(x + 2)² + (y - 3)² = 25
2.
Center: (1, 1)
Radius: 6/2 = 3
Standard form/ equation: (x - 1)² + (y - 1)² = 9
Standard form:
(x - 1)² + (y - 1)² = 3²
(x - 1)² + (y - 1)² = 9
Hope this helps!
#1
Centre(-2,3)Radius=5=rEquation:-
(x-h)²+(y-k)²=r²(x+2)²+(y-3)²=5²(x+2)²+(y-3)²=25★More simply.
x²+4x+4+y²-6y+9=25x²+y²+4x-6y=12#2
Centre(1,1)Radius=3Equation
(x-1)²+(y-1)²=3²(x-1)²+(y-1)²=9★BRAINLIEST! and MAX POINTS! PLUS 200 POINTS FOR A GOOD JOB!!
Given the following numbers:
π,2√5,√8,√3,√27
part A. Approximate the square root terms using the perfect squares approximation method. Your answer should be a mixed fraction. Make sure to show your work.
Please note pi does not need to be approximated by the perfect squares approximation method as it is not a square root.
part B. Order the numbers from least to greatest. Please show your answer using the original symbols and radicals provided. You may use decimals or fractions as part of your work for figuring it out.
Answer:
Part A)
0.47/1=0.47x100/1x100=47/100\
Part B)
0.47=47/99
Part C)
0.47=47/99
-------------------------------------------------------------------------------------------------------------
this is what I got for the first problem
Part A, 2√5)
5=2.2360679775 5=2x2.2360679775=4.472135955=4.47
Part A, √8)
2 3
V4 8 v9
2 4/5
Part A, √3)
1 2
V1 3 v4
1 2/3 Part A, √27)
5 6
V25 27 v39
5 2/14
-------------------------------------------------------------------------------------------------------------
Part B)
1 2/3 2 3/5 4.47 5 2/14
and this is what I got for the second problem
Step-by-step explanation:
Hope tis helps
Express the number 68,708 in word form and expanded form.
Word form ?
Expanded form ?
Consider this quadratic equation. 2x2 − 1 = 3x + 4 Which equation correctly applies the quadratic formula?
Answer:
[tex]\frac{-(-3)+-\sqrt{(-3)^2-4(2)(-5)}}{2(2)}[/tex]
Step-by-step explanation:
Quadratic formula: [tex]\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
[tex]2x^2-1=3x+4\\\\2x^2-3x-5=0\\\\\\frac{-(-3)+-\sqrt{(-3)^2-4(2)(-5)}}{2(2)} \\\frac{3+-\sqrt{9+40} }{4}[/tex]
[tex]x = \frac{3+-7}{4}[/tex]
Hope this helps and God bless!
The sum of the measures of the interior angles of a polygon is given. How
many sides does the polygon have?
3) 3060
4) 6480
Sides:
Sides:
Answer:
19sides if sum is 3060
38sides if sum is 6480
help I have to turn this is tomorrow and I don’t know how to do it
Step-by-step explanation:
The area of the triangular base is: 19
square units
How to calculate the base area
The given parameters are:
Volume = 27.36 cubic units
Height = 2.88 unit
The volume of a triangular prism is:
V = 0.5 * B *h
Where B represents the base area.
So, we have:
27.36 = 0.5 * B * 2.88
27.36 B * 1.44 -
Solve for B
B = 19
Hence, the area of the triangular base is: 19 square units
The function f is defined by f(x) = x^2 + 3x -10 , if f(x + 5) = x^2 + kx + 30, k=
Answer:
k = 13
Step-by-step explanation:
substitute x = x + 5 into f(x) , that is
f(x + 5) = (x + 5)² + 3(x + 5) - 10 ← expand squared factor using FOIL
= x² + 10x + 25 + 3x + 15 - 10
= x² + 13x + 30
compare this with f(x + 5) = x² + kx + 30
for the 2 expressions to be equal , then k = 13
Find the midpoint of the segment with the given endpoints.
G(–4, 4) and H(2, 10)
Answer:
Midpoint (-1,7)
Step-by-step explanation:
To find a midpoint, average the x's and then average the y's (add and divide by 2)
The x-coordinate of the midpoint is: (-4+2)/2
= -2/2
= -1
and the y-coordinate is:
(4+10)/2
= 14/2
= 7
So the midpoint is:
(-1,7)
Answer:
(-1, 7)
Step-by-step explanation:
Midpoint of a line segment
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}[/tex]
[tex]\textsf{let}\:(x_1,y_1)=(-4,4)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(2,10)[/tex]
[tex]\implies \textsf{Midpoint}=\left(\dfrac{2+(-4)}{2},\dfrac{10+4}{2}\right)=(-1,7)[/tex]