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Given: Different angles in degrees and in terms of pi. The different angles are:
[tex]\begin{gathered} a)714^0 \\ b)\frac{23\pi}{5} \\ c)120^0 \\ d)\frac{31\pi}{6} \end{gathered}[/tex]To Determine: The equivalence of the given angles
The equivalent of degree and pi is given as
[tex]\begin{gathered} 2\pi=360^0 \\ \pi=\frac{360^0}{2} \\ \pi=180^0 \\ 360^0=2\pi \\ 1^0=\frac{2\pi}{360^0} \\ 1^0=\frac{1}{180}\pi \end{gathered}[/tex][tex]\begin{gathered} a)714^0 \\ 1^0=\frac{1}{180}\pi \\ 714^0=\frac{714^0}{180^0}\pi \\ 714^0=3\frac{29}{30}\pi \\ 714^0=\frac{119\pi^{}}{30} \end{gathered}[/tex][tex]\begin{gathered} b)\frac{23\pi}{5} \\ 1\pi=180^0 \\ \frac{23\pi}{5}=\frac{23}{5}\times180^0 \\ \frac{23\pi}{5}=828^0 \end{gathered}[/tex][tex]\begin{gathered} c)120^0 \\ 1^0=\frac{\pi}{180} \\ 120^0=120\times\frac{\pi}{180} \\ 120^0=\frac{2\pi}{3} \end{gathered}[/tex][tex]\begin{gathered} d)\frac{31\pi}{6} \\ 1\pi=180^0 \\ \frac{31\pi}{6}=\frac{31}{6}\times180^0 \\ \frac{31\pi}{6}=930^0 \end{gathered}[/tex]ALTERNATIVELY
A revolution is 360 degree
[tex]\begin{gathered} a)714^0 \\ \text{Multiples of 360 degre}e \\ 2\times360^0=720^0 \\ \text{equivalent of 714 degre}e\text{ would be} \\ 720^0-714^0=6^0 \end{gathered}[/tex][tex]undefined[/tex][tex]\begin{gathered} a)714^0=\frac{119\pi}{30} \\ b)\frac{23\pi}{5}=828^0 \\ c)120^0=\frac{2\pi}{3} \\ d)\frac{31\pi}{6}=930^0 \end{gathered}[/tex]Related Questions
Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
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The derivative of the function f(x) = -5x²+3x-2 is -10x+3.
Given the function is f(x) = -5x²+3x-2
Differentiate with respect to x.
d/dx -5x²+3x-2 = d/dx (-5x²) + d/dx(3x) - d/dx(2)
using the power rule d/dx [xⁿ] = nxⁿ⁻¹
⇒ d/dx -5x²+3x-2 = -5(2)x²⁻¹ + 3(1) - 0
⇒ d/dx -5x²+3x-2 = -10x+3
The power rule states that the derivative of xn is nx(n-1) for every x if n is a positive integer, regardless of whether you are thinking of derivatives at a point (numbers) or derivatives on an interval (functions).
Hence we get the derivative as -10x+3.
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Newton's Second Law, F=m.a, describes the relationship between an object's mass, a force acting on it, and the resulting acceleration, where: F is force, in Newtons m is mass, in kilograms a is acceleration, in meters per second squared A young boy and his tricycle have a combined mass of 30 kilograms. If the boy's sister gives him a push with a force of 60 Newtons, what is his acceleration? 1 2 meter per second squared 2 meters per second squared 30 meters per second squared 90 meters per second squared
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Newton's Second Law, F=m.a, describes the relationship between an object's mass, a force acting on it, and the resulting acceleration, where: F is force, in Newtons m is mass, in kilograms a is acceleration, in meters per second squared A young boy and his tricycle have a combined mass of 30 kilograms. If the boy's sister gives him a push with a force of 60 Newtons, what is his acceleration? 1 2 meter per second squared 2 meters per second squared 30 meters per second squared 90 meters per second squared
we have that
F=m*a
we have
m=30 kg
F=60 N
substitute in the formula
60=30*a
solve for a
a=60/30
a=2 m/s^2
therefore
the answer is 2 meters per second squaredFind decimal notation for 100%
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The decimal notation of percentage is the quotient of the percentage divided by 100.
So it follows that :
[tex]\frac{100\%}{100}=1[/tex]The answer is 1
The table shows the amount of water used daily to water the fairways at Fairlawn Golf Course. To the nearest tenth,determine the mean absolute deviation of the data. A. 2.3 B. 7.7 C. 10 D. 12.3
Answers
Answer:
2.3
Explanation:
The formula for calulating mean deviation is expressed as:
[tex]\frac{1}{n}\sum ^n_{i\mathop=1}|x_i-m|[/tex]where;
m is the mean of the data set
Xi are individual values
n is the total sample space
Get the mean;
n = 7
mean = (10+12+11+15+9+8+5)/7
mean = 70/7
mean = 10
Get the mean deviation:
Mean deviation = (10-10)+(12-10)+(11-10)+(15-10)+(9-10)+(8-10)+(5-10)/7
Since the values is in modulus |xi - m| will give a positive value, hence;
Mean deviation = (0+2+1+5+1+2+5)/7
Mean deviation = 16/7
Mean deviation = 2.28
Mean deviation = 2.3 (to the nearest tenth)
Which options show polynomial 1 bring divided into polynomial 2? SELECT ALL THAT APPLY
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Hello. This is an exercise about polynomials.
In this specific question, we will see about the division of polynomials:
We have two polynomials:
• First: 2x
,• Second: 6x²-10x
Now, we'll have to divide the first by the second. We have some ways to write this:
The third and fourth options are wrong because it divides the second polynomial by the first, while the question asks the first divided by the second.
TASK 2: Awards DinnerTran is in charge of the school's Awards Dinner. She set up the multi-purpose room with a stage in front and round tables for parents, students, and family membersto sit around for dinner. Below is the floor plan that she drew for the event.StageCLUE Illuminate EducationIncSign out11US 01:09hp
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According to the image each table has an amount of 8 seats, and there are
rectangle rstw has diagonals RT and SW that intersect at Z. If RZ= 5x+8 and SW= 11x-3 find the value of x.
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Answer:
19
Explanation:
We know that the diagonals of a rectangle are always equal, therefore RT = SW.
So if RZ = 5x + 8 and SW = 11x - 3, lets's go ahead and find x as shown below;
[tex]\begin{gathered} 2(5x+8)=11x-3 \\ 10x+16=11x-3 \\ 16+3=11x-10x \\ 19=x \\ \therefore x=19 \end{gathered}[/tex]A population forms a normal distribution with a meanof μ = 85 and a standard deviation of o = 24. Foreach of the following samples, compute the z-score forthe sample mean.a. M=91 for n = 4 scoresb. M=91 for n = 9 scoresc. M=91 for n = 16 scoresd. M-91 for n = 36 scores
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In this problem, we have a population with a normal distribution with:
• mean μ = 85,
,• standard deviation σ = 24.
We must compute the z-score for different samples.
The standard deviation of a sample with mean M and size n is:
[tex]σ_M=\frac{σ}{\sqrt{n}}.[/tex]The z-score of the sample is given by:
[tex]z(M,n)=\frac{M-\mu}{\sigma_M}=\sqrt{n}\cdot(\frac{M-\mu}{\sigma})[/tex]Using these formulas, we compute the z-score of each sample:
(a) M = 91, n = 4
[tex]z(91,4)=\sqrt{4}\cdot(\frac{91-85}{24})=0.5.[/tex](b) M = 91, n = 9
[tex]z(91,9)=\sqrt{9}\cdot(\frac{91-85}{24})=0.75.[/tex](c) M = 91, n = 16
[tex]z(91,16)=\sqrt{16}\cdot(\frac{91-85}{24})=1.[/tex](d) M = 91, n = 36
[tex]z(91,9)=\sqrt{36}\cdot(\frac{91-85}{24})=1.5.[/tex]Answera. z = 0.5
b. z = 0.75
c. z = 1
d. z = 1.5
2/(x - 1) - 1/(x + 1) - 3/(x ^ 2 - 1)
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The first step to solve this problem is to solve the substraction between the first two fractions:
[tex]undefined[/tex]Use the fact that 521•73=38, 033.Enter the exact product of 5.21•7.3
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Answer: 38.033
5.21 x 7.3
= 38.033
help me please if you can A.(0, 3)B. (-1, 5)C.(1, 1.5)
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Answer:
A. (0, 3)
C. (1, 1.5)
Explanation:
A point is a solution to the system if it satisfies both inequalities.
So for each option, we get:
Replacing (x, y) = (0, 3)
y ≥ -2x + 3
3 ≥ -2(0) + 3
3 ≥ 3
y ≤ -x² - x + 4
3 ≤ -0² - 0 + 4
3 ≤ 4
Since both inequalities are satisfied, (0, 3) is a solution.
For (x, y) = (-1, 5)
y ≥ -2x + 3
5 ≥ -2(-1) + 3
5 ≥ 2 + 3
5 ≥ 5
y ≤ -x² - x + 4
5 ≤ -(-1)² - (-1) + 4
5 ≤ -1 + 1 + 4
5 ≤ 4
Since 5 is not lower than 4, (-1, 5) is not a solution
For (x, y) = (1, 1.5)
y ≥ -2x + 3
1.5 ≥ -2(1) + 3
1.5 ≥ -2 + 3
1.5 ≥ 1
y ≤ -x² - x + 4
1.5 ≤ -(1)² - (1) + 4
1.5 ≤ -1 - 1 + 4
1.5 ≤ 2
Since both inequalities are satisfied, (1, 1.5) is a solution.
Therefore, the answers are
A. (0, 3)
C. (1, 1.5)
How many true, real number solutions does the equation n + 2 = -16-5n have?solution(s)
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The equation is
n + 2 = - 16 - 5n
By collecting like terms, we have
n + 5n = - 16 - 2
6n = - 18
Dividing both sides of the equation by 6, we have
6n/6 = - 18/6
n = - 3
It has only one solution
A local band was interested in the average song time for rock bands in the 1990s. They sampled eight different rock bands and found that the average time was 3.19 minutes with a standard deviation of 0.77 minutes.
Calculate the 95% confidence interval (in minutes) for the population mean.
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The 95% confidence interval (in minutes) for the population mean is of:
(2.55, 3.83).
What is a t-distribution confidence interval?The bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the parameters are described as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The distribution is used when the standard deviation of the population is not known, only for the sample.
In the context of this problem, the values of the parameters are given as follows:
[tex]\overline{x} = 3.19, s = 0.77, n = 8[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 8 - 1 = 63 df, is t = 2.3646.
Then the lower bound of the confidence interval is calculated as follows:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 3.19 - 2.3646\frac{0.77}{\sqrt{8}} = 2.55[/tex]
The upper bound is calculated as follows:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 3.19 + 2.3646\frac{0.77}{\sqrt{8}} = 3.83[/tex]
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Given AFGH ~ ALMN, which must be true? Select all that apply.A.FGLMFHLNB. FH ~ LNC.mZFmZLmZGmZMD. GHMNE. mZH ^mZN
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what is 9/36 simplified?
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Answer:
1/4
Step-by-step explanation:
it can be simplified by dividing both the numerator and denominator with 9.
[tex] \displaystyle \large{ \sf{ \frac{9}{36}}} [/tex]
[tex]\displaystyle \large{ \sf{ \frac{9}{36} = \frac{ \cancel9}{ \cancel3 \cancel6} }}[/tex]
[tex]\displaystyle \large{ \bf{ = \frac{1}{4} }}[/tex]
simplest form is 1/4
How many solutions does the following equation have? - 6(x + 7) = - 4x – 2 А. No solutions B.Exactly one solution C.Infinitely many solutions
Answers
ANSWER
Exactly one solution.
EXPLANATION
We are given the equation:
-6(x + 7) = -4x - 2
To find the number of solutions, we have to solve for x:
-6x - 42 = -4x - 2
Collect like terms:
-6x + 4x = 42 - 2
-2x = 40
x = 40 / -2
x = -20
Therefore, the equation has exactly one solution.
Write the equation for the quadratic function in vertex form & standard form with the given vertex that passes through the given point.Vertex (2, -8) through the point (4, 3)
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We will have the following:
[tex]\begin{gathered} y=a(x-2)^2-8\Rightarrow3=a(4-2)^2-8 \\ \\ \Rightarrow3=4a-8\Rightarrow4a=11 \\ \\ \Rightarrow a=\frac{11}{4} \end{gathered}[/tex]So, the equation in vertex form is:
[tex]y=\frac{11}{4}(x-2)^2-8[/tex]And in standard form:
[tex]\begin{gathered} y=\frac{11}{4}(x^2-4x+4)-8\Rightarrow y=\frac{11}{4}x^2-11x+11-8 \\ \\ \Rightarrow y=\frac{11}{4}x^2-11x+3 \end{gathered}[/tex]***Explanation***
We know that the quadratic expression in vertex form follows:
[tex]y=a(x-h)^2+k[/tex]Where (h, k) is the vertex of the expression. Now, we know that the vertex is (2, -8), so we replace those values and we obtain:
[tex]y=a(x-2)^2+(-8)\Rightarrow y=a(x-2)^2-8[/tex]Now, in order to determine "a" we must replace one point (That is not the vertex) in the expression and solve for "a", and we are told that the point (4, 3) is in one of the solutions, so:
[tex]\begin{gathered} 3=a(4-2)^2-8\Rightarrow3=a(2)^2-8 \\ \\ \Rightarrow11=4a\Rightarrow a=\frac{11}{4} \end{gathered}[/tex]Thus, the expression in vertex form is then:
[tex]y=\frac{11}{4}(x-2)^2-8[/tex]And to determine the standard form, we simply expand the equation in vertex form:
[tex]y=\frac{11}{4}(x^2-4x+4)-8\Rightarrow[/tex]My answer is correct or no please check
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Answer:
D) 5 minus a number M
hope this helps!
Answer:
Yep. You got it right. Good job!
Step-by-step explanation:
740In the table on the right there are grades that were earned by students on a midtermbusiness math exam What percent of the students earned a grade below 80?83977084986685687783958879648890859396The percent of students with grade below 80 is(Round to the nearest whole number as needed)
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Notice that the number of students that got a grade below 80 is:
[tex]7,[/tex]and the total number of students is:
[tex]20.[/tex]Therefore, we have to determine what percentage 7 represents from 20. To determine the percentage that x represents from y, we can use the following expression:
[tex]\frac{x}{y}*100.[/tex]Finally, we get that 7 represents the
[tex]\frac{7}{20}*100=35\%,[/tex]of 20.
Answer:
[tex]35\%.[/tex]Find the coordinates of the vertex of the graph of y=4-x^2 indentify the vertex as a maximum or minimum point A.(2,9);maximumB.(0,4);minimumC.(0,4);maximum D.(2,0);minimum
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Let's begin by identifying key information given to us:
[tex]\begin{gathered} y=4-x^2 \\ y=-x^2+4 \\ a=-1,b=0,c=4 \\ x_v=-\frac{b}{2a}=-\frac{0}{2(-1)}=0 \\ y_v=-\frac{b^2-4ac}{4a}=-\frac{0^2-4(-1)(4)}{4(-1)} \\ y_v=-\frac{0+16}{-4}=\frac{-16}{-4}=4 \\ y_v=4 \\ \\ \therefore The\text{ vertex of the equation is }(0,4) \end{gathered}[/tex]To know if the vertex is the maximum or minimum point, we will follow this below:
[tex]\begin{gathered} y_v=4 \\ \Rightarrow This\text{ is a minimum point} \end{gathered}[/tex]Hence, the answer is B.(0,4); minimum
For these problems, please show your algebraic work using logarithms. 1. Determine the doubling time for each situation listed below. a. A population is growing according to P = P_0e^0.2t b. A bank account is growing by 2.7% each year compounded annually.
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Answer: We need to find the doubling time for population growth:
Population growth is given by
[tex]P=P_oe^{(0.2)t}[/tex]Where:
[tex]\begin{gathered} P\rightarrow\text{final} \\ P_o\rightarrow I\text{nitial} \end{gathered}[/tex]For the population to double, it implies that:
[tex]P=2P_o[/tex]Therefore:
[tex]\frac{P}{P_o}=\frac{2P_o}{P_o}=2=e^{(0.2)t}[/tex]Solving for time "t" gives:
[tex]2=e^{(0.2)t}\rightarrow\ln (2)=(0.2)t\rightarrow t=\frac{\ln (2)}{(0.2)}=3.46u[/tex]in a triangle one angle is three times the smallest angle and the third angle is 45 more than twice the smallest angle. find the measure of all 3 angles. Hint: the angles of a triangle add up to 180.
Please show me full steps. I need help.
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The angles are 22.5°, 67.5° and 90°.
How to calculate the angle?Let the smallest angle = x
Total angles in a triangle = 180°
One angle is three times the smallest angle. This will be 3x.
The third angle is 45 more than twice the smallest angle. This will be:
= (2 × x) + 45
= 2x + 45
The angles will be:
x + 2x + 45 + 3x = 180
6x + 45 = 180
Collect like terms
6x = 180 - 45
6x = 135
Divide
x = 135 / 6
x = 22.5°
Smallest angle = 22.5°
The other angles will be calculated by substitutibg 22.5° for x. This will be:
3x = 3 × 22.5 = 67.5°
Also, 2x + 45 = 2(22.5) + 45 = 90°
This illustrates the concept for angles in a triangle.
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in a recent year the annual salary of the governor of New York was 1790000 during the same year the annual salary of the governor of Tennessee was 940000 less write and solve an equation to find the annual salary of the government of Tennessee in that year
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Step 1 : Let's review the information given to us to answer the problem correctly:
• Annual salary of the governor of New York = $ 1,790,000
,• Annual salary of the governor of Tennessee = $ 940,000
Step 2: Let x to represent the annual salary of the governor of New York
and let's find the ratio of the salary of the governor of Tennessee, as follows:
940,000/1,790,000 = 0.525
Step 3: Now, let's write the equation for calculating the salary of the governor of Tennessee for any given year, this way:
• 0.525x = Annual salary of the governor of Tennessee
,•
Step 4: If the salary of the governor of New York for the next year is 2,000,000, then we can calculate the salary of the governor of Tennessee, this way:
0.525x = 0.525 * 2,000,000 = 1,050,000
The annual salary of the governor of Tennessee woudl be 1,050,000
Can I get help w this pleaseThe dimensions of a rectangular prism are quadrupled.if the original surface area was 225ft^2 was is the new surface area?
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Answer:
Concept:
Doubling the dimensions of a prism will increase the new area by 4 times the original area
Tripling the the dimensions of the prism will increase the new area by 9 times the original area
Quadrupling will increase the new area by 16 times the original area
Given that the original area given is
[tex]=225ft^2[/tex]The new area therefore will be
[tex]\begin{gathered} 16\times225 \\ =3600ft^2 \end{gathered}[/tex]Hence,
The final answer will be
[tex]\rightarrow3600ft^2[/tex]After a translation, the image of P(-3, 5) is P'(-4, 3). Identify the image of the point (1, 6) after this same translation.
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The image of the point (1, 6) after the translation is (0, 4).
What is named as translation?In geometry, translation refers to a function that shifts an object a specified distance. The object is not elsewhere altered. It has not been rotated, mirrored, or resized.Every location of the object should be relocated in the same manner and at the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, as well as the object that after translation is referred to as the image.For the given question,
The image of point P(-3, 5) after a translation is P'(-4, 3).
In this, there is a shift of 1 units to the left of x axis and shift of 2 units up on the y axis.
Thus, do the same translation for the point (1, 6).
After translation image will be (0, 4)
Thus, image of the point (1, 6) after the translation is (0, 4).
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Find the area of the triangle below.9 cm6 cm2 cm
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We recall that the area of a triangle is defined by the product of the triangle's base times its height divided by 2.
So we notice that in our image, we know the height (6 cm), and we also know the base of the triangle (2 cm)
Therefore the triangles are is easily estimated via the formula:
[tex]\text{Area}=\frac{base\cdot height}{2}=\frac{2\cdot6}{2}=6\, \, cm^2[/tex]Then the area is 6 square cm.
The volume of a right circular cylinder with a radius of 4 in. and a height of 12 in. is ___ π in^3.
Answers
For the given right cylinder:
Radius = r = 4 in
Height = h = 12 in
The volume of the cylinder =
[tex]\pi\cdot r^2\cdot h=\pi\cdot4^2\cdot12=192\pi[/tex]So, the answer will be the volume is 192π in^3
identify the slope: 6x - 2y = -6
Answers
The slope = 3
Explanations:Note that:
The slope - Intercept form of the equation of a line takes the form y = mx + c
where m is the slope and
c is the intercept
The given equation is:
6x - 2y = -6
The equation can be re-written as:
2y = 6x + 6
2y / 2 = 6x/2 + 6/2
y = 3x + 3
The slope, m = 3
The intercept, c = 3
Y intercept=3
simplify x⁹ divided by x^5
Answers
Answer:
[tex]x^{4}[/tex]
Step-by-step explanation:
Whenever it comes to the division of the same variable, we subtract their powers in order to get the correct answer:
[tex]x^{9}/x^{5}[/tex]
[tex]x^{9-5}[/tex]
[tex]x^{4}[/tex]
At one time, it was reported that 27.9% of physicians are women. In a survey of physicians employed by a large health system, 45 of 120 randomly selected physicians were women. Is there sufficient evidence at the 0.05 level of significance to conclude that the proportion of women physicians in the system exceeds 27.9%?Solve this hypothesis testing problem by finishing the five steps below.
Answers
SOLUTION
STEP 1
The hull hypothesis can written as
[tex]H_0\colon p=0.279[/tex]The alternative hypothesis is written as
[tex]H_1\colon p>0.279[/tex]STEP 2
The value of p will be
[tex]\begin{gathered} \hat{p}=\frac{X}{n} \\ \hat{p}=\frac{45}{120}=0.375 \\ \text{where n=120, x=}45 \end{gathered}[/tex]STEP3
From the calculations, we have
[tex]\begin{gathered} Z_{\text{cal}}=2.34 \\ \text{Z}_{\text{los}}=0.05 \end{gathered}[/tex]We obtained the p-value has
[tex]\begin{gathered} p-\text{value}=0.0095 \\ \text{level of significance =0.05} \end{gathered}[/tex]STEP4
Since the p-value is less than the level of significance, we Reject the null hypothesis
STEP 5
Conclusion: There is no enought evidence to support the claim
