Answer: y=-22
Step-by-step explanation:
A group of friends wants to go to the amusement park. They have no more than $115 to spend on parking and admission. Parking is $15, and tickets cost $25 per person, including tax. Write and solve an inequality which can be used to determine xx, the number of people who can go to the amusement park
Step-by-step explanation:
A group of friends wants to go to the amusement park. They have no more than $115 to spend on parking and admission. Parking is $15, and tickets cost $25 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park.
115 ≥ 25p + 15
115 ≥ 25p + 15
subtract 15 from both sides:
115 - 15 ≥ 25p + 15 - 15
100 ≥ 25p
divide both sides by 25:
100/25 ≥ 25p/25
4 ≥ p
4 people
The number of people who can go to the amusement park is 4.
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number lineby their size.
Given that, the money to be spend, is no more than $115 to spend on parking and admission.
Parking is $15, and tickets cost $25 per person, including tax.
we need to determine the maximum number of people that can go to the park,
115 ≥ 25p + 15
115 ≥ 25p + 15
subtract 15 from both sides:
115 - 15 ≥ 25p + 15 - 15
100 ≥ 25p
divide both sides by 25:
100/25 ≥ 25p/25
4 ≥ p
Hence, the number of people who can go to the amusement park is 4.
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Triangle ABC has vertices A(-6, 6), B(4, 2), and C(-4, 0).
Which statement about triangle ABC is true?
A. Since none of the sides are congruent, it is not a right triangle.
B. Since none of the sides have slopes that are negative reciprocals, it is not a right triangle.
C. Since two of the sides have slopes that are negative reciprocals, it is a right triangle.
D. Since two of the sides are congruent, it is a right triangle.
The statement that is true about the triangle ABC with vertices A(-6, 6), B(4, 2), and C(-4, 0) is C. Since two of the sides have slopes that are negative reciprocals, it is a right triangle.
How to check if the triangle is right triangleRight triangles are triangles with have perpendicular relationships
The lines will be checked for perpendicularity by calculating the slopes, if any two slopes are negative reciprocals then they are perpendicular and the triangle is a right triangle'
the points A(-6, 6), B(4, 2), and C(-4, 0)
Using point A(-6, 6) and B(4, 2)
m = (y₂ - y₁) / (x₂ - x₁)
m = (4 - 6) / (2 - -6)
m = -1/2
Using point B(4, 2), and C(-4, 0)
m = (y₂ - y₁) / (x₂ - x₁)
m = (4 - -4) / (2 - 0)
m = 2
Comparing the slopes shows that slopes calculated are negative reciprocals
2 and -1/2Therefore the triangle is a right triangle
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Solve for x: x^2 + 6√3 x – 9 = 0
Step-by-step explanation:
use this equation : if , ax² + bx + c = 0 [tex] x \: = \frac{ - b \: \frac{ + }{ } \sqrt{ {b}^{2} - 4ac} \: }{2a} [/tex]so here, a = 1 b = 6√3 c = -9
let's use the formula .......
[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} \sqrt{36 \times 3 - 4(1)( - 9)} }{2(1)} [/tex]
[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} \sqrt{108 \: + 36} }{2} [/tex]
[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} \sqrt{144} }{2} [/tex]
[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} 12 }{2} [/tex]
[tex]x \: = \: \frac{ - 6 \sqrt{3} + 12 }{2} [/tex] OR .......[tex]x \: = \: \frac{ - 6 \sqrt{3} - 12 }{2} [/tex]
so , X = -3√3 +6 ............ or X = -3√3 -6 ............Explain how comparing the values of two signed numbers is different than comparing their absolute value?
The difference between the value of two signed numbers and the absolute value is that
signed numbers does not neglect the signs, they can be positive or negative while absolute value gives the positive valueIn a number line signed numbers have specific positions and directions while absolute values ranges from the zero to the positiveWhat are signed numbers?Positive and negative numbers are referred to as signed numbers. The number is automatically regarded as positive if no sign is present.
On a number line, positive numbers are those to the right of zero. Negative numbers are those to the left of 0
What are absolute values?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
A number can never have a negative absolute value.
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Three positive numbers are in the ratio 7:3:2. The sum of the least number and the greatest number exceeds twice the remaining number by 30. Find the three numbers.
The three numbers that are in the ratio 7:3:2 are 70, 30, and 20.
What is the ratio?A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
So, let 7x, 3x, and 2x be the three numbers.
7x+2x = 9x is the product of the lowest and greatest number.
In accordance with:
9x-30=2(3x)
To make the equation easier:
9x-30=6x
30 extra on both sides:
9x=6x+30 or,9x-6x=30
3x=30, x=10,
So, the numbers will be:
7x=7(10) = 70
3x=3(10) = 30
2x=2(10) = 20
Therefore, the three numbers that are in the ratio 7:3:2 are 70, 30, and 20.
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Which of the following techniques might be most useful in helping a restaurant determine how to position itself in the marketplace?
a. factor analysis
b. multiple regression analysis
c. conjoint analysis
d. perceptual mapping
Let A (t) = 2 cot-3 cot1, 0 ≤t ≤ 2. 1. Factorize A(t). 2. Hence, olve the equation A(t) = 0 for 0 ≤t≤ 2. (4 mark)
Answers to both the subparts are as follows:
(A) In order to factor A(t), we obtain A(t) = -cost + 1.
(B) t = 1.57 after solving the equation A(t) = 0 for 0 ≤ t ≤ 2.
What are equations?Two expressions are combined by the equal sign to form a mathematical statement known as an equation.
For instance, a formula might be 3x - 5 = 16.
After solving this equation, we learn that the value of the variable x is 7.
(A) Factorize A(t):
A(t) = 2cost - 3cost + 1
After assembling the cost terms, we have:
A(t) = cost(2 - 3) + 1
A(t) = cost(- 1) + 1
A(t) = -cost + 1
In order to factor A(t), we obtain A(t) = -cost + 1.
(B) Solving equation A(t) = 0 for 0 ≤t≤ 2:
Since A(t) = -cost + 1
When we solve A(t) = 0 for 0 ≤ t ≤ 2, we get:
A(t) = 0
-cost + 1 = 0
-cost = -1
cost = 1
If we take the inverse cosine, we get:
t = cos⁻¹(1)
t = π/2
t = 3.142/2
t = 1.571
t ≅ 1.57
t = 1.57 after solving A(t) = 0 for 0 t 2
Therefore, answers to both the subparts are as follows:
(A) In order to factor A(t), we obtain A(t) = -cost + 1.
(B) t = 1.57 after solving the equation A(t) = 0 for 0 ≤ t ≤ 2.
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Complete question:
Let A (t) = 2 cost-3 cost+1, 0 ≤t ≤ 2
A. Factorize A(t).
B. Hence, solve the equation A(t) = 0 for 0 ≤t≤ 2.
via gelato is a popular neighborhood gelato shop. the company has provided the following cost formulas and actual results for the month of june: fixed element per month variable element per liter actual total for june revenue $ 13.00 $ 72,540 raw materials $ 4.75 $ 30,330 wages $ 5,700 $ 1.50 $ 14,560 utilities $ 1,730 $ 0.30 $ 3,800 rent $ 2,700 $ 2,700 insurance $ 1,450 $ 1,450 miscellaneous $ 660 0.45 $ 2,990 while gelato is sold by the cone or cup, the shop measures its activity in terms of the total number of liters of gelato sold. for example, wages should be $5,700 plus $1.50 per liter of gelato sold and the actual wages for june were $14,560. via gelato expected to sell 6,000 liters in june, but actually sold 6,200 liters.
Via Gelato total revenue for the month of June as the the details of expenses is equal to $7870.
As given in the question,
Total revenue is:
= (6200 × 13) - 72,540
=$ 8060
Details of all expenses are as follow:
Expense on raw material:
= (6200 × 4.75) -30,330
= -$880
Wages :
= (6200 ×1. 50) + 5,700 - 14,560
= $440
Utilities:
= (6200 × 0.30) +1730 - 3,800
= -$210
Rent:
= (2700-2700)
= 0
Insurance :
= (1450-1450)
= 0
Miscellaneous :
= (6200 × 0.45) + 660 -2,990
= $460
Total expense
=-$190
Net operating income :
=$ [8060-190]
=$7870
Therefore, Via Gelato's total revenue of the June month is equal to $7870.
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I need help fast please!!
Name the Property of Congruence that justifies the statement:
A. Symmetric Property
B. Transitive Property
C. Reflexive Property
D. none of the above
Answer:
A. Symmetric Property
Step-by-step explanation:
The Symmetric Propertry states that if x = y, then y = x.
Since XY = WX, and WX = XY, its the Symmetric Property.
what is the statement of |×+1|+5=2
Step-by-step explanation:
|x+1|=2-5
|x+1|= -3
statement doesn't have solution
what is the actual explanation of what happens when you subtract a negative number from another negative number
2(vh)/k=r Solve equation for v in terms of all other variables involved
The equation v in terms of other variables is v = kr/2h
What is the subject of an equation?It is a variable which is expressed in terms of other variables involved in the formula.
Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.
2(vh) / k = r
by cross multiplication
2(vh) = kr
divide both sides by 2h
v = kr/2h
In conclusion, v in terms of other variables is kr/2h
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twenty high school students took an examination and received the following scores: 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73 determine what percent of the students scored within ( ) one standard deviation of the mean
70% of students had scores that were within (±) one standard deviation of the mean.
Explain the term standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.For the stated question-
Total number of students = 20
Scores received; 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73.
Mean = Sum of all/ Total number
Mean x = 79.7
standard deviation = 8.7
Thus, (±) one standard deviation SD of the mean becomes;
-1 SD; 79.7 - 8.7 ≈ 70.994
+1 SD; 79.7 + 8.7 ≈ 88.406
Thus, 71 to 88
Percentage = scores between 71 to 88/ total scores
Percentage = 14/20 x 100 %
Percentage = 70%
Thus, 70% of students had scores that were within (±) one standard deviation of the mean.
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A student reads at a constant rate in her chapter book, where the red fern grows. This can be described by the equation y=1/2x. Complete the chart below.
(Pls help)
The chart can be completed by substituting the value of x and y in the given equation in two variable y = 1/2 x
What are Linear Equations in Two Variables?
The linear equations in two variables are the equations in which each of the two variables are of the highest exponent order of 1 and have one, none, or infinitely many solutions. The standard form of a two-variable linear equation is ax + by + c = 0 where x and y are the two variables.
According to the given question:
(Check the attachment below for complete question)
The given function is y = x/2
Let x be the minutes taken by the student and y be the pages read by him.
The chart can be completed by substituting the value of x that is minutes taken in the given equation to find the value of y. (Check attachment below)
If the teacher recommended that student must be read 20 min each night then the page read by the student is y = 20/2 = 10 pages.
If he reads 18 pages then time taken by him is x = 2×18 = 36 min.
If there are 245 pages then the time taken by the student is
x= 2×245 = 490 min
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3 Isosceles Trapezoid
128°
y is to the left of it
X is diagonal to it
What is x and y
Answer:
x = 52°y = 128°Step-by-step explanation:
Base angles are congruent.
[tex]\tt y=128^o[/tex]
Let's solve for x first:-
[tex]\tt x+y=180^o[/tex]
[tex]\tt x=180-y[/tex]
[tex]\tt x=180-128[/tex]
[tex]\tt x=52^o[/tex]
Therefore, x = 52° and y = 128°
_________________
Hope this helps you!
Have a nice day! :)
What could be the right answer for this question? with explanation pls. :))
Answer:
x ≤ -5
Step-by-step explanation:
Treat this EXACTLY like you would an equation:
-3(x+4) ≥ x+8
-3x - 12 ≥ x + 8
-4x - 12 ≥ 8
-4x ≥ 20
Except here (when dividing BOTH sides by a negative):
-4x ≥ 20 ⇒ x ≤ -5
w + 2 + 2(w + 3)
HELP FASTTTT
Answer:
Step-by-step explanation:
=w + 2 + 2w + 6
= 3w + 8
3w = -8
w =-8/3
unlike the coefficient of determination, the sample correlation coefficient in a simple linear regression . multiple choice can be greater than 1 measures the percentage of variation explained by the regression line indicates whether the slope of the regression line is positive or negative is a proportion
the regression line indicates whether the slope of the regression line is positive or negative is a proportion will be between 0 to 1
Regression is a statistical method that links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether variations in the dependent variable are related to variations in one or more of the explanatory variables.
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16. if alexa's car can typically travel 300 miles on a full tank of gasoline, and if her car's tank can hold 18 gallons, then at this rate how far should the car be able to travel on 12 gallons of gasoline?
The distance covered by the car with 12 gallons of gasoline is 200 miles.
Given,
Distance travelled by a car with full tank gasoline = 300 miles
The capacity of the car's tank = 18 gallons
We have to find the distance covered by the car with 12 gallons of gasoline;
Here,
x be the distance covered by the car with 12 gallons of gasoline
Then,
300/18 = x/12
x = (300 x 12) / 18
x = (300 x 2) / 3
x = 100 x 2
x = 200 miles
That is,
The car will cover 200 miles with 12 gallons of gasoline.
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Ue the right triangle and the given information to olve the triangle. A = 3; b = 64\deg ; find b, c, and a
The value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.
Define the term trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.For the given question-
The length of the side are-
a = 3 units
Angle B = 64°.
Then,
Applying trigonometric properties-
Tan B = b/a
b = a tan B
b = 3 tan 64°
b = 12.47 units
Now,
Sin B = b/c
c = b sin B
c = 12.47 sin 64°
c = 11.21 units.
Thus, the value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.
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The length of a rectangle is two feet greater than twice its width. If the perimeter is 25 feet, find the width which of the following is correct 25=2L+2(2+2W)
Answer:
w=7/2=3.5
Step-by-step explanation:
width =w
length = l = 2w+2
25=2(l+w)= 2(2w+2+w) =2(3w+2)=6w+4
25=6w+4
6w=21
w= 21/6 = 7/2
onstruct a normal probability plot for the following sample of observations on coating thickness for low-viscosity paint. 0.810.870.901.051.111.141.301.30 1.481.481.591.601.661.691.781.84
A sample observation results in a point estimate of 0.53 for the mean value of paint thickness.
The mean value theorem states that there is one point on a curve where the tangent is parallel to the secant running through the two points.
A low-viscosity paint sample with the following thickness is provided to us.
0.810.870.901.051.111.141.301.301.481.481.591.601.661.691.781.84
a) Point estimate of the mean value of coating thickness.
To estimate the mean coating thickness, we use the mean value of the sample.
mean= sum of all observations/total number of observations
mean=8.16/16
mean=0.53
Question:Construct a normal probability plot for the following sample of observations on coating thickness for low-viscosity paint. 0.810.870.901.051.111.141.301.30 1.481.481.591.601.661.691.781.84 Determine the z percentile associated with each sample observation. (Round your answers to two decimal places.)
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Please I need help on this I don’t get how to do it, show your explanation please and thank you!
Answer:
B/A = 1/2
Step-by-step explanation:
You want the scale factor between the two figures shown.
Scale factorThe scale factor is the ratio of the length in one figure to the corresponding length in the other figure. Often, we're interested in the scale factor B/A, which is what A dimensions need to be multiplied by in order to match the B dimensions.
ApplicationYou can pick any corresponding dimensions. Often, it is convenient to choose a short one, so you don't have to count so many grid squares.
We can choose the line from the center, where the lines cross, up and to the right to the upper right corner. In the A figure, that line goes 2 squares to the right and 2 squares up. In the B figure, that line goes 1 square right and 1 square up. Then the scale factor is ...
(B dimension)/(A dimension) = 1/2
We can choose to look at the lengths of that line (A: 2√2; B: √2), or the x-dimension (A: 2; B: 1) or the y-dimension (A: 2; B: 1). All the measurements are proportional, so we get the same ratio for any pair of corresponding measures.
The scale factor B/A is 1/2.
__
Additional comment
The horizontal magenta lines in the attached figure are another possibility for determining the scale factor. B/A = 2/4 = 1/2.
You need to be careful to understand what scale factor you want. Sometimes it is described as "A to B", which can be ambiguous.
Here, the ratio of an A dimension to a B dimension is A : B = 2 : 1. The same wording can be interpreted to mean "the scale factor that multiplies A to transform it to B." That is the scale factor we have shown.
two websites sell the same type of headphones. website a website b e47.68 16.95 cost of headphones cost of postage including the cost of postage which website is cheaper and by how much? e49.95 14.39
Website B is cheaper then website A.
What are headphones?
A user wears headphones, which are a pair of small loudspeaker drivers, on or near their head over their ears.
They function as electroacoustic transducers, converting an electrical signal into an associated sound.
People can listen to music and carry on conversations at any time and from any location thanks to headphones. It is impossible to overstate how simple it is to use headphones and how much mobility they provide.
There are two types of headphones, website A and website B.
First to find the cost for website A.
Cost of website A = Cost of headphone + cost of postage
= 47.68 + 16.96
Cost of website A = 64.63
Cost of website B = Cost of headphone + cost of postage
= 49.95 + 14.39
Cost of website B = 64.34
The cost of website B is less than the cost of website A.
Hence, website B is cheaper then website A.
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create a table of values and graph the following function rule. you must find at least 4 points in your table/graph. then, determine if the function is linear or non-linear, explaining your reasoning. show your work. y=2x^2-5.
then answer if the function is linear or nonlinear. explain?
please someone answer this ASAP I will give brainlist and 100 points!!!!! please.
The function y = 2x² - 5 is a nonlinear equation and the table of values is
x 0 1 2 3
y -5 -3 5 13
How to determine the category of the equation?From the question, we have the following equation that can be used in our computation:
y = 2x² - 5
As a general rule, a linear equation can take any of the following forms
Slope-intercept form: y = mx + xStandard form: Ax + Bx = CPoint slope form: y - Y = m(x - X)By comparing y = 2x² - 5 to the above forms, we can see that the equation does not take any of the forms represented above
This means that the function is not a linear function
i.e. The function is a nonlinear function
Also, we set x = 0, 1, 2 and 3
So, we have
y = 2(0)² - 5= -5
y = 2(1)² - 5= -3
y = 2(2)² - 5= 5
y = 2(3)² - 5 = 13
So, the table of values is
x 0 1 2 3
y -5 -3 5 13
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a rectangular lot measures 60 feet wide and has an area of 1,200 square yards. what is the depth of the lot?
The depth of the given rectangular lot is 60 yards.
Here, we are given that the area of a rectangular lot is 1,200 square yards.
Further the width of the lot is 60 feet
As the area and the width are given in different units, we first need to convert them into the same units.
Now, 1 foot = 0.33 yards
⇒ 60 feet = 0.33*60 yards
= 20 yards
Further, we know that the area of a rectangle is given by the formula-
area = length × breadth
Thus,
1,200 = 20 × breadth
1,200/20 = breadth
breadth = 60 yards
Thus, we find that the depth of the given rectangular lot is 60 yards.
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1. Marcus is training for a bike race and has biked 25 miles this week. He needs to bike at least
80 miles this week to complete his training. How many miles should Marcus bike on each of the 5
remaining days this week?
Answer: 11 miles each day for the remaining 5 days
Step-by-step explanation:
First, you subtract the miles already done (25) from the total (80) to get 55 (miles left to do) then next divide 55 by 5 (days left), and then your left with 11. Finally, check the work and see how 11x5=55 then 55+25=80.
That's how to get the answer :)
If x = 2, y = -5 and z = -7, then find the value of the following expression. (4x^3-10)/((〖3y〗^2+5)-(〖4x〗^3 (z^2-8))/((y^3+5)))
The value of the mentioned expression is -43.24.
To solve the expression, firstly rewriting the equation followed by keeping the values of x, y and z at their respective places.
Equation = (4x³ - 10)/(3y² + 5) - (4x³ (z² - 8))/(y³ + 5)
Now keeping the values of each variable in the equation
Equation = (4×2³ - 10)/(3×(-5)²) - (4×2³ ((-7)² - 8))/((-5)³ + 5)
Taking cube and square on Right Hand Side of the equation
Equation = (4×8 - 10/(3×15)) - (4×8 (49 - 8))/(25 + 5)
Solving the bracket first where we will perform multiplication on the Right Hand Side
Equation = (32 - 10/45) - ((32 × 41)/30)
Equation = 22/45 - 1312/30
Now performing division on Right Hand Side of the equation
Equation = 0.49 - 43.73
Performing subtraction on Right Hand Side of the equation
Equation = -43.24
Hence, the value is -43.24.
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In recent years, only 79% of the fruit sold at Fred's Fruit stand has been any good. Fred recently started buying fruit from new farmers and wants to know if there is a statistically significant increase in the percentage of good fruit. In a random sample of 475 pieces, 85 were bad.
The conclusion does not change if the significance level went from 7% to 5%.
According to the given situation, 79% of the fruits sold are good and whether there is an increase in the percentage of good fruit is to be tested. If there is no increase in percentage of good fruit, p = 0.79 and if there is an increase in percentage of good fruit, p > 0.79.
The test statistic is given by z = (X - µ)/(σ/√n)
In the given data, µ = 0.79 and σ = √(0.79(1-0.79) = 0.407
In a random sample n = 475 and 85 are bad.
Good fruits = 475 – 85 = 390
X = 390/475 = 0.8211
Hence,
z = (0.8211 – 0.79)/(0.407/√475) = 1.66
From the z-table, p value is 0.9515.
The p value of the test that no increase in percentage of good fruits = 1 – 0.9515 = 0.0485
If the p-value is less than 0.05 it is statistically significant. As 0.0486 is less than 0.05 and 0.07 there is sufficient evidence to conclude that there is a statistically significant increase in the percentage of good fruit. It is true for each significance level. Hence, the change in significance levels does not change the conclusion.
Note: The question is incomplete. The complete question probably is: In recent years, only 79% of the fruit sold at Fred's Fruit stand has been any good. Fred recently started buying fruit from new farmers and wants to know if there is a statistically significant increase in the percentage of good fruit. In a random sample of 475 pieces, 85 were bad. How would the conclusion change if the significance level went from 7% to 5%?
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if f(x)= 5x+7 then what is f(7)
A. 64
B. 42
C. 19
Answer:
f(7)= 42
Step-by-step explanation:
we fill in 7 where x is
f(7)=5(7)+7
f(7)=35+7
f(7)=42
Hopes this helps please mark brainliest