The test static value is 1.44 and its associated p-value is 0.1335.
Given that the problem deals with the concept of test for single proportion. The parameter of the interest is the population proportion of graduates with GPA of 3.00 or below is less than 0.09.
Let the population proportion be p=0.09.
Let the number of graduates in a sample be n=260.
Let the number of students have a GPA of 3.00 or below be x=20.
Based on the known data, the null and alternative hypothesis are,
H₀:p≥0.09
H₁:p<0.09
The sample proportion of students have a GPA of 3.00 or below is,
[tex]\begin{aligned}\hat{p}&=\frac{x}{n}\\ &=\frac{20}{260}\\ &=0.07\end[/tex]
Under the null hypothesis, the test static value is,
[tex]\begin{aligned}z&=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\ &=\frac{0.07-0.09}{\sqrt{\frac{0.09(1-0.09)}{260}}}\\ &=\frac{-0.02}{0.018}\\ &=-1.11\end[/tex]
The p-value for the left-tailed test is
p-value=p(z<-1.11)
p-value=0.1335
Hence, the value of the test statistic and its associated p-value for the proportion of graduates with a GPA of 3.00 or below is less than 0.09. are 1.44 and 0.1335.
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Joe is building a post for his mailbox. To find the correct dimensions, he needs to expand this expression:
Answer:
c.) [tex]x^{3} -16x^{2} +75x-108[/tex]
Step-by-step explanation:
Check the attachment.
What is the smallest sample size that guarantees that the margin of error is less than 1% when constructing a 97% confidence interval for a population proportion
In order to get 97% confidence level, with confidence interval of
+/- 1%, and standard deviation of 0.5 our sample size should be 11,772 samples
A confidence interval for a population mean, when the population standard deviation is known based on the conclusion of the Central Limit Theorem that the sampling distribution of the sample means follow an approximately normal distribution.
Accordingly, the Necessary Sample Size is calculated as follows:
Necessary Sample Size = [tex](Z-score)^{2} . StdDev*(1-StdDev) / (Margin Of Error)^{2}[/tex]
Given:-
At 97% confidence level Z-score = 2.17 Assuming standard deviation = 0.5, margin of error (confidence interval) of +/- 1%.Substituting in the given formula we get
Necessary Sample Size =
= ((2.17)² x 0.5(0.5)) / (0.01)²
= (4.7089x 0.25) / .0001
= 1.177225 / 0.0001
= 11,772.25
Hence in order to get 97% confidence level, with confidence interval of
+/- 1%, and standard deviation of 0.5 our sample size should be 11,772
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A silo is to be built by attaching a hemisphere roof onto a circular cylinder. The hemisphere part of the silo is constructed by a material costing $100 per square foot, and the sides are constructed with a different material costing $75 per square foot. The volume of the silo must be held to 5000 cubic feet. What radius and height, to two decimal places, will minimize the cost of the construction
The radius and height, in two decimal places are mathematically given as
r=10.60
What is the radius and height, in two decimal places?Generally, the equation for the volume is mathematically given as
[tex]V=\pi r^{2} h+\frac{2}{3} \pi r^{3}[/tex]
Therefore
[tex]5000 &=\pi 0^{2} h+\frac{2}{3} \pi r^{3}[/tex]
[tex]V(r, h) &=\pi r^{2} h+\frac{2}{3} \pi r^{3}-5000 \\\nabla V &=\left\langle 2 \pi r h+2 \pi r^{2}, \pi r^{2}\right\rangle \\[/tex]
[tex]\cos t &=100\left(2 \pi r^{2}\right)+75(2 \pi r h) \\\\\cos t &=200 \pi r^{2}+150 \pi r h \\\\\nabla C(r, h) &=\langle 400 \pi r+150 \pi h, 150 \pi r\rangle[/tex]
Using Lagrange method
[tex]$\langle 400 \pi \gamma+150 \pi \gamma h, 150 \pi \gamma\rangle=\lambda\left\langle 2 \pi \gamma h+2 \pi \gamma^{2}, \pi r^{2}\right\rangle$[/tex]
[tex]$400 \pi r+150 \pi r=\left(2 \pi r h+2 \pi r^{2}\right) \lambda$[/tex]
[tex]$400 \pi \gamma+150 \pi h=300 \pi h+300 \pi r \\\\[/tex]
[tex]$400 \pi r-300 \pi r=150 \pi h$[/tex]
[tex]$160 \pi r=150 \pi h \quad \\\\\\[/tex]
with
[tex]h=\frac{2}{3} r $[/tex]
[tex]$\pi r^{2} h+\frac{2}{3} \pi r^{3}=5000$[/tex]
[tex]\pi r}\left(\frac{2}{3} r \right)+\frac{2}{3} \pi^{3}=5000$[/tex]
[tex]$\frac{4 \pi \gamma^{3}}{3}=5000 \quad[/tex]
[tex]r^{3}=\left(\frac{5000 \times 3}{4 \pi}\right)$[/tex]
r=10.60
In conclusion, the radius and height, in two decimal places is
r=10.60
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12 A pilot needs to know the maximum height an aircraft can fly at. The cabin has been tested and is safe to a height of 15679 m. Round this height appropriately: a) to a whole number of kilometres b) to a whole 100 m.please help me
Manuel is blowing up balloons for a party at his house .he blows up 30 balloons in 10 minutes.how many balloons does he blow up in one minute ?
Answer:
it is 3 i think
Step-by-step explanatplease mark brainlest
can someone help me solve this
Answer:
Step-by-step explanation:
Answer:
26.9 ft
Step-by-step explanation:
So this answer is going to require one of the trigonometric functions, which is the ratio of sides of a triangle. So I attached a diagram to my answer, which is depicting the given information and hopefully this should be able to help a bit.
Anyways, we know the hypotenuse, an angle, and the opposite side of the angle. There is a trigonometric function which is defined as: [tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]. We can use the sine function to solve for the opposite side. So let's plug in known values into this equation:
Known Values: theta=85 degrees, hypotenuse = 27 ft
[tex]sin(85)=\frac{opposite}{27 ft}[/tex]
Multiply both sides by 27 ft]
[tex]sin(85)*27ft=opposite[/tex]
Now you can approximate the value of sin(85) using your calculator, and make sure it's in degree mode not radian mode.
[tex]0.996194698*27ft\approx opposite[/tex]
Simplify
[tex]26.8973 ft\approx opposite[/tex]
Rounding this to one decimal place makes it
[tex]26.9 ft\approx opposite[/tex]
NEED HELP RN LIKE ASAPP PLEASE!!
Answer:
Step-by-step explanation:
To answer this, you also need to click the transversal pic above.
67. Extensions
Find the equation of the line that passes through the following points: (a, 0) and (c, d)
Answer:
Equation of a line passing through two point (a, 0) and (c, d) is given by [tex]$y=\frac{d}{c-a} x-\frac{a d}{c-a}$[/tex].
Step-by-step explanation:
In the question, it is given that a line passes through (a, 0) and (c, d).
It is asked to write the equation of line.
To do so, first find the values which are given in the question and put it in the formula of the equation of line passing through two points.
Step 1 of 2
Passing point of the line is (a, 0).
Hence, [tex]$x_{1}=a$[/tex] and
[tex]$$y_{1}=0 \text {. }$$[/tex]
Also, Passing point of the line is (c, d).
Hence, [tex]$x_{2}=c$[/tex] and
[tex]$$y_{2}=d \text {. }$$[/tex]
Step 2 of 2
Substitute the above values in the formula of equation of line passing through two point given by [tex]$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left(x-x_{1}\right)$[/tex].
[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left(x-x_{1}\right)$$\\ $y-0=\frac{d-0}{c-a}(x-a)$\begin{aligned}&y=\frac{d}{c-a}(x-a) \\&y=\frac{d}{c-a} x-\frac{d a}{c-a}\end{aligned}$$[/tex]
Hence, [tex]$y=\frac{d}{c-a} x-\frac{d a}{c-a}$[/tex].
Find the slope of the line that passes through the pair of points listed below.
(4,5) , (6,2)
Answer:
-3/2
Step-by-step explanation:
gradient= y2-y1 over x2-x1
2-5 over 6-4
which equals to -3 over 2
Answer:
-3/2.
Step-by-step explanation:
Slope of a line joining the points (x1, y1) and (x2, y2) is:
(y2 - y1) / (x2 - x1) so here we have
Slope = (2 - 5)/(6 - 4)
= -3/2
III- Hallar el módulo del vector
a (2,6)
[tex]\sqrt{2^{2}+6^{2}}=\sqrt{4+36}=\sqrt{40}=\boxed{2\sqrt{10}}[/tex]
Mixed Practice
In the following exercises, solve.
358. The length of one leg of a right triangle is three more than the other leg. If the hypotenuse is 15, find the lengths of the two legs.
Answer:
9 units and 12 units to nearest hundredth.
Step-by-step explanation:
Let one leg be x units long then the other = x+3 units.
By Pythagoras:
x^2 + (x+3)^2 = 15^2 = 225
2x^2 + 6x + 9 = 225
2x^2 + 6x - 216 =0
x^2 + 3x - 108 = 0
(x - 9)(x + 12) = 0
x = 9
So the other 2 legs are 9 and 12.
What is the probability that the manufacturing unit has carbon emission beyond the permissible emission level and the test predicts this?
The probability that the manufacturing unit has carbon emissions beyond the permissible emission level is 0.2975
Given that the probability that carbon emissions from the company’s factory exceed the permissible level is 35% and the accuracy of the test is 85%.
The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.
Event A: The given Carbon emission beyond to the given permissible emission level.
Event B: Test predicts this.
To get the probability of this problem, first we need to divide by 100 the given values.
A=35/100
A=0.35
The probability of event A is P(A)=0.35
And the probability is P(B|A)=85/100=0.85
Now, we will use the conditional probability formula, we get
P(B|A)=P(A∩B)/P(A)
0.85=P(A∩B)/0.35
P(A∩B)=0.85×0.35
P(A∩B)=0.2975
Hence, the probability that the manufacturing unit has carbon emissions beyond the permissible emission level and the test predicts is0.2975.
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find the root of the function f(x)= 1/(1/3)
Answer:
Hello, look at the picture
Nina, Shanti and Belle run a 1000 m race at a constant speed. When Nina crossed the inish line irst,
she was 200 m ahead of Shanti and 400 m ahead of Belle. When Shanti crossed the inish line, how far
ahead of Belle was she?
When Shanti had crossed the finish line, she was a distance of 250 m ahead of Belle
How to calculate Constant Speed?We are given;
Length of Race = 1000 m
When nina crossed the finish line, she was 200 m ahead of Shanti and 400 m ahead of Belle.
Thus;
Shanti had run 4/5 of the race when Nina finished.
So, if Nina's time was x, then by variation, we can say that;
Time it took Shanti to finish the race = 5/4x
So, Belle had run 5/4 * 600 = 750 meters when Shanti finished.
Thus, means Shanti was; 1000 - 750 = 250m ahead of Belle.
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Which exponential function is represented by the table
Answer:
for x = 0 ; we have f(x) = 0,5
We can eliminate the first and the last proposal because
f(x) = 0,2(0,5ˣ) ⇒ f(0) = 0,2(0,5⁰) = 0,2 × 1 = 0,2 ≠ 0,5
f(x) = 0,2(0,2ˣ) ⇒ f(0) = 0,2(0,2⁰) = 0,2 × 1 = 0,2 ≠ 0,5
Try for x = 1, we have f(x) = 0,1
f(x) = 0,5(5ˣ) ⇒ f(1) = 0,5 × 5 = 2,5 ≠ 0,1
f(x) = 0,2(0,5ˣ) ⇒ f(1) = 0,2(0,5) = 0,1 ⇒ ok
So the answer is f(x) = 0,2(0,5ˣ)
Diego inicia un viaje por carretera de 12 horas con la batería de su teléfono al 75%. Dado su uso normal, ¿su teléfono durará todo el viaje?
Based on Diego's normal usage of his phone, if the battery is at 75%, the phone will not last the whole trip.
How long will the phone battery last?First find out how long each percentage of battery life lasts:
= 15 / 100
= 0.15 hours
If Diego is going on a 12 hour trip with 75%, the length of time it would last is:
= 0.15 x 75
= 11.25 hours
This is less than the 12 hours required so the phone will not last the whole trip.
Rest of question:
At 100%, the battery can go for 15 hours.
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The following diagram shows a semicircle ABC with centre O and a right-angled triangle ACD.
Given the radius is 3.5 cm, calculate the perimeter, in cm, of the whole diagram.
A 36 B 60 C 67 D 72
Answer:
Since the radius is 3.5, to figure out the length on the diameter/side of the triangle, we have to multiply it by 2:
3.5 x 2 = 7
Now we can use the Pythagorean theorem to figure out the length of the other side of the triangle.
a^2 + b^2 = c^2
7^2 + b^2 = 25^2
49 + b^2 = 625
b^2 = 576
b = 24cm
Now that we have all the lengths of the triangle, using the radius, we can calculate the arc of the semi circle using the following formula:
(π + 2)r
(π + 2)3.5
3.5π + 7 = 18cm
Now we can add all of the lengths excluding the diameter of the circle since we want to calculate the perimeter:
25 + 24 + 18 = 67cm
Therefore, the correct answer would be C.
what function is graphed?
The answer is B.
the graph of x²+2 (quadratic) has domain values less than 1 because the circle in the graph is an open circle
The graph of -x+2 (linear) has domain values greater than or equal to 1 because the circle in the graph is a closed circle
Hope it helps!
3. It snowed 80 inches over 10 days. What is the rate? What about the unit rate?
Find the area of the shaded region. (Object is not drawn to scale.) GEOMETRY PLS HELPPPP
Answer:
101.5 cm
Step-by-step explanation:
You find the area of the rectangle and then the area of the triangle. Then, you subtract the area of the rectangle and the area of triangle.
A manager measured the number of goods, y, that his company produced in x hours. The company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45 goods.
Which equation, in point-slope form, correctly represents the goods produced by the company after x hours?
The equation, in point-slope form is (y - 45) = 5(x - 9) option first is correct.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
A manager measured the number of goods, y, that his company produced in x hours.
The slope:
m = 5
From the problem:
The point (9, 45) will satisfy the line.
(y - 45) = 5(x - 9)
Thus, the equation, in point-slope form is (y - 45) = 5(x - 9) option first is correct.
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Sherry Lebito bought 500 shares of stock at a quoted price of 83 1/4 What was the total purchase price?
$
A year later Sherry sold her stock at a quoted price of 95 1/2.
(b) Did she have a capital gain or a capital loss?
(c) How much of a gain or loss did she experience?
$
The total purchase price is $41,625.00
Capital gain was recorded
The capital gain is $41,625.00
What is total initial initial investment?
Was a capital gain or loss made?
What is the dollar value of gain or loss recorded?
Cost per share=$83.25(note 1/4=0.25)
Total purchase price=purchase price per share*number of shares
Total purchase price=$83.25*500
Total purchase price=$41,625.00
The fact that the price at which Sherry sold the stocks a year later is more than the initial purchase price of $83.25, means that a capital gain was recorded, in other words, she bought low and sold high.
The capital gain can be computed as the total selling price(selling price per stock multiplied by the number of shares sold) minus the total purchase price.
total selling price=$95.50(i.e. 1/2=0.500
total selling price=$95.50*500
total selling price=$47,750.00
capital gain=$47,750.00-$41,625.00
capital gain=$6,125.00
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Time to paint the living room. The room measures 20 feet wide by 30 feet long by 12
feet high. There are two doors, 7 feet high by 3 feet wide, and four windows, each 4 feet
high by 3 feet wide. I'm going to paint the walls and ceiling with two coats of paint at 25
cents per square foot. What will it cost?
The cost to paint the walls and the ceiling is $855
How much will it cost?First, we need to find the area that will be painted.
The area of two of the walls is:
A = 20ft*12ft = 240ft²
The area of the other two walls:
A' = 30ft*12ft = 360ft²
The area of the ceiling is:
A'' = 20ft*30ft = 600ft²
We also need to subtract the areas of the two doors and the 4 windows.
Each door is 7ft by 3ft, so the area of each door is:
a = 7ft*3ft = 21ft²
Each window is 4ft by 3ft:
a' = 4ft*3ft = 12ft²
Then the total area that will be painted is:
area = 2A + 2A' + A - 2a - 4a'
area = 2*( 240ft²) + 2*(360ft²) + 600ft² - 2*(21ft²) - 4*(12ft²)
area = 1,710 ft²
We know that we need two coats of paint to cover that area, and the cost per square foot of paint is $0.25, then the total cost is:
C = $0.25*2*(1,710) = $855
The cost to paint the walls and the ceiling is $855
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Bob's password consists of a non-negative single-digit number followed by a letter and another non-negative single-digit number (which could be the same as the first one). What is the probability that Bob's password consists of an odd single-digit number followed by a letter and a positive single-digit number
9/20 is the probability that Bob's password consists of an odd single-digit number followed by a letter and a positive single-digit number
It is given that bob's password consists of a non-negative single-digit number followed by a letter and another non-negative single-digit number (which could be the same as the first one).
P (odd single digit number ) = ( 5 odd single digits / 10 non-negative single digits) = (5/10) = 1/2
P (positive single digit number ) = (9 positive single digits / 10 non-negative single digits) = 9/10
The total probability is (1/2) (9/10) = 9/20
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HELP PLEASE ILL GIVE THE BRAINLIEST TO THE FIRST PERSON WHO ANSWERS <3
factor completely.
25d^8−80d^4+64=
Answer:
[tex](5d^4-8)^2[/tex]
Step-by-step explanation:
[tex]\textsf{Let }\:u=d^4[/tex]
[tex]\implies 25d^8-80d^4+64=25u^2-80u+64[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex] :
[tex]\implies ac=25 \cdot 64=1600[/tex]
[tex]\implies b=-80[/tex]
Two numbers that multiply to 1600 and sum to -80 are:
-40 and -40
Rewrite b as the sum of these two numbers:
[tex]\implies 25u^2-40u-40u+64[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 5u(5u-8)-8(5u-8)[/tex]
Factor out the common term (5u - 8):
[tex]\implies (5u-8)(5u-8)[/tex]
Simplify:
[tex]\implies (5u-8)^2[/tex]
Substitute back [tex]u=d^4[/tex]
[tex]\implies (5d^4-8)^2[/tex]
Therefore:
[tex]25d^8-80d^4+64=(5d^4-8)^2[/tex]
Let's see
25d⁴-80d⁴+645²(d⁴)²-2(5)(d⁴)(8)+8²(5d⁴)²-(2)(5d⁴)(8)+8²(5d⁴-8)²Used formula
(a+b)²={a²+2ab+b²)Sprinter #1 is running at a speed of 96 inches/second. Sprinter #2 is running at a speed of 475
feet/minute. Who will win the race? Give reason for your answer.
Answer:
Sprinter #1
Step-by-step explanation:
Sprinter #1 is running at 96/12 feet per second: 8 feet per second
Sprinter #2 is running at 475/60 feet per second: approximately 7.9 feet per second
Sprinter #1 covers more distance per second.
8. What is the domain of [tex]\frac{x}{x^{2} +20x+75}[/tex] ? Hint: try factoring the polynomial.
9. What is the domain and range of [tex]\sqrt{13x-7}+1[/tex] ?
Please hurry! I really need help with this!
Answer:
8. Domain: (-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)
9. Domain: [7/13, ∞)
Range: [1, ∞)
Step-by-step explanation:
Question 8
Given rational function:
[tex]f(x)=\dfrac{x}{x^2+20x+75}[/tex]
Factor the denominator of the given rational function:
[tex]\implies x^2+20x+75[/tex]
[tex]\implies x^2+5x+15x+75[/tex]
[tex]\implies x(x+5)+15(x+5)[/tex]
[tex]\implies (x+15)(x+5)[/tex]
Therefore:
[tex]f(x)=\dfrac{x}{(x+15)(x+5)}[/tex]
Asymptote: a line that the curve gets infinitely close to, but never touches.
The function is undefined when the denominator equals zero:
[tex]x+15=0 \implies x=-15[/tex]
[tex]x+5=0 \implies x=-5[/tex]
Therefore, there are vertical asymptotes at x = -15 and x = -5.
Domain: set of all possible input values (x-values)
Therefore, the domain of the given rational function is:
(-∞, -15) ∪ (-15, -5) ∪ (-5, ∞)
---------------------------------------------------------------------------------
Question 9
Given function:
[tex]f(x)=\sqrt{13x-7}+1[/tex]
Domain: set of all possible input values (x-values)
As the square root of a negative number is undefined:
[tex]\implies 13x-7\geq 0[/tex]
[tex]\implies 13x\geq 7[/tex]
[tex]\implies x\geq \dfrac{7}{13}[/tex]
Therefore, the domain of the given function is:
[tex]\left[\dfrac{7}{13},\infty\right)[/tex]
Range: set of all possible output values (y-values)
[tex]\textsf{As }\:\sqrt{13x-7}\geq 0[/tex]
[tex]\implies \sqrt{13x-7}+1\geq 1[/tex]
Therefore, the range of the given function is:
[1, ∞)
Giving 100 points.
Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.
Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions.
1. Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that x represents the number of $1 increases in the cost of the buffet.
2. To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create an inequality in standard form that represents the restaurant owner’s desired revenue.
3. Which possible buffet prices could Noah could charge and still maintain the restaurant owner’s revenue requirements?
Answer:
1. Cost per customer: 10 + x
Average number of customers: 16 - 2x
[tex]\textsf{2.} \quad -2x^2-4x+160\geq 130[/tex]
3. $10, $11, $12 and $13
Step-by-step explanation:
Given information:
$10 = cost of buffet per customer16 customers choose the buffet per hourEvery $1 increase in the cost of the buffet = loss of 2 customers per hour$130 = minimum revenue needed per hourLet x = the number of $1 increases in the cost of the buffet
Part 1
Cost per customer: 10 + x
Average number of customers: 16 - 2x
Part 2
The cost per customer multiplied by the number of customers needs to be at least $130. Therefore, we can use the expressions found in part 1 to write the inequality:
[tex](10 + x)(16 - 2x)\geq 130[/tex]
[tex]\implies 160-20x+16x-2x^2\geq 130[/tex]
[tex]\implies -2x^2-4x+160\geq 130[/tex]
Part 3
To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:
[tex]\implies -2x^2-4x+160\geq 130[/tex]
[tex]\implies -2x^2-4x+30\geq 0[/tex]
[tex]\implies -2(x^2+2x-15)\geq 0[/tex]
[tex]\implies x^2+2x-15\leq 0[/tex]
[tex]\implies (x-3)(x+5)\leq 0[/tex]
Find the roots by equating to zero:
[tex]\implies (x-3)(x+5)=0[/tex]
[tex]x-3=0 \implies x=3[/tex]
[tex]x+5=0 \implies x=-5[/tex]
Therefore, the roots are x = 3 and x = -5.
Test the roots by choosing a value between the roots and substituting it into the original inequality:
[tex]\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144[/tex]
As 144 ≥ 130, the solution to the inequality is between the roots:
-5 ≤ x ≤ 3
To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.
[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an increase in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers increases per hour.]
Cost per customer:
[tex]x =0 \implies 10 + 0=\$10[/tex]
[tex]x=3 \implies 10+3=\$13[/tex]
Therefore, the possible buffet prices Noah could charge are:
$10, $11, $12 and $13.
Can someone pls help me out on these geometry questions? Just fill in the blanks, ASAP pls
Question 5
1) Given
2) Definition of congruent segments
3) Reflexive property of equality
4) Addition property of equality
5) Substitution
6) Commutative property of addition
7) Segment addition postulate
8) Substitution
9) Segments with equal measure are congruent
Question 6
1) Given
3) Segment addition postulate
4) Substitution
5) Subtraction property of equality
7) SSS
Write the property that best matches the following
The property that best matches the equation is the associative property.
What is an associatve property?It should be noted that the associative property simply implies that the way the factors are grouped in a multiplication problem doesn't change the product.
In this case, since it's illustrated that (5 × 3) × 2 = (2 × 3) × 5. They both will give a value of 40.
In this case, the associative property is illustrated.
The complete question is:
Write the property that best matches the following: (5 × 3) × 2 = (2 × 3) × 5.
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