Answer:
The price p could be any of $8 or $15 .
Step-by-step explanation:
The equation is a relationship between the numbers of pencil sharpener x can sell each week and the price of each sharpener p.
x = 2300 - 100p
xp = 12000
therefore,
x = 12000/p
insert the value of x in the equation
x = 2300 - 100p
12000/p = 2300 - 100p
12000/p + 100p - 2300 = 0
multiply through by p
12000 + 100p² - 2300p = 0
100p² - 2300p + 12000 = 0
divide through by 100
p² - 23 + 120 = 0
Find the number that we can multiply to give 120 and add to give - 23. The number are -15 and - 8.
p² - 8p - 15p + 120 = 0
p(p - 8) - 15(p - 8) = 0
(p - 8)(p - 15)
p = 8 or 15
x = 2300 - 100p
x = 2300 - 100(8)
x = 2300 - 800
x = 1500 pencil sharpener sold
or
x = 2300 - 100(15)
x = 2300 - 1500
x = 800 pencil sharpener sold
The price could be any of $8 or $15 .
What does the “equity” of a tax mean?
Answer:
Equity of taxation means each citizen pays an amount of tax equal to their income and ability to pay the tax.
Answer:
C) The tax is paid equally by everyone
Step-by-step explanation:
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
The correct answer would be A
(I am not guessing I had the same quiz before)
This Question: 4 pts
1 of 11 (0 complete)
Music Preferences
Students at a high school were polled to determine the type of music they preferred. There were 1960 students who
completed the poll. Their responses are represented in the circle graph.
Rap 916
Alternative 46
Rock and Roll 279
Country 183
Jazz 32
Other 89
About What % of the students who completed the poll preferred rock and roll music.
(Round to one decimal place as needed.)
Answer:
The percentage of the students who completed the poll preferred rock and roll music.
P(RR) = 0.1423 = 14.23 %
Step-by-step explanation:
Explanation:-
Given total number of students n(S) = 1960
Given the Students at a high school were polled to determine the type of music they preferred.
Rap 916
Alternative 46
Rock and Roll 279
Country 183
Jazz 32
Other 89
Let ' RR' be the event of Rock and Roll preferred music
given Rock and Roll = 279
n( RR) = 279
The percentage of the students who completed the poll preferred rock and roll music.
[tex]P(RR) = \frac{n(RR)}{n(s)} = \frac{279}{1960}[/tex]
P(RR) = 0.1423 = 14.23 %
Solve the system of equations.
3x + 3y + 6z = 6
3x + 2y + 4z = 5
7x + 3y + 32 = 7
a. (x = 2, y = -2, z = 0)
b. (x = 3, y=-3, z = 3)
c. (x = 1, y = - 1,2= 1)
d. (x = 0, y = 0, z = 2)
Answer:
The answer is option c
x = 1 y = - 1 z = 1
Hope this helps.
Round 1040 to the nearest hundred.enter your answer in the box below
Answer:
1000
Step-by-step explanation:
For rounding questions, you want to look at the place value to the right of the digit it wants you to round to. If that place value to the right of the digit you need to round is less than 5, you round down. If the place value to the right of the digit you need to round is 5 or greater, then you round up. In your situation, the place value you want to round is the hundreds place, so we need to look at the tens value. The tens value is 4, which is less than 5, so we round down. Therefore, the answer would be 1000.
A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mean 3125 and standard deviation 250. Calculate the approximate 90th percentile for the distribution of the total contributions
Answer:
The 90th percentile for the distribution of the total contributions is $6,342,525.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For sums of size n, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sqrt{n}*\sigma[/tex]
In this question:
[tex]n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250[/tex]
The 90th percentile for the distribution of the total contributions
This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.28 = \frac{X - 6328125}{11250}[/tex]
[tex]X - 6328125 = 1.28*11250[/tex]
[tex]X = 6342525[/tex]
The 90th percentile for the distribution of the total contributions is $6,342,525.
Serena wants to determinethe area of the lawn the grass part of her front yard using the information given in the diagram below Serena knows that she needs to divide by 9 to change the units from square yards so she writes the expression below to determine the area of grass in square yards
Answer:
The answer is 295 square yards.
Step-by-step explanation:
[48(72-12)-15^2] divide by 9
3456-576-225 divide by 9
Subtract 3456 by 576
2880-255
2655 divide by 9
=295 square yards.
Hope this helped!
The answer is 295 square yards.
What is the area of square space?To find the area of square , take the square of side.
Given expression is [48(72-12)-15^2] divide by 9 .
Let the unknown area is x.
x = {48 * 60 - 15^2 } divide by 9
x = 2880 - 225 divide by 9
x = 2655 divide by 9
x =295 square yards.
Hence, The answer is 295 square yards.
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The following data summarizes results from 945 pedestrian deaths that were caused by accidents. If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated.
Pedestrian
intoxicated not intoxicated
Driver intoxicated 64 68
not intoxicated 292 521
Answer:
37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
945 accidents.
In 64 of them, the pedestian was intoxicated.
In 292 of them, the driver was intoxicated.
Probability that the pedestrian was intoxicated or the driver was intoxicated.
(64+292)/945 = 0.3767
37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.
In a lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $350, which is a profit of $349. If you lose, you lose $1. Your probability of winning is 0.001. What is the expected value of your profit
Answer:
The expected value of profit is -$0.65.
Step-by-step explanation:
The rules of the lottery are as follows:
You pay $1 and pick a number from 000 to 999.If your number comes up, you win $350, which is a profit of $349.If you lose, you lose $1.The probability of winning is, P (W) = 0.001.
Then the probability of losing will be,
P (L) = 1 - P (W)
= 1 - 0.001
= 0.999
Let the random variable X represent the amount of profit.
The probability distribution table of the lottery result is as follows:
Result X P (X)
Win +349 0.001
Lose -1 0.999
The formula to compute the expected value of X is:
[tex]E(X)=\sum X\cdot P(X)[/tex]
Compute the expected value of profit as follows:
[tex]E(X)=\sum X\cdot P(X)[/tex]
[tex]=(349\times 0.001)+(-1\times 0.999)\\\\=0.349-0.999\\\\=-0.65[/tex]
Thus, the expected value of profit is -$0.65.
7+2x/3=5 im stuck on this question pls hhelp my homework is due soon pls help
The value of X is 4
please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
(a) Use a linear approximation to estimate f(0.9) and f(1.1). f(0.9) ≈ f(1.1) ≈ (b) Are your estimates in part (a) too large or too small? Explain. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too large. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too small. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too large. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too small.
Answer:
(Missing part of the question is attached)
[tex]L(x)=2x+3[/tex]
Estimates are too large.
Step-by-step explanation:
Suppose the only information we know about the function is:
[tex]f(1)=5[/tex]
where the graph of its derivative is shown in the attachment
(a)If the function [tex]f\\[/tex] is differentiable at point [tex]x=1[/tex] , the tangent line to the graph of [tex]f[/tex] at 1 is given by the equation:
[tex]y=f(1) +f'(1)(x-1)[/tex]
So we call the linear function:
[tex]L(x)=f(1) +f'(1)(x-1)[/tex]
We know the [tex]f(1)=5[/tex] as it is given in the question, and [tex]f'(1)=2[/tex] from the graph attached. Substitute in the equation of [tex]L(x)[/tex].
[tex]L(x)=5+2(x-1)\\L(x)=5+2x-2\\L(x)=2x+3\\[/tex]
(b)At x=1, [tex]f'(x)[/tex] is positive but it is decreasing. However. if we draw the tangent lines, we see that the tangent lines are becoming less steeper, so the tangent lines lie above the curve [tex]f[/tex]. Thus, The estimates are too large.
Please help!!! Which of the following is equal to the rational expression when x ≠ -2 or 3? x^2+5x+6/x^2-x-6
Answer:
see below
Step-by-step explanation:
These are always simplified by cancelling common factors from numerator and denominator. In order to do that, you have to factor the expressions. The restrictions on x give a clue as to the factors of the denominator.
[tex]\dfrac{x^2+5x+6}{x^2-x-6}=\dfrac{(x+3)(x+2)}{(x-3)(x+2)}=\boxed{\dfrac{x+3}{x-3}}[/tex]
The best possible statement to your question is x+3 / x-3
Find the area of a circle with radius, r = 19cm.
Give your answer rounded to 3 SF.
math question is attached below
and show your work
Answer:
[tex]V = \frac13 \pi r^2 h[/tex]
117.81
Step-by-step explanation:
r is half the diameter so 2.5 cm
h is 18
fill in and get:
V = [tex]\frac13 \pi \cdot 6.25 \cdot 18 \approx 117.81 cm^3[/tex]
"A 12-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 33 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 55 feet from the wall?"
Answer:
Step-by-step explanation:
The question has typographical errors. The correct question is:
"A 12-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the wall?
Solution:
The ladder forms a right angle triangle with the ground. The length of the ladder represents the hypotenuse.
Let x represent the distance from the top of the ladder to the ground(opposite side)
Let y represent the distance from the foot of the ladder to the base of the wall(adjacent side)
The bottom of the ladder is sliding along the pavement directly away from the building at 3ft/sec. This means that y is increasing at the rate of 3ft/sec. Therefore,
dy/dt = 3 ft/s
The rate at which x is reducing would be
dx/dt
Applying Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side², it becomes
x² + y² = 12²- - - - - - - -1
Differentiating with respect to time, it becomes
2xdx/dt + 2ydy/dt = 0
2xdx/dt = - 2ydy/dt
Dividing through by 2x, it becomes
dx/dt = - y/x ×dy/dt- - - - - - - - - - 2
Substituting y = 5 into equation 1, it becomes
x² + 5 = 144
x² = 144 - 25 = 119
x = √119 = 10.91
Substituting x = 10.91, dy/dt = 3 and y = 5 into equation 2, it becomes
dx/dt = - 5/10.91 × 3
dx/dt = - 1.37 ft/s
On Sunday, a local hamburger shop sold a combined of 572 hamburger and cheeseburger. The number of cheeseburgers sold was three times the number of hamburger sold. How many hamburger were sold on Sunday
The freezer contains vanilla and chocolate ice cream. Chocolate ice cream contains 12 servings less than vanilla. How many servings of vanilla ice cream are in the freezer if there are a total of 40 servings of ice cream? (Solve by building an equation)
Answer:
26 servings
Step-by-step explanation:
Let the number of servings of vanilla ice cream be x.
Number of servings of chocolate ice cream
= x -12
(since it has 12 servings less than vanilla)
Total servings= servings of chocolate+ vanilla
x + x-12= 40
2x -12 =40 (simplify)
2x= 40 +12 (+12 on both sides)
2x= 52 (simplify)
x= 52 ÷2
x= 26
Therefore, there are 26 servings of vanilla ice cream in the freezer.
divide 41000 into two parts such that their amounts at 50% compound interest compounded annually in 2 and 3 years are equal
Answer:24600 , 16400
Step-by-step explanation:
Let the first part be x
So, second part will be 41000 - x
For amount x
SI = prt / 100
SI = x * 0.50 * 2
SI = 1x
For amount 41000 - x
SI = (41000-x) * 0.50 * 3
SI = 61500 - 1.5x
1x = 61500 - 1.5x
1.5x + x = 61500
2.5x = 61500
x = 61500 / 2.50 = 24600 for 2 years
2nd part = 41000 - 24600 = 16400 for three years
I need help please help me
Answer:
Option 2
Step-by-step explanation:
Cost of book= 6.50
Shipping= 4.99
Total= 82.99
Equation:
6.50x+4.99= 82.99
Option 2 is correct
3/5 of a juice drink is made of real juice. What percent of the drink is
real juice?
Answer:
60%
Step-by-step explanation:
Percent means out of 100
Changing 3/5 to a denominator of 100
3/5*20/20
60/100
The percent is 60 %
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
D. F(x) = 2(x-3)^2 + 3
Step-by-step explanation:
We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)
We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.
The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.
Our two equations left are:
B. F(x) = 2(x+3)^2 + 3
D. F(x) = 2(x-3)^2 + 3
Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.
y = 2(3+3)^2 + 3 =
2(6)^2 + 3 =
2·36 + 3 =
72 + 3 =
75
That one didn't give us a y value of 3.
y = 2(3-3)^2 + 3 =
2(0)^2 + 3 =
2·0 + 3 =
0 + 3 =
3
This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:
D. F(x) = 2(x-3)^2 + 3
Hopefully this helps you to understand parabolas better.
A box on a 20 degree incline is shown with vectors radiating from a point in the center of the box. The first vector points up and parallel to the surface of the incline, labeled F Subscript f s Baseline. A second vector points toward the center of the earth, labeled F Subscript g Baseline = 735 N. A third vector is perpendicular to and away from the surface of the incline from the point, labeled F Subscript N Baseline. A fourth vector is broken into 2 components, one parallel to the surface and down the incline, labeled F Subscript g x Baseline, and one perpendicular to the surface and into the surface, labeled F Subscript g y Baseline.
A box at rest on a ramp is in equilibrium, as shown.
What is the force of static friction acting on the box? Round your answer to the nearest whole number. N
What is the normal force acting on the box? Round your answer to the nearest whole number.
The images to solve this problem is in the attachment.
Answer: [tex]F_{fs}[/tex] = 671.0 N; [tex]F_{N}[/tex] = 300 N
Step-by-step explanation: From the image in the attachment and knowing that the box is in equilibrium, i.e., the "sum" of all the forces is 0, it is possible to conclude that:
[tex]F_{fs}[/tex] = [tex]F_{gx}[/tex] and [tex]F_{N}[/tex] = [tex]F_{gy}[/tex]
Using trigonometry, shown in the second attachment, the values for each force are:
Force of Static Frictionsin 20° = [tex]\frac{F_{gx} }{F_{g} }[/tex]
[tex]F_{gx}[/tex] = [tex]F_{g}[/tex]. sin(20)
[tex]F_{gx}[/tex] = 735.0.913
[tex]F_{gx}[/tex] = 671.0
Normal Forcecos 20° = [tex]\frac{F_{gy} }{F_{g} }[/tex]
[tex]F_{gy}[/tex] = [tex]F_{g}[/tex]. cos (20)
[tex]F_{gy}[/tex] = 735.0.408
[tex]F_{gy}[/tex] = 300
The force of static friction is 671N and normal force is 300N
Answer:
Static force is 251 and the Normal force is 691.
Step-by-step explanation:
Hope this helps!! Have a great day!! :)
Suppose you
earn $10.30 per hour and work 24 eight-hour
days in a month. How much do you earn in that month?
Answer:1977.60
Step-by-step explanation:
24x8= 192
192x 10.30= 1977.60
A supervisor records the repair cost for 14 randomly selected refrigerators. A sample mean of $79.20 and standard deviation of $10.41 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
( $74.623, $83.777)
The 90% confidence interval is = ( $74.623, $83.777)
Critical value at 90% confidence = 1.645
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $79.20
Standard deviation r = $10.41
Number of samples n = 14
Confidence interval = 90%
Using the z table;
The critical value that should be used in constructing the confidence interval.
z(α=0.05) = 1.645
Critical value at 90% confidence z = 1.645
Substituting the values we have;
$79.20+/-1.645($10.42/√14)
$79.20+/-1.645($2.782189528308)
$79.20+/-$4.576701774067
$79.20+/-$4.577
( $74.623, $83.777)
The 90% confidence interval is = ( $74.623, $83.777)
Graph the line y=-2x+5
Hope this helps!! :)
Solve the problem. When going more than 38 miles per hour, the gas mileage of a certain car fits the model where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what speed will the car average 15 miles per gallon? (Round to nearest whole number.)
Answer:
73 mph
Step-by-step explanation:
The question seems to be incomplete because the model is missing, I found a similar question with the addition of the model, so if we can solve it (see attached image).
We have that the model would be:
y = 43.81 - 0.395 * x
We need to solve for x, if y = 15
Replacing:
15 = 43.81 - 0.395 * x
Solving for x we have:
0.395 * x = 43.81 - 15
0.395 * x = 28.81
x = 28.81 / 0.395
x = 72.9
We are asked to round to the nearest number therefore x = 73.
The car will average 15 miles per gallon at the speed of 73 miles per hour.
Alguien me puede ayudar con esto por favor!!!!
Answer:
8 + 15i
Step-by-step explanation:
(-2 + 3i) + 2(5 + 6i) =
= -2 + 3i + 10 + 12i
= 8 + 15i
Louis had 19 dogs. He feeds them with 38 pounds of biscuits. If there are 4 more
dogs, then how much more pounds of biscuit are needed?
Answer:
14
Step-by-step explanation:
Answer:
Which of these factors will affect the friction on a road
Step-by-step explanation:
Twice the length of the rectangle exceeds three times the width of the rectangle by one centimeter and if one-third of the difference of the length and the width is one centimeter.find the dimension.
The dimensions of the rectangle are given as 4cm and 1cm respectively.
What is a rectangle?A rectangle is a type of parallelogram having equal diagonals.
All the interior angles of a rectangle are equal to the right angle.
The diagonals of a rectangle do not bisect each other.
Suppose the length of rectangle be x.
And, the width be y.
Then, the following equations can be written as per the information given as,
2x - 3y = 1 (1)
And, 1/3(x - y) = 1
⇒ x - y = 3 (2)
Multiply equation (2) by 2 and subtract from (1) to get,
2x - 3y - 2(x - y) = 1 - 2 × 3
⇒ -5y = -5
⇒ y = 1
Substitute y = 1 in equation (2) to get,
x - 1 = 3
⇒ x = 4
Hence, the dimensions are 4cm and 1cm respectively.
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What is the value of y ??????????????
Answer & Step-by-step explanation:
For this problem we can just set up an equation and equal it to 180.
(2y) + (y + 10) + 50 = 180
Combine like terms.
3y + 60 = 180
Subtract 60 from 180.
3y = 120
Divide 120 by 3.
y = 40
So, the value of y is 40°