Cop
16
7. A company finds that if it charges x dollars for a cell phone, it can expect to sell
1,000-2x phones. The company uses the function r defined by
r(x) = x (1,000 - 2x) to model the expected revenue, in dollars, from selling cell
phones at x dollars each.
rain
26.361
a. Use graphing technology to graph the function r. Sketch the graph here and
show the coordinates of the vertex and any intercepts.
150,000
nit of
revenue (dollars)
*S
125,000
WERE
100,000
75,000
50,000
25,000
dhizib sri
b. What do the x-intercepts mean in this situation?
3
100 200 300 400 500
price per phone (dollars)
trative
IM Mathematics
600
16x3
c. Is 0 ≤ x ≤ 600 an appropriate domain for the function r? Explain your
reasoning.
d. At what price should the company sell their phones to get the maximum
revenue? Explain your reasoning.
The price at which the company should sell its phones to get the maximum revenue is $250
What is Maximum Revenue?Attaining peak yields is the preeminent rate of profits that a commerce or congregation can accumulate from its action, products, or amenities within a determined span.
It is where the firm or collective is accruing the most money achievable, harnessing its present facilities, marketplace appeal, pricing methods, along with other specifics.
In order to attain maximum revenue, an enterprise must focus on refining its sales and networking campaigns, developing its wares or services, determining and honing in on precise shoppers, and optimizing its expenses as well as costs efficaciously.
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Given the polynomial 2x3 − 5x2 + 6x − 15, rewrite the polynomial as a product of binomials. a. (x2 + 3)(2x − 5) b. (x2 + 3)(2x + 5) c. (x2 − 3)(2x − 5)
d. (x2 − 3)(2x + 5)
The polynomial 2x³ − 5x² + 6x − 15 as a product of binomials is option (a) (x² + 3)(2x − 5).
To factor the polynomial 2x³ − 5x² + 6x − 15 into a product of binomials, we can use the technique of polynomial factorization by grouping.
Factor out the greatest common factor (GCF) from the first two terms and the last two terms separately
2x³ − 5x² + 6x − 15 = x²(2x − 5) + 3(2x − 5)
Notice that we have a common binomial factor of (2x − 5) in both terms. Factor out this common binomial factor
2x³ − 5x² + 6x − 15 = (2x − 5)(x² + 3)
Therefore, the polynomial 2x³ − 5x² + 6x − 15 can be factored as the product of binomials (2x − 5) and (x² + 3).
So, the correct option is (a) (x² + 3)(2x − 5).
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What is the value of x?
sin 25° = cos x°
(a) 50
(b) 155
(c) 75
(d) 25
(e) 65
A baker evenly divides 30 pounds of cookie dough into 7 containers. How many pounds will he put into each container? record the remainder as a fraction
If baker evenly divides "30" pounds of cookie dough in 7 containers, then each container will contain approximately 4.29 pounds.
To find the amount of cookie dough that the baker will put into each container, we divide the total amount of dough by the number of containers.
The total amount of cookie dough is = 30pounds,
The total number of containers is = 7 containers.
Cookie dough in each container is = 30/7 containers = 4.2857... pounds,
≈ 4.29 pounds,
Therefore, the baker will put approximately 4.29 pounds of cookie dough into each of the 7 containers, if he evenly divides 30 pounds of dough among them.
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I need help ASAP or before 3:06
The exponential equation that represents the function is 3x².
What is the equation of the function?The finite difference between two consecutive values of f(x) is given by:
Δf(x) = f(x+1) - f(x)
Δf(-6) = f(-5) - f(-6) = 75 - 108 = -33
Δf(-5) = f(-4) - f(-5) = 48 - 75 = -27
Δf(-4) = f(-3) - f(-4) = 27 - 48 = -21
Δf(-3) = f(-2) - f(-3) = 12 - 27 = -15
The second finite differences are:
Δ²f(-6) = Δf(-5) - Δf(-6) = 6
Δ²f(-5) = Δf(-4) - Δf(-5) = 6
Δ²f(-4) = Δf(-3) - Δf(-4) = 6
Since the second finite differences are constant, the function is a quadratic polynomial of the form;
f(x) = ax² + bx + c
f(-6) = 108 = 36a - 6b + c
f(-5) = 75 = 25a - 5b + c
f(-4) = 48 = 16a - 4b + c
The final equation becomes;
36a - 6b + c = 108 ---- (1)
25a - 5b + c = 75 ------ (2)
16a - 4b + c = 48 -------- (3)
solve the equation, using crammers rule,
a = 3, b = 0, c = 0
f(x) = 3x²
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what are the odds, in a hand of five cards, of getting two matching pairs of one type of card, and three matching pairs of another?
The probability of odds of getting two matching pairs of one type of card, and three matching pairs of another in a hand of five cards are extremely low.
To calculate the odds, we can first calculate the number of ways to get two matching pairs of one type of card, which is (13 choose 2) × (4 choose 2)² since we need to choose 2 ranks out of 13, and then 2 suits out of 4 for each of those ranks. This equals 78,624.
Next, we calculate the number of ways to get three matching pairs of another type of card, which is (11 choose 3) × (4 choose 2)³, since we need to choose 3 ranks out of the remaining 11, and then 2 suits out of 4 for each of those ranks. This equals 15,024. Finally, we multiply the two probabilities to get the overall odds: (78,624 × 15,024) / (52 choose 5) = 0.000016.
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Factor the trinomial and show your work.
x^2 - 10x + 9
Answer:
[tex](x - 9)(x - 1)[/tex]
Step-by-step explanation:
We can factor the trinomial using the rule:
IF [tex]x^2 + cx + d = (x + a)(x + b)[/tex],
THEN [tex]a + b = c[/tex] and [tex]a \cdot b = d[/tex].
We know that -9 and -1 add to -10. They also multiply to 9.
Therefore, we can factor [tex]x^2 - 10x + 9[/tex] as:
[tex]\boxed{(x - 9)(x - 1)}[/tex]
The factors of the given trinomial are (x-9)(x-1).
What is trinomial?Trinomial is a polynomial having 3 terms. At least one variable and one operation (addition, subtraction, multiplication, division) must be present in an algebraic expression.
Given that, a trinomial x² - 10x + 9, we need to find the factors,
So,
x² - 10x + 9
= x² - 9x - x + 9
= x(x-9) -1(x-9)
= (x-9)(x-1)
Hence, the factors of the given trinomial are (x-9)(x-1).
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Instructions 1 Given the following information, answer the questions. Output per worker is 100 K VN The savings rate is 20%. The depreciation rate is 4%. Question 1 1 pts Calculate output per worker il capitale workeris 40.000 0 DO Question 2 1 pts Calculate Investment per werkeri coital per workers O,000. Hint Use your answer to the previous question D Question 3 1 pts Calculate the amount of depreciation or worker cooper workeris 40,000 D Question 4 1 pts Calculate netestit capital or workeris 40.000 Question 5 1 pts Is capital per weer growing, tating or staying the son of capitale workers 40.000 Grow For Site D Question 1 pts Castle capitair wurer D Question 7 1 pts Calculate net investment if capital per worker is 360,000.
The answers based on the given information:
1. Output per worker (Y/L) is given as 100. Capital per worker (K/L) is given as 40,000.
2. Investment per worker (I/L) can be calculated using the savings rate (s). I/L = s * (Y/L). Since the savings rate is 20% (0.20), I/L = 0.20 * 100 = 20.
3. Depreciation per worker can be calculated using the depreciation rate (d) and capital per worker (K/L). Depreciation per worker = d * (K/L). Since the depreciation rate is 4% (0.04), Depreciation per worker = 0.04 * 40,000 = 1,600.
4. Net investment per worker can be calculated by subtracting depreciation per worker from investment per worker. Net investment per worker = (I/L) - Depreciation per worker = 20 - 1,600 = -1,580.
5. Since the net investment per worker is negative, capital per worker is decreasing.
7. If capital per worker is 360,000, net investment can be calculated by multiplying the savings rate by the new output per worker (assuming it stays the same) and then subtracting the depreciation. Net investment = (s * (Y/L)) - (d * 360,000) = (0.20 * 100) - (0.04 * 360,000) = 20 - 14,400 = -14,380.
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Gabriel is younger than Moussa. Their ages are consecutive even integers. Find
Gabriel's age if the product of their ages is 120.
Answer: Gabriel is 10 years old.
Step-by-step explanation:
Let x represent Gabriel's age and x+2 represent Moussa's age.
x(x+2)=120
x^2+2x=120
x^2+2x-120=0
(Factor quadratic equation): (x-10)(x+12)=0
x=10, x=-12 --> (age can't be negative)
Gabriel is 10 years old.
a manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 433 gram setting. it is believed that the machine is underfilling the bags. a 11 bag sample had a mean of 429 grams with a standard deviation of 26 . assume the population is normally distributed. a level of significance of 0.02 will be used. specify the type of hypothesis test.
We used a standard deviation to determine whether the bag filling machine was underfilling the bags at the 433 gram setting that is falls within the range of -2.76 to 2.76
To determine whether we should reject or fail to reject the null hypothesis, we will use a hypothesis test with a level of significance of 0.02.
Plugging in the values from the problem, we get:
t = (429 - 433) / (26 / √11)
t = -1.38
To determine whether we should reject or fail to reject the null hypothesis, we will compare the calculated t-value to the critical t-value from the t-distribution table.
Looking up the critical t-value with 10 degrees of freedom and a level of significance of 0.01, we find a value of ±2.76.
Since our calculated t-value of -1.38 falls within the range of -2.76 to 2.76, we fail to reject the null hypothesis.
This means that there is not enough evidence to conclude that the bag filling machine is underfilling the bags at the 433 gram setting.
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Orange traffic cones come in a variety of sizes. Approximate the volume, in cubic inches, of a traffic cone that has a height of 2 feet and a diameter of 14 inches.
The volume of the orange traffic cones is 102.63 in³ respectively.
What is a cone?A cone is a recognizable three-dimensional geometric shape with a smooth and curving surface that is directed upward in mathematics. The
Greek word "konos," which denotes a peak or a wedge, is the source of the English word "cone."
The apex is the pointy end, while the base is the level area.
So, the cone volume is:
V=πr²h/3
Now, insert values as follows:
V=πr²h/3
V=π7²2/3
V=102.63
Therefore, the volume of the orange traffic cones is 102.63 in³ respectively.
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where is the blue dot on the number line?
Step-by-step explanation:
its -7.4
because each gap means 0.1
Prism P and prism Q are similar.
The ratio of the surface area of prism P to the surface area of prism Q is 1 : 3.
The volume of prism Q is 86
c
m
3
.
Calculate the volume of prism P.
The volume of prism P is calculated as: 16.55 cm³.
What is the volume of the prism?Similar figures are defined as those figures that the same shape, but the sizes are different.
The parameters given are:
- Prism P and prism Q are similar.
- Ratio of the surface area of the prism P to Q = 1 : 3
We also have:
Volume of prism Q = 86 cm³
Scale factor of height of the prism would be square root of surface area of the prism.
Scale factor of volume of the prism would be the cube of the height of the prism.
Let volume of prism P be V(P)
Let the volume of the prism Q be V(Q).
Thus:
V(P) / V(Q) = 1 / (√3)³
V(P) = V(Q) / (√3)³
= 86 / (√3)³
= 16.55 cm³
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Express 9 in simplest radical form
Answer & Explanation
Well when we say “ radical form “ just means putting it in square root
“ [tex]\sqrt{}[/tex] “
Square root of 9 is a whole number since it is not a decimal then it can be multiplied by itself to get the original number. The actual value of square root of 9 is 3. “ √9 = ±3 “
If we square root +3 or -3, the resulting value will be equal to 9. Shown:
[tex](+3)^{2} = 9[/tex]
[tex](-3)^2 = 9[/tex]
Does not matter any order.
A company manufactures water bottles the list below describes the number of water bottles manufactured in three months
.February 4,100 water bottles
. March 7% more water bottles than in February
.April: 500 more water bottles than in march
what is the percent increase to the nearest percent in the number of water bottles the company manufactured from February to April?
Answer:
19%
Step-by-step explanation:
First, find how many water bottles were manufactured in March:
4,100 x 1.07 = 4387
Add 500 to the March number
4387 + 500= 4887
Then divide the April number by February
4887/4100= 1.19195
This means that there is a 19 percent increase of water bottles manufactured from February to April
Alexi's restaurant bill is $58, and he wants to leave a 20 percent tip. Which expression represents the total amount that
Alexi needs to pay?
$58(0.20) + $58
$58(0.20)
$58(20) + $58
$58(20)
Answer:
20/100=0.20
0.20$(58) +$58
option A
what is the measure of angle X
Answer:
The answer for x is 28°
Step-by-step explanation:
x+62=90°
x=90-62
x=28°
Refer to the regular square pyramid shown. 13. B = ? 14. L.A. = ? 15. T.A. = ? 16. V = ?
The total surface area of the pyramid is 1,296 unit².
The lateral surface area (L.A) of the pyramid is 19.21 unit².
The volume of pyramid is 120 unit³.
What is the surface area of the pyramid?The surface area of the pyramid is calculated as follows;
T.S.A = 2bh + b²
where;
b is the base of the triangular faceh is the height of each triangular faceIn then diagram, we where given, base, b = 24 units, height = 15 units, then the surface area of the pyramid is calculated as follows;
T.S.A = 2 x 24 x 15 + 24²
T.S.A = 1,296 unit²
The lateral surface area is calculated as
L.A = √(b²/4 + h²)
L.A = √(24²/4 + 15²)
L.A = 19.21 unit²
The volume of pyramid is calculated as;
V = ¹/₃BH
V = ¹/₃ x 24 x 15
V = 120 unit³
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How to do this teacher didn’t explain well
Refer to the attached images.
Evaluate the following expressions for y= -3 how do I solve this?
To evaluate the expressions 2(y+6)/3 and (4y+64)/(-3) for y=-3, we substituted -3 for y and simplified. The first expression evaluates to 2, and the second evaluates to approximately -17.333.
To evaluate the expressions 2(y+6)/3 and (4y+64)/(-3) for y=-3, we can simply substitute -3 for y in each expression and simplify
2(y+6)/3 = 2(-3+6)/3
Now, simplifying by simple subtraction and then multiply,
= 2(3)/3 = 6/3 = 2
Therefore, when y=-3, the value of 2(y+6)/3 is 2.
Now, substituting the value of y =-3
(4y+64)/(-3) = (4(-3)+64)/(-3) = (-12+64)/(-3) = 52/(-3) = -17.333...
Therefore, when y=-3, the value of (4y+64)/(-3) is approximately -17.333.
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(Help!)
An object in the shape of a rectangular prism has a length of 8 inches, a width of 7 inches, and a height of 5 inches. The object's density is 20.7 grams per cubic centimeter. Find the mass of the object to the nearest gram.
The requried, rounding to the nearest gram, mass of the object is 95,297 g.
First, we need to find the volume of the rectangular prism:
Volume = length x width x height = 8 in x 7 in x 5 in = 280 cubic inches
Next, we need to convert the volume to cubic centimeters since the density is given in grams per cubic centimeter:
1 cubic inch = 16.3871 cubic centimeters
280 cubic inches = 280 x 16.3871 = 4594.628 cubic centimeters
Finally, we can calculate the mass of the object using the density formula:
Density = mass/volume
Density x volume
mass = 20.7 g/cm³ x 4594.628 cm³ ≈ 95,296.7 g
Rounding to the nearest gram, the mass of the object is 95,297 g.
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Which angle forms a corresponding angle with ∠2?
Answer:
6,3,7
Step-by-step explanation:
this is because they are all obtuse angles please help me i have a brain fart on meidan of 45, 52, 57, 42, 54, 58.
In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and the other 200,745 children were given a placebo. Among those in the treatment group, 33 developed polio, and among those in the placebo group, 115 developed polio. If we want to use the methods for testing a claim about two population proportions to test the claim that the rate of polio is less for children given the Salk vaccine, are the requirements for a hypothesis test satisfied?a. The requirements are satisfied; the samples are simple random samples that are independent, and for each of the two groups, the sample size is at least 1000.b. The requirements are not satisfied; the difference between the rates of those that developed polio in the two groups is not statistically significant.
The requirements for a hypothesis test are satisfied.
To test the claim that the rate of polio is less for children given the Salk vaccine, we need to check if the requirements for a hypothesis test about two population proportions are met. The requirements are:
1. The samples are simple random samples and independent.
2. For each of the two groups, the sample size is at least 1000.
In this case, the study involved 401,974 children who were randomly assigned to two groups: the treatment group with 201,229 children and the placebo group with 200,745 children. This satisfies the first requirement, as the samples are simple random samples and independent. The sample size for both groups is also larger than 1000, meeting the second requirement.
Therefore, the requirements for a hypothesis test are satisfied, and we can proceed with testing the claim that the rate of polio is less for children given the Salk vaccine.
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A toy store sells individual marbles in a variety of colors and sizes.
What is the probability that a randomly selected marble is purple or small?
The probability that a randomly selected marble is purple or small is: 0.5254
How to find the probability from the table?The total number of big marbles = 34 marbles
The total number of small marbles = 25 marbles
The total number of red marbles = 22 marbles
The total number of Green Marbles = 11 marbles
The total number of purple marbles = 16 marbles
The total number of blue marbles = 10 marbles
Total number of all marbles = 59 marbles
Thus, the probability that a randomly selected marble is purple or small is:
P(purple or small) = (16/59) + (25/59)
= 31/59 = 0.5254
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Laura is wrapping a gift that measures 6 inches by 13.5 inches by 3 inches. How much wrapping paper will she need to wrap the gift?
Responses
The amount of wrapping paper for the gift is A = 279 inches²
Given data ,
To calculate the amount of wrapping paper Laura will need to wrap the gift, we need to find the total surface area of the gift.
The surface area of a rectangular box is given by the formula:
Surface Area = 2 x (length x width + length x height + width x height)
Given that the length of the gift is 6 inches, the width is 13.5 inches, and the height is 3 inches, we can substitute these values into the formula:
Surface Area = 2 x (6 x 13.5 + 6 x 3 + 13.5 x 3)
Surface Area = 2 x (81 + 18 + 40.5)
Surface Area = 2 x 139.5
The surface area of a rectangular box = 279 inches²
Hence , Laura will need 279 inches² of wrapping paper to wrap the gift
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PLEASE HELP ME WITH THIS ASSIGNMENT PLEASE!!
I'm rather busy right now but I'll try my best to help you out
1. Radius is 6 because 12/2 = 6
2. Formula is πr^2
im really sry i wasnt able to help out alot but i hope you can understand it a little better
Write a function in the form y=Mx+b for the line that contains the points (6.4,2.6)and(5.2,9)
Answer:
y=-5.3x+36.73
Step-by-step explanation:
Which one of the following sets of horizontal forces can keep a body in equilibrium ? (a) 12 N, 24 N and 48 N (b) 50 N, 75 N and 150 N (d) 35 N, 35 N and 35 N. (c) 45 N, 90 N and 450 N
The sum of horizontal forces acting on a body in equilibrium must be zero.
(a) 12 N + 24 N + 48 N = 84 N ≠ 0, so not in equilibrium.
(b) 50 N + 75 N + 150 N = 275 N ≠ 0, so not in equilibrium.
(c) 45 N + 90 N + 450 N = 585 N ≠ 0, so not in equilibrium.
(d) 35 N + 35 N + 35 N = 105 N = 0, so this set of forces can keep a body in equilibrium.
Therefore, the correct answer is (d) 35 N, 35 N, and 35 N.
The owner of a health club decides to reduce the $35 membership fee by $5. What is the approximate percent
decrease in the fee?
O The percent decrease is approximately 0.14%.
O The percent decrease is approximately 0.85%.
O The percent decrease is approximately 14%.
O The percent decrease is approximately 85%.
Answer:
0.14%
Step-by-step explanation:
Daniel randomly surveyed 120 students at his school and found that 96 of them have at least one sibling. Based on these data, how many of the 425 students at his school would be expected to have at least one sibling?
The probability of a student having at least one sibling, based on the survey results is 0.8.
Daniel surveyed 120 students at his school and found that 96 of them have at least one sibling. This means that the probability of a student having at least one sibling, based on the survey results, is 96/120 or 0.8.
There are 425 students at Daniel's school, so if we multiply this number by the probability of having at least one sibling (0.8), we can estimate that approximately 340 students at the school have at least one sibling.
To estimate the number of students at Daniel's school who have at least one sibling, we can use this probability to make a prediction.
If we assume that the probability of a student having at least one sibling is the same for all students at the school, then we can apply this probability to the total number of students.
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