3. Above are pictures of a regular pyramid and prism, both with square bases. One side of the
base of the pyramid has a length of 10 inches, one side of the base of the prism has a length of
10 inches, both solids have a height of 12 inches. The pyramid has a slant height of 13 inches.
Show ALL your work!
a. Which one has the larger surface area and by how much?
b. Which has the larger volume and by how much?

Answers

Answer 1

Let's calculate the surface area and volume for both the pyramid and the prism and compare the results.

a. Surface Area:

The surface area of a regular pyramid is given by the formula:

SA_pyr = Base Area + (1/2) * Perimeter of Base * Slant Height

The base area of the pyramid is the area of a square, which is equal to one side length squared:

Base Area_pyr = (10 inches)² = 100 square inches

The perimeter of the base is the sum of all four sides:

Perimeter of Base_pyr = 4 * 10 inches = 40 inches

Plugging the values into the formula, we have:

SA_pyr = 100 square inches + (1/2) * 40 inches * 13 inches
SA_pyr = 100 square inches + 20 inches * 13 inches
SA_pyr = 100 square inches + 260 square inches
SA_pyr = 360 square inches

Now, let's calculate the surface area of the prism. The surface area of a prism with a square base is given by the formula:

SA_prism = 2 * Base Area + Perimeter of Base * Height

The base area of the prism is the area of a square, which is equal to one side length squared:

Base Area_prism = (10 inches)² = 100 square inches

Plugging the values into the formula, we have:

SA_prism = 2 * 100 square inches + 40 inches * 12 inches
SA_prism = 200 square inches + 480 square inches
SA_prism = 680 square inches

Therefore, the pyramid has a surface area of 360 square inches, and the prism has a surface area of 680 square inches.

The prism has a larger surface area by:
680 square inches - 360 square inches = 320 square inches.

b. Volume:

The volume of a regular pyramid is given by the formula:

V_pyr = (1/3) * Base Area * Height

Plugging the values into the formula, we have:

V_pyr = (1/3) * 100 square inches * 12 inches
V_pyr = 400 cubic inches

The volume of a prism with a square base is given by the formula:

V_prism = Base Area * Height

Plugging the values into the formula, we have:

V_prism = 100 square inches * 12 inches
V_prism = 1200 cubic inches

Therefore, the pyramid has a volume of 400 cubic inches, and the prism has a volume of 1200 cubic inches.

The prism has a larger volume by:
1200 cubic inches - 400 cubic inches = 800 cubic inches.

To summarize:

a. The prism has a larger surface area by 320 square inches.
b. The prism has a larger volume by 800 cubic inches.

Related Questions

PLease HELP!! Brainliest answer

PLease HELP!! Brainliest answer

Answers

Answer:

3

Step-by-step explanation:

15:5

9:HE

15/5 = 9/HE

15HE = 45

HE = 3

What is the solution to this equation?
X-8 = 15
O A. x= 17
O B. x = 23
O c. x = 13
O D. x = 7

Answers

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{ x = 23}}}}}\)

Option B is correct.

Step-by-step explanation:

\( \star{ \text{ \: \: x - 8 = 15}}\)

\( \text{Step \: 1 \: : Move \: 8 \: to \: right \: hand \: side \: and \: change \: its \: sign}\)

\( \hookrightarrow{ \sf{x = 15 + 8}}\)

\( \text{Step \: 2 \: : Add \: the \: numbers \: : 15 \: and \: 8}\)

\( \hookrightarrow{ \sf{x = 23}}\)

\( \sf{ \: The \: value \: of \: x \: is \: 23.}\)

\( \sf{Hope \: I \: helped !}\)

\( \sf{Best \: regards!!}\)

~\( \sf{TheAnimeGirl}\)

wich inequality does the graph sow HURRY

wich inequality does the graph sow HURRY

Answers

Answer: The correct answer is A)

how many cups of granulated sugar in a 5 pound bag

Answers

There are approximately 11.25 cups of granulated sugar in a 5 pound bag.

To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.

First, we multiply the number of pounds (5) by the conversion factor:

5 pounds * 2.25 cups/pound = 11.25 cups

Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.

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The critical F value with 6 numerator and 60 denominator degrees of freedom at a = .05 is a. 3.74.
b. 1.96.
c. 2.25.
d. 2.37.

Answers

The critical F value with 6 numerator degrees of freedom and 60 denominator degrees of freedom at a significance level of 0.05 is approximately 2.37.

To find the critical F value with 6 numerator and 60 denominator degrees of freedom at a significance level of 0.05, we need to refer to the F-distribution table or use statistical software. The critical F value represents the value beyond which we reject the null hypothesis in an F-test.

In this case, the numerator degrees of freedom (df1) is 6 and the denominator degrees of freedom (df2) is 60. The significance level (alpha) is 0.05.

Using the F-distribution table or statistical software, we find that the critical F value corresponding to a significance level of 0.05, with 6 numerator degrees of freedom and 60 denominator degrees of freedom, is approximately 2.37.

Therefore, the correct answer is d. 2.37.

The F-distribution is a probability distribution that arises in statistical inference when comparing variances or conducting analysis of variance (ANOVA) tests. It has two parameters, the numerator degrees of freedom (df1) and the denominator degrees of freedom (df2). The F-distribution is right-skewed and its shape depends on the degrees of freedom.

In hypothesis testing, the critical F value is used to determine whether the observed F statistic is statistically significant. If the calculated F statistic exceeds the critical F value, we reject the null hypothesis and conclude that there is evidence of a significant difference between the groups being compared. On the other hand, if the calculated F statistic is lower than the critical F value, we fail to reject the null hypothesis.

It is important to consult the F-distribution table or use statistical software to find the specific critical F value corresponding to the given degrees of freedom and significance level, as these values can vary depending on the specific parameters of the F-distribution.

In summary, the critical F value with 6 numerator degrees of freedom and 60 denominator degrees of freedom at a significance level of 0.05 is approximately 2.37. This value is crucial in determining the statistical significance of the observed F statistic in hypothesis testing involving these degrees of freedom.

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Tiana is selling handmade jewelry to earn money for camp. Bracelets sell for $10 and necklaces sell for $15. She needs to make at least $350 to cover the cost of camp. Use b = number of bracelets and n = number of necklaces, write an inequality to represent the situation.

(Please…I literally have a test soon )

Answers

Answer: n>b so they only need to sell 2b and 32n to cover the cost of camp.

Step-by-step explanation:

4 a bucket being filled with water is 3/8 full after 24 seconds. at the same rate, how many more seconds will it take to fill the bucket?

Answers

Answer: To fill the whole bucket, it will take 64 seconds so the remaining time is 40 seconds

Step-by-step explanation: As we are given 3/8 th part of the bucket is filled in 24 seconds. So by simply applying the unitary method we can say -

3/8 th part -----> 24 seconds

To fill the whole bucket multiply both sides by 8/3 in order to make the 1 unit of the bucket on the L.H.S, we get

1 bucket ----> 64 seconds.

The remaining times as it already passes 24 seconds and 3/8 th part of the bucket is filled, 64-24 seconds i.e 40 seconds is remaining in which bucket is full.

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On a coordinate plane, a curved line with a maximum value of (negative 1, 2) crosses the x-axis at (negative 3, 0) and (1, 0), and crosses the y-axis at (0, 1.5).
What are the x-intercepts of the graphed function?

(–3, 0) and (0, 1.5)
(–3, 0) and (1,0)
(–1, 2) and (1, 0)
(0, 1.5) and (1, 0)

Answers

9514 1404 393

Answer:

  (–3, 0) and (1,0)

Step-by-step explanation:

The x-intercepts are where the curve crosses the x-axis. Your problem statement tells you ...

  "crosses the x-axis at (negative 3, 0) and (1, 0)"

This means the x-intercepts are (-3, 0) and (1, 0).

Answer:

The answer would be B= (–3, 0) and (1,0)

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part Tutorial Exercise A population of protozoa develops with a constant relative growth rate of 0.469 per member per day. On day zero the population consists of five members. Find the population size after seven days. Part 1 of 3 Since the relative growth rate is 0.469, then the differential equation that models this growth is dP = 0.469p dt 0.469P X Part 2 of 3 We know that P(t) = P(O)ekt, where P(O) is the population on day zero, and k is the growth rate. Substitute the values of P(O) and k into the equation below. P(t) = P(O)ekt Submit Skip.(you cannot come back)

Answers

The population size of the protozoa after seven days, starting with an initial population of five members and a constant relative growth rate of 0.469 per member per day, can be calculated using the formula\(P(t) = 5 * e^{(0.469 * 7)\).

Part 1 of the question establishes that the relative growth rate of the protozoa population is 0.469 per member per day. This information helps us define the differential equation that represents the growth: dP/dt = 0.469P.

Part 2 introduces the exponential growth formula for population growth, which states that \(P(t) = P(0)e^{kt\) where P(t) is the population size at time t, P(0) is the initial population size, k is the growth rate, and e is the base of the natural logarithm.

To find the population size after seven days, we substitute the given values into the formula: \(P(t) = 5 * e^{(0.469 * 7)\). Evaluating this expression yields the final answer, which represents the population size of the protozoa after seven days.

Note: The calculation itself is not included in the answer as the model response is limited to explaining the approach.

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3. Calculating the mean when adding or subtracting a constant A professor gives a statistics exam. The exam has 50 possible points. The s 42 40 38 26 42 46 42 50 44 Calculate the sample size, n, and t

Answers

The sample consists of 9 exam scores: 42, 40, 38, 26, 42, 46, 42, 50, and 44. The mean when adding or subtracting a constant A professor gives a statistics exam is √44.1115 ≈ 6.6419

To calculate the sample size, n, and t, we need to follow the steps below:

Find the sum of the scores:

42 + 40 + 38 + 26 + 42 + 46 + 42 + 50 + 44 = 370

Calculate the sample size, n, which is the number of scores in the sample:

n = 9

Calculate the mean, μ, by dividing the sum of the scores by the sample size:

μ = 370 / 9 = 41.11 (rounded to two decimal places)

Calculate the deviations of each score from the mean:

42 - 41.11 = 0.89

40 - 41.11 = -1.11

38 - 41.11 = -3.11

26 - 41.11 = -15.11

42 - 41.11 = 0.89

46 - 41.11 = 4.89

42 - 41.11 = 0.89

50 - 41.11 = 8.89

44 - 41.11 = 2.89

Square each deviation:

\((0.89)^2\) = 0.7921

\((-1.11)^2\) = 1.2321

\((-3.11)^2\) = 9.6721

\((-15.11)^2\) = 228.6721

\((0.89)^2\) = 0.7921

\((4.89)^2\) = 23.8761

\((0.89)^2\) = 0.7921

\((8.89)^2\) = 78.9121

\((2.89)^2\) = 8.3521

Find the sum of the squared deviations:

0.7921 + 1.2321 + 9.6721 + 228.6721 + 0.7921 + 23.8761 + 0.7921 + 78.9121 + 8.3521 = 352.8918

Calculate the sample variance, \(s^2\), by dividing the sum of squared deviations by (n-1):

\(s^2\) = 352.8918 / (9 - 1) = 44.1115 (rounded to four decimal places)

Calculate the sample standard deviation, s, by taking the square root of the sample variance:

s = √44.1115 ≈ 6.6419 (rounded to four decimal places)

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The mass of the Rock of Gibraltar is 1.78-102 kilograms. The mass of the Antarctic iceberg is 4.55-103 kilograms. Approximately how many more kilograms is the mass of the Antarctic iceberg than the mass of
the Rock of Gibraltar? Show your work and write your answer in scientific notation (10 points)

Answers

4.372 × \(10^{13}\) more kilograms the mass of the Antarctic iceberg than the mass of the Rock of Gibraltar.

Mass of the Antarctic iceberg = 4.55 × \(10^{13}\)  

Mass of the rock of Gibraltar  = 1.78 × \(10^{12}\)  

Excessive mass of Antarctic Icebergs than the rock of Gibraltar,

4.55 × \(10^{13}\)  - 1.78 × \(10^{12}\)  

Subtract easily both should be in the same power of ten,

= 4.55 × \(10^{13}\)  - 1.78 × \(10^{12}\)  

= 43.72  × \(10^{12}\)  

= 4.372 × \(10^{13}\)

Scientific notation is used to express quantities that are either too large or too little to be represented by decimals. Scientific format, standard index format, and standard format are other terms for the same thing.

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show that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

Answers

We have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

What is rectangle?

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Let A and B be two sets in a generalized rectangle R, i.e., R = A x B. The boundary of R, denoted by bd(R), is defined as the closure of the set of points that are not in the interior of R. In other words, bd(R) = cl(R) \ int(R), where cl(R) is the closure of R and int(R) is the interior of R.

To show that bd(R) is the union of finitely many closed generalized rectangles with volume zero, we first note that the closure of R can be expressed as the union of R and its boundary, i.e., cl(R) = R ∪ bd(R). Therefore, it suffices to show that R can be expressed as the union of finitely many closed generalized rectangles with volume zero and that bd(R) can also be expressed as the union of finitely many closed generalized rectangles with volume zero.

Let (a,b) be a point in R. Then there exists an open ball B((a,b), r) around (a,b) that is contained in R, where r > 0. Without loss of generality, we can assume that r is small enough so that B((a,b), r) is a generalized rectangle. Since B((a,b), r) is open, it follows that int(R) is the union of all such generalized rectangles. Therefore, R can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such generalized rectangles.

Next, we show that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero. Let (a,b) be a point in bd(R). Then every open ball B((a,b), r) around (a,b) contains points both in R and in the complement of R. By definition of bd(R), the closure of B((a,b), r) intersects both R and the complement of R. Therefore, B((a,b), r) can be expressed as the union of two closed generalized rectangles, one contained in R and one contained in the complement of R. It follows that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such balls B((a,b), r) and their decompositions into closed generalized rectangles.

Therefore, we have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

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Solve each equation in the interval from 0 to 2π. Round your answer to the nearest hundredth.

20 cost=-8

Answers

The solutions of the equation 20cosθ=-8 in the interval from 0 to 2π are 0.785 and 5.236, rounded to the nearest hundredth.

To solve the equation, we divide both sides by 20 to get cosθ=-0.4. The cosine function has a period of 2π, so all solutions of the equation can be found by adding multiples of 2π to the solution cosθ=-0.4.

The solutions in the interval from 0 to 2π are then cosθ=-0.4+2πk, where k is an integer. When k=0, we get cosθ=-0.4. When k=1, we get cosθ=-0.4+2π=0.785. When k=2, we get cosθ=-0.4+4π=5.236.

The solutions cosθ=-0.4 and cosθ=5.236 are both in the interval from 0 to 2π. When rounded to the nearest hundredth, these solutions are 0.785 and 5.236, respectively.

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PLEASE HELP ME!!!
Which line has an x-intercept of 4?

PLEASE HELP ME!!! Which line has an x-intercept of 4?

Answers

Answer:

-2x + 2y = -8

Step-by-step explanation:

2y=2x-8

y=x-4

0=x-4

x=4

Hopefully this helps :) Let me know if you need me to explain it better.

Answer:

-2 x + 2 y = -8

Step-by-step explanation:

radikool

What is the equation of the linear relationship that has a slope of 200 and a y-intercept of 100?

Answers

The linear equation from the given data can be constructed as y=200x+c

What is the slope-intercept form of a line?

The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line

Given here: The slope of a line is 200 and the y-intercept as 100

We know the slope intercept form of a line s given by y=mx+c

Thus substituting the values we get

y=200x+100

Hence, The linear equation from the given data is y=200x+c

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A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. He wants to construct the 95% confidence interval with a maximum error of 0.19 reproductions per hour. Assuming that the mean is 12.6 reproductions and the variance is known to be 3.61 what is the minimum sample size required for the estimate? Round your answer up to the next integer.

Answers

Answer:

the minimum sample size required is 139

Step-by-step explanation:

To construct a 95% confidence interval with a maximum error of 0.19 reproductions per hour, we need to use the t-distribution. The t-distribution is used when the population variance is unknown and the sample size is small.

To find the minimum sample size required, we need to use the following formula:

n = (t_(α/2,df) * s / E)^2

where:

n is the minimum sample size

t_(α/2,df) is the critical value of the t-distribution for a confidence level of 95% (α = 0.05) and df is the degrees of freedom

s is the standard deviation of the population

E is the maximum error allowed

We are given that the mean is 12.6 reproductions and the variance is 3.61. The standard deviation is the square root of the variance, so the standard deviation is 1.9.

To find the critical value of the t-distribution, we need to know the degrees of freedom. The degrees of freedom is equal to the sample size minus 1. Since we don't know the sample size yet, we will use a symbol (let's use "df") to represent the degrees of freedom in the formula.

Plugging the values into the formula, we get:

n = (t_(0.025,df) * 1.9 / 0.19)^2

To find the critical value of the t-distribution, we need to use a t-table or a computer program. Looking up the critical value in a t-table or using a computer program, we find that the critical value for a 95% confidence level and df = 9 is 2.262.

Plugging this value into the formula, we get:

n = (2.262 * 1.9 / 0.19)^2

Simplifying the expression, we get:

n = (11.868)^2

n = 138.7

The minimum sample size required is 138.7. Since we can't have a fractional number of samples, we need to round up to the next integer, which is 139.

Therefore, the minimum sample size required is 139.

Mr. and Mrs. Tournas know that their son will attend a college, in 14 years, that they estimate to cost approximately $250,000. How much should they deposit now if they assume that they can earn 8.5% compounded annually?
a) $72,083.41
b) $76,055.32
c) $75,450.20
d) $79,785.45

Answers

Answer: D

Step-by-step explanation:

We will try it to determine how much the need to save using the exponential function. In an exponential function,we need the start up amount and the common difference.

We know that the common difference is is 1.085  because if they will earn 8.5% interest plus 100% .

So  1.085 raised to the number of years times a number has to equal 250,000

x * 1.085^14 = 250,000   now solve for x

3.13340357495x = 250,000

x = 79785.44544 Rounded to the nearest cent is $79785.45

Find the difference!

Find the difference!

Answers

Answer:

2x + 10

_______

x^3 - 4x

Step-by-step explanation:

this is the answer

How many sides does a rectangular pyramid

Answers

Answer:

Step-by-step explanation:

A rectangular pyramid has five sides. It consists of a rectangular base and four triangular faces that meet at a common vertex or apex.


≧◉◡◉≦

Allan can make 8 pizzas in 15 minutes at the pizza restaurant where he works. If the number of pizzas varies directly with minutes, how many pizzas can Allan make in 3 hours? Please Help

Answers

Answer:

96 pizzas

Step-by-step explanation:

Allan can make 8 pizzas in 15 minutes at the pizza restaurant where he works.

We are told that;

If the number of pizzas varies directly with minutes,

P ∝ M

P = kM

Hence:

8 = 15k

k = 8/15

How many pizzas can Allan make in 3 hours?

Convert 3 hours to minutes

1 hour = 60 minutes

3 hours = x

x = 3 × 60

x = 180 minutes

Hence,

M = 180 minutes

k = 8/15

P = kM

P = 8/15 × 180

P = 96 pizzas

Therefore, Allan can make 96 pizzas in 3 hours

Nina bought a computer mouse for $9.30. She paid with a $20 bill. How much change did she get back?
A.
$11.70
B.
$10.70
C.
$9.70
D.
$29.30

Answers

Answer: B. 10.70

Step-by-step explanation:

So we are given how much she spent and how much it costed.

So if the mouse costed $9.30 but she paid with 20 we would just subtract

9.30 - 20 = 10.7 or 10.70

(You could also check this by adding- 10.70 + 9.30 = 20 )

So she got 10.70 change back

Fill in the blanks with the appropriate justifications (reasons) for the steps used in solving the equation. Statements 1.x/2-9=-4 given 2. x/2=-13 3 x=-26 what are the justifications for 2 and 3​

Answers

Therefore, the justification for step 2 is "Addition Property of Equality" and the justification for step 3 is "Multiplication Property of Equality".

What is equation?

An equation is a mathematical statement that shows the equality of two expressions, usually separated by an equal sign. It means that the expressions on both sides of the equal sign represent the same value or quantity. Equations can involve one or more variables and may have different degrees of complexity. They are commonly used to model various real-world situations and to solve problems in mathematics, science, engineering, and other fields.

Here,

2. To isolate the variable term, add 9 to both sides. This yields:

x/2 - 9 + 9 = -4 + 9

Simplifying the left side, we get:

x/2 = 5

3. To solve for x, multiply both sides by 2. This yields:

x/2 * 2 = 5 * 2

Simplifying both sides, we get:

x = -10

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HELP PLEASE!! not sure about it!!

HELP PLEASE!! not sure about it!!

Answers

Answer:

y=2/4x+4

or

y=1/2x+4

Step-by-step explanation:

:)))

While having his kitchen remodeled, vijay discusses the options with his contractor. there are 3 countertops and 3 sinks to choose from. for the appliances, there are 3 brands in his price range. how many different kitchens can vijay design?

Answers

Vijay can design 84 different kitchens using combination.

What is the combination?

The combination is a method of choosing things from a collection where, unlike permutations, the order of the choices is irrelevant.

The formula for combination is ⁿ\(C_{r}\)=\(\frac{n!}{r!(n-r)!}\) where 0 ≤ r ≤ n.

Given that Vijay has to choose 3 countertops and 3 sinks from 3 brands.

To find the number of kitchens he can design.

No. of ways in which kitchens can be designed using 3 countertops and 3 sinks can be (3×3).

So, n = 9

He need to chose from 3 brands so r = 3.

No. of kitchens he can design = \(=\frac{n!}{r!(n-r)!}\)

= \(\frac{9!}{3!(9-3)!}\)

= \(\frac{9!}{3!(6)!}\)

= \(\frac{9.8.7}{3.2.1}\)

= 84

Therefore, Vijay can design 84 different kitchens.

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Which of the following expressions is equivalent to "eight groups of four"?
A 8+4
B. (8 + 4)
C. 8 x 4
D. 4°

Answers

Answer:

Hey mate,here is your answer. Hope it helps you.

Step-by-step explanation:

The answer is c- 8 x 4. As there are 8 groups of 4 the easiest way to calculate is by multiplying them both. Repeated addition is known as multiplication.

a department store holds a year-end clearance sale that includes a 19.8% discount on cosmetics. find the sale price of a bottle of perfume if its original price was $50.07.

Answers

The sale price of a bottle of perfume is $40.16 if its original price was 50.07%.

What is discount?

By paying a charge or fee, a debtor might purchase the right to postpone payments to a creditor for a predetermined length of time through the financial mechanism known as discounting. In essence, the party who is currently owing money purchases the right to postpone payment until a later time.

Let the original price of the perfume bottle is, $50.07

The sale on the cosmetics is 19.8%.

So, the discount on the perfume bottle is,

50.07 x 0.198 = 9.91368

Therefore, the sale price of perfume is,

$50.07 - $9.91368 = $40.15614

Hence, the sale price of perfume is, $40.16

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A function f is defined by f(x)= 3-8x³/ 2
(7.1) Explain why f is a one-to-one function.
(7.2) Determine the inverse function of f.

Answers

7.1 . The function f(x) = (3 - 8x³) / 2 is one-to-one.

7.2 . The inverse function of f(x) = (3 - 8x³) / 2 is f^(-1)(x) = ∛[(2x - 3) / -8].

(7.1) To determine if the function f(x) = (3 - 8x³) / 2 is one-to-one, we need to show that each unique input (x-value) produces a unique output (y-value), and vice versa.

Let's consider two different inputs, x₁ and x₂, where x₁ ≠ x₂. We need to show that f(x₁) ≠ f(x₂).

Assume f(x₁) = f(x₂), then we have:

(3 - 8x₁³) / 2 = (3 - 8x₂³) / 2

To determine if the two sides of the equation are equal, we can cross-multiply:

2(3 - 8x₁³) = 2(3 - 8x₂³)

Expanding both sides:

6 - 16x₁³ = 6 - 16x₂³

Subtracting 6 from both sides:

-16x₁³ = -16x₂³

Dividing both sides by -16 (since -16 ≠ 0):

x₁³ = x₂³

Taking the cube root of both sides:

x₁ = x₂

Since x₁ = x₂, we have shown that if f(x₁) = f(x₂), then x₁ = x₂. Therefore, the function f(x) = (3 - 8x³) / 2 is one-to-one.

(7.2) To find the inverse function of f(x) = (3 - 8x³) / 2, we need to swap the roles of x and y and solve for y.

Let's start with the original function:

y = (3 - 8x³) / 2

To find the inverse, we'll interchange x and y:

x = (3 - 8y³) / 2

Now, let's solve for y:

2x = 3 - 8y³

2x - 3 = -8y³

Divide both sides by -8:

(2x - 3) / -8 = y³

Take the cube root of both sides:

∛[(2x - 3) / -8] = y

Therefore, the inverse function of f(x) = (3 - 8x³) / 2 is:

f^(-1)(x) = ∛[(2x - 3) / -8]

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Let f(x) and g(x) be quasiconcave functions defined on R show that the function h(x) = min{f(x), g(x)} is also quasiconcave.

Answers

The function h(x) = min{f(x), g(x)} is quasiconcave when f(x) and g(x) are quasiconcave functions defined on R. This can be explained by considering the properties of quasiconcave functions and the properties of the minimum operator.

To show that h(x) = min{f(x), g(x)} is quasiconcave, we need to demonstrate that for any two points x1 and x2 in the domain of h(x), and for any t between 0 and 1, the inequality h(tx1 + (1-t)x2) ≥ min{h(x1), h(x2)} holds.

Let's consider two arbitrary points, x1 and x2, in the domain of h(x). Since f(x) and g(x) are quasiconcave, we know that for any t between 0 and 1, the inequalities f(tx1 + (1-t)x2) ≥ min{f(x1), f(x2)} and g(tx1 + (1-t)x2) ≥ min{g(x1), g(x2)} hold.

Now, let's analyze h(tx1 + (1-t)x2). By definition, h(tx1 + (1-t)x2) = min{f(tx1 + (1-t)x2), g(tx1 + (1-t)x2)}. Since min{a, b} ≤ a and min{a, b} ≤ b for any real numbers a and b, we have h(tx1 + (1-t)x2) ≤ f(tx1 + (1-t)x2) and h(tx1 + (1-t)x2) ≤ g(tx1 + (1-t)x2).

Combining these inequalities with the quasiconcave property of f(x) and g(x), we have h(tx1 + (1-t)x2) ≥ min{f(x1), f(x2)} and h(tx1 + (1-t)x2) ≥ min{g(x1), g(x2)}. Therefore, h(x) = min{f(x), g(x)} satisfies the quasiconcave property.

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Please help! Will pick Brainliest for the right answer!!!

Please help! Will pick Brainliest for the right answer!!!

Answers

Answer:

3/5

4/3

2/1

3/1

Step-by-step explanation:

turn them to ratios and fractions and try to simplify

3/5=3/5

4/3=4/3

2/1=2/1

6/2=3/1

so put the end results in order

so all of them have a bigger numerator than denominator, except one. 3/5. Thats the slowest one.

4/3 isn't quite 2 wholes, but 2/1 is, so 4/3 is second last and 2/1 is second.

3/1 is the first.

Convert 8100 mg to grams
help me ?

Answers

It would be 8.1 grams

Answer:

8.1g, mg->g is divide by 1000 :)

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