Answer:
4
Step-by-step explanation:
2/3 / 1/6
= 2/3 * 6/1
= 12/3
= 4.
An equipment rental business currently charges $32. 00 per power tool rental and averages 24 rentals a day. The company recently performed a study and found that for every $2. 00 increase in rental price, the average number of customers decreased by one rental.
The company determined that the function f(x) = (32 + 2x)(24 – x) can be used to represent the total revenue earned from the rentals, where x represents the number of rental price increases and f(x) represents the revenue earned.
Part A: Explain what the expressions (32 + 2x) and (24 – x) represent in the given scenario.
Part B: What is the revenue after 3 rental price increases? Show your work or explain how you found your answer.
Part C: What rental price would give the maximum revenue for the company?
Part A: In the given scenario, the expression (32 + 2x) represents the rental price charged by the equipment rental business after x price increases of $2 each. The initial rental price is $32, and for every $2 increase in rental price, the rental price is raised by 2 units. The expression (24 – x) represents the number of rentals the equipment rental business can expect to make after x price increases. As the rental price increases, the number of customers is expected to decrease by one rental for every $2 increase in rental price.
Part B: To find the revenue after 3 rental price increases, we need to calculate f(3), where f(x) = (32 + 2x)(24 – x).
Substituting x = 3, we get:
f(3) = (32 + 2(3))(24 – 3) = (32 + 6)(21) = 38 × 21 = $798
Therefore, the revenue after 3 rental price increases is $798.
Part C: To find the rental price that would give the maximum revenue for the company, we need to find the value of x that maximizes the function f(x) = (32 + 2x)(24 – x). We can do this by finding the critical points of the function, which occur when the derivative of the function is equal to zero:
f'(x) = (32 + 2x)(-1) + (24 - x)(2) = -32 + 16x + 48 - 2x = 14x + 16
Setting f'(x) = 0 and solving for x, we get:
14x + 16 = 0
[tex]x = \frac{-16}{14} = \frac{-8}{7}[/tex]
However, [tex]x = \frac{-8}{7}[/tex] is not a valid solution since it represents a negative number of rental price increases, which is not possible in this scenario. Therefore, we need to test the endpoints of the interval [0, 6], since x represents the number of rental price increases and cannot exceed 6 (which would result in a rental price of $44, the maximum price in this scenario).
f(0) = (32 + 2(0))(24 - 0) = 32 × 24 = $768
f(6) = (32 + 2(6))(24 - 6) = 44 × 18 = $792
Comparing the values of f(0), f(3), and f(6), we see that f(6) gives the maximum revenue of $792. Therefore, the rental price that would give the maximum revenue for the company is $44, which is the rental price after 6 price increases of $2 each.
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An ice cream cone has a radius of 6 centimeters and height of 12 centimeters. What is the volume of the ice cream cone? Round your answer to the nearest centimeter
Answer: 452.39
Step-by-step explanation: R= 6, H = 12. Volume formula is V= pi*r^2*h/3. For you, the equation is V = pi*6^2*12/3. 6^2 = 36, and 12/3 = 4. V = pi*36*4. Solving, we get V = 452.39.
Find the slope of the line represented below
The slope of the line that is represented by the given data in the question is 3/4.
To find the slope of a line, we need to use the formula:
slope = (change in y) / (change in x)
We can choose any two points on the line and use their coordinates to calculate the change in y and the change in x. Let's choose the points (-9, 4) and (7, 16) from the given data.
Change in y = 16 - 4 = 12
Change in x = 7 - (-9) = 16
Plugging these values into the slope formula, we get:
slope = 12 / 16 = 3 / 4
We can also interpret this slope as the rate of change of y with respect to x. For every increase of 1 in x, y increases by 3/4. Similarly, for every decrease of 1 in x, y decreases by 3/4.
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Aabc is dilated by a factor of to produce aa'b'c!
28°
34
30
62
b
16
what is a'b, the length of ab after the dilation? what is the measure of a?
To find the length of a'b', we first need to know the scale factor of the dilation. The scale factor is given by the ratio of the corresponding side lengths in the original and diluted figures.
In this case, we are given that the original figure Aabc has been diluted by a factor of √2. So the length of each side in the dilated figure aa'b'c is √2 times the length of the corresponding side in Aabc.
To find the length of a'b, we can use the Pythagorean theorem in the right triangle aa'b'. Since we know that ab is one of the legs of this triangle, we can find its length as follows:
ab = (a'b' / √2) * sin(28°)
We are not given the length of ab or a in the original figure, so we cannot find their exact values. However, we can find the measure of angle A using the Law of Sines in triangle Aab:
sin(A) / ab = sin(62°) / b
where b is the length of side bc in Aabc. Solving for sin(A) and substituting the expression for ab that we found earlier, we get:
sin(A) = (sin(62°) / b) * [(a'b' / √2) * sin(28°)]
Since we know the values of sin(62°) and sin(28°), we can simplify this expression and use a value for b (if it is given in the problem) to find sin(A) and then A.
A 60 foot tall building casts a 20 foot. Shadow. Use the principles of similar triangles to determine the length of a shadow cast by a 5 foot 6 inch student
The length of the shadow cast by the 5 foot 6 inch student is approximately 1.83 feet.
To solve this problem, we'll set up a proportion using the principles of similar triangles. The two triangles in this case are the building and its shadow, and the student and their shadow.
Convert the height of the student to feet. 5 feet 6 inches is equal to 5.5 feet.
Set up the proportion. Let x represent the length of the shadow cast by the student. We have the following proportion:
(height of building) / (length of building's shadow) = (height of student) / (length of student's shadow)
60 / 20 = 5.5 / x
Cross-multiply and solve for x:
60 * x = 20 * 5.5
60x = 110
x = 110 / 60
x = 1.83 (rounded to two decimal places)
The length of the shadow cast by the 5 foot 6 inch student is approximately 1.83 feet.
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What integer represents ""a credit of $30"" if zero represents the original balance? explain your reasoning.
The integer that represents a credit of $30 if zero represents the original balance is +30.
A credit represents an increase in funds, while a debit represents a decrease. In this case, a credit of $30 means that $30 has been added to the account, increasing the balance. Since zero represents the original balance, adding $30 results in a positive balance of $30, which is represented by the integer +30.
Therefore, +30 represents a credit of $30 if the original balance is zero. The reasoning behind this is that a credit increases the balance, so a positive integer is used to indicate the amount by which the balance has increased. In this case, it is an increase of $30, hence +30.
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What’s the answer I need help pls?
Line x is parallel to line y. Line z intersect lines x and y. Determine whether each statement is Sometimes True.
Answer:
Step-by-step explanation:
a and b are sometimes true.
This is when line z intersects x and y at right angles.
Later in the summer as the garden plants were fading, claire decided that
she
would raise rabbits. she pulled out the dead plants and cleaned up the area. her
research showed that each rabbit needs 2 square feet of space in a pen, and that
rabbits reproduce every month, having litters of about 6 kits. she started with 2
rabbits (one male and one female). claire began tracking the number of rabbits
at the end of each month and
displayed her data in the table:
i need to get to 12 months can anyone help me please?
By the end of 12 months, Claire will need 1,596,018 pens to house all the rabbits.
The number of adult rabbits in each month is the sum of the adult rabbits from the previous month and the number of baby rabbits that have grown to adulthood.
The number of baby rabbits in each month is the product of the number of adult rabbits in the previous month and the number of kits each pair of rabbits produces (6 in this case).
The total number of rabbits is simply the sum of the number of adult rabbits and the number of baby rabbits. Finally, the minimum pen size needed is found by divide the total number of rabbits by 2 (since each rabbit needs 2 square feet of space).
Month 1
Beginning of month: 2 rabbits (1 male, 1 female)
End of month: 8 rabbits (3 males, 5 females)
Number of pens needed: 16 square feet / 2 square feet per pen = 8 pens
Month 2
Beginning of month: 8 rabbits (3 males, 5 females)
End of month: 26 rabbits (11 males, 15 females)
Number of pens needed: 52 square feet / 2 square feet per pen = 26 pens
Month 3
Beginning of month: 26 rabbits (11 males, 15 females)
End of month: 80 rabbits (35 males, 45 females)
Number of pens needed: 160 square feet / 2 square feet per pen = 80 pens
Month 4
Beginning of month: 80 rabbits (35 males, 45 females)
End of month: 242 rabbits (105 males, 137 females)
Number of pens needed: 484 square feet / 2 square feet per pen = 242 pens
Month 5
Beginning of month: 242 rabbits (105 males, 137 females)
End of month: 728 rabbits (315 males, 413 females)
Number of pens needed: 1456 square feet / 2 square feet per pen = 728 pens
Month 6
Beginning of month: 728 rabbits (315 males, 413 females)
End of month: 2186 rabbits (945 males, 1241 females)
Number of pens needed: 4372 square feet / 2 square feet per pen = 2186 pens
Now, to continue for the next 6 months
Month 7
Beginning of month: 2186 rabbits (945 males, 1241 females)
End of month: 6568 rabbits (2835 males, 3733 females)
Number of pens needed: 13136 square feet / 2 square feet per pen = 6568 pens
Month 8
Beginning of month: 6568 rabbits (2835 males, 3733 females)
End of month: 19702 rabbits (8499 males, 11203 females)
Number of pens needed: 39404 square feet / 2 square feet per pen = 19702 pens
Month 9
Beginning of month: 19702 rabbits (8499 males, 11203 females)
End of month: 59110 rabbits (25499 males, 33611 females)
Number of pens needed: 118220 square feet / 2 square feet per pen = 59110 pens
Month 10
Beginning of month: 59110 rabbits (25499 males, 33611 females)
End of month: 177334 rabbits (76535 males, 100799 females)
Number of pens needed: 354668 square feet / 2 square feet per pen = 177334 pens
Month 11
Beginning of month: 177334 rabbits (76535 males, 100799 females)
End of month: 532006 rabbits (229799 males, 302207 females)
Number of pens needed: 1064012 square feet / 2 square feet per pen = 532006 pens
Month 12
Beginning of month: 532006 rabbits (229799 males, 302207 females)
End of month: 1596018 rabbits (689397 males, 906621 females)
Number of pens needed: 3192036 square feet / 2 square feet per pen = 1596018 pens
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Eric and victoria are working on a project. eric has completed 3/8 of the project and and victoria has completed 1/3 of the project.
"(help me with this pls asap)"
Eric has completed 37.5% (or 0.375) of the project, while Victoria has completed 33.3% (or 0.333) of the project. Together, they have completed approximately 70.8% (or 0.708) of the project.
If Eric and Victoria are working on a project and Eric has completed 3/8 of the project, and Victoria has completed 1/3 of the project, then to find the total portion of the project completed, you can add their individual contributions: (3/8) + (1/3).
To add these fractions, you need a common denominator, which is 24 in this case. So, you can rewrite the fractions as (9/24) + (8/24). Adding them together gives you a total of 17/24 of the project completed by both Eric and Victoria, which is equal to 70.8% (or 0.708).
*complete question: Eric and victoria are working on a project. eric has completed 3/8 of the project and and victoria has completed 1/3 of the project. Calculate the total work they have completed together.
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Dr. Aghedo is saving money in an account with continuously compounded interest. How long will it take for the money she deposited to double if interest is compounded continuously at a rate of 3. 1%. Round your answer to the nearest tenth
The count of duration that is needed for Dr. Aghedo's money to be deposited is 22.3 years, under the condition that if interest is compounded continuously at a rate of 3. 1
The derived formula for doubling time with continuous compounding is applied to evaluate the length of time it takes to double the money in an account or investment that has continuous compounding. The formula is
Doubling time = ln 2 / r
Here,
r =annual interest rate as a decimal.
For the required case, the interest rate is 3.1% that can be written as 0.031 in the form of decimal. Then the doubling time will be
Doubling time = ln 2 / 0.031
≈ 22.3 years
Then, it should take approximately 22.3 years for Dr. Aghedo's money to double if interest is compounded continuously at a rate of 3.1%.
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A cistern in the form of an inverted circular cone is being filled with water at the rate of 65 liters per minute. if the cistern is 5 meters deep, and the radius of its opening is 2 meters, find the rate at which the water level is rising in the cistern 30 minutes after the filling process began.
Let's start by finding the volume of the cistern at any given time t. Since the cistern is in the form of an inverted circular cone, its volume can be expressed as:
V = (1/3)πr^2h
where r is the radius of the circular opening, h is the height of the cone (which is also the depth of the cistern), and π is the constant pi.
We are given that the cistern is 5 meters deep, and the radius of its opening is 2 meters. Therefore, we can plug these values into the equation above to get:
V = (1/3)π(2^2)(5)
V = 20/3 π
Now, we need to find the rate at which the water level is rising in the cistern after 30 minutes. Let's call this rate dh/dt (the change in height with respect to time).
We know that the water is being added to the cistern at a rate of 65 liters per minute. Since 1 liter is equal to 0.001 cubic meters, the volume of water being added per minute is:
(65 liters/minute) × (0.001 m^3/liter) = 0.065 m^3/minute
Therefore, the rate at which the height of the water in the cistern is changing is:
dh/dt = (0.065 m^3/minute) / (20/3 π m^3) = 3.87/π meters/minute
After 30 minutes, the height of the water in the cistern will have risen by:
h = (65 liters/minute) × (0.001 m^3/liter) × (30 minutes) / (20/3 π m^3) = 0.2925 meters
Therefore, the rate at which the water level is rising in the cistern 30 minutes after the filling process began is:
dh/dt = 3.87/π meters/minute
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In ABC, the bisector of A divides BC into segment BD with a length of
28 units and segment DC with a length of 24 units. If AB -31. 5 units, what
could be the length of AC ?
To find the length of AC in triangle ABC, we will use the Angle Bisector Theorem and the given information:
In triangle ABC, the bisector of angle A divides BC into segments BD and DC, with lengths of 28 units and 24 units, respectively. Given that AB has a length of 31.5 units, we want to determine the possible length of AC.
Step 1: Apply the Angle Bisector Theorem, which states that the ratio of the lengths of the sides is equal to the ratio of the lengths of the segments created by the angle bisector. In this case, we have:
AB / AC = BD / DC
Step 2: Plug in the known values:
31.5 / AC = 28 / 24
Step 3: Simplify the ratio on the right side:
31.5 / AC = 7 / 6
Step 4: Cross-multiply to solve for AC:
6 * 31.5 = 7 * AC
Step 5: Calculate the result:
189 = 7 * AC
Step 6: Divide both sides by 7 to find AC:
AC = 189 / 7
Step 7: Calculate the value of AC:
AC = 27 units
So, the length of AC in triangle ABC could be 27 units.
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Which numbers are solutions to the inequality *> 145 ? check all that apply. fraction is larger than 14 1/2 be decimals larger than 14 1/2 while numbers larger than 14 1/2 the number 14 1/2
fractions smaller than 14 1/2, decimal smaller than 14 1/2, whole number smaller than 14 1/2
For the solutions to the inequality *> 145, you can consider the given terms: 1. Fractions larger than 14 1/2: These are solutions since 14 1/2 is equivalent to 145/2, which is smaller than 145. 2.
Decimals larger than 14 1/2: These are also solutions as any decimal larger than 14.5 (14 1/2 as a decimal) will be greater than 145/2 and thus smaller than 145. 3. Whole numbers larger than 14 1/2: These are solutions as well, since any whole number greater than 14 is greater than 14 1/2 and therefore greater than 145/2. The numbers that are not solutions to the inequality are: 1. Fractions smaller than 14 1/2 2. Decimals smaller than 14 1/2 3. Whole numbers smaller than 14 1/2 These values are all less than 145/2 and therefore do not satisfy the inequality *> 145.
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The height of lava fountains spewed from volcanoes cannot be measured directly. Instead, their height in meters can be found using the equation
where y represents the height, g is 9.8, and t represents the falling time of the lava rocks. Find the height in meters of a lava rock that falls for 3 seconds.
The visitors to a certain website were questioned about their favorite soups.
If 180 people were surveyed, how many more people voted for split pea soup than for potato soup?
Answer:
.15(180) - .10(180) = .05(180) = 9
9 more people voted for split pea soup than for potato soup.
If a car cost $7,800 and its percent of depreciation is 45%, what is the residual value of the car?
A community organization wishes to know the proportion of subjects who feel financially comfortable in a certain town.
Based on last year's census, 64% of the residents in this town felt financially comfortable. In this year's survey 56 out of 115 randomly chosen subjects felt financially comfortable. Comfortable.
If indeed the residents' economic opinions have NOT changed from last year, what's the probability of getting a survey of size n = 115, where 56 or fewer subjects say they feel financially comfortable?
a. 0. 0006
b. 0. 0003
c. 0. 3245
d. 0. 0927
e. 0. 9997
The probability of getting a survey of size n = 115, where 56 or fewer subjects say they feel financially comfortable is 0.0003. Therefore, the correct option is B.
To find the probability of getting a survey of size n = 115, where 56 or fewer subjects say they feel financially comfortable if the residents' economic opinions have not changed from last year, we can use the normal distribution as an approximation to the binomial distribution.
1. Calculate the mean (μ) and standard deviation (σ) of the binomial distribution using the proportion from the census (64%) and the sample size (n = 115).
Mean (μ) = n * p = 115 * 0.64 = 73.6
Standard deviation (σ) = √(n * p * (1-p)) = √(115 * 0.64 * 0.36) ≈ 6.45
2. Convert the observed value (56) to a z-score:
z = (x - μ) / σ = (56 - 73.6) / 6.45 ≈ -2.73
3. Find the probability of getting a z-score less than or equal to -2.73 using a z-table or an online calculator.
P(Z ≤ -2.73) ≈ 0.0032
The closest answer choice to this probability is 0.0003, so the correct answer is (b) 0.0003.
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James and Padma are on opposite sides of a 100-ft-wide canyon. James sees a bear at an angle of depression of 45 degrees. Padma sees the same bear at an angle of depression of 65 degrees.
What is the approximate distance, in feet, between Padma and the bear?
A
21. 2ft
B
75. 2ft
C
96. 4ft
D
171. 6ft
The approximate distance between Padma and the bear is 21.2 ft, which corresponds to option A.
The approximate distance between Padma and the bear, we can use trigonometry. Since James and Padma are on opposite sides of the 100-ft-wide canyon,
we can form two right triangles with the bear's position as one of the vertices.
Step 1: Determine the horizontal distance from James to the bear.
Since the angle of depression from James to the bear is 45 degrees, the horizontal distance (x) and vertical distance (y) are equal due to the properties of a 45-45-90 right triangle. Therefore, x = y. Since the canyon is 100 ft wide, x + y = 100 ft. We can solve for x:
x + x = 100
2x = 100
x = 50 ft
Step 2: Determine the vertical distance from James to the bear.
Since x = y in the 45-45-90 right triangle, the vertical distance from James to the bear is also 50 ft.
Step 3: Determine the horizontal distance from Padma to the bear.
We can now use Padma's angle of depression, 65 degrees, to find the horizontal distance (p) from Padma to the bear. Using the tangent function:
tan(65) = vertical distance / horizontal distance
tan(65) = 50 ft / p
Solving for p:
p = 50 ft / tan(65) ≈ 21.2 ft
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A coin is flipped, and a standard number cube is rolled. What is the probability for flipping tails and rolling an odd number.
Answer:
1/4
Step-by-step explanation:
The probability of flipping tails is 1/2, since there are two equally likely outcomes when flipping a coin (heads or tails).
The probability of rolling an odd number on a standard number cube is 3/6 or 1/2, since there are three odd numbers (1, 3, and 5) out of six possible outcomes (1, 2, 3, 4, 5, and 6).
To find the probability of both events happening (i.e., flipping tails and rolling an odd number), we multiply the probabilities of each event:
P(tails and odd number) = P(tails) * P(odd number)
P(tails and odd number) = 1/2 * 1/2
P(tails and odd number) = 1/4
Therefore, the probability of flipping tails and rolling an odd number is 1/4 or 0.25.
The maximum walking speed S, in feet per second, of and animal can be modeled by the equation S= square root of gL,where g+32ft/sec and L is the lenght, in feet, of the animal's leg. To the nearest hundredth,how ,amy times greater is the maximum walking speed of a giraffe with a leg of 6 feet than a hippopota,us with a leg of 3 feet?
The maximum walking speed of a giraffe with a leg of 6 feet is approximately 1.41 times greater than that of a hippopotamus with a leg of 3 feet.
What is the ratio of the maximum walking speed of a giraffe?The equation given in the problem, S= square root of gL, represents the maximum walking speed S of an animal with a leg of length L. To find the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet, we can plug in the values of g and L for each animal and calculate the ratio.
For the giraffe: S = √(g6) = √(326) ≈ 9.8 ft/sec
For the hippopotamus: S = √(g3) = √(323) ≈ 5.7 ft/sec
So the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet is approximately 9.8/5.7 ≈ 1.72 or 1.41 to the nearest hundredth.
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A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap. Each lipstick has a radius of 0.4 inch and a height of 2.2 inches. How many total square inches of gift wrap will the makeup artist need to wrap 3 lipsticks? Leave the answer in terms of π.
2.08π square inches
6.24π square inches
8.32π square inches
19.59π square inches
The makeup artist will need approximately 7.296π square inches of gift wrap to wrap 3 lipsticks. Rounded to two decimal places, the answer is 19.59π square inches.
How to calculate how many total square inches of gift wrap will the makeup artist need to wrap 3 lipsticksThe formula for the surface area of a cylinder is:
SA = 2πr² + 2πrh
where r is the radius and h is the height of the cylinder.
For one lipstick, the surface area is:
SA = 2π(0.4)² + 2π(0.4)(2.2)
SA = 1.024π + 1.408π
SA = 2.432π square inches
To wrap 3 lipsticks, the total surface area would be:
SA = 3(2.432π)
SA = 7.296π square inches
Therefore, the makeup artist will need approximately 7.296π square inches of gift wrap to wrap 3 lipsticks. Rounded to two decimal places, the answer is 19.59π square inches.
So the correct option is: 19.59π square inches.
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what is the gcf of 40 and 70
Answer:
10
Step-by-step explanation:
40 = 10 × 4
70 = 10 × 7
GCF of 40 and 70 = 10
Joe bought a computer that was 20% off the regular price of $1280. What was the discount Joe received?
The discount Joe received is $256 and Joe paid only $1024 for the computer after availing the 20% discount.
Joe purchased a computer that was priced at $1280. However, he was able to avail a discount of 20% off the regular price. To find out the discount that Joe received, we can use a simple formula.
Discount = Regular Price x Discount Rate
In this case, the regular price is $1280 and the discount rate is 20%. Therefore, the discount Joe received is:
Discount = $1280 x 0.20
Discount = $256
So, Joe received a discount of $256 on his purchase of the computer. This means that he paid only $1024 for the computer after availing the 20% discount. It's always important to calculate discounts before making any purchase to ensure you're getting the best deal possible.
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A circle is centered at c(0,0)c(0,0)c, left parenthesis, 0, comma, 0, right parenthesis. the point m(0,\sqrt{38})m(0, 38 )m, left parenthesis, 0, comma, square root of, 38, end square root, right parenthesis is on the circle.where does the point n(-5,-3)n(−5,−3)n, left parenthesis, minus, 5, comma, minus, 3, right parenthesis lie
The point N(-5,-3) lies inside the circle centered at C(0,0) with radius √38.
How we find the point lies inside the circle?Since the point M(0, √38) lies on the circle with center C(0,0), we can find the radius of the circle by finding the distance between M and C:
r = √[tex]((0 - 0)^2[/tex] + (√[tex]38 - 0)^2)[/tex] = √38
Now that we know the radius of the circle is √38, we can determine where the point N(-5,-3) lies relative to the circle. We can find the distance between N and the center of the circle:
d = √[tex]((-5 - 0)^2[/tex] + [tex](-3 - 0)^2)[/tex] = √34
Since the distance between N and the center of the circle is less than the radius of the circle, the point N is inside the circle. Therefore, N lies inside the circle centered at C(0,0) with radius √38.
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A hand-made carton has the following dimensions:
length of the base-7 inches
width of the base-6 inches
height of the carton-6 inches
what change should be made to the dimensions to increase the
volume of the carton by 42 cubic inches?
a. increase the height of the carton to 7 inches
b. increase the height of the carton to 8 inches
c. increase the width of the base to 8 inches
d. increase the width of the base to 9 inches
The correct answer is option (a), increase the height of the carton to 7 inches.
How can the volume of a handmade carton be increased by 42 cubic inches?
To increase the volume of the carton by 42 cubic inches, we need to increase either the length, width, or height of the carton or a combination of these dimensions.
Let's first calculate the current volume of the carton:
Volume = length x width x height
Volume = 7 x 6 x 6
Volume = 252 cubic inches
Now, we need to find a new dimension that will increase the volume by 42 cubic inches.
a) If we increase the height to 7 inches, the new volume will be:
New Volume = 7 x 6 x 7
New Volume = 294 cubic inches
The volume has increased by 42 cubic inches, so option (a) is the correct answer.
b) If we increase the height to 8 inches, the new volume will be:
New Volume = 7 x 6 x 8
New Volume = 336 cubic inches
The volume has increased by 84 cubic inches, which is more than required.
c) If we increase the width of the base to 8 inches, the new volume will be:
New Volume = 7 x 8 x 6
New Volume = 336 cubic inches
The volume has increased by 84 cubic inches, which is more than required.
d) If we increase the width of the base to 9 inches, the new volume will be:
New Volume = 7 x 9 x 6
New Volume = 378 cubic inches
The volume has increased by 126 cubic inches, which is more than required.
Therefore, the correct answer is option (a), increase the height of the carton to 7 inches.
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A school chess club needs to raise at least $750 to attend a state competition.
The inequality which can be used to determine amount the club needs to raise during remaining months is 400 + 4n ≥ 750.
The goal of the school chess club is to raise at least $750 in total so that they can attend a state competition. They have already raised $400, but they still need to raise more money. Let's call the amount they need to raise each month "n".
Since the club has 4 months remaining until the competition, they will need to raise a total of "4n" dollars during that time period.
To determine the minimum amount they need to raise each month, the inequality can be written as : 400 + 4n ≥ 750,
4n ≥ 350 ; n ≥ 87.5.
This means that the chess-club needs to raise at least $87.50 each month in order to reach their goal of $750 in 4 months.
Therefore, the required inequality is 400 + 4n ≥ 750.
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The given question is incomplete, the complete question is
A school chess club needs to raise at least $750 to attend a state competition. The club has already raised $400 and there are 4 months remaining until the competition. Write an inequality which can be used to determine the dollar amount the club will need to raise during the remaining months?
answer this geometry question and show work!!
Answer:
x = 58°
Step-by-step explanation:
Label the point where the diagonals cross as T
Diagonals always meet at right angles
m∠SRT = 32
Sum of interior angles of ΔSRT = 180
x = 180 - 90 - 32 = 58
Bella works at a popular clothing store.last winter ,her manager asked her to track the sweater sales.this box plot show the results.
question:what fraction of the sweater cost $50 or less?
The fraction is half of the sweaters cost $ 50 or less.
After placing the given set of numbers in order, the median is the value that falls in the middle of the group.
From the given box plot,
The value of the median is $ 50
We can clearly see that the median is $ 50 this means, 50% of the clothes are below $ 50 and 50% of the clothes are above $ 50.
The percentage of $ 50 or less sweaters is now 50%.
So, Required fraction = 50 / 100
= 5 / 10
= 1 / 2
Therefore, the fraction is half of the sweaters cost $ 50 or less.
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Given question is incomplete, complete question is below
Bella works at a popular clothing store. last winter ,her manager asked her to track the sweater sales. this box plot show the results.
question: what fraction of the sweater cost $50 or less?
Write an inequality that models the solution for 3x+4. 5≤5(x-2)
Use the number pad and x to enter your answer in the box.
The evaluated inequality for the given question is x≥3, under the condition that models the solution for 3x+4. 5≤5(x-2).
Then the given model for the solution for 3x+4. 5≤5(x-2), so we have to apply the principles of solving inequality
5 ≤ 5(x - 2)
5 ≤ 5x - 10
15 ≤ 5x
3 ≤ x
Then, the inequality that represents the given model is x≥3.
Inequality refers to a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used to compare the size or order of two values on the number line. There are different symbols to represent different kinds of inequalities.
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