Question Details
To earn full credit, you must show ALL
of your steps and calculation leading to
your solution. You will be assessed on
your mathematical communication, use
of mathematics and accuracy of your
results.
A rectangular prism and a square
pyramid were joined to form a
composite figure. What is the surface
area of the figure?
Answers
Answer: the surface area of the composite figure is 195 square units.
Step-by-step, explanation/work:
To find the surface area of the composite figure, we need to calculate the surface area of the rectangular prism and the square pyramid separately, and then add them together.
Let's first find the surface area of the rectangular prism. A rectangular prism has six faces, each of which is a rectangle. The formula for the surface area of a rectangular prism is:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism.
Let's assume that the rectangular prism has dimensions of 4 units by 6 units by 8 units. Then, the surface area of the rectangular prism is:
SA_rectangular prism = 2(4*6) + 2(4*8) + 2(6*8) = 120 square units
Next, let's find the surface area of the square pyramid. A square pyramid has five faces: a square base and four triangular faces. To find the surface area of a square pyramid, we need to find the area of the square base and the area of each of the four triangular faces, and then add them together. The formula for the surface area of a square pyramid is:
SA = l^2 + 2lh
where l is the length of one side of the square base, and h is the height of the pyramid.
Let's assume that the square pyramid has a base of 5 units and a height of 10 units. Then, the surface area of the square pyramid is:
SA_square pyramid = 5^2 + 2(5*10) = 75 square units
Now that we have calculated the surface area of both the rectangular prism and the square pyramid, we can add them together to find the total surface area of the composite figure:
SA_composite figure = SA_rectangular prism + SA_square pyramid
SA_composite figure = 120 + 75
SA_composite figure = 195 square units
Related Questions
What is the equation of a straight line that passes through (2, 0)
and has a gradient of −3 ?
Answers
Answer:
Step-by-step explanation:
La ecuación de una línea recta que pasa a través de un punto \ ((x_1,y_1)\) y tiene un gradiente \ (m\) se puede escribir en la forma punto-pendiente1:
\ [y - y_1 = m (x - x_1)\]
En tu caso, el punto es \ ((2,0)\) y el gradiente es \ (-3\). Sustituyendo estos valores en la fórmula anterior, obtenemos:
\ [y - 0 = -3 (x - 2)\]
Simplificando esta ecuación, obtenemos:
\ [y = -3x + 6\]
Esta es la ecuación de la línea recta que buscas.
Espero que te haya sido útil. ¿Tienes alguna otra pregunta?
Espero que te haya sido útil.
a distribution of values is normal with a mean of 128.3 and a standard deviation of 80.9.find p36, which is the score separating the bottom 36% from the top 64%. p36 = ___
Answers
The score separating the bottom 36% from the top 64%. p36 = 97.43
To find the score that separates the bottom 36% from the top 64%, we need to find the z-score corresponding to the 36th percentile and then use it to calculate the corresponding raw score.
First, we find the z-score using a standard normal table or calculator:
z = invNorm(0.36) = -0.379
Next, we use the formula:
z = (x - mu) / sigma
where x is the raw score, mu is the mean, and sigma is the standard deviation.
Plugging in the given values, we get:
-0.379 = (x - 128.3) / 80.9
Solving for x,
x = -0.379 * 80.9 + 128.3 = 97.43
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Y=6-x4/3algebraic method
Answers
Answer:
Step-by-step explanation:
An employee makes $15 per hour for up to 40 hours per week. For every hour over 40 hours worked in a week, the employee's pay is 1 1/2 regular hourly pay. The employee has to pay 30% of his income in taxes.
What is the employee's net pay after taxes if he works 52.5 hours in one week? Enter the answer in the box.
Answers
The employee's net pay after taxes if he works 52.5 hours in one week is $616.875.
What is the net pay?The net pay is the difference between the gross periodic pay or earnings less statutory deductions, including income taxes.
Normal hourly rate = $15
Normal weekly hours = 40 hours
Overtime rate = 1¹/₂ of $15 = $22.50
Income tax rate = 30%
Total hours worked in one week = 52.5 hours
Overtime hours = 12.5 (52.5 - 40)
Normal weekly gross pay = $600 ($15 x 40)
Overtime pay = $281.25 ($22.50 x 12.5)
Total pay for the week = $881.25
Income tax = $264.375 ($881.25 x 30%)
Net pay = $616.875 ($881.25 - $264.375)
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La raíz cuadrada de 81 dividida en el cuadrado de 3
Answers
Answer:
27 duh lord help them please and me
what is the answer to this math equation i am very bad at division and dont understand it (564873 / 5) * 2 + 6
Answers
Answer:
225955.2
Step-by-step explanation:
How much pure alcohol must a pharmacist add to 10cm^(3) of a 8% alcohol solution to strengthen it to a 80% solution? cubic centimeters
Answers
36 cm³ of pure alcohol is added to 10 cm of an 8% alcohol solution to strengthen it to an 80% solution.
What is the solution?
A particular kind of homogenous mixture made up of two or more substances is known as a solution. A solute is a substance that has been dissolved in a solvent, which is the other substance in the mixture.
Here, we have
Given: a pharmacist adds 10cm^(3) of an 8% alcohol solution to strengthen it to an 80% solution.
Let x represent the volume of pure alcohol (100%) in cm³ needed to be added.
x × 100% + 10 cm³ × 8% = 80% × (x + 10 cm³)
x × 1 + 10 × 0.08 = 0.8 × (x + 10)
x + 0.8 = 0.8x + 8
0.2x = 7.2
x = 36 cm³
Hence, 36 cm³ of pure alcohol is added to 10 cm of an 8% alcohol solution to strengthen it to an 80% solution.
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the graph of y=f(x) is shown below find all values of x where f(x)=1
Answers
the values of x where f(x) = 1 for the function y = x^2 - 2x + 1 are x = 0 and x = 2.
general steps to find all values of x where f(x) = 1 for a given function y = f(x):
1. Set f(x) equal to 1: f(x) = 1.
2. Solve the equation for x. This may involve algebraic manipulation or using techniques such as factoring, completing the square, or using the quadratic formula, depending on the form of the equation.
3. If the equation has multiple solutions, list them all as the values of x where f(x) = 1. If the equation has no solutions, then there are no values of x for which f(x) = 1.
For example, if the function is y = x^2 - 2x + 1, then setting f(x) = 1 gives:
x^2 - 2x + 1 = 1
Simplifying this equation by subtracting 1 from both sides, we get:
x^2 - 2x = 0
Factoring out x, we get:
x(x - 2) = 0
This equation is satisfied when either x = 0 or x = 2. Therefore, the values of x where f(x) = 1 for the function y = x^2 - 2x + 1 are x = 0 and x = 2.
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How can I solve this?
Answers
Answer:
Step-by-step explanation:
first.. simplify
5.9x^2 + 8.5x +4.5x^2+5x (add the others together in a different problem)
then subtract the two numbers (i hope this helps!)
Help!! please!!!!!!!!PLEASE!!!!!!!PLEASE PLEASE M BEEGGNG.
Answers
The independent events are given below:
Rolling a dice and flipping a coin:
Spinning two spinners each round:
The Dependent EventsGrabbing an S out of the scrabble bag and then grabbing an M:
These are dependent events because the outcome of the first event affects the outcome of the second event. The number of possible outcomes for the second event depends on the outcome of the first event.
For example, if the S is not replaced in the bag after it is picked, then the probability of picking an M on the second draw will be different if an S was picked on the first draw.
Pulling a candy, eating it, and pulling another out of a bag:
These are dependent events because the outcome of the first event affects the outcome of the second event. After one candy is removed from the bag, the total number of candies in the bag decreases, which affects the probability of selecting a certain type of candy on the second draw.
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Solve the formula 3x+4y=10 for y
Answers
Answer:formula 3x + 4y = 10 can be solved for y as y = (10 - 3x) / 4.
Step-by-step explanation:
To solve for y, we need to isolate y on one side of the equation.
3x + 4y = 10
Subtract 3x from both sides:
4y = 10 - 3x
Divide both sides by 4:
y = (10 - 3x) / 4
Which angle between -0° and -36° is coterminous with 887?
Answers
Answer:
Step-by-step explanation:
To find the coterminal angle with 887, we can add or subtract any multiple of 360°.
Adding a multiple of 360°:
887 + n(360)
where n is an integer.
Subtracting a multiple of 360°:
887 - n(360)
where n is an integer.
To find the angle between -0° and -36°, we need to subtract a multiple of 360° from 887 to get an angle between -0° and -36°.
887 - n(360) = -x
where x is the angle between -0° and -36°.
We can solve for x:
x = 887 - n(360)
We want x to be negative, so we need to choose a value of n such that 887 - n(360) is less than 0.
If we set n = 3, then:
x = 887 - 3(360) = 47
So, the angle between -0° and -36° that is coterminal with 887 is 47 degrees.
If it is 10:41 now what time will it be in 18 hours 17 minutes
Answers
Answer : 04:48 AM
:)
Answer:
4:58
Step-by-step explanation:
10+18 = 28
28/12 = 2 r4
41+17 = 58
20. There are 100 packs of 100 sheets of paper on a table. Melissa must transfer 82 sheets from each
pack onto a cart. She can count at a maximum speed of 3 sheets per second and needs a minimum of 3
seconds more for putting each pack onto a cart. What is the minimum amount of time she will need to
accomplish the task?
a) 15 minutes
b) 8 minutes
c) 10 minutes
d) 12 minutes
e) 13 minutes
Answers
The minimum time that Melissa will need to accomplish the task are 15 minutes.
How much time will Melissa require to complete this task?To start let's calculate the time she needs to count the sheets Melissa will transfer:
Sheets to be counted: 18 (Melissa can just count 18 sheets rather than 82 as there are 100 sheets in a pack) 100 - 82 = 18.
Time to count 3 sheets: 1 second
1 second = 3 sheets
x = 18 sheets
x = 18 x 1 / 3 = 6 seconds
6 seconds + 3 seconds to transfer the package = 9 seconds
Finally, let's calculate the total time by multiplying by the number of packs.
9 x 100 = 900 seconds / 60 = 15 minutes.
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I need help Area of a circle
Answers
Answer:
The formula
Step-by-step explanation:
just do pi times the circle's radius squared.
(pi x r squared)
The regular price of a color TV is $445.81. During a sale, Hill TV is selling the TV for $393.36. Determine the percent decrease in the price of the TV.
Answers
The regular price of the TV is $445.81, and the sale price is $393.36.
To find the percent decrease in the price, we can use the formula:
percent decrease = (original price - sale price) / original price x 100%
Substituting the given values, we get:
percent decrease = ($445.81 - $393.36) / $445.81 x 100%
percent decrease = $52.45 / $445.81 x 100%
percent decrease = 0.1175 x 100%
percent decrease = 11.75%
Therefore, the percent decrease in the price of the TV is 11.75%.
In a circle with radius 7, an angle measuring π radians intercepts an arc. Find the length of the arc in simplest form.
Answers
Answer: the length of an arc intercepted by an angle in a circle is L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.
Using this formula, we can find the length of the arc intercepted by an angle of π radians in a circle with radius 7:
L = rθ = 7π/1 = 7π
Therefore, the length of the arc is 7π units. This is already in its simplest form since π is a constant that cannot be simplified further.
Step-by-step explanation:
Question 7 of 10
Which equation matches the graph of the greatest integer function given
below?
8
6
t
et
1
-8-6-4-20 2 4
-2
-4
-6
-8
1
OA. y-1x1-3
OB. y-[x]-1
OC. y-[x]+3
OD. y-[x]+1
6 8
Answers
The graph represents B) y = [x] - 1.
What is equatiοn?In algebra, an equatiοn is defined as a mathematical assertiοn that shοws the equality οf twο mathematical expressiοns. Fοr example, the equatiοn 3x + 5 = 14 is made up οf the twο equatiοns 3x + 5 and 14, which are divided by the wοrd "equal."
The Greatest Integer Functiοn is denοted by y = [x].
Fοr all real numbers, x, the greatest integer functiοn returns the largest integer less than οr equal tο x. In essence, it rοunds dοwn a real number tο the nearest lοwest integer.
In the plοt οf y = [x], the plοt starts frοm οrigin because
y = [0] = 0.
But, in the questiοn, all the line are shifted 1 units dοwnward, as it starts frοm (0, -1).
i.e fοr every values οf x, y decreases 1 units. Hence, 1 must be subtracted.
Therefοre, this graph represents B) y = [x] - 1.
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Solve the inequality 8k−(2k−1)≥7k−21, and write the solution in interval notation.
Answers
Answer:
k∈(-∞;22]
Step-by-step explanation:
I added a photo of my solution
PLEASE HELP ME!!! THANK YOU
Answers
The interval notation for the solution set is (-∞, -4] and the number line is on the image at the end.
How to find the solution set of the ienquality?Here we want to find the solution set of the inequality below:
x ≤ -4
First let's do the interval notation. This will be the set that contains all the numbers from negative infinity to -4 (with -4 included, so we need to have a closed set at that end)
This is written as:
(-∞, -4]
The use of the symbols [ ] means that the element belongs to the set.
Now to the number line, we will have a closed circle at x = -4 (because it is a solution) and a line that goes to the left of it. You can see an example in the graph at the end.
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solve for x show ur work pls
Answers
The value of the variable x for the similar triangle ∆MST is 9 which makes option D correct.
How to solve for the value of x for the triangle ∆MSTThe triangles MLK and MST are similar, this implies that the length MS of the smaller triangle is similar to the length MK of the larger triangle
and the length MT of the smaller triangle is similar to the length ML of the larger triangle
so;
14/21 = (x + 5)/21
by comparison of both sides of the equation, we have that;
14 = x + 5
x = 14 - 5 {subtract 5 from both sides}
x = 9
Therefore, the value of the variable x for the similar triangle ∆MST is 9.
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If h(x) = 5 + x and k (x) = StartFraction 1 Over x EndFraction, which expression is equivalent to (k circle h) (x)?\
A: StartFraction (5 + x) Over x EndFraction
B: StartFraction 1 Over (5 + x) EndFraction
C: 5 + (StartFraction 1 Over x EndFraction)
D: 5 + (5 + x)
Answers
Answer:
B: (k circle h)(x) = StartFraction 1 Over (5 + x) EndFraction
Step-by-step explanation:
To find the expression that is equivalent to (k circle h)(x), we first need to find k(h(x)).
k(h(x)) = k(5 + x) = 1/(5 + x)
Therefore, the expression that is equivalent to (k circle h)(x) is 1/(5 + x), which is option B:
(k circle h)(x) = StartFraction 1 Over (5 + x) EndFraction
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Answer:
16
Step-by-step explanation:
Because this is a right triangle the two angles besides the right angle add up to 90°
33 + 3x + 9 = 90
Combine like terms
42 + 3x = 90
Isolate the x ( subtract 42 from both sides)
3x = 48
Divide both sides by 3
x = 16
Answer:
X= 16
Step-by-step explanation:
right angle = 90°
And we have 33° already
90 + 33 = 123
Triangle is 180
180 - 123 = 57
Write in an equation
57 = 3x + 9
57- 9 = 48
48= 3x
48/ 3 = 16
X= 16
Molly is 54 3/4 inches tall. Nancy is 1 1/2 inches taller than Molly and Jane is 1 1/5 inches taller than Nancy. How tall is Jane?
Answers
Answer:
Jane is 57 9/20 inches tall.
Step-by-step explanation:
54 3/4 + 1 1/2 = 55 + (3/4 + 1/2) = 55 + (3/4 + 2/4) = 55 + 5/4 = 56 1/4 inches
Nancy is 56 1/4 inches tall.
Then Jane is 1 1/5 inches taller than Nancy:
56 1/4 + 1 1/5 = 57 + (1/4 + 1/5) = 57 + (5/20 + 4/20) = 57 + 9/20 = 57 9/20 inches so therefore
Jane is 57 9/20 inches tall.
Luis plays basketball for WVC. For the free throws, he makes the
shot 75% of the time. He must now attempt two free throws. Probability that Luis makes the first
shot is 0.75. The probability Luis makes the second shot is 0.75. The probability Luis makes the
second free throw given that he made the first is 0.85. Calculate the probability that Luis makes
both free throws.
Please write your answer as a decimal. Round your answer to the third decimal place.
Answers
Let's use the conditional probability formula to calculate the probability that Luis makes both free throws:
P(both free throws) = P(makes first) * P(makes second | makes first)
We are given that:
P(makes first) = 0.75
P(makes second | makes first) = 0.85
So we can substitute these values in the formula:
P(both free throws) = 0.75 * 0.85
P(both free throws) = 0.6375
Therefore, the probability that Luis makes both free throws is 0.6375, or 0.638 rounded to the nearest thousandth.
help pls show ur work
Answers
22. 3.9 feet tall at the highest point.
23. 12.6 inches long.
24. 76.6 feet tall.
25. The height of the formation is 50.3m.
What is trigonometry?Trigonometry studies the relationships between sides and angles of triangles.
22. To calculate the height of the ramp, David can use the concept of trigonometry. The formula for finding the height of a right triangle is h = opposite side/sin(angle).
The opposite side is 3.5 feet and the angle is 20°.
Therefore, h = 3.5/sin(20°) = 3.9 feet. The ramp needs to be 3.9 feet tall at the highest point, rounded to the nearest tenth.
23. To calculate the length of the springboard, Eric can use the concept of trigonometry.
The opposite side is 6 inches and the angle is 14.5°. Therefore, a = 6/tan(14.5°) = 12.6 inches. The springboard is 12.6 inches long.
24. To calculate the height of the roller coaster, the concept of trigonometry can be used.
The opposite side is 98 feet and the angle is 55°.
Therefore, h = 98/sin(55°) = 76.6 feet. The roller coaster is 76.6 feet tall when it reaches the top of the first hill.
25. To calculate the height of the formation, Diego can use the concept of trigonometry.
The opposite side is 43m and the angle is 36°. Therefore, h = 43/sin(36°) = 50.3m.
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Here’s the question
Answers
The value of 2 miles = 3520 yards and 3 miles = 5280 yards. 2 yards = 6 feet and 3 yards = 9 feet. 2 feet = 2 x 12 inches = 24 inches and 3 feet = 36 inches.
What is SI unit conversion?The International System of Units (SI) units may be used in trade and commerce, grants and other business-related activities, educational information, and as guidelines in publications to improve understanding of the metric system. The SI units may be interpreted or modified for use in the United States by the Secretary of Commerce through the National Institute of Standards and Technology.
Multiply the number of miles by 1760:
1 mile = 1760 yards
2 miles = 2 x 1760 yards = 3520 yards
3 miles = 3 x 1760 yards = 5280 yards
Multiply the number of yards by 3, since there are 3 feet in a yard.
1 yard = 3 feet
2 yards = 2 x 3 feet = 6 feet
3 yards = 3 x 3 feet = 9 feet
Multiply the number of feet by 12, since there are 12 inches in a foot.
1 foot = 12 inches
2 feet = 2 x 12 inches = 24 inches
3 feet = 3 x 12 inches = 36 inches
Hence, the value of 2 miles = 3520 yards and 3 miles = 5280 yards. 2 yards = 6 feet and 3 yards = 9 feet. 2 feet = 2 x 12 inches = 24 inches and 3 feet = 36 inches.
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marking as brainlist please help!!
Answers
Answer:
x=7 and 1/6
Step-by-step explanation:
LOOK AT THE PICTURE! Because the transversal (line that goes through A and B) is straight, then:
(Angle C)+(20x+10)=180 deg
Angle C=(180 deg)-20x+10 deg
Angle C=170-20x
We know that 4x+2 is equal to angle C (marked in the picture) because of alternate interior angles are congruent theorem. So:
170-20x=4x+2
172=24x
x=7 and 1/6
What is the least number of plums that can be shared equally among 6, 9 or 12 children? (A) 27 (B) 36 (C) 54 (D) 72
Answers
The least number of plums that can be shared equally among 6, 9, or 12 children is the smallest common multiple (LCM) of 6, 9, and 12.
Prime factorizing each number, we get:
6 = 2 * 3 9 = 3 * 3 12 = 2 * 2 * 3
Taking the highest power of each prime factor, the LCM is:
LCM = 2 * 2 * 3 * 3 = 36
Therefore, the least number of plums that can be shared equally among 6, 9, and 12 children is 36, which is option (B).
Answer:
Step-by-step explanation: answer is choice B or 36
That would be finding the Lcm of least common multiple of the three numbers. Which is 36
hope it helps!
Three grams of musk oil are required for each bottle of Mink Caress, a very popular perfume made by a small company in western Siberia. The cost of the musk oil is $1.50 per gram. Budgeted production of Mink Caress is given below by quarters for Year 2 and for the first quarter of Year 3:
Answers
Cost of Raw Materials for 4 years is = $ 297,000 $ 459,000 $ 630,000 $ 423,000
Define Budgeted productionBudgeted production refers to the expected level of production that a company plans to achieve during a specific period of time, typically a year. It is a key component of the budgeting process and involves estimating the amount of goods or services that a company will produce and sell in the upcoming period, based on various factors such as market demand, production capacity, and available resources.
Part 1:Direct Materials Budget in Bottles & Grams
Year 2
First Second Third Fourth Total
Budgeted production, 60,000 90,000 150,000 100,000 450,000
Add Desired Ending Inventory
20 % 0f the Production 18,000 30,000 20,000 14,000 82,000
Less Beginning Inventory
36,000/ 3 12,000 18,000 30,000 20,000 80,000
D.
Materials 66,000 102,000 140,000 94,000 452,000
Grams in a Bottle 3 3 3 3 3
Raw Materials 198,000 306,000 420,000 282,000 1356,000
Costs $1.50 $1.50 $1.50 $1.50 1.50
Costs Raw Materials $ 297,000 $ 459,000 $ 630,000 $ 423,000
Total Raw Material Cost is $2,034,000.
Part 2:"Unit cost of raw materials"
Direct Materials Budget in Bottles & Grams
Year 2 Year 3
First Second Third Fourth First
Budgeted production
Production = 60,000 90,000 150,000 100,000 70,000
Desired Ending Inventory
20 % of the Production = 18,000 30,000 20,000 14,000
Less Beginning Inventory
36,000/3 = 12,000/18,000 30,000 20,000 14,000 for musk oil.
D.
Materials Budget = 66,000 102,000 140,000 94,000
Grams in a Bottle = 3 3 3 3
gms = 198,000 306,000 420,000 282,000 for raw materials
Costs(given) = $1.50 $1.50 $1.50 $1.50
Costs of Raw Materials are $ 297,000, $ 459,000, $ 630,000, and $ 423,000 for 4 years.
Therefore, the correct answer are :
Total Raw Material Cost is $2,034,000.
Cost of Raw Materials for 4 years is = $ 297,000 $ 459,000 $ 630,000 $ 423,000
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The complete question is:
Three grams of musk oil are required for each bottle of Mink Caress, a very popular perfume made by a small company in western Siberia. The cost of the musk oil is $1.50 per gram. Budgeted production of Mink Caress is given below by quarters for Year 2 and for the first quarter of Year 3:
Year 2 Year 3
First Second Third Fourth First
Budgeted production, in bottles 60,000 90,000 150,000 100,000 70,000
Musk oil has become so popular as a perfume ingredient that it has become necessary to carry large inventories as a precaution against stock-outs. For this reason, the inventory of musk oil at the end of a quarter must be equal to 20% of the following quarters production needs. Some 36,000 grams of musk oil will be on hand to start the first quarter of Year 2.
Required:
Prepare a direct materials budget for musk oil, by quarter and in total, for Year 2. (Round "Unit cost of raw materials" answers to 2 decimal places.)