Answer:
V(x) = 4x³ - 96x² + 576xStep-by-step explanation:
Cut out square on each corner has side of x.
When folded up the height of the box becomes same as the side of the cut-out square.
Sides of the base of the box are:
24 - 2x cm as it is folded on both sides.The volume of the box which is the right square prism is:
V = Bh = a²h, where B- base area, a- side of the base, h- height.Substitute the values and find the volume:
V(x) = (24 - 2x)(24 - 2x)x = 4x³ - 96x² + 576xThere are two different mountains in the
state of Washington that get record snowfall.
One winter season, Mount Ranier received
1,224 inches of snow. Mount Baker received
1,140 inches of snow. What is the total
snowfall of these two mountains?
Answer:
2364 in
Step-by-step explanation:
1,224+1,140=2364
1 Over 25
One-fifth
1
25
Answer:
25
Step-by-step explanation:
Divide: 5 : 1/5 = 5/1 · 5/1 = 5 · 5/1 · 1 = 25/1 = 25 Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1/5 is 5/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.In other words - five divided by one fifth is twenty-five.
I hope this helps! Thanks!
what is a rate and a unit rate
Answer: a unit rate is how much would you pay for one item and a rate is a fixed price for a good or service
Step-by-step explanation:
In a survey of 95 pet owners, 56 said they own a dog, and 37 said they own a cat. 34 said they own both a dog and a cat? How many owned a dog but not a cat?
Based on the number of people who said they own a dog and those who owned both a cat and a dog, the number of people who own a dog but not a cat are 22 people.
How to find those who own a dog?To find the number of people who own a dog but not a cat, the formula is:
= Number of people who own a dog - Number of people who own both a dog and a cat
Solving for the number who own a dog and no cats is:
= 56 - 34
= 22 people
In conclusion, 22 people own a dog but not a cat.
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solve Question 4.........
Answer:
5/16
Step-by-step explanation:
9/16 - 1/4 = 9-4/16 = 5/16
Write an expression that represents the paycheck total for
any number of hours worked.
Answer: h x 5
Step-by-step explanation: it is going by 5 every hour and every hour you get paid goes up by 5$. so I would say h x 5 or pt x 5
hw pt
40 / 8.50 . 40
pt = paycheck total
hw= hours worked
A hairdresser is making 4 hair bows. She needs 13/16 yards for each bow. If she has 6 1/8 yards of ribbon, how much will be leftover after making the bows?
Answer:
2 7/8 yards
Step-by-step explanation:
Given 6 1/8 yards of ribbon, you want the leftover amount after making 4 bows that use 13/16 yards each.
Quantity usedIf each of 4 bows takes 13/16 yards, the amount required for bows is ...
4×13/16 = 13/4 . . . . yards
Quantity remainingThe amount left over is the difference between the starting amount and the amount used:
6 1/8 - 13/4 = 49/8 -26/8 = 23/8 = 2 7/8
The hairdresser has 2 7/8 yards of ribbon remaining.
__
Additional comment
Your calculator can work this problem, too.
Based on what you learned about Gerya in the article you read today, how can scientists study Mars if they can't directly
observe what is happening there?
I
Even though scientists can't directly observe what is happening on Mars, they can send satellites to orbit Mars which can document the various aspects of Mars and its geography.
How can we observe Mars?Thanks to massive strides in space technology, humans have been able to study Mars all the way from Earth without having to observe the planet directly.
The main way they can do this is by positioning satellites around Mars which will orbit the planet. These satellites will record and observe things such as the composition of the atmosphere of Mars and how its terrain works.
In conclusion, scientists can use satellites to observe Mars.
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One jar of jam weighs 516 g what is the weigh of 7 jars of jam?
if 1 jar of jam is 516 then 7 jars of jam is 3612 g
-42-3y + 4z = 1
-4y+ 2z = -2
-5z = -5
Find the unique solution to this system of equations. Give your answer as a point. (x, y, z)
The point (x,y,z) = (₋1,3,₋1) is the solution of the equations.
Given the system of equations are:
2x ₊ y ₊ 3z = ₋2 .....eq(1)
x ₋ y ₋ z = ₋3 ...... eq(2)
3x ₋ 2y ₊ 3z = ₋ 12 .... eq(3)
Solving equation 1 and 2.
2x ₊ y ₊ 3z = ₋2
x ₋ y ₋ z = ₋3
Multiply eq(1) by 1 and eq(2) by 2, we get:
2x ₊ y ₊ 3z = ₋2
2x ₋ 2y ₋ 2z = ₋6
⁻ ⁺ ⁺ ⁺
hence sign changes, then we get:
3y ₊ 5z = 4 ... eq(a)
now solving equation 2 and 3.
x ₋ y ₋ z = ₋3
3x ₋ 2y ₊ 3z = ₋ 12
Multiply eq (2) by 3 and eq (3) by 1.
₋3x ₊ 3y ₊ 3z = 9
3x ₋ 2y ₊ 3z = ₋ 12
sign changes, and we get:
y ₊ 6z = ₋3 ..... eq(b)
y = ₋3 ₋ 6z
substitute y value in eq(a)
3(₋3₋6z) ₊ 5z = 4
₋9 ₋ 18z ₊ 5z = 4
₋13z = 13
z = ₋1
substitute z value in eq(b)
y ₊ 6(₋1) = ₋3
y ₋ 6 = ₋3
y = 3
substitute y and z values in eq (2)
x ₋ (3) ₋ (₋1) = ₋3
x ₋ 3 ₊ 1 = ₋3
x ₋ 2 = ₋3
x = ₋3 ₊ 2
x = ₋1
Therefore the solution to the system of equations is: (₋1,3,₋1)
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your question is incomplete.Please find the missing content here:
2x ₊ y ₊ 3z = ₋2
x ₋ y ₋ z = ₋3
3x ₋ 2y ₊ 3z = ₋ 12
Find the unique solution to this system of equations. Give your answer as a point. (x, y, z)
Ken invested $10,000 in two bank accounts. One of the accounts pays 4% annual interest, and the
other account pays 6% annual interest. If the combined interest earned in both accounts after a
year was $514, how much money was invested in each account?
Ken invested $5,700 in the 6% account, and the other $4,300 in the 4% account.
How much money was invested in each account?Let's define the variables:
x = amount of money on the 4% account.y = amount of money on the 6% account.We know that Ken invested $10,000 in total, so:
x + y = 10,000
And the interest in one year is:
x*0.04 + y*0.06 = 514
Then we have a system of equations:
x + y = 10,000
x*0.04 + y*0.06 = 514
To solve it we start by isolating one of the variables in one of the equations, isolating x we will get:
x = 10,000 - y
Replacing that in the other equation we get:
(10,000 - y)*0.04 + y*0.06 = 514
400 - y*0.04 + y*0.06 = 514
400 + y*0.02 = 514
y = (514 - 400)/0.02 = 5,700
Then Ken invested $5,700 in the 6% account, and the other $4,300 in the 4% account.
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please help I cannot find the answer
Answer:
1.55 lbs
Step-by-step explanation:
take 6 ⅕ and divide it by 4 since there are 4 bags, you can also turn it into a decimal (6.2)
Answer:
1.55lbs of cat food in each bag
Step-by-step explanation:
question 1) simply divide the total amount of cat food by the number of bags it is placed in.
6 1/5lb divided by 4
[tex]6 \frac{1}{5} \div 4[/tex]
when dividing fractions, the divisor is flipped over and the sign changes to multiplication.
[tex]6 \frac{1}{5} \times \frac{1}{4} [/tex]
[tex] \frac{31}{5} \times \frac{1}{4} [/tex]
therefore=
[tex] \frac{31}{20} [/tex]
or as a decimal 1.55lbs
What is the solution to 4(3x - 6) + 16 < -32
Answer:-2
Step-by-step explanation:add 8 to both sides 12x-8<-32=-2
Gina might buy 10 oranges and _ apples
The number of apples that Gina can buy is 15 apples.
How to illustrate the information?From the information, it was stated that the ratio of orange to apples is 2:3.
In this case, let the number of apples be represented by x
Therefore, the number of will be:
2/3 = 10/x
Cross multiply
2x = 10 × 3
2x = 30
Divide
x = 30 / 2
x = 15
Therefore, the number of apples that Gina can buy is 15 apples.
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The ratio of orange to apples is 2:3. Gina might buy 10 oranges and _ apples
HELP ASP SHOW UR WORK YOULL GET BRAINLEST
Answer:
x = 8
Step-by-step explanation:
Subtract
44
from both sides
2
Simplify
3
Add
8x
to both sides
4
Simplify
5
Divide both sides by the same factor
6
Simplify
On a test of 80 items, Pedro got 91% correct. (There was partial credit on some items.) How many items did he get correct? incorrect?
Answer:
Step-by-step explanation:
to find this answer you have to know how to make a percent of something to a normal value so to make 91% to a decimal value you divide by 100. That is 0.91. Then you multipy 0.91 x 80=72.8
He got 72 questions right
A tringle is shown.
The triangle is translated 5 units down, then reflected over the x-axis.
Select the Polygon tool. Then, click the points of the triangle vertices to create the triangle by connecting the sides.
The triangle was translated 5 units down and then reflected over the x axis to get (-1, 2), (2, 6) and (-5, 8)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Transformation is the movement of a point either up, down, left or right in the coordinate plane.
The triangle shown has vertices at (-1, 3), (2, -1) and (-5, -3). It was translated 5 units down to get (-1, -2), (2, -6) and (-5, -8). It is then reflected over the x axis to get (-1, 2), (2, 6) and (-5, 8)
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How many cubes of dimensions 15, 30 and 15 cm will be need to form a cube? please give step by step answer to write in exam
4 cuboids of dimensions 15, 30, and 15 cm will be needed to form a cube
The volume of the cuboid is l×b×h where l is length, b is breath and h is the height
The volume of given cuboid = l b h
= 15× 30 ×15
= 6750 cm3
The volume of a cube is a3 where a is the edge of the cube
The edge of the cube can be 30cm
The volume of cube= [tex]a^{3}[/tex]
= [tex]30^{3}[/tex]
= 27000 [tex]cm^3[/tex]
To find out the number of cuboids to be required to form a cube will be the volume of the cube divided by the volume of a cuboid
No of cuboids required = (volume of the cube)/(volume of the cuboid)
= 27000/ 6750
= 4
So, 4 cuboids of 30 ×15 ×15 are required to make a cube whose edge is 30cm
The correct question is How many cuboids of dimensions 15, 30, and 15 cm will be needed to form a cube
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Which of the relations shown does NOT represent y as a function of x?
The graph which does not represent y as a function of x is (B) as a line drawn can't touch the graph at two points.
The function that dose not show y as a function of x.
Y is a function of X, means that a certain variable magnitude or phenomenon Y is determined/caused by another magnitude or phenomenon X, such that the behavior of X will affect that of Y. In logic, a function symbol is a logical symbol that may be applied to an object term to produce another object term.
If a vertical line is drawn such that it touches more than one place, then it is not a function of x.
Here also if a vertical line will be drawn it will touch two places in the curve.
So, in figure B, y is not a function of x.
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As a line created can't touch the graph at two locations, graph (B) does not represent y as a function of x.
The function that hides y's relationship to x.
A variable's magnitude or phenomena Y is determined by or caused by a different variable's magnitude or phenomenon X, meaning that X's behavior will have an impact on Y's. A function symbol in logic is a logical symbol that can be used to transform one object term into another.
A vertical line is not a function of x if it is drawn so that it touches many locations.
In this instance as well, a vertical line drawn here will strike the curve twice.
Y is not a function of x in figure B, therefore.
Karen puts a fence around an L shaped garden with dimensions 2.1ft by 7.8ft by 5.5ft by2.7ft how many feet of fencing will she need
Karen while putting a fence around the L shaped garden will need about 22.3 ft which is the exact perimeter of this field, with its dimensions as given as 2.1ft by 7.8ft by 5.5ft by2.7ft of the garden.
In arithmetic, how do you handle perimeter?Any kind of closed path that covers, encircles, or outlines a full one-dimensional length or a two-dimensional shape is called as a perimeter.
The circumference of a circle or an ellipse is referred to as its perimeter. There are varied uses in real life for the perimeter calculations.
For example, in case of a rectangle, there are two equal lengths and two equal widths in a rectangle. Then we must sum up all the lengths of the rectangle’s four sides in order to get its final perimeter.
Since there are like two of each side length, it is easy to accomplish this perimeter by simply adding the length and width and then multiplying the result by two.
In this problem,
Total perimeter = 2.1 + 5.1 + 2.1 + 2.5 + 2.7 + 7.8
= 22.3 ft
Thus, the perimeter has been calculated in total as 22.3 ft.
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A researcher post a newspaper ad for 20$ for 5 people
Answer:
100$
Step-by-step explanation:
5x20=100
If x varies inversely as y, then find the constant of variation if y = 9 and x =
8.
The constant of variation is 72.
Constant of Variation: What is it?In a direct variation, the constant of variation is the constant (unchanged) ratio of the two variables. The formula for direct variation is. where k is the variational constant and y=kx (or y=kx).
being that
x = 8
y = 9
If x varies in opposition to y, then
x*y = fixed
which means
x*y = k (where we assume constant as k) (where we take constant as k)
Inputting the values of x and y now yields,
8*9 = k
72 = k
Consequently, 72 is the constant of variation.
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LAST QUESTION JUST HELP ME PLS I BEG U
describe a real-world situation where you can apply finding the unit rate
A real-world situation where you can apply the unit rate is finding the cost of a single can of soda from a pack of soda.
How can you use the unit rate?The unit rate refers to the price of a single item out of a number or group of items. It is found by dividing the total price of the group of items by the number of items in the group.
In a real-world scenario, you might see a pack of soda priced at $5.20 and you need to know the price of a single can of soda. You can find this by the formula:
= Price of soda pack / Number of soda cans
= 5.20 / 6
= $0.87
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Write the range of the graph using interval notation.
Answer:
[0, infinity)
Step-by-step explanation:
The range is the set of y-values.
I’m so confused can someone help me pls
Answer:
In so confused to here's a picture that might help a little bit
Anthony want to have $250,000 in 8 years. If her account is paying 14% interest compounded continuously, how much should she invest in now?
The principal investment required to get a total amount of $250,000.00 rounded to the nearest cent is $81569.95.
What is the principal investment required to get the given accrued amount?The formula for calculating compound interest is expressed as;
A = P(1 + r/n)^(n*t)
P = A / e^(r*t) compounded continuously
Given the data in the question;
Accrued amount A = $250,000Time t = 8 yearsAnnual interest = 14% = 14/100 = 0.14compounded continuouslyPlug the given values into the equation above and solve for P
P = A / e^(r*t)
P = 250,000 / e^( 0.14 × 8 )
P = 250,000 / e^( 1.12)
P = 250,000 / e^( 1.12)
P = $81569.95
Therefore the principal investment required to get a total amount of $250,000.00 rounded to the nearest cent is $81569.95.
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The drawing represents a soccer field with goal areas on either end. The scale for the drawing is5m for each grid unit
Answer:
it got sides and all the sides are 5cm
find the value of the variable and the measure of each labeled angle!
x=
x=
simplified =
please help me im struggling
Answer:
Hello! X should equal 17 and each measured angle would be at 37 degrees.
Step-by-step explanation:
(x + 20) = (4x - 31)
Solve.
x = 17
Plug it in.
(17 + 20) = (4(17) - 31)
Solve.
37 = 37
Hope this helps! Xx
A trial is one specific execution of an experiment.
t or f
Answer:
Step-by-step explanation:
f
an elevation
elevation of 20.5 m
of 15 m and an
The angle of elevation made from the eyes of the observer to the top of the tower is 45°.
What is defined as the term angle of elevation?The angle of elevation is the angle formed by the horizontal line of sight and the upward line of sight.
For the given question;
The height of the observer is 1.5 meters.The height of the tower is given as 22 meters.The distance of the tower from the observer is 20.5 meter.The angle of elevation of the top of the tower to the eyes of the observer is needed.
Thus, for this subtract the height of the observer to the height of tower;
height from the eyes to the tower is 22 - 1.5 = 20.5 m.
Thus, apply the trigonometric rule to calculate the angle;
tan Ф = perpendicular/base
perpendicular is the height of tower from the eyes of boy = 20.5 meter.
base is the distance of the tower from the boy = 20.5 meter.
Put the values;
tan Ф = 20.5/20.5
tan Ф = 1
Ф = 45°.
Thus, the angle of elevation made by the eyes of the observer to the top of the tower is 45°.
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The complete question is -
An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.
