The hexagonal prism below has a height of 9 units and a volume of 216.9 units. Find the area of one of its bases.

Answers

Answer 1

Answer:

The answer is 24.1 unit²

Step-by-step explanation:

Volume of prisms=cross sectional area×h

cross sectional area=Volume of prisms/height

A=216.9/9

A=24.1 unit²


Related Questions

Firm A calculates the cost of a job using the formula=500+30t,where t represents the number of days to complete the job. Firm B calculates the cost of a job using the formula=260+48t​

Answers

Answer

I think its a

Step-by-step explanation:

If the reaction starts with 35.2 grams of Ca(OH)2 and 20.7 grams of H2SO4, find the limiting reactant and show your work to support your decision.

Answers

The limiting reactant in the reaction between 35.2 grams of Ca(OH)₂ and 20.7 grams of H₂SO₄ is H₂SO₄. This was determined by calculating the moles of each reactant and comparing them to the stoichiometric ratio of the reaction.

To determine the limiting reactant, we need to calculate the amount of product that can be formed from each reactant.

First, let's write the balanced chemical equation for the reaction between Ca(OH)₂ and H₂SO₄

Ca(OH)₂ + H₂SO₄ → CaSO₄ + 2H₂O

Next, let's calculate the amount of product that can be formed from each reactant

For Ca(OH)₂:

Molar mass of Ca(OH)₂ = 74.09 g/mol

1 mole of Ca(OH)₂ reacts with 1 mole of H₂SO₄ to produce 1 mole of CaSO₄

Moles of Ca(OH)₂ = 35.2 g / 74.09 g/mol = 0.475 mol

Moles of H₂SO₄ = 20.7 g / 98.08 g/mol = 0.211 mol

Moles of CaSO₄ that can be formed from Ca(OH)₂ = 0.475 mol

Moles of CaSO₄ that can be formed from H₂SO₄ = 0.211 mol

For H2SO4

Molar mass of H₂SO₄ = 98.08 g/mol

Moles of CaSO₄ that can be formed from H2SO4 = 0.211 mol

Since the amount of CaSO₄ that can be formed from Ca(OH)₂ is greater than the amount that can be formed from H₂SO₄, Ca(OH)₂ is the excess reactant and H₂SO₄ is the limiting reactant.

Therefore, H₂SO₄ is the limiting reactant

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Which expression is equivalent to 6√8 √√2?

A. 48√/2
B. 24
C. 24√2
D. 48

Answers

Answer:

[tex]6 \sqrt{8} \sqrt{2} = 6 \sqrt{16} = 6(4) = 24[/tex]

B is the correct answer.

F(x)=3x-1 and g(x)=x+2, find (f+g)(x)

Answers

Answer:

4x+1

Step-by-step explanation:

3x-1+(x+2)

3x-1+x+2

Collect Like Terms: 3x+x-1+2

= 4x+1

You're at a clothing store that dyes your clothes while you wait. The store offers
4 different articles of clothing and 3 colors.
If you randomly choose the article of clothing and the color, which of these diagrams can be used to find all of the possible outcomes?
Choose all answers that apply:

Answers

Answer:

Both.

Step-by-step explanation:

They both are the same diagram. Just rearranged.

A child that is 4.5 feet tall is standing in the playground. The sun is shining and the child casts a shadow 10 feet long. At the same time, a tree casts a shadow that is 24 feet long. How tall is the tree?

Answers

Answer:

The tree is 10.8 feet

---------------------------

The formed triangles are similar right triangles.

They have equal ratios of corresponding sides.

Let the tree is t feet high, then we have ratios:

t/4.5 = 24/10

Solve it for t:

t/4.5 = 2.4t = 4.5*2.4t = 10.8

Answer:

10.8 feet

Step-by-step explanation:

The problem involves using proportions to find the height of the tree, based on the height of the child and the lengths of the two shadows.

To set up the proportion, first recognize that the ratio of the height of the child to the length of their shadow is the same as the ratio of the height of the tree to the length of its shadow.

This can be written mathematically as:

[tex]\boxed{\sf \dfrac{height\;of\;the\;child}{child\;shadow\;length}=\dfrac{height\;of\;the\;tree}{tree\;shadow\;length}}[/tex]

Let the height of the tree be x.

Given the height of the child is 4.5 feet, the length of the child's shadow is 10 feet, and the length of the tree's shadow is 24 feet:

[tex]\begin{aligned}\sf \dfrac{height\;of\;the\;child}{child\;shadow\;length}&=\sf \dfrac{height\;of\;the\;tree}{tree\;shadow\;length}\\\\\dfrac{4.5}{10}&=\dfrac{x}{24}\end{aligned}[/tex]

To solve for x, multiply both sides of the equation by 24 and simplify:

[tex]24 \cdot \dfrac{4.5}{10}=24 \cdot \dfrac{x}{24}[/tex]

     [tex]\dfrac{108}{10}=x[/tex]

     [tex]10.8=x[/tex]

Therefore, the height of the tree is 10.8 feet.

Write the equation of the line in slope intercept form, that is perpendicular to the line shown and passes through the point J(-1,3).

Answers

Answer:y=-4x-1

Step-by-step explanation:

The equation of the line in slope-intercept form that is perpendicular to the line passing through (-2,6) and (-3,2) and passes through point (-1,3) is

x - 4y = -11

We have,

From the figure,

(-2, 6) and (-3, 2)

So,

The slope of the given line.

slope = (change in y) / (change in x)

slope = (2 - 6) / (-3 - (-2))

slope = -4 / -1

slope = 4

Since the two lines are perpendicular, the slope of the new line will be the negative reciprocal of the slope of the given line.

The slope of the new line = -1/4

Now that we know the slope of the new line, we can use the point-slope form of the equation of a line to find the equation of the line that passes through point J(-1,3):

y - y1 = m(x - x1)

where m is the slope and (x1,y1) is the point through which the line passes.

Substituting the values.

y - 3 = (-1/4)(x - (-1))

Simplifying.

y - 3 = (-1/4) (x + 1)

Multiplying by -4 to get the equation into slope-intercept form.

-4y + 12 = x + 1

Simplifying:

x - 4y = -11

Therefore,

The equation of the line in slope-intercept form that is perpendicular to the line passing through (-2,6) and (-3,2) and passes through point (-1,3) is

x - 4y = -11

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find the square root of 7

Answers

The value of the square root of 7 is,

⇒ √7 = 2.645

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

WE have to given that;

To find the value of the square root of 7 .

Since, the square root of 7 is,

⇒ √ 7

⇒ 2.645

Thus, The value of the square root of 7 is,

⇒ √7 = 2.645

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The school asked students to help decide what to name the school gym. Each student was given a list of six names and asked to choose one. What type of graph would be the most appropriate to graph the results?

Answers

Answer:

Step-by-step explanation:

I'd suggest a bar graph. Some may suggest a pie chart, but it can be visually difficult to quickly tell the difference in sizes between slices of the pie in pie charts when there are a lot of options. With a bar graph, it is usually very easy to see which bar is the tallest.  

A restaurant automatically charges a 20% gratuity if a party has 6 or more people. How much gratuity is added to a party of 6 on a $141 bill.

Answers

Answer:

Therefore, $28.20 is added as gratuity to the $141 bill for a party of 6.

Step-by-step explanation:

If a party has 6 or more people, a 20% gratuity is automatically charged. So in this case, the gratuity is:

20% of $141 = (20/100) x $141 = $28.20

Therefore, $28.20 is added as gratuity to the $141 bill for a party of 6.

Please help meeeeeeeee

Answers

Answer:

936m3

Step-by-step explanation:

6×6×2=72m3

9×16×6=864m3

72+864=936m3

what is the volume of a rectangular prism with a length of 4m, width of 6.5m and height of 1.2m

Answers

The volume of the rectangular prism is 31.2 [tex]m^{3}[/tex].

To find the volume of a rectangular prism, we multiply the length, width, and height of the prism.

Given that the length of the rectangular prism is 4m, the width is 6.5m, and the height is 1.2m, we can find the volume as follows:

Volume = length x width x height

= 4m x 6.5m x 1.2m

= 31.2 cubic meters

Therefore, the volume of the rectangular prism is 31.2 cubic meters.

To understand what this means, imagine filling the rectangular prism with cubic blocks, each having a volume of 1 cubic meter. We would need to place 31.2 of these blocks to completely fill the prism. Another way to think about it is that the prism could hold 31.2 cubic meters of water, if filled to the brim without any spillage.

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What is the sine of 0?
(Need help)

Answers

The angle of sinθ between the horizontal vector (1, 0) and the slant vector (15/17, -8/17) is sin⁻¹(8/17), which is approximately 29.11 degrees.

To find the angle of sinθ between a horizontal vector and a slant vector, we can use the dot product formula:

a · b = |a| |b| cos(θ)

where a and b are vectors, |a| and |b| are their magnitudes, and theta is the angle between them.

In this case, the horizontal vector is (1, 0) and the slant vector is (15/17, -8/17).

The magnitude of the horizontal vector is 1, and the magnitude of the slant vector is:

|b| = sqrt((15/17)² + (-8/17)²) = sqrt(225/289 + 64/289) = sqrt(289/289) = 1

The dot product of the two vectors is:

a · b = (1)(15/17) + (0)(-8/17) = 15/17

So we have:

15/17 = (1)(1) cos(θ)

cos(θ) = 15/17

To find sin(θ), we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

sin²(θ) = 1 - cos²(θ) = 1 - (15/17)² = 64/289

Taking the square root of both sides, we get:

sin(theta) = sqrt(64/289) = 8/17

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ABCD is a rhombus. A has coordinates (2,- 4) and C (-2, 4). Find the equation of the diagonal
BD.

Answers

Answer:

[tex]y =\dfrac{1}{2}x[/tex]

Step-by-step explanation:

General slope-intercept form of a straight line is
y = mx + b
where m = slope, b = y-intercept

The diagonals of a rhombus bisect each other at 90°

The equation of diagonal AC can be found as follows

Slope of AC = [tex]\dfrac{4 - (-4)}{-2 - 2} = \dfrac{8}{-4} = - 2\\[/tex]

Therefore the diagonal AC has the equation
y = -2x + b

where b is the y intercept

We can find b by plugging in (-2, 4) into the above equation:
4 = -2(-2) + b

4 = b + b

b = 0

So the equation of the diagonal is y = -2x

This passes through the origin (0,0)

Since A and C are equidistant from the origin, the origin is the midpoint of the diagonal AC

Since the other diagonal BD has to bisect this diagonal at 90°, it too has to pass through the midpoint (0, 0)

The slope of a line perpendicular to y = mx + b is -1/m

Therefore the slope of the perpendicular line to y = -2x is - (1/-2) = 1/2 and the y-intercept is 0 since it passes through the origin

Therefore the equation of diagonal BD is
[tex]y =\dfrac{1}{2}x[/tex]

what is the actual lenght if length of drawing is 8.6cm and scale is 1cm of 50km?

Answers

Answer:

Step-by-step explanation:

To determine the actual length represented by a given length on a drawing, you need to use the scale ratio. In this case, the scale is 1 cm : 50 km. This means that 1 cm on the drawing represents 50 km in actual length.

To find the actual length represented by a length of 8.6 cm on the drawing, we can set up a proportion:

1 cm : 50 km = 8.6 cm : x

To solve for x, we can cross-multiply:

1 * x = 50 * 8.6

x = 430 km

Therefore, the actual length represented by a length of 8.6 cm on the drawing is 430 km.

Suppose z varies inversely with t and that z = 10 when t = 12. What is the value of z when t = 5?

Answers

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"z" varies inversely with "t"}}{z = \cfrac{k}{t}}\hspace{5em}\textit{we also know that} \begin{cases} z=10\\ t=12 \end{cases} \\\\\\ 10=\cfrac{k}{12}\implies 120 = k\hspace{9em}\boxed{z=\cfrac{120}{t}} \\\\\\ \textit{when t = 5, what's "z"?}\qquad z=\cfrac{120}{5}\implies z=24[/tex]

PLEASE HELP!!! MARKING BRAINLIST

Answers

Answer:

P = (3^2)/(4^2) = 9/16 = .5625 = 56.25%

This probability is about .56.

Tami has two jobs and can work at most 20 hours each week. She works as a server and makes $6 per hour. She also tutors and makes $12 per hour. She needs to earn at least $150 a week. Review the included image and choose the graph that represents the system of linear inequalities.


A.
Graph A

B.
Graph B

C.
Graph C

D.
Graph D

Answers

Graph B represents the system of linear inequalities the best.

Hence the correct option is (B).

Let Tami needs to work x hours per week as server and y hours per week as tutors.

So it is given that she can work at most 20 hours a week.

So, the suitable inequality to describe the situation:

x + y [tex]\le[/tex] 20 ............. (i)

Now the corresponding equation of this above inequality is,

x + y = 20

x/20 + y/20 = 1

comparing to inception form of straight line we can say that the equation says about a line which cuts axes at (20, 0) and (0, 20) respectively.

since (0, 0) gives 0 + 0 = 0 [tex]\le[/tex] 20 is true.

So the solution area towards origin.

It is also given that she makes $6 per hour as server and makes $12 per hour as tutor and she needs to earn at least $150.

The best suited inequality for this condition,

6x + 12y [tex]\ge[/tex] 150 .................(ii)

The corresponding equation of the above inequality:

6x + 12y = 150

6x/150 + 12y/150 = 1

x/25 + y/(12.5) = 1

So it is the line cuts the axes at (25, 0) and (0, 12.5) respectively.

since (0, 0) gives 6*0 + 12*0 = 0 [tex]\ge[/tex] 150 is not true so the solution area for this inequality towards opposite of origin along the straight line.  

So Graph B represents the system of linear inequalities the best.

Hence the correct option is (B).

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please help me with theses!! need to get it done asap.

Answers

Answer:

Question 1 : Pierre is right

Question 2 : 0.85 (because 1 - 0.15 = 0.85)

Question 3 : Less than 1

Step-by-step explanation:

can someone please do #7

Answers

The numeric value of f(a) + f(h) for f(x) = x² - 5x + 3 is given as follows:

A. f(a) + f(h) = a² + h² - 5a - 5h + 6.

How to calculate the numeric value of a function or of an expression?

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is defined as follows:

f(x) = x² - 5x + 3.

Hence the numeric values are given as follows:

f(a) = a² - 5a + 3.f(h) = h² - 5h + 3.

The only like term is the 3 for both expressions, hence the addition is given as follows:

f(a) + f(h) = a² + h² - 5a - 5h + 6.

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If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?

Answers

Answer:

f(g(x)) = x is the correct graph.

what is the answer? –162 ÷ (–9)

Answers

Answer:

To sum up, 162/9 = 18.

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 9 on the left side and the dividend 162 on the right side like this:

9 ⟌ 1 6 2

Step 2:

The divisor (9) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:

0

9 ⟌ 1 6 2

Step 3:

Multiply the divisor by the result in the previous step (9 x 0 = 0) and write that answer below the dividend.

0

9 ⟌ 1 6 2

0

Step 4:

Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.

0

9 ⟌ 1 6 2

- 0

1

Step 5:

Move down the 2nd digit of the dividend (6) like this:

0

9 ⟌ 1 6 2

- 0

1 6

Step 6:

The divisor (9) goes into the bottom number (16), 1 time(s). Therefore, put 1 on top:

0 1

9 ⟌ 1 6 2

- 0

1 6

Step 7:

Multiply the divisor by the result in the previous step (9 x 1 = 9) and write that answer at the bottom:

0 1

9 ⟌ 1 6 2

- 0

1 6

9

Step 8:

Subtract the result in the previous step from the number written above it. (16 - 9 = 7) and write the answer at the bottom.

0 1

9 ⟌ 1 6 2

- 0

1 6

- 9

7

Step 9:

Move down the last digit of the dividend (2) like this:

0 1

9 ⟌ 1 6 2

- 0

1 6

- 9

7 2

Step 10:

The divisor (9) goes into the bottom number (72), 8 time(s). Therefore put 8 on top:

0 1 8

9 ⟌ 1 6 2

- 0

1 6

- 9

7 2

Step 11:

Multiply the divisor by the result in the previous step (9 x 8 = 72) and write the answer at the bottom:

0 1 8

9 ⟌ 1 6 2

- 0

1 6

- 9

7 2

7 2

Step 12:

Subtract the result in the previous step from the number written above it. (72 - 72 = 0) and write the answer at the bottom.

0 1 8

9 ⟌ 1 6 2

- 0

1 6

- 9

7 2

- 7 2

0

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 162 divided by 9 calculated using Long Division is:

18

0 Remainder

Jim spends $16 each time he travels the toll roads. He started the month with $224 in his toll road account. The amount, (in dollars), that he has left in the account after T trips on the toll roads is given by the following function.
A(t)=224-16t
How much money does Jim have left in the account after 8 trips on the toll roads?How many trips on the toll roads can he take until his account is empty?

Answers

first multiply 16*8=128
then subtract 224-128=96
money left after 8trips is $96
then he can take 6 more trips
(96/16=6trips)

Find an equation of the line.Write the equation in the standard form.
Through (7,3)​; parallel to 8x−y=9.

Answers

As the line is parallel to the given line, the slopes of both lines are equal.

The given line 8x − y = 9 can be written in slope-intercept form as:

y = 8x - 9

Comparing with y = mx + b, we get slope m = 8.

Therefore, the slope of the line we need to find is also 8.

Using the point-slope form of the equation of a line, we have:

y - y1 = m(x - x1)

where (x1, y1) = (7, 3) and m = 8.

Substituting the values, we get:

y - 3 = 8(x - 7)

y - 3 = 8x - 56

y = 8x - 53

This is the equation of the line in slope-intercept form. To convert it to standard form, we move all the variables to the left-hand side:

-8x + y = -53

Therefore, the equation of the line in standard form is:

8x - y = 53.

GRADE O7 MATHEMATICS MCA / MATHEMATICS MCA / 22 OF 49
42%
The table shows the average annual precipitation over a 30-year period for 7 states. The values for Michigan and Nebraska are missing.
• When the missing values are included, the range for the data is 18.1.
• The mean of the values for Michigan and Nebraska is 28.2 inches.
• Michigan has a greater amount of annual precipitation than Nebraska.
• Indiana has the greatest average annual precipitation.
What are the missing values?
Drag the numbers into the table.

Answers

Answer:

Michigan: 32.8

Nebraska: 23.6

Step-by-step explanation:

8 apple pies and 3 blueberry muffins cost €14.
6 apple pies and a blueberry muffin cost €8.
Work out the total cost of an apple pie and a blueberry
muffin.

Answers

The total cost of an apple pie and a blueberry muffin is €3. An apple pie costs €1 and a blueberry muffin costs €2.

To tackle this issue, we can utilize an arrangement of conditions. We should let "a" address the expense of one fruity dessert, and "b" address the expense of one blueberry biscuit.

Then we can compose two conditions in light of the data given:

8a + 3b = 14

6a + b = 8

The principal condition addresses the expense of 8 fruity desserts and 3 blueberry biscuits, which is equivalent to €14. The subsequent condition addresses the expense of 6 fruity desserts and 1 blueberry biscuit, which is equivalent to €8.

Presently we can tackle this arrangement of conditions utilizing replacement. We can detach b in the subsequent condition:

b = 8 - 6a

We can then substitute this articulation for b into the primary condition:

8a + 3(8 - 6a) = 14

Working on this situation, we get:

8a + 24 - 18a = 14

Joining like terms, we get:

-10a + 24 = 14

Deducting 24 from the two sides, we get:

-10a = - 10

Partitioning by - 10, we get:

a = 1

Now that we know the expense of one fruity dessert, we can substitute this worth back into the second condition to settle for b:

6(1) + b = 8

Improving on this situation, we get:

6 + b = 8

Taking away 6 from the two sides, we get:

b = 2

Consequently, a fruity dessert costs €1 and a blueberry biscuit costs €2. The complete expense of a fruity dessert and a blueberry biscuit is €3.

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A woman deposits $300 in a savings account that pays 6% annually. If she withdraws all the money in the account after 120 days, how much does she withdraw (rounded to the nearest dollar)?

Answers

The woman will withdraw $300 given 6%   interest rate annually.

We can use the formula for simple interest to solve this problem:

I = Prt

where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years. Since the interest rate is given as an annual rate, we need to convert it to a daily rate by dividing by 365:

r = 0.06/365 = 0.00016438356

The time in years is 120/365 = 0.3287671233 years. Now we can plug in the values and solve for I:

I = 300 * 0.00016438356 * 0.3287671233 = 0.01699999999

The interest earned is $0.017, which is negligible. Therefore, the woman will withdraw the entire principal plus any interest earned, which is:

300 + 0.017 = $300.02

Rounding to the nearest dollar, the woman will withdraw $300.

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AABC DEF. What sequence of transformations will move AABC onto ADEF?

A. A dilation by a scale factor of 2, centered at the origin, followed by
a 90° clockwise rotation about the origin

B. A dilation by a scale factor of centered at the origin, followed by
the translation (x, y) - (x+4, y-2)

C. A dilation by a scale factor of, centered at the origin, followed by
a 180° clockwise rotation about the origin

D. A dilation by a scale factor of 2, centered at the origin, followed by
a reflection over the y-axis

Answers

The ΔABC is dilated with scale factor 1/2 followed by

a 180° clockwise rotation about the origin.

Hence option (C) is correct.

From the given figure;

The image shrinks while moving ABC to DEF.

And the scale factor is defined as the proportion of the new image's size to that of the previous image.

Since we know

The image contracts if the scale factor is between 0 and 1.

To acquire the position of DEF we have to rotate the triangle 180 degree in clockwise direction about the origin.

Since 1/2 lies between 0 and 1.

Therefore,

It dilated clockwise at 180 degree with scale factor 1/2.

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Gabrielle needs several rectangular outside walls of her house repainted. The north-facing
wall is 22 feet wide by 10 feet tall, the south-facing wall is 15 feet wide by 20 feet tall, and
the wall by her patio is 8 feet wide by 10 feet tall. The painter charges $5 per square foot to
paint outside walls.
How much will it cost Gabrielle
to have the outside walls repainted?

Answers

Answer:

$3000

Step-by-step explanation:

22×10=220

15×20=300

8×10=80

220+300+80=600ft²

5×600=$3000

Select the real-world situation that can be represented by 4m+ 2.
A. Bentley swims 4 more than 2 times the laps Dan swims.
B. Grace bikes 2 more than 4 times the miles Jamie bikes.
C. An online company charges a $4 shipping fee and $2 per item for
a purchase.
OD. A music download website has a membership fee of $4 and
charges $2 for each download.

Answers

Step-by-step explanation:

The real-world situation that can be represented by 4m+2 is option D, where a music download website has a membership fee of $4 and charges $2 for each download.

Here, "4m" represents the total cost of downloading "m" songs at a cost of $2 per song, and "2" represents the fixed cost of the membership fee. So, the total cost of downloading "m" songs along with the membership fee can be represented by the expression 4m + 2.

Other Questions
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