4. The surface area of a cube is 486 in. Find the volume inside the cube but outside of
an inscribed sphere. Round to the nearest tenth.

The missing values of the average annual precipitation over a 30-year period for Michigan and Nebraska are:

The average annual precipitations over a 30-year period for Michigan and Nebraska are calculated as follows:

The range of the data is 18.1 inches

Indiana has the greatest average annual precipitation of 41.7 inches

Hence, the smallest value = 41.7 - 18.1

The smallest value = 23.6 inches

From the table, this would be the value of either Michigan or Nebraska.

Also, the mean of the values for Michigan and Nebraska is 28.2 inches.

Let the unknown value be y

Hence; (23.6 + y) / 2 = 28.2

y = 56.4 - 23.6

y = 32.8 inches

Since Michigan has a greater amount of annual precipitation than Nebraska, the average annual precipitation over a 30-year period for Michigan and Nebraska is 32.8 inches and 23.6 inches respectively.

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Step-by-step explanation:

The dressmaker's expected value can be calculated as follows:

E(X) = (1/5) x $76 + (6/11) x (-$31)

E(X) = $15.20 - $16.36

E(X) = -$1.16

Therefore, the dressmaker's expected value is -$1.16, which means that on average, the dressmaker can expect to lose $1.16 for each dress they create.

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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The value of the square root of 7 is,

⇒ √7 = 2.645

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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Answer:

936m3

Step-by-step explanation:

6×6×2=72m3

9×16×6=864m3

72+864=936m3

The domain and range of the cube root function is all real numbers because the cube root of any real number is defined.

The domain of the cube root function is all real numbers because the cube root of any real number is defined. However, in certain situations, such as when the function is being used in a real-world context, there may be practical restrictions on the domain of the function.

The range of the cube root function is also all real numbers because every real number has a unique real cube root. Specifically, the range of the cube root function includes negative and positive real numbers, as well as zero.

It's important to note that the domain and range of a function can be affected by any restrictions or conditions that apply to the function, which may depend on the specific context in which the function is being used. However, for the cube root function as a mathematical concept, the domain and range are as stated above.

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Answer:

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

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:

Solve it for t:

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.

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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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]

Answer:

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

This probability is about .56.

Answer:

Michigan: 32.8

Nebraska: 23.6

Step-by-step explanation:

Answer: 70

Step-by-step explanation: The circles total angles will be 360. From here we just subtract 360-140-150 to get our answer of 70.

Answer:

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

B is the correct answer.

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.

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:

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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Logan will pay $18.02 more if he buys the wooden stacking toy instead of the plastic stacking toy.

The cost of the plastic stacking toy is 1/3 the cost of the wooden stacking toy:

Cost of plastic toy = (1/3) x $25.50 = $8.50

If Logan buys the wooden toy, he will pay:

Cost of wooden toy = $25.50

To find the amount of sales tax on either toy, we can multiply the cost of the toy by the tax rate of 6%:

Sales tax = 6% x cost of toy

Sales tax on the wooden toy = 6% x $25.50 = $1.53

Sales tax on the plastic toy = 6% x $8.50 = $0.51

If Logan buys the wooden toy, he will pay an extra:

Total cost difference = Cost of wooden toy - Cost of plastic toy + Sales tax on wooden toy - Sales tax on plastic toy

Total cost difference = ($25.50 - $8.50) + ($1.53 - $0.51)

Total cost difference = $17 + $1.02

Total cost difference = $18.02

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The probability the number chosen is even, give that it is greater than 1 is 1/2.

The numbers include 1,2,3,4,5,6,

Let P (E) = probability of chosing even number is

P (E) = (Required outcome)/(Total outcome)

Required outcome = numbers of even number

Total outcome = total numbers

P (E) = 3/6

P (E) = 1/2

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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.

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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The inequality that represents the number of each type of calculator she can buy will be 25x + 65y ≤ 800

Given that teacher needs to purchase some scientific calculators for $25 each and some graphing calculators for $65 each.

Consider that x equal the number of scientific calculators and y equal the number of graphing calculators she buys She can only spend up to $800 for the calculators.

The inequality that represents the situation becomes as;

25x + 65y ≤ 800

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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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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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Answer:

Both.

Step-by-step explanation:

They both are the same diagram. Just rearranged.

Answer:

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

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:

Answer

I think its a

Step-by-step explanation:

Answer:

4x+1

Step-by-step explanation:

3x-1+(x+2)

3x-1+x+2

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

= 4x+1

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

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.  

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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