If the height of this prism is 10 cm, what is the surface area
of the rectangular prism?
Surface Area = 2lw + 2lh + 2wh
5 cm
5 cm

The Euler's formula solved for the variable V gives . V = 2 + E − F. Option 2

The subject of a formula is the variable or variables that represent the quantity being calculated or solved for.

In mathematical formulas, the subject is typically denoted by a letter or symbol, and the formula shows the relationship between the subject and other variables or constants in the equation.

From the information given, we have that;

V − E + F = 2

To make the variable, V, the subject, take the steps

collect the variable E

V + F = 2 + E

Now, collect the F variable

V = 2 + E - F

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The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%. Here, we have to depend on the principles of standard normal distribution to find the percentage of probability,


Let us take  z-score for a starting salary of $31,000 as

z = (31000 - 25000) / 5000
= 1.2

Now after using a standard normal distribution table , the probability of a z-score of 1.2 or greater is approximately 0.1151
Converting it into percentage
0.1151 x 100
= 11.51%
The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%.

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The coordinates for the dilated figure would be A'(-2, 2), B'(-2, -1), C'(2, -1), and D'(2, 2).

The kind of dilation that was done is called a reduction.

When you dilate a figure with a scale factor k = 1/3, you are performing a reduction, because the scale factor is between 0 and 1. In this case, the dilation will shrink the original figure by a factor of 1/3.

To find the coordinates of the dilated points, multiply the x and y coordinates of each point by the scale factor (1/3):

A' = (-6 x 1/3, 6 x 1/3) = (-2, 2)

B' = (-6 x 1/3, -3 x 1/3) = (-2, -1)

C' = (6 x 1/3, -3 x 1/3) = (2, -1)

D' = (6 x 1/3, 6 x 1/3) = (2, 2)

The coordinates of the dilated figure are A'(-2, 2), B'(-2, -1), C'(2, -1), and D'(2, 2). This type of dilation is a reduction, as the figure becomes smaller.

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Answer:

The answer to your problem is, B. 0.125

Step-by-step explanation:

Here is something that is simple so you will not forget easily.

( Just replace the numbers like how you shown in fraction )

= [tex]\frac{125}{1000}[/tex]

= 125 ÷ 1000

= 0.125

Simple but effective

0.125 is the answer.

Thus the answer to your problem is, B. 0.125

Friday's practice session was 3 and 153/896 hours longer than

To find out how much longer Friday's practice session was than Wednesday's, we need to subtract Wednesday's practice time from Friday's practice time.

Friday's practice time is 2 3/7 hours. To make it easier to subtract, we can convert this mixed number to an improper fraction:

2 3/7 = (2 × 7 + 3) / 7 = 17/7

Now we can add this to Wednesday's practice time, which is already in improper fraction form:

1 1/8 = (1 × 8 + 1) / 8 = 9/8

Adding these two fractions, we get:

17/7 + 9/8

To add these fractions, we need to find a common denominator. The smallest number that both 7 and 8 divide into is 56, so we can convert both fractions to have 56 as the denominator:

17/7 × 8/8 = 136/56

9/8 × 7/7 = 63/56

Now we can add the numerators:

136/56 + 63/56 = 199/56

This is the total practice time for both Wednesday and Friday. To find out how much longer Friday's practice session was than Wednesday's, we need to subtract Wednesday's practice time from this total:

199/56 - 9/8

To subtract fractions, we need to find a common denominator again:

199/56 - 9/8 = (199/56) × (8/8) - (9/8) × (7/7) = 1425/448 - 63/56

Now we can subtract the numerators:

1425/448 - 63/56 = 2841/896

This is the difference between Friday's practice time and Wednesday's practice time, expressed as an improper fraction. To convert this back to a mixed number, we can divide the numerator by the denominator:

2841 ÷ 896 = 3 with a remainder of 153

So the answer is Friday's practice session was 3 and 153/896 hours longer than Wednesday's practice session.

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the answer to the problem is that one angle measures 19.1 degrees and its complementary angle measures 70.9 degrees.

How to solve the question?

Let's first define the problem. Complementary angles are two angles whose sum is 90 degrees. Let x be the measure of one of the angles, then the measure of its complementary angle is 90 - x. According to the problem, one angle measures 51.8 degrees less than its complementary angle, so we can write:

x = (90 - x) - 51.8

Simplifying this equation, we get:

2x = 90 - 51.8

2x = 38.2

x = 19.1

Therefore, one angle measures 19.1 degrees and its complementary angle measures 90 - 19.1 = 70.9 degrees.

We can check that these angles are indeed complementary by verifying that their sum is 90 degrees:

19.1 + 70.9 = 90

So the answer to the problem is that one angle measures 19.1 degrees and its complementary angle measures 70.9 degrees.

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The volume of the prism with given dimensions in the figure is equal to 612√3 cubic millimeter.

The dimensions of the triangular prism are,

Base of the triangle  'B' = 12mm

let us consider 'h' be the height of the triangle base.

Which intersect base at midpoint

height of the triangle 'h' = √ 12² - 6²

                                        = √108

                                        = 6√3mm

Side length of the prism 'l' = 17mm

Volume of the triangular prism

= ( 1/2 ) × Base × height × length of the side

= ( 1/2 ) × B × h × l

Now , substitute the values we have,

⇒ Volume of the triangular prism  = (1/2) × 12 × 17 × 6√3

⇒ Volume of the triangular prism  = 612√3 cubic millimeter.

Therefore, the volume of the triangular prism is equal to 612√3 cubic millimeter.

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Answer: 22

Step-by-step explanation:

So since Margo missed 24.6% of 90 free throws, you have to find 24.6% of 90. The easiest way to do this is to do 90 multiplied by 0.246.

To multiply by percentages in general, move the decimal point to the left by two places. For example, if it said 82.6, the decimal point would go to the left two places and be 0.826.

Back to the original question...

so 90 multiplied by 0.246 is 22.14. If you can use a calculator, this is easy, if not just do the usual multiplication.

Then, this rounds to 22, and the problem is complete!

However, each beaker would have the following if there were, say, five beakers: 2.5 units of water are equal to 8.5/5.

Typically, it is expressed in geometric units, which including cubic metres (m3), cubic centimetres (cm3), or cubic feet (ft3), depending on the length unit being used. A formula that is based on an object's shape can be used to determine its volume. The volume of such a rectangular prism, for instance, can be determined by utilizing the formula V = lwh, where l stands for length, w for width, and h for height. A cylinder's volume can be calculated using the formula V = r2h, where r denotes the circle of the base and h the height.

given

We can simply sum the numbers supplied to determine the total volume of water in all the beakers:

1/4 x 6 + 3/4 x 2 + 1/2 + 1 1/4 + 1 1/2 + 1 3/4

= 1.5 + 1.5 + 0.5 + 1.25 + 1.5 + 1.75 (converting mixed values to improper fractions)

= 8.5

8.5 units of water are therefore present in all of the beakers.

Each beaker will have 8.5 divided by the number of beakers if this water is distributed equally among them.

We are unable to provide a precise response since we are unsure of the number of beakers.

However, each beaker would have the following if there were, say, five beakers: 2.5 units of water are equal to 8.5/5.

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Okay so Jack started with 50 chocolates, and ended with 2.

The simple way to calculate it would be by realizing that Jack only distributed 48 chocolates. We can find how many times 3 fits into 48 by dividing [tex]48\div3=16[/tex].

Using algebra, we substitute the value we want to find with [tex]x[/tex]. Here what we want to find is the number of friends that were at Jack's party.

We know that he started with 50 chocolates, then distributed [tex]3\times[/tex] the number of friends present (which is [tex]x[/tex]).

We write that down as [tex]50-3x[/tex]

(It's minus because when chocolates are distributed, Jack is taking away from what he has.)

We know that after this, there were only 2 chocolates left, so it's

[tex]\underline{\bold{50-3x=2}}[/tex]

Then we proceed by moving all the numbers to the right until only [tex]x[/tex] is left:

[tex]-3x=2-50[/tex]

[tex]-3x=-48[/tex]

[tex]x=\dfrac{-48}{-3}[/tex]

[tex]\boxed{\bold{x=16}}[/tex]

Conclusion: The number of people that attended the party was 16.

angle 1 = 90-( angle 2 ) and angle 2 = 90-( angle 1) ( diagonal property of rectangle)

A diagonal of a rectangle divides it into two congruent right triangles. The diagonals of a rectangle are the same length.

If the diagonal of a rectangle diveds it into two congruent triangles, then triangle OST is congruent to Triangle QRT.

Therefore angle 1 = 90-angl2

represent angle 1 by x and angle 2 by y

therefore x = 90-y

and y = 90-x

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For a production company of total 24 workers, who works in different shifts. The probability that all 6 workers are selected from the same shift is equals to the 0.0019.

We have a company with faculty working in different shifts. Total number of workers in company = 10 + 8 + 6 = 24

Number of workers work in day shift = 10

Number of workers work in swing shift= 8

Number of workers work in graveyard shift = 6

Now, 6 workers are randomly selected from among 24. That is any of group of 6 can be selected. Number of possible ways to select 6 out of 24 = ²⁴C₆=134,596.

Number of ways to select a group of 6 workers from morning shift = ¹⁰C₆ = 210

Number of ways to select a group of 6 workers from swing shift = ⁸C₆= 56

Number of ways to select a group of 6 workers from graveyard shift = ⁶C₆ = 1

Now, probability to select the group of 6 from morning shift = [tex]\frac{210}{134596}[/tex]

Probability to select the group from morning shift = [tex]\frac{56}{134596}[/tex]

Probability to select the group from graveyard shift=[tex]\frac{1}{134596}[/tex].

Total probability for selecting a group of 6 workers from same shift [tex]= \frac{210}{134596} + \frac{56}{134596} + \frac{1}{134596} [/tex]

[tex]= \frac{267}{134596}[/tex]

= 0.00198

Hence, required probability is 0.0019.

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Complete question:

a production company factory 10 workers on day shift , 8 workers on swing shift and 6 workers on graveyard shift. A quality control team select 6 workers for in depth interviews.. Suppose the selection made in such a way that any particular group of 6 workers has same chance to selecting as does any other group( drops 6 slips without replacement from among 24 )

what is the probability that all 6 workers are selected from the same shift, again, assume the employees are selected sequentially and not all at once. round your answer to four decimal places. save your answer as p all same.

Answer:

- w - 24

Step-by-step explanation:

- 4(w + 6) + 3w ← multiply each term in the parenthesis by - 4

= - 4w - 24 + 3w ← collect like terms

= (- 4w + 3w) - 24

= - w - 24

Answer:

500 ≥ 245.50

500 - 245.50 ≥ 0

254.50 ≥ 0

Therefore, she needs to deposit at least $245.50 to avoid a fee.

Step-by-step explanation:

Let x be the least amount of money she needs to deposit to avoid a fee.

The balance in her checking account after writing the check would be (500 - 245.50) = 254.50.

To avoid a fee, the balance must be greater than or equal to 500, so we can write the inequality as:

x + 254.50 ≥ 500

Solving for x, we get:

x ≥ 500 - 254.50

x ≥ 245.50

The small two above the radical symbol indicates that the square root of a mathematical number or expression is being taken, which means that the number under the radical must be squared to obtain the original number

Therefore,the correct answer is True.

An expression is a mathematical phrase that combines numbers, variables, and operations to create a value. It can include arithmetic, algebraic, or trigonometric operations and may contain parentheses, exponents, or radicals.

The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √ and is a type of radical.

According to the given information:

The correct answer is True.

The radical symbol, which looks like a division bar with a dot on top, is used to denote a root operation in mathematics. The index or degree of the root indicates the number of times the root must be multiplied by itself to obtain the number under the radical. In the case of the square root, the index is 2, which means that the number under the radical must be squared to obtain the original number.

Therefore, when the radical symbol has a small two above it, it is indicating that the square root of the number or expression below the radical is being calculated. The result of the square root operation is always a positive number, since the negative sign is indicated separately outside the radical symbol.

For example, the square root of 25 is written as √25 = 5, since 5 squared is equal to 25. Similarly, the square root of 4 is written as √4 = 2, since 2 squared is equal to 4.

In summary, the small two above the radical symbol indicates that the square root of a mathematical number or expression is being taken, which means that the number under the radical must be squared to obtain the original number.

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Using the calculus rule, we can rewrite the total derivative (dx/dz) at constant y as the sum of two partial derivatives.

The total derivative (dx/dz) at constant y can be rewritten as the sum of two partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y

Apply the chain rule
The chain rule in calculus allows us to find the derivative of a function with respect to another variable, by considering how the intermediate variables change.

In this case, we want to find (dx/dz) at constant y.

The chain rule states:
(dx/dz) = (dx/dy)*(dy/dz) + (dx/dz) at constant y
Identify the partial derivatives:
Since we want to rewrite (dx/dz) as a sum of two partial derivatives, we will keep the terms (dx/dy) and (dy/dz) as partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y
Final answer
The total derivative (dx/dz) at constant y can be rewritten as the sum of two partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y.

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Explanation: We subtract the given value from 1

1-0.31 = 0.69

The complement of an event is the complete opposite.

Example: heads vs tails

Thus, the value of x for the given set of similar triangles is found as: x = 42.

Triangles that are similar to one another in terms of shape but not always in terms of size.

Identical triangles always have congruent corresponding angles and proportional corresponding sides. Two angles must share the same measure in order to be congruent.

The triangles both have proportional equivalent sides. Hence, each pair of corresponding sides' ratios is the same. The scale factor is the name of this ratio.

In smaller triangle. applying angle sum property :

Let the unknown angle be y

y + 126 + 16 = 180

y = 180 - 142

y = 38

For the given similar triangles:

The corresponding angles are also equal.

So,

on the straight line:

16 + 3x + 38 = 180 (linear pair)

3x = 180 - 54

x = 126/3

x = 42

Thus, the value of x for the given set of similar triangles is found as: x = 42.

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Answer:

x = 63° and y =153°

Step-by-step explanation:

a streght line measure 180° so in the given we sum up

90° + x + 27°=180° then solve x

and for y u will sum up 90° and x then u will get by vertical opposite angle

The function has a minimum value of -2 that occurrs at x = -1

Given that

g(x) = 2x^2 + 4x

This is a quadratic function with a positive leading coefficient (2), which means that it opens upward and so it has a minimum value.

We can find the vertex of the parabola (the point where it changes direction) by using the formula:

x = -b/2a

where a and b are the coefficients of the quadratic function.

In this case, a = 2 and b = 4, so:

x = -4/(2*2) = -1

To find the corresponding y-value (the minimum value of the function), we substitute x = -1 into the function:

g(-1) = 2(-1)^2 + 4(-1) = -2

Therefore, the minimum of the parabola is at the point (-1, -2).

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Answer:

86.3

Step-by-step explanation:

To find the two possible values of x, we can use the law of sines, which states that:

asinA​=bsinB​=csinC​

where A, B, and C are the angles of the triangle and a, b, and c are the opposite sides.

In this case, we are given A = 50°, a = 10 cm, and b = 9 cm. We can use the law of sines to find sin B:

10sin50°​=9sinB​

sinB=109sin50°​≈0.6904

Now, we can use the inverse sine function to find B:

B=sin−1(0.6904)≈43.7°

However, this is not the only possible value for B. Since the sine function is positive in both quadrant I and quadrant II, there is another angle with the same sine value but in quadrant II. This angle is the supplement of B:

B′=180°−B≈180°−43.7°=136.3°

This means that there are two possible triangles that satisfy the given information: one with B = 43.7° and one with B = 136.3°.

To find x, we need to find C for each triangle using the fact that the sum of angles in a triangle is 180°:

C=180°−A−B≈180°−50°−43.7°=86.3°

C′=180°−A−B′≈180°−50°−136.3°=−6.3°

However, C’ is not a valid angle for a triangle because it is negative. Therefore, we can ignore this possibility and conclude that there is only one possible value for x:

x=C≈86.3°

18x9=162

18 cubes and 9 layers of the 18 cubes. so thats just eighteen, nine times.

The length of each side is 2√6 cm.

We have,

Length of diagonal of square = 4√3 cm

Now, To compute the length of a side of a square Divide d by √2.

So, length of each side

= 4√3 / √2

= 4√6/ 2

= 2√6

Thus, the length of each side is 2√6 cm.

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The calculated value of the total cost of the sour cream and butter is $2.69.

To calculate the total cost of sour cream and butter, we need to multiply the weight of each item by its respective price per kilogram and then add the results.

The cost of 0.6 kilograms of sour cream is:

0.6 kg * $2.15/kg = $1.29

The cost of 1.4 kilograms of butter is:

1.4 kg * $1.00/kg = $1.40

Adding these two costs together, we get:

$1.29 + $1.40 = $2.69

Therefore, the total cost of the sour cream and butter is $2.69.

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Answer:

(- 2, 16 )

Step-by-step explanation:

y = 8x + 32 → (1)

y = - 8x → (2)

substitute y = 8x + 32 into (2)

8x + 32 = - 8x ( add 8x to both sides )

16x + 32 = 0 ( subtract 32 from both sides )

16x = - 32 ( divide both sides by 16 )

x = - 2

substitute x = - 2 into either of the 2 equations and evaluate for y

substituting into (2)

y = - 8(- 2) = 16

solution is (- 2, 16 )

Answer:

[tex]0.42[/tex]÷[tex]7[/tex]

Step-by-step explanation:

First, let's count the number of colored squares in the hundredth-grid.

There are a total of 42 hundredth-squares.

Since this is measured in hundredths, the number it represents is 0.42.

Each of the different colors represents a separate group that 0.42 is being divided into. There are 7 separate groups.

Since 0.42 is being divided into 7 groups, the equation that is being represented is:

[tex]0.42[/tex]÷[tex]7[/tex]

As per the concept of simple interest, the interest amount earned after three years is $306.

To calculate the interest amount earned, we can use the formula:

I = P * r * t

Where:

I = interest earned

P = principal amount

r = interest rate per year (as a decimal)

t = time period in years

Plugging in the values from the problem, we get:

I = $1200 * 0.085 * 3

I = $306

This means that after three years, the bond will be worth the principal amount plus the interest earned, which is:

$1200 + $306 = $1506

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