An office manager needs to cover the front face of a rectangular box with a label for shipping. the vertices of the face are (-5, 8), (3, 8), (-5, -4), and (3, -4). what is the area, in square inches, of the label needed to cover the box?
98 in2
48 in2
40 in2
20 in2​

The probability of taking the smallest ball at least once during 4 tries can be calculated as 1 minus the probability of not taking the smallest ball in any of the 4 tries. Since each try is independent and the probability of not taking the smallest ball in a single try is 9/10, the probability of not taking it in all 4 tries is (9/10) * (9/10) * (9/10) * (9/10) = 0.6561. Therefore, the probability of taking the smallest ball at least once during 4 tries is 1 - 0.6561 = 0.3439, or approximately 34.39%.

To find the probability of not taking the smallest ball in any of the 4 tries, we need to calculate the probability of not selecting the smallest ball in each try and then multiply them together.

In each try, there are 9 balls remaining that are not the smallest ball, out of a total of 10 balls. Therefore, the probability of not taking the smallest ball in a single try is 9/10.

Since the tries are independent events, we can multiply the probabilities together to find the probability of not taking the smallest ball in all 4 tries.

After calculating this probability, we subtract it from 1 to obtain the probability of taking the smallest ball at least once during the 4 tries.

In this case, the probability of not taking the smallest ball in all 4 tries is (9/10) * (9/10) * (9/10) * (9/10) = 0.6561.

Finally, subtracting this value from 1 gives us the probability of taking the smallest ball at least once, which is 1 - 0.6561 = 0.3439, or approximately 34.39%.

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Answer:

Volume : 300

Surface Area : 280

Step-by-step explanation:

Volume : 6*5*10

Surface Area : 50+50+30+30+60+60

Answer:

36)

[tex]f(x) = \frac{1}{x + 3} - 1[/tex]

The equation of the function is y = 1/(x + 3) - 1

From the question, we have the following parameters that can be used in our computation:

The reciprocal function shifted down one unit and left three units

The equation of the reciprocal function is represented as

y = 1/x

When shifted down one unit, we have

y = (1/x) - 1

When shifted left three units, we have

y = 1/(x + 3) - 1

Hence, the equation of the function is y = 1/(x + 3) - 1

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Based on the pattern we identified, the next term in the sequence would be 55.

The sequence should be 7, 10, 19, 34, 55

To identify the pattern and determine what comes next in the given sequence (7, 10, 19, 34), we need to examine the relationship between the terms and look for a consistent pattern.

If we calculate the differences between consecutive terms, we get:

10 - 7 = 3

19 - 10 = 9

34 - 19 = 15

By examining the differences, we notice that they are increasing by 6 each time.

This suggests that the sequence might be formed by adding an increasing number to each term.

Let's calculate the next difference:

15 + 6 = 21

Now, let's add this difference to the last term of the sequence:

34 + 21 = 55

Therefore, based on the pattern we identified, the next term in the sequence would be 55.

To summarize:

7, 10, 19, 34, 55

It's important to note that without further context or information, this pattern is just one of the possibilities and may not be the only correct answer.

Additional terms or a different pattern may emerge if more information is provided.

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Answer:

?

Step-by-step explanation:

?

The correct answer is: O How to produce? How much to produce?

The statement "A manufacturing firm employs workers to monitor and maintain specialized machines making small metal parts" answers the economic questions of "How to produce?" and "How much to produce?"

How to produce: The statement indicates that the manufacturing firm has chosen to employ workers to monitor and maintain specialized machines. This suggests that they have made a decision regarding the production process and how they will go about manufacturing the small metal parts.

How much to produce: The fact that the manufacturing firm has employed workers to monitor and maintain the machines implies that they have determined a level of production that is deemed appropriate or necessary. The number of workers and the capacity of the machines can influence the quantity of small metal parts produced.

Therefore, the correct answer is: O How to produce? How much to produce?

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Answer:

Based on the values in the table, it can be observed that changing the radius of the sphere has a direct effect on the surface area of the sphere. As the radius increases, the surface area also increases.

Step-by-step explanation:

In general, multiplying the radius of a sphere by a factor of x will result in the surface area of the sphere being multiplied by a factor of x^2. This is because the surface area of a sphere is given by the formula:

Surface Area = 4πr^2

When the radius is multiplied by a factor of x, the new radius becomes xr. Substituting this into the formula, we get:

New Surface Area = 4π(xr)^2

= 4πx^2r^2

= x^2(4πr^2)

Therefore, the surface area of the sphere is multiplied by a factor of x^2 when the radius is multiplied by a factor of x. This relationship shows that the surface area increases at a faster rate than the radius.

Naomi will take approximately 93 quarters (around 23 years and 3 months) to save $100,000 by making quarterly payments of $1,500 with a 4.4% interest rate.

Doubling her payment amount would save her time, but the exact time saved would require recalculating with the new payment amount.

To calculate the time it will take for Naomi to reach her goal of $100,000, we can use the future value formula for a series of periodic payments:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future value (goal amount) = $100,000

P = Payment amount per period = $1,500

r = Interest rate per period = 4.4% per year / 4 (quarterly compounding) = 1.1% per quarter

n = Number of periods (quarters) to reach the goal (what we need to find)

Plugging in the values, we have:

$100,000 = $1,500 * [(1 + 0.011)^n - 1] / 0.011

Simplifying the equation, we have:

[(1 + 0.011)^n - 1] = $100,000 * 0.011 / $1,500

[(1.011)^n - 1] = 0.073333...

Now, we can solve this equation for n using logarithms:

n = log(0.073333...) / log(1.011)

Using a financial calculator or an online calculator, we find that n ≈ 92.33 quarters.

Since Naomi is making quarterly payments, we round up to the next whole number, giving us a total of 93 quarters.

Therefore, it will take Naomi approximately 93 quarters (or around 23 years and 3 months) to reach her goal of $100,000.

Doubling her payment amount to $3,000 per quarter would indeed save her time in reaching her goal. The higher payment amount means she would accumulate the desired amount faster. However, to determine the exact time saved, we would need to recalculate using the same formula as above with P = $3,000. The time saved will depend on the specific calculation result.

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Reason:

Tangent is the ratio of opposite over adjacent.

The side 'a' is opposite reference angle 52, while c is adjacent to this angle.

Using a calculator, tan(52) = 1.27994 approximately.

Answer:

Tan 52°

Step-by-step explanation:

Since the Tangent of angle is given by the ratio of opposite to the adjacent.

So, Here

Tan 52°= opposite/adjacent

Tan 52°=a/c

Therefore, the ratio of a/c is Tan 52°

The probability of randomly selecting either a diamond or a 3 from the bag is 100%.

Random selection refers to the process of selecting elements from a group with equal probability of selection.

Probability is a measure of the likelihood of an event occurring, which is usually expressed as a fraction or a decimal.

When it comes to random selection of a diamond or 3, we can use probability to determine the likelihood of either event occurring.

For instance, suppose we have a bag containing 10 numbered balls: 5 of them are diamonds and 5 are threes.

To find the probability of randomly selecting a diamond, we divide the number of diamonds by the total number of balls: P(Diamond) = Number of diamonds/ Total number of balls = 5/10 = 0.5 or 50%

This means that the probability of randomly selecting a diamond from the bag is 50%.

To find the probability of selecting either a diamond or a 3, we add the probability of selecting a diamond to the probability of selecting a 3, since the events are mutually exclusive: P(Diamond or 3) = P(Diamond) + P(3) = 5/10 + 5/10 = 1

This means that the probability of randomly selecting either a diamond or a 3 from the bag is 100%.

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Answer:

34.63

Step-by-step explanation:

The 2 in 34.6285 marks the hundredths place

We can round by seeing what number is to the right of it which is 8.

Since 8 is larger than 5, we round up by 1.

Thus, 34.63 is our answer

The answer is:

34.63

Work/explanation:

Rounding to the nearest hundredth means rounding to 2 decimal places (DP).

So we have 2 decimal places, and the 3rd one matters too because it will determine the value of the 2nd DP.

The third DP is 8. Since it's greater than 5, then the value of the 2nd DP will be rounded up. I will add 1 to it.

Remember that we round up when the digit that we're rounding to is followed by another digit that is greater than or equal to 5.

So we round :

[tex]\bf{34.6285 =\!=\!\!\! > 34.63}[/tex]

Answer:

[tex]f(x) = - 3 {x}^{2} - 6x - 1[/tex]

=================================================

Explanation

I'll use the distance formula.

[tex](x_1,y_1) = (1,3) \text{ and } (x_2, y_2) = (-2,7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-(-2))^2 + (3-7)^2}\\\\d = \sqrt{(1+2)^2 + (3-7)^2}\\\\d = \sqrt{(3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

The distance is 5 units.

Answer:

5

Step-by-step explanation:

Jessica squeezed 235 cups of juice, Barry made 221 cups of juice, and the best estimate for the amount of juice Barry made is 198 cups.

Jessica and Barry squeezed oranges for juice. Jessica squeezed 235 cups of juice. Barry made 14 cups less than Jessica. Barry estimated that Jessica squeezed about 212 cups of juice. The best estimate for the amount of juice Barry made is 198 cups.

There are different ways to approach this problem, but one possible method is to use subtraction to find out how much juice Barry actually made, and then compare it to the estimated amount. If Jessica squeezed 235 cups of juice and Barry made 14 cups less, then Barry made 235 - 14 = 221 cups of juice.

This is the exact amount of juice that Barry made, but it may not be a convenient answer if we are looking for an estimate that is close to Barry's estimate of 212 cups of juice. One way to get such an estimate is to round 221 to the nearest ten or hundred. For example, if we round to the nearest ten, we get 220, which is only 8 cups away from Barry's estimate.

Alternatively, if we round to the nearest hundred, we get 200, which is only 12 cups away from Barry's estimate. Therefore, the best estimate for the amount of juice Barry made is 198 cups, which is obtained by rounding down to the nearest ten. This estimate is only 14 cups away from Barry's estimate, and it is also easy to compute mentally.

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Answer:

x=30 degrees, 2x=60 degrees, 3x=90 degrees

Step-by-step explanation:

in a triangle the sum of angles is 180 so

x+2x+3x=180

6x=180

x=180/6

x=30

so the angle x is 30 degrees, the angle that is 2x is 60 degrees and the angle the angle 3x is 90

Answer: C

Step-by-step explanation:

the x - 2 means go right 2

the +3 means go up 3

Answer:

the solution would be X=3 as 3.1 represents 3×1.

The calculated equation of the line is y = -2x + 3

From the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

(1, 1) and (0, 3)

The equation of the line is calculated as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 3

Using the points, we have

m + 3 = 1

So, we have

m = -2

This means that

y = -2x + 3

Hence, the equation of the line is y = -2x + 3

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Answer:

1. x = 18

2. x = 31

Step-by-step explanation:

1. Angles in a quadrilateral sum to 360°.

360 -(60 +130 +70) = 360 -260 = 100

So, x +82 = 100. x = 100 -82 = 18

2. Angles in a triangle sum to 180°. 180 -(29 +75) = 180 -104 = 76.

So, -17 +3x = 76. 3x = 93. x = 93/3 = 31

The incorrect phrases in the paragraph are as follows:

Since ∠AMC is a right angle,  ∠BMC and  ∠CMD are complementary.

Since  ∠BMD is a right angle,  ∠AMB and  ∠BMC are complementary.

To identify the wrong phrases, note that a right angle is an angle that forms 90° when inclined to another line. Also, complementary angles are those whose sum is 90°.

A close look at the angles will show that ∠BMD is a right angle but ∠BMC and  ∠CMD are complementary. Also, the following is correct: ∠AMC is a right angle,  ∠AMB and  ∠BMC are complementary.

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The total length of electric wire in both rolls is 166.76 meters.

To find the total length of electric wire in both rolls, we need to add the lengths of the two rolls together.

The first roll contains 80m 20cm of wire. We can convert this to meters by noting that 1 meter is equal to 100 centimeters. Therefore, the length of the first roll is:

80m 20cm = 80 meters + (20 centimeters / 100) meters

= 80 meters + 0.20 meters

= 80.20 meters

Similarly, the second roll contains 86m 56cm of wire. Converting this to meters:

86m 56cm = 86 meters + (56 centimeters / 100) meters

= 86 meters + 0.56 meters

= 86.56 meters

To find the total length, we add the lengths of both rolls:

Total length = 80.20 meters + 86.56 meters

= 166.76 meters

Therefore, the total length of electric wire in both rolls is 166.76 meters.

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The solutions to the absolute value equations are:

1. b. x = 1, -19.      2. a. no solution.     3. c. x = 5, -9.

1. |3x+9| = 30

To solve this equation, we isolate the absolute value expression by considering two cases: 3x+9 = 30 and -(3x+9) = 30. Solving both equations, we find x = 7 and x = -19, respectively. Thus, the answer is b. x = 1, -19.

2. |2x+11| = -13

An absolute value cannot be negative, so there is no solution to this equation. The answer is a. no solution.

3. |x + 2| + 4 = 11

To solve this equation, we isolate the absolute value expression by subtracting 4 from both sides, resulting in |x + 2| = 7. Considering two cases: x + 2 = 7 and -(x + 2) = 7, we solve for x and find x = 5 and x = -9, respectively. Thus, the answer is c. x = 5, -9.

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the answer is

w = -3/2 u + 2

Answer:

f(0) = 1

f(1) = 21.1

Step-by-step explanation:

Do as the problem says:

[tex]f(0)=4^{2.2(0)}=4^0=1\\f(1)=4^{2.2(1)}=4^{2.2}\approx21.1[/tex]

Answer:

X intercepts: (-2, 0), (2, 0)

Y intercept: (0, 4)

Edited because I forgot to put in point form earlier. Depends on whether your teacher wants it in point form. If not, ignore the 0s.

Step-by-step explanation:

X intercepts are the points where a line crosses the x axis. Y intercepts are the points where a line crosses the y axis.

Answer:

A. x-intercept: (-2,0), (2,0)

A. y-intercept: (0,4)

Step-by-step explanation:

If you want to find the x and y-intercept of a line, you need to know its equation. But don't worry, it's not as hard as it sounds. Here are some tips to help you out.

One type of equation is y = mx + c, where m is the slope and c is the y-intercept. This means that the line crosses the y-axis at c. To find the x-intercept, just plug in y = 0 and solve for x. You'll get x = -c/m. Easy peasy!

For example, if the equation is y = 2x + 4, then the y-intercept is 4 and the x-intercept is -2.

Another type of equation is ax + by + c = 0, where a, b and c are constants. To find the x-intercept, plug in y = 0 and solve for x. You'll get x = -c/a. To find the y-intercept, plug in x = 0 and solve for y. You'll get y = -c/b. Piece of cake!

For example, if the equation is 3x + 2y - 6 = 0, then the x-intercept is 2 and the y-intercept is -3.

Now you know how to find the x and y-intercept of a line from its equation.Let us understand the calculations to find the x and y intercept, through the steps in the below table.

Answer:

y= -4

Step-by-step explanation:

To find the value of y when x = 6, we can substitute x = 6 into the equation and solve for y:

4(6) + y = 20

24 + y = 20

y = 20 - 24

y = -4

Therefore, when x = 6, y is equal to -4.