Signed numbers are also called directed numbers true or false

length, l=16in

width, b=13in

thickness, t=3in

To Find:-

Area of wrapping paper required.

Explanation:-

Since, wrapping paper is to be wrapped over the whole rectangular box.Therefore, we have to calculate the total surface area of the rectangular box.



Therefore, 590 of paper is required to wrap the whole rectangular box.

1) The scale factor of dilation is 1/3

2) The orientation is preserved in dilation of A to A'

3) The congruence is not preserved in dilation of A to A'

We know that the scale factor is nothing but the ratio of the size of the transformed image to the size of the original image.

Here from the attached graph we can observe that the square A is transformed to A'

The side length of square A is 18 units and the side length of square A' is 6

So, the scale factor would be,

r = A' / A

r = 6/18

r = 1/3

We know that a dilation preserves the shape and orientation of the figure, but changes the size of he figure.

So, the dilations do not preserve congruence, as it changes the size of a figure.

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Answer:θ≈2.15

θ≈4.13 are correct

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

3u^2 - 2u - 2 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3, b = -2, and c = -2. Substituting these values, we get:

u = (2 ± sqrt(4 + 24)) / 6

u = (2 ± 2sqrt(7)) / 6

Simplifying this expression, we get:

u = (1 ± sqrt(7)) / 3

Therefore, either:

The number of ways of selecting 3 items from a total of 7 items, where order does not matter is (a) 35 ways.

The number of ways to choose three items from a group of seven, where order does not matter, is given by the combination formula:

⇒ C(n,r) = n!/(r! × (n-r)!),

where n is = total number of items, and r is = number of items to be chosen,

We have, total items (n) = 7 and items to be selected (r) = 3.

Substituting the values,

We get;

⇒ C(7,3) = 7!/(3! × (7-3)!),

⇒ 7!/(3! × 4!),

⇒ (7 × 6 × 5)/(3 × 2 × 1),

⇒ 35 ways.

Therefore, the correct option is (a).

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The new coordinates of dilated rectangle by scale factor of 1/4 are J(1, 2), K(3, 2), L(3, 1), and M(1, 1) we can draw figure.

We are given the coordinates of the vertices of a rectangle J(4,8), K(12,8), L(12,4), and M(4,4).

To dilate the rectangle by a scale factor of 1/4, we need to multiply each coordinate by 1/4.

Multiplying each x-coordinate by 1/4

x-coordinate of J: 4 * 1/4 = 1

x-coordinate of K: 12 * 1/4 = 3

x-coordinate of L: 12 * 1/4 = 3

x-coordinate of M: 4 * 1/4 = 1

Multiplying each y-coordinate by 1/4

y-coordinate of J: 8 * 1/4 = 2

y-coordinate of K: 8 * 1/4 = 2

y-coordinate of L: 4 * 1/4 = 1

y-coordinate of M: 4 * 1/4 = 1

Therefore, the coordinates of the dilated rectangle are: J(1,2), K(3,2), L(3,1), and M(1,1).

Using these new coordinates, we can draw the dilated rectangle by plotting the four vertices on a coordinate plane.

The dilated rectangle has the same shape and orientation as the original rectangle, but it has been reduced in size by a scale factor of 1/4.

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The calculated radius of the cone is 5 inches

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

Volume = 109.95 cubic inches

Height = 4.2 inches.

The volume is calculated as

V = 1/3 * 3.14 * r^2h

So, we have

1/3 * 3.14 * r^2 * 4.2 = 109.95

So, we have

r^2 = 3 * 109.95/(4.2 * 3.14)

So, we have

r^2 = 25.01

Take the square roots

r = 5

Hence, the radius is 5 inches

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Answer: Maryanne's conjecture could have been that the perimeter of the image of the triangle will be the same as the perimeter of the original triangle.

Step-by-step explanation:

a) The percent of the scores are between 72 and 87 is 77.45%

b) The probability that a score is greater than 77 is 84.13%

c) The probability that a score is less than 82 or greater than 92 is 52.28%

d) About 5 students scored outside two standard deviations of the mean.

a) To find the percent of scores between 72 and 87, we first need to standardize these scores. We can do this by subtracting the mean (82) and dividing by the standard deviation (5). This gives us:

z = (72 - 82) / 5 = -2

z = (87 - 82) / 5 = 1

We can then use a table of standard normal probabilities (also called a z-table) to find the probability of a score being between -2 and 1. This probability is 0.7745, or 77.45%

b) To find the probability that a score is greater than 77, we again need to standardize the score:

z = (77 - 82) / 5 = -1

Using the z-table, we can find the probability of a score being greater than -1 (which is the same as the probability of a score being less than or equal to 77). This probability is 0.1587, or 15.87% (rounded to two decimal places). To find the probability of a score being greater than 77, we subtract this probability from 1:

P(score > 77) = 1 - P(score <= 77) = 1 - 0.1587 = 0.8413, or 84.13%

c) To find the probability that a score is less than 82 or greater than 92, we can break this into two separate probabilities:

P(score < 82) + P(score > 92)

We can standardize these scores as follows:

z = (82 - 82) / 5 = 0

z = (92 - 82) / 5 = 2

Using the z-table, we can find the probabilities associated with these z-scores:

P(score < 82) = P(z < 0) = 0.5 (from the symmetry of the standard normal distribution)

P(score > 92) = P(z > 2) = 0.0228

Adding these probabilities together gives us:

P(score < 82 or score > 92) = 0.5 + 0.0228 = 0.5228, or 52.28%

d) Two standard deviations from the mean in either direction would be:

82 - (2 x 5) = 72

82 + (2 x 5) = 92

So any score below 72 or above 92 would be considered outside two standard deviations. To find how many students scored outside this range, we need to find the total proportion of scores that fall outside this range and multiply by the total number of scores.

To find the proportion of scores outside the range, we can use the same approach as in part c):

P(score < 72 or score > 92) = P(z < -2 or z > 2) = P(z < -2) + P(z > 2)

Using the z-table, we find:

P(z < -2) = 0.0228

P(z > 2) = 0.0228

Adding these probabilities together gives us:

P(score < 72 or score > 92) = 0.0228 + 0.0228 = 0.0456

So 4.56% of scores fall outside the range of 72 to 92. To find the number of students who scored outside this range, we can multiply this proportion by the total number of scores:

0.0456 x 120 = 5.472 ≈ 5

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Answer:

second option

Step-by-step explanation:

the volume of a cone is calculated as

[tex]\frac{1}{3}[/tex] πr²h

the volume of a sphere is calculated as

[tex]\frac{4}{3}[/tex] πr³

then the volume of a hemisphere is

[tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex] πr³ = [tex]\frac{2}{3}[/tex] πr³

then the volume (V) of the composite solid is

V = [tex]\frac{1}{3}[/tex] πr²h + [tex]\frac{2}{3}[/tex] πr³

a) The total number of balls in a bag is 9.

b) The probability that the first ball chosen is orange is 1/3.

c) The probability that the 2nd ball is also orange is 1/4.

d) The probability that both balls are orange is 1/12.

Given that:

Balls, White = 6 and Orange = 3

a) The total of ping-pong balls in the bag at the start is calculated as,

Total ball = 6 + 3

Total ball = 9

b) The probability that the first ball chosen is orange is calculated as,

P(Orange) = 3/9

P(Orange) = 1/3

c) There will be 8 balls in the bag, of which 2 are orange if the first ball selected was an orange ball. Then the probability is calculated as,

P(Orange) = 2/8

P(Orange) = 1/4

d) The product rule of probability may be used to determine the likelihood that the first and second balls are both orange:

P(Orange and Orange) = 1/3 x 1/4

P(Orange and Orange) = 1/12

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Answer:

Step-by-step explanation:

y=-2x+2

Answer:

4(x-1)=2(6-2x)

4x-4=12-4x

4x+4xd=12+4

8x=16

x=2

Answer:

x=2

Step-by-step explanation:

Step 1: Distribute

To solve this problem, the first step is distributing the four and the 2.

[tex]4(x-1)=2(6-2x)\\\\4x-4=12-4x[/tex]

So this is our simplified problem.

Step 2: Solve for x

Step 2a: Add 4x to both sides:

(This is because we do not have two variables in the equation, making it easier to solve.

[tex]4x+4x-4=12-4x+4x\\\\8x-4=12+0\\\\8x-4=12[/tex]
Step 2b: Add 4 to both sides:

(We do this to leave the variable on one side and the constant on the other. )

[tex]8x-4+4=12+4\\\\8x+0=16\\\\8x=16[/tex]

Step 2c: Divide both sides by 8:

(The reason why we do this is to isolate the variable without any coefficient in front.)

[tex]\frac{8x}{8} =\frac{16}{8} \\\\x=2[/tex]

Answer:

it is b got it right on my test

Step-by-step explanation:

The required graph that shows Ellen's steps where her mean steps for a week is 10000 is graph 2 where the data are as,

Day 1 = 11000 , Day 2 = 9000, Day 3 = 10000, Day 4 = 12000, Day 5 = 8000, Day 6 ≈ 10000, Day 7 ≈ 10000

Mean of ungrouped data is the average of all the values of the observation in the data set.

Mean = (Summation of all values in data set)/ (Number of observations)

Here there are 7 observations and the mean number of steps is 10000.

For graph 1 the values for each day of the week are as,

Day 1 = 8000 , Day 2 = 9000, Day 3 = 12000, Day 4 = 2000, Day 5 = 6000, Day 6 = 10000, Day 7 = 10000

Thus, the mean number of steps is = (8000+ 9000+ 12000+ 2000+ 6000+ 10000 + 10000) / 7

= 8143 (approximately) ≠ 10000

For graph 2 the values for each day of the week are as,

Day 1 = 11000 , Day 2 = 9000, Day 3 = 10000, Day 4 = 12000, Day 5 = 8000, Day 6 ≈ 10000, Day 7 ≈ 10000

Thus, the mean number of steps is = (11000+ 9000+ 10000+ 12000+ 8000+ 10000 + 10000) / 7

= 10000

For graph 3 the values for each day of the week are as,

Day 1 = 7000 , Day 2 = 14000, Day 3 = 11500, Day 4 = 10000, Day 5 = 4500, Day 6 = 6000, Day 7 = 11000

Thus, the mean number of steps is = (7000+ 14000+ 11500+ 10000+ 4500+ 6000 + 11000) / 7

= 9143 (approximately) ≠ 10000

For graph 4 the values for each day of the week are as,

Day 1 = 8000 , Day 2 = 9000, Day 3 = 9500, Day 4 = 10000, Day 5 = 9000, Day 6 = 7000, Day 7 = 11000

Thus, the mean number of steps is = (8000+ 9000+ 9500+ 10000+ 9000+ 7000 + 11000) / 7

= 9071 (approximately)  ≠ 10000

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As pumpkins cost $0.60 per pound Diego will pay $7.68 for his pumpkin.

To find out how much Diego will pay for his pumpkin, we need to multiply the weight of the pumpkin by the cost per pound:

Cost = weight × cost per pound

In this case, the weight is 12.8 pounds and the cost per pound is $0.60:

Cost = 12.8 pounds × $0.60/pound

Simplifying the expression, we get:

Cost = $7.68

Therefore, Diego will pay $7.68 for his pumpkin.

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Some questions that can be asked on the Expenditures and Consumptions behaviours and attitudes of polytechnic Students in a questionnaire are:

One must carefully consider the purpose of a questionnaire, as well as the information required before starting to design it. Also crucial are factors such as the target audience, number and type of questions (i.e., multiple-choice or open-ended), and its format (e.g., Likert scale).

The way in which questions are organized plays an important role, such that people can easily comprehend them and respond accurately while finishing the survey as fast as needed. Concludingly, logical sequencing of questions should be ensured for the overall design to make sense from beginning to end.

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The value of a in the equation 60°a = [? ]° is dependent on the value of [? ].

To solve for a in the equation 60°a = [? ]°, we need to isolate a on one side of the equation. We can do this by dividing both sides of the equation by 60°:

60°a / 60° = [? ]° / 60°

This simplifies to:

a = [? ]° / 60°

Since we don't have the value of [? ]°, we cannot determine the exact value of a. However, we can simplify the expression by canceling out the ° units:

a = [? ] / 60

Therefore, the value of a is dependent on the value of [? ].

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In the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.

We have a right triangle with an unknown angle θ (measured in degrees), the opposite side length of 16 units, and a hypotenuse length of 21 units. We're given the formula for calculating the sine of an angle:

sin(θ) = opposite / hypotenuse

By substituting the values we know, we get:

sin(x) = 16 / 21

x = sin⁻¹(16 / 21)

x ≈ 49.6°

Therefore, in the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.

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Answer:

[tex]1 \frac{7}{20} [/tex]

Step-by-step explanation:

Well you should find a common denominator for 10, 4 and 5 first to be able to mix them. Let's take 20 because it's the smallest number we can convert 10, and 4 and 5 to.

So

[tex] \frac{3 \times 2}{10 \times 2} + \frac{1 \times 5}{4 \times 5} + \frac{4 \times 4}{5 \times 4} [/tex]

And you get

6/20 + 5/20 + 16/20 (now you can add them because they all have 20 as denominator) so = 27/20 = 1 7/20

The total number of employees in the company is 297 if  ratio of union members to nonunion members working for a company is 4 to 7

The given ratio of union members to nonunion members, which is 4 to 7. This means that for every 4 union members, there are 7 nonunion members.

We are also given that there are 108 union members working for the company.

The total number of employees in the company be "x".

Let us from a proportional equation

4/11 = 108/x

To solve for x, we can cross-multiply and simplify:

4x = 1188

x = 297

Therefore, the total number of employees in the company is 297.

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It seems there are two numbers missing between "15 cm summ" and "12 cm". Please provide the complete values so I can help you solve the problem.

The area of the given triangle is expressed as: 25.6 in²

We are only given two sides of the triangle and an angle and so we must find the length of the third side to be able to find the area. The length of the third side is gotten from cosine rule to get:

a = √(14.1² + 7.2² - 2(14.1 * 7.2)*cos 30.3)

a = 8.68 in

In order for us to calculate the area of triangle which has 3 sides, we will have to utilize the Heron's Formula.

From the formula, the area of a triangle (A) that has 3 sides a, b, and c is calculated via the formula:

A = √[s(s - a)(s - b)(s - c)]

where:

s denotes the semi-perimeter of the specific triangle given by the formula: s = (a + b + c)/2.

s = (8.68 + 14.1 + 7.2)/2

s = 14.99 in

Thus:

Area = √[14.99(14.99 - 8.68)(14.99 - 14.1)(14.99 - 7.2)]

Area = 25.6 in²

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Let’s solve this problem by setting the cost of the two companies equal to each other and solving for the amount of sugar. Let x be the amount of sugar in tons.

The cost for the first company is 5500 + 200.25x and the cost for the second company is 4995 + 225.50x.

Setting these two expressions equal to each other, we get:

5500 + 200.25x = 4995 + 225.50x

Solving for x, we get:

25.25x = 505

x = 20

So, the two companies charge the same when the amount of sugar is 20 tons.

The cost when the two companies charge the same is:

5500 + 200.25 * 20 = $9505

So, when the two companies charge the same, the cost is $9505.

Received message. Let's solve this problem by setting the cost of the two companies equal to each other and solving for the amount of sugar. Let x be the amount of sugar in tons. The cost for the first company is 5500 + 200.25x and the cost for the second company is 4995 + 225.50x. Setting these two expressions equal to each other, we get: 5500 + 200.25x = 4995 + 225.50x Solving for x, we get: 25.25x = 505 x = 20 So, the two companies charge the same when the amount of sugar is **20 tons**. The cost when the two companies charge the same is: 5500 + 200.25 * 20 = $9505 So, when the two companies charge the same, the cost is **$9505**.

The value of u -v is 6i - 10j.

We have,

u = 4i-3j, and v= -2i+ 7j.

So, u - v

= (4i - 3j) - (-2i + 7j)

= 4i - 3j + 2i - 7j

= (4i + 2i) + (-3j - 7j)

= 6i - 10j

Thus, the resultant vector is 6i - 10j.

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Answer:

For this question, you can use the simultaneous equation to solve this problem.

Equation 1 reads: x + y = 34. (There are 34 notes in total.)

Equation 2: 5x + 10y = 235 (The notes are worth a total of $235.)

To find x in terms of y, we can apply equation 1:

x = 34 - y

When we use this expression to replace x in equation 2, we obtain:

5(34 - y) + 10y = 235

By condensing and figuring out y, we get at:

y = 15

There are 15 $10 bills in the wallet as a result.

The estimate of the population mean is 80 and the variability in the distribution is 120

Here, we have

The dot plots

From the dot plots, we can see that the data are normally distributed

This means that the mean, the median and the mode are equal

From the distribution of the random variable, we have the following readings

Hence, the estimate of the population mean is 80

Here, we use the range

So, we have

Variability = Highest - Least

This gives

Variability = 140 - 20

Variability = 120

So, the variability in the distribution is 120

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Answer:

  0.67 million miles per day

Step-by-step explanation:

You want the average rate of change of the function d(t) = ∛(6t²) on the interval [4, 8], where d is in millions of miles, and t is in days.

The average rate of change of the function on the interval [a, b] is given by ...

  rate of change = (d(b) -d(a))/(b -a)

As the table in the attachment shows, this is approximately ...

  rate of change = (7.268 -4.579)/(8 -4) ≈ 0.67

The average rate of change on the interval 4 ≤ t ≤ 8 is about 0.67 million miles per day.

__

Additional comment

Mercury has an orbit of about 88 days at a distance of roughly 36 million miles from the Sun. Already at that distance, the General Theory of Relativity comes into play, making predictions from Newtonian physics somewhat problematic. It is unlikely this formula has any relation to reality for t much less than 200.

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1) Note the the linearization of th function f(X) at a =1 is l(x) = 2x-3
2) since l(x) = 2x-3, f(1.01) is = - 0.98

Linearization is the process of converting a nonlinear function's gradient with respect to all variables into a linear representation at that moment.

for the  above prompt , we have to use the formula:

l (x) =  f(a) + f' (a) (x-a)

where  (a) is the value fo the function at point a

and f' (a)  is the derivative of the function evaluated at point  a.


Using a =  1, f(a) becomes:


f(1)  = 2 (1) ⁵ - 8 (1) + 5

f (1) =-1


f(x) = 10x⁴ -8

So f' (1 ) when evalutated will give us the slope of the tangent line at x =1

Thus,

f (1 ) = 10 (1)⁴ -8

= 2

Hence substituting all the values into th e linearization formula we get:

l(x) = f( 1) + f '(1) (x-1)

= -1 + 2 *( x-1 )
= -1 + 2x - 2
= 2x -3

This means that the linearization of the function f(x ) at a= 1 is l(x) = 2x-3


b) Given the l(x) above, f(1.01) gives us:

l(x) = 2x -3
= 2 (1.01) -3
= - 0.98

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Answer:

x is 25

Step-by-step explanation:

There is a common ratio between the sides. In this case, 35/28 is 1.25. This is the number you have to multiply to 20. 1.25 * 20 = 25.

Answer:

True, a cone has an apex which is the point where the sides of the cone meet to form a tip.

The measure of WY using trigonometric identities is 5.4405.

We have,

Using trigonometric identities,

tan 33 = YW/√70

Now,

√70 = 8.37

tan 33 = 0.65

Substituting,

0.65 = YW/8.37

YW = 0.65 x 8.37

YW = 5.4405

Thus,

The measure of WY is 5.4405.

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