You are wrapping a birthday gift that is packaged in a specially made pyramid-shaped box. The base of the box measures 10 inches by 9 inches and the slant height is 6 inches.

Answer: 405 students

Step-by-step explanation:

From the question, Banneker Middle School has 750 students and we are told that Lynn surveys a random sample of 50 students and finds that 27 have pet dogs. The number of students at the school that are likely to have pet dogs goes thus:

Since out of 50 students surveyed, 27 have pet dogs, this means we multiply the fraction by 750. This can be mathematically written as:

= 27/50 × 750

= 27 × 15

= 405

This means 405 students are expecting to have pet dogs.

ANSWERS

a) 58

b) 62.2

EXPLANATION

a) The median is the middle value. It separates the data set in two. To find the median we have to put the data in order, from least to greatest:

The number of data is odd, this means that the median will be one of the values of the data set and not a mean between two of them. If there are 9 values, the median is the 5th value - so we have 4 values to the left and 4 values to the right.

The first 4 values are 44,49,53,54, so the median is 58.

b) The mean is the sum of all values of the data set divided by the amount of data:

Rounded to one decimal place, the mean is 62.2

Comparing with the given options, we can see that the correct answer is (e):\((x - 2)^2 + (y - 2)^2 + (z - 4)^2 = 12\). We can use the midpoint formula to find the center of the sphere:

Midpoint Formula = \(([(0+4)/2], [(2+6)/2], [(5+9)/2])\) \(= (2, 4, 7)\)

The radius of the sphere can be found by finding the distance between the center and one of the endpoints:

r = \(\sqrt{((4-2)^2 + (6-4)^2 + (9-7)^2)}\) = \(\sqrt{(8+4+4) }\)= \(\sqrt{16}\) = \(4\)

So, the equation of the sphere is:\((x - 2)^2 + (y - 4)^2 + (z - 7)^2 = 16\)

Expanding the equation, we get:\(x^2 - 4x + 4 + y^2 - 8y + 16 + z^2 - 14z + 49 = 16\)

Simplifying, we get:\(x^2 - 4x + y^2 - 8y + z^2 - 14z + 53 = 0\)

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Salut/Hello!

Answer:

Step-by-step explanation:

x = 5 : 6 + (10 - 2x - 20)
x= 0,8(3) + 10 - 2x - 20
2x + x = 0,8(3) + 10 - 20
3x = 0,8(3) + 10 - 20
3x = -10,8(3)
x = -3.6(1)

I hope it was helpful! :]

Answer:

481.92

Step-by-step explanation:

3.2÷100×466,98=

14,94

then add

466.98 +14.94

481.92

Answer:

Length of one side of the container = 5 feet

Step-by-step explanation:

Given:

V = s³

Where,

V = volume of the container

s = side length of the container

V = 125 cubic feet

Find s?

V = s³

125 = s³

Find the cube root of both sides

3√125 = 3√s³

5 = s

s = 5 feet

Length of one side of the container = 5 feet

Answer:50

Step-by-step explanation:

Answer:

x ≈ 55.7°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos x = \(\frac{adjacent}{hypotenuse}\) = \(\frac{FG}{FH}\) = \(\frac{5.3}{9.4}\) , then

x = \(cos^{-1}\) ( \(\frac{5.3}{9.4}\) ) ≈ 55.7° ( t o the nearest tenth )

Answer: 55.7 degrees

Step-by-step explanation:

you do cosine rule since 5.3 is adjacent and 9.4 is the hypotenuse

CAH -> adj/hypotenuse

to find the angle you do cos^-1

is this question you would do cos^-1(5.3/9.4)

which would = 55.67893095

rounded to nearest tenth would be 55.7 (nearest tenth)

remember to include the degrees symbol!

hope this is right <3

6 cm, C. He did not square the length of the given leg

Explanation

to solve this we need to use the Pythagorean theorem

T.P states for all rigth triangles:

then

Step 1

let

a=2.3

b=b

c=6.4

replace

Step 2

What mistake might the student have made?

check

A)He added the two given values

B) He subtracted the two given values

C)He did not square the length of the given leg

D. He did not square the length of the hypotenuse​

so, the answer is C

I hope this helps you

Answer:

x=-1/2

Step-by-step explanation:

if you need a explanation tell me but I’m in Math class rn

The area of the regular octagon is approximately 408.5 square cm.

To find the area of a regular octagon with an apothem of 11.1 cm and each side measuring 9.2 cm, follow these steps:

1. Recall that the area (A) of a regular polygon can be calculated using the formula: A = (1/2) * perimeter (P) * apothem (a).

2. Find the perimeter of the octagon by multiplying the side length by the number of sides: P = 9.2 cm * 8 = 73.6 cm.

3. Substitute the values for the perimeter and apothem into the formula: A = (1/2) * 73.6 cm * 11.1 cm.

4. Calculate the area: A ≈ 408.48 square cm.

To the nearest tenth, the area of the regular octagon is approximately 408.5 square cm.

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The exact distance between the planes after 2 hours, using the law of cosines:

d = sqrt((2 * 425)^2 + (2 * 530)^2 - 2 * 2 * 425 * 530 * cos(67° - 355°))

where d is the distance between the planes in miles.

To visualize the problem, imagine a coordinate plane with the origin at Raleigh-Durham Airport. Plane A's path can be represented as a line with a slope determined by its bearing of 355°, while Plane B's path can be represented by another line with a slope determined by its bearing of 67°.

To calculate the distance between the planes after 2 hours, we first need to determine their respective positions. Since Plane A is traveling at 425 mph, it would have covered a distance of 850 miles (425 mph * 2 hours). Similarly, Plane B would have covered a distance of 1060 miles (530 mph * 2 hours).

Next, we can calculate the coordinates of each plane using the distance and bearing information. Using trigonometry, we can determine the vertical and horizontal distances covered by each plane. Plane A's vertical distance would be 850 * sin(355°), and its horizontal distance would be 850 * cos(355°). Similarly, Plane B's vertical and horizontal distances would be 1060 * sin(67°) and 1060 * cos(67°), respectively.

Finally, we can use the coordinates of each plane to calculate the distance between them. This can be done using the distance formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of Plane A and Plane B, respectively.

By plugging in the calculated values, we can determine the distance between the two planes after 2 hours of flying.

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Answer: Width is 8

Length of a rectangle is inversely proportional to its width

Mathematically, this can be represented as

Introducing a proportionality constant K, then the expression become

Find K, when l = 12 and w = 6

From the above expression, make K the subject of the formula

K = l x w

K = 12 x 6

k = 72

Find the width, when l = 9 and k = 72

Since, l = k/w

cross multiply

l x w = k

lw = k

Divide both sides by l

w = k/l

w = 72/9

w = 8

The answer is 8

To solve this problem, we need to use the Poisson distribution formula, which is:
P(X = k) = (e^-λ * λ^k) / k
where λ is the average rate of defects per unit length (in this case, per 100 meters), and k is the number of defects we're interested in.

First, we need to find the rate of defects per meter, which is:
λ' = λ / 100 = 0.02 defects/meter
Next, we need to find the probability of having more than 2 defects between meters 20 and 75. We can do this by finding the probability of having 0, 1, or 2 defects in that range, and subtracting that from 1 (the total probability).
Let X be the number of defects in the range from meter 20 to meter 75. Then, X follows a Poisson distribution with mean:
μ = λ' * (75 - 20) = 1.1 defects
Now, we can use the Poisson formula to calculate the probabilities:
P(X = 0) = (e^-1.1 * 1.1^0) / 0! = 0.3329
P(X = 1) = (e^-1.1 * 1.1^1) / 1! = 0.3647
P(X = 2) = (e^-1.1 * 1.1^2) / 2! = 0.2006
Therefore, the probability of having more than 2 defects between meters 20 and 75 is:
P(X > 2) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
P(X > 2) = 1 - (0.3329 + 0.3647 + 0.2006)
P(X > 2) = 0.102

So the probability of having more than 2 defects in that range is approximately 0.102, or 10.2%.

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To solve this problem, we need to use the Poisson distribution formula, which is:
P(X = k) = (e^-λ * λ^k) / k
where λ is the average rate of defects per unit length (in this case, per 100 meters), and k is the number of defects we're interested in.

First, we need to find the rate of defects per meter, which is:
λ' = λ / 100 = 0.02 defects/meter
Next, we need to find the probability of having more than 2 defects between meters 20 and 75. We can do this by finding the probability of having 0, 1, or 2 defects in that range, and subtracting that from 1 (the total probability).
Let X be the number of defects in the range from meter 20 to meter 75. Then, X follows a Poisson distribution with mean:
μ = λ' * (75 - 20) = 1.1 defects
Now, we can use the Poisson formula to calculate the probabilities:
P(X = 0) = (e^-1.1 * 1.1^0) / 0! = 0.3329
P(X = 1) = (e^-1.1 * 1.1^1) / 1! = 0.3647
P(X = 2) = (e^-1.1 * 1.1^2) / 2! = 0.2006
Therefore, the probability of having more than 2 defects between meters 20 and 75 is:
P(X > 2) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
P(X > 2) = 1 - (0.3329 + 0.3647 + 0.2006)
P(X > 2) = 0.102

So the probability of having more than 2 defects in that range is approximately 0.102, or 10.2%.

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Answer:

100+15p < 25p

Step-by-step explanation:

Note that

> means greater than

< means less than

≥ means greater than or equal to  

≤ less than or equal to  

total cost of travelling = cost to rent a bus + total cost of ticket for p persons

100 + 15p

they want to spend less than an average cost of 25 per p people

they want to spend less than 25p

since they dont want to spend less than 25p, < would be used

100+15p < 25p

Answer:

True

Step-by-step explanation:

Two points are always collinear.

Therefore, points Z and R are collinear.

The probability that the next chew Henry removes from the bag will be cherry or watermelon is 8/11.

The probability of Henry selecting a cherry or watermelon chew can be found by adding the number of times he selected a cherry chew and the number of times he selected a watermelon chew, and then dividing that sum by the total number of experiments:

Probability of selecting a cherry or watermelon chew = (Number of cherry chews + Number of watermelon chews) / Total number of experiments

Probability of selecting a cherry or watermelon chew = (20 + 20) / 55

Probability of selecting a cherry or watermelon chew = 40/55

To simplify the fraction, we can divide both the numerator and denominator by 5:

Probability of selecting a cherry or watermelon chew = 8/11

Therefore, the probability that the next chew Henry removes from the bag will be cherry or watermelon is 8/11.

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Answer:

pm+2=8

Step-by-step explanation:

Given,

m=3

p=3

We know,

pm+2=3(3)+2

=3×3+2

=6+2

=8

The given double integral is ∫ ∫ (x² + y²)dx dy, and we need to evaluate it over the region in the positive quadrant where x+y≤1.

To evaluate this double integral, we can first determine the limits of integration for both x and y based on the given region. In the positive quadrant, x and y both range from 0 to 1.

Now, integrating the inner integral with respect to x, we get:

∫ (x² + y²)dx = (1/3)x³ + y²x + C1,

where C1 is the constant of integration.

Next, we integrate the resulting expression with respect to y:

∫ [(1/3)x³ + y²x + C1] dy = (1/3)x³y + (1/3)y³x + C1y + C2,

where C2 is another constant of integration.

Finally, we evaluate this double integral over the given region by substituting the limits of integration:

∫∫ (x² + y²)dx dy = ∫[0 to 1] ∫[0 to 1-x] (x² + y²)dy dx.

Performing the integration, we can find the numerical value of the double integral within the given region.

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Answer:

2.29883

formula

\(c = 2 \times \pi \times r\)

solving for (r) radius

\(r = \frac{c}{2\pi} = \frac{14.44}{2 \times \pi} \)

= 2.29883

Answer:

\(\frac{729}{64}\)

Step-by-step explanation:

step 1

(- \(\frac{3}{2}\) )² = - \(\frac{3}{2}\) × - \(\frac{3}{2}\) = \(\frac{9}{4}\)

step 2

(\(\frac{9}{4}\) )³ = \(\frac{9^3}{4^3}\) = \(\frac{729}{64}\)

The radical form of the given exponential form of a number 11x^(1/4) is written as ( 11 ) × \(\sqrt[4]{x}\).

As given in the question ,

Given exponential form is equal to :

11x^(1/4)

Using th formula to convert exponential form into radical form in standard form we have :

( y )^ ( a / b ) = \(\sqrt[b]{y^{a} }\)

Here y is equal to x

a is equal to 1

b is equal to 4

Substitute the value of the given expressions in the formula we have,

11x^(1/4)

= ( 11 ) ×  [x^(1/4) ]

= ( 11 ) × \(\sqrt[4]{x^{1} }\)

Any thing raise to one is the number or variable itself the required radical form is equal to:

=  ( 11 ) × \(\sqrt[4]{x}\)

Therefore, the radical form of the given expression 11x^(1/4) is given by :

( 11 ) × \(\sqrt[4]{x}\).

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Answer:

3

Step-by-step explanation:

There are 4.5 diamonds, which represent 9 hours in total.

This corresponds to 9/3 = 3 circles.

Answer:

3 circles

Step-by-step explanation:

For the pig, it's 4.5 squares. Each square is two hours, and 4.5*2 is 9. Each circle is 3 hours, and 9 divided by 3 is 3. Therefore, the answer is 3 circles.

Answer:

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

According to the diagram we have:

1) Angles w and 138° form a linear pair, hence:

2) Angles 19°, x and w form a right angle, hence:

Answer: Let's start by finding how many truffles Davion sold in small boxes:

Number of truffles in small boxes = 12 truffles/box * 32 boxes = 384 truffles

To find how many truffles Davion sold in large boxes, we can subtract the number of truffles in small boxes from the total number of truffles sold:

Number of truffles in large boxes = Total number of truffles - Number of truffles in small boxes

= 1032 truffles - 384 truffles

= 648 truffles

Since each large box contains 24 truffles, we can find the number of large boxes Davion sold by dividing the total number of truffles in large boxes by the number of truffles per large box:

Number of large boxes = Number of truffles in large boxes / Number of truffles per large box

= 648 truffles / 24 truffles/box

= 27 boxes

Therefore, Davion sold 27 large boxes of truffles last week.

Answer:

I don't know how to solve it

Answer:

x^2 + 3x + 9 + 7/x-3

To calculate the annual payment required to pay off a five-year, $25,000 loan at an interest rate of 3.50 percent EAR, we can use the formula for calculating the equal annual payment for an amortizing loan.

The formula is: A = (P * r) / (1 - (1 + r)^(-n))

Where: A is the annual payment,

P is the loan principal ($25,000 in this case),

r is the annual interest rate in decimal form (0.035),

n is the number of years (5 in this case).

Substituting the given values into the formula, we have:

A = (25,000 * 0.035) / (1 - (1 + 0.035)^(-5))

Simplifying the equation, we can calculate the annual payment:

A = 6,208.61

Therefore, the annual payment required to pay off the five-year, $25,000 loan at an interest rate of 3.50 percent EAR is $6,208.61.

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The x and y coordinates of point C are -2.6 and 5.2, respectively

The coordinate of the points are given as:

\(A = (-4,8)\)

\(B =(2,-4)\)

The ratio is given as:

\(m :n = 3 : 10\)

The point at the given ratio is calculated as:

\(C = (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})\)

So, we have:

\(C = (\frac{3 \times 2 + 10 \times -4}{3+10},\frac{3 \times -4 +10 \times 8}{3+10})\)

Simplify

\(C = (\frac{-34}{13},\frac{68}{13})\)

\(C = (-2.6,5.2)\)

Hence, the x and y coordinates of point C are -2.6 and 5.2, respectively

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Answer:

a

Step-by-step explanation:

Answer:

i am not sure man

Step-by-step explanation: