Jacque is using a soup can for a school project and wants to paint it. If the can is 11 cm tall and has a diameter of 9 cm, at least how many square centimeters of paint is needed? Approximate using π = 3.14.

374.45 cm2
139.50 cm2
699.44 cm2
438.03 cm2

Answer: 3.5 cm

Step-by-step explanation:

SA for cone = [tex]\pi[/tex]rs + [tex]\pi[/tex]r²        r=radius=9     s=slant height (not height)

A(cone) = 9[tex]\pi[/tex]s + 81[tex]\pi[/tex]

SA for a cylinder = 2[tex]\pi[/tex]rh +2[tex]\pi r^{2}[/tex]      r=6     h = 18

A(cyl) = 2([tex]\pi[/tex])(6)(8) + 2([tex]\pi[/tex])6²

           = 96[tex]\pi[/tex] + 72[tex]\pi[/tex]

           =168[tex]\pi[/tex]

Set the 2 areas equal to each other to solve for slant height

9[tex]\pi[/tex]s + 81[tex]\pi[/tex] = 168[tex]\pi[/tex]

9[tex]\pi[/tex]s=87[tex]\pi[/tex]

s=87/9

this is slant height, now you use pythagorean to solve for h

(87/9)²=9²+h²

h=3.5

Answer:

a) The mode is 6 (which occurs the most times--18).

b) Since there are 50 observations, the median is the value halfway between observations 25 and 26 when the data are arranged in order. That value is 6.

c) (4(2) + 5(10) + 6(18) + 7(14) + 8(6))/50 =

312/50 = 6.24 peas/pod

The number 0. 07129813 corrected to 2 decimal places is 0.07

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

0.07129813

Corrected to 2 decimal places means that we leave only two digits after the decimal points

using the above as a guide, we have the following:

0.07129813  = 0.07

Hence, the solutuion is 0.07

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Answer:

Step-by-step explanation:

Sol'n,

Here,

The length of all sides of sq= height = h

Height of triangle=h

Base length of triangle=b

Now, We know that,

The entire figure is a trapezium,

so, Area of Trap.= 1/2 * h(length of diagonal one + length of diagonal 2)

or, 80 = 1/2 * h* {h +(b+h)}[ since here, the length of second diagonal is sum of the base and length of one side of sq]

or, 160 = h (2h+b)

2h^2 + hb - 160 = 0....(I)

Hence, I is the required eqn....

The Equation for Area of figure is area of Figure, h² + 1/2(h)(b) = 80

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given:

We have the figure consist of one square and one right triangle.

Now, Area of Figure,

= Area of square + area of Triangle

[tex]\dfrac{= \text{length} \times \text{width +}}{\times \text{base} \times \text{height}} =[/tex]

[tex]= 16 \times 12 + \dfrac{1}{2} \times 10 \times 20[/tex]

[tex]= 192+ 100[/tex]

[tex]=292 \ \text{unit}^2[/tex]

and, if the square with height, h, units and a right triangle with height, h units, and a base length, b units.

Then, area of Figure = h² + 1/2(h)(b) = 80 square units.

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a) The length of its edge is; 8 units.

b) The volume of the sphere is; 268.083 cubic units.

c) The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage is 52.4 %.

A. We have been given that the volume of the cube is 512 cubic units.

We have to find the length of its edge. So, Let the length of an edge of a cube be a units.

Then, the volume of the cube = (length of edge)3

the volume of the cube = 512 cubic units.

So, (length of edge)3 = 512 cubic units

So,Length of edge = Cube root of 512 cubic units = 8 units

Thus, the diameter of the sphere = 8 units.

Hence, the radius of the sphere = 8 / 2 = 4 units

B. The volume of the sphere = (4 / 3)πr36

= (4 / 3) × π × 4^3

= 4/3 × 3.14 × 64= 268.08 cubic units

C. The fraction of the cube that is taken up by the sphere = volume of sphere/volume of cube

= 268.08 / 512= 67 / 128

So, the percentage of the cube taken up by the sphere is,

= (67 / 128) × 100= 52.34% (approx)

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Answer:

Step-by-step explanation:

To solve this problem, we need to use the distributive property to simplify the expression inside the parentheses first, then combine like terms:

2x + 6 + 5x - 7 = 4x - 8

7x - 1 = 4x - 8 (combine like terms)

7x - 4x = -8 + 1 (subtract 4x from both sides)

3x = -7 (combine constants)

x = -7/3

Therefore, the solution to the equation 2(x + 3) + 5(x - 1) = 4(x - 2) - 8 is x = -7/3.

We can be 90% confident that the true average number of sick days for an employee who is 28 years old falls between 4.31 and 9.85 days per year, based on the provided data

First, we can plug in the value of 28 for Age in the regression line equation to get the estimated average number of sick days for an employee who is 28 years old:

Next, we can use the standard error to calculate the margin of error for a 90% confidence interval:

Finally, we can construct the confidence interval by adding and subtracting the margin of error from the estimated average number of sick days:

Confidence interval = 7.079032 ± 2.767462 = (4.31157, 9.84649)

Therefore, we can be 90% confident that the true average number of sick days for an employee who is 28 years old falls between 4.31 and 9.85 days per year, based on the provided data.

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Complete Question:

The estimated regression line and the standard error are given. Sick Days=14.310162−0.2369(Age) se=1.682207 Find the 90% confidence interval for the average number of sick days an employee will take per year, given the employee is 28. Round your answer to two decimal places.

Employee 1 2 3 4 5 6 7 8 9 10

Age 30 50 40 55 30 28 60 25 30 45

Sick Days 7 4 3 2 9 10 0 8 5 2.

To find the limit of cos(x)/(1-sin(x)) as x approaches (π/2)+, we can use l'Hospital's Rule.

First, we can take the derivative of both the numerator and denominator with respect to x: lim cos(x)/(1 − sin(x)) x → (π/2)+ = lim [-sin(x)/(cos(x))] / [-cos(x)] x → (π/2)+ = lim sin(x) / [cos(x) * cos(x)] x → (π/2)+

Now, plugging in (π/2)+ for x, we get: lim sin(π/2) / [cos(π/2) * cos(π/2)] x → (π/2)+ = 1 / (0 * 0) = undefined

Since the denominator approaches 0 as x approaches (π/2)+, and the numerator is bounded between -1 and 1, the limit does not exist.

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The correct interpretation of the 95% confidence interval is that if Peggy were to repeat her sampling process many times and calculate a 95% confidence interval each time

Approximately 95% of those intervals would contain the true population means the height of young women aged 18 to 24 in the US. In other words, we can be 95% confident that the true population means height falls within the interval that Peggy calculated from her sample of 2,000 young women.

The correct interpretation is that there is a 95% chance that the true population mean height falls within the calculated interval.

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The probability that a single randomly selected value is greater than 203.4 is approximately 0.556.

To solve this problem, we need to use the properties of the normal distribution and probability.

First, we know that the population has a normal distribution with a mean of 208.5 and a standard deviation of 35.4. This means that the distribution of sample means will also be normal with a mean of 208.5 and a standard deviation of 35.4/sqrt(236), which is approximately 2.3.

Next, we want to find the probability that a single randomly selected value is greater than 203.4. To do this, we need to standardize the value using the formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the population mean, and σ is the population standard deviation.

Plugging in the values we have:

z = (203.4 - 208.5) / 35.4 = -0.144

This means that the value of 203.4 is 0.144 standard deviations below the mean.

Using a standard normal distribution table or calculator, we can find the probability of a value being less than -0.144, which is the same as the probability of a value being greater than 0.144. This probability is approximately 0.556.

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The measure of the angles of the isosceles triangle is x = 36°

Given data ,

Let the measure of one angle of the isosceles triangle be = 108°

where , the isosceles triangle has three acute angles, meaning that the angles are less than 90°

So , let the measure of the unknown angle be x

And , x + x + 108 = 180

Subtracting 108 on both sides , we get

2x = 72

Divide by 2 on both sides , we get

x = 36°

Hence , the angle of isosceles triangle is x = 36°

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The complete question is attached below :

One angle of an isosceles triangle measures 108°. What measures are possible for the other two angles? Choose all that apply.

The probability that a randomly selected passenger car gets more than 35 mpg is approximately 38.4%.

To find the probability that a randomly selected passenger car gets more than 35 mpg, we need to use the normal distribution with a mean of 33.7 mpg and a standard deviation of 4.4 mpg.

First, calculate the z-score for 35 mpg using the formula:

z = (X - μ) / σ

where X is the value (35 mpg), μ is the mean (33.7 mpg), and σ is the standard deviation (4.4 mpg).

z = (35 - 33.7) / 4.4
z ≈ 0.295

Now, we use a z-table or calculator to find the probability for a z-score of 0.295. The table shows the probability to the left of the z-score, so we need to find the complement to get the probability of a car getting more than 35 mpg.

P(Z > 0.295) = 1 - P(Z ≤ 0.295)
P(Z > 0.295) ≈ 1 - 0.616
P(Z > 0.295) ≈ 0.384

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An expression that is equivalent to ∛18⁴ is (b) (18)³/⁴

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

∛18⁴

Applying the law of indices, we have

∛18⁴ = (18⁴)¹/³

Evaluate

So, we have

∛18⁴ = (18)³/⁴

Hence, the solution is (18)³/⁴

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Answer:

[tex] {3}^{2} + {4}^{2} = {5}^{2} [/tex]

[tex] {(3 \times 2)}^{2} + {(4 \times 2)}^{2} = {(5 \times 2)}^{2} [/tex]

[tex] {6}^{2} + {8}^{2} = {10}^{2} [/tex]

3-4-5 is a Pythagorean triple.

Multiplying each of these numbers by 2, we obtain 6-8-10, which is a Pythagorean triple.

Answer:  [tex]12\frac{1}{2}[/tex] inches

Step-by-step explanation:

set common denominators.

[tex]3\frac{1}{5}[/tex] = [tex]3\frac{4}{20}[/tex]

add up all sides =  [tex]3\frac{4}{20}[/tex] + [tex]3\frac{4}{20}[/tex] + [tex]3\frac{1}{20}[/tex] + [tex]3\frac{1}{20}[/tex] = [tex]12\frac{10}{20}[/tex] = [tex]12\frac{1}{2}[/tex]

Answer:

12.5 inches

Step-by-step explanation:

To find perimeter you must plus all the sides. To add fractions they must have the same denominator which we can change by finding the common denominator.

To solve this expression, we can first simplify the expression inside the parenthesis by combining like terms:

(x + 2y) + (x + 2y)^2 = (x + 2y) + x^2 + 4xy + 4y^2

Now we can distribute the A to each term inside the parenthesis:

A(x + 2y) + A(x^2 + 4xy + 4y^2)

Next, we can simplify each term:

A(x + 2y) = Ax + 2Ay

A(x^2 + 4xy + 4y^2) = Ax^2 + 4Axy + 4Ay^2

Putting these simplified terms back together, we get:

Ax + 2Ay + Ax^2 + 4Axy + 4Ay^2

This is the final simplified expression.

Answer:

[tex]x = \sqrt{ {17}^{2} - {15}^{2} } = \sqrt{289 - 225} = \sqrt{64} = 8[/tex]

So x = 8 = 8.0

In the given graph, the length of the segment "AB" is 6.32units.

We have to find length of segment "AB", which means we have to find the distance between the end-points "A" and "B",

From the graph, the end-points of the segment "AB" are :

A ⇒ (-2,4) and B ⇒ (4,2),

So, the length(distance) between these two points can be calculated by the formula : √((x₂-x₁)² + (y₂-y₁)²);

Considering (-2,4) as (x₁, y₁) and (4,2) as (x₂, y₂);

We get,

Length(distance) = √((4-(-2))² + (2-4)²);

Length = √(6² + (-2)²); = √(36 + 4);

Length = √40 ≈ 6.32 units.

Therefore, the length of the segment is 6.32 unis.

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[tex]\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{ns^2}{4}\cot\left( \frac{180}{n} \right) ~~ \begin{cases} n=\stackrel{sides'}{number}\\ s=\stackrel{side's}{length}\\[-0.5em] \hrulefill\\ n=5\\ s=14 \end{cases}\implies A=\cfrac{(5)(14)^2}{4}\cot\left( \frac{180}{5} \right) \\\\\\ A=36\cot(20^o)\implies A\approx 98.91~m^2 \\\\\\ A=245\cot(36^o)\implies A\approx 337.21~in^2[/tex]

Make sure your calculator is in Degree mode.

Heart = 1

Water = 2

star = 4

Step-by-step explanation:

Heart x water = water, so heart is probably 1.

Water x water=star and water + water= star so water is 2. Star is 4

Answer:

heart= 1
tear= 2
star=4

leaf=2
diamond=3
circle=6

Step-by-step explanation:

if heart x tear equals tear one of those numbers has to be one.

so heart equals 1
tear + tear= star and tear x tear= star
only number that work are 2 since 2+2=4 and 2x2=4

leaf +leaf +leaf = circle
so plug in 2 for the leaves. 2+2+2=6
2x ____=6 plug in 3 so diamond is 3
3+3=6 so those are the correct choices.

Answer: 68

Step-by-step explanation:

All the angles of a triangle add up to 180

so 32 + 80 + x = 180  or 180-32-80=x

x = 68

Answer:

x= 68

Step-by-step explanation:

80+ 32+ x= 180

112 +x= 180

x= 180-112

x= 68

The statements that are true about Triangle HNR are;

a. The value of x is 2,

b. The value of y is 6 and

e. The length of KH is 7.6

To find the value of y for triangle HRN, we have to pick out coordinates that have y value in them and they are;  KR = (0.5y + 3.2) and KW = (2y - 8.9). The centroid divides the medians of a triangle into segments with a 2:1

KW : KR = 1:2

(2y - 8.9)/ (0.5y + 3.2) = 1/2

We multiply KW by 2 for the cross exchange, it becomes

4y - 17.8 = 0.5y + 3.2

3.5y = 21

We divide 3.5 and 21 by 3.5 to find the value of y

y = 6

We can then look for the length of KN which is

0.5 x 6 + 3.2 = 6.2

Therefor KR is 6.2

To find the value of x, we take the coordinates that have x in them.

KN = (5x -5.2), KT = (7.1x - 11.8)

7.1 x - 11. 8/ 5x - 5.2 = 1/2
14.2x - 23.6 = 5x -5.2

9.2x = 18.4

x = 2

To find the length of KN, we say

KN = 5 × 2 - 5.2 = 4.8

To find the value of w, we take the coordinates with w values and they are  KD = (9w -23.2) and KH = (4.5w - 5.9).

(9w -23.2)/(4.5w - 5.9) = 1/2

18w - 46.4 = 4.5w - 5.9

13.5w = 40.5

w = 40.5/13.5

w = 3

The length of KH becomes

4.5 × 3 - 5.9

KH = 7.6

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The solution to the given proportion is x = 6

A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio may be written as: 1: 3 (for every one boy, there are three girls).

To determine if a connection is proportional, examine the ratios between the two variables. The connection is proportionate if the ratio is always the same. The connection is not proportional if the ratio changes.

To solve the proportion, we state:

x/3 = 6/3

x / 3 = 2

x = 2 x 3

x = 6

Thus, the solution to the proportion is x = 6

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Solve the given proportion.

x/3 = 6/3

The expression: lim θ→π/2 sin(θ)/(4cos(2θ)) = sin(π/2)/(4cos(2π/2)) = 1/4.

The limit is 1/4.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

We can begin by directly substituting π/2 into the expression and see that we get an indeterminate form of 0/0:

lim θ→π/2 (1 - sin(θ))/(1 + cos(2θ)) = (1 - sin(π/2))/(1 + cos(2π/2)) = 0/0.

To apply l'Hospital's Rule, we take the derivative of the numerator and denominator with respect to θ:

lim θ→π/2 (1 - sin(θ))/(1 + cos(2θ)) = lim θ→π/2 (-cos(θ))/(−2sin(2θ))

Now we can directly substitute π/2 into the expression:

lim θ→π/2 (-cos(θ))/(−2sin(2θ)) = (-cos(π/2))/(−2sin(2π/2)) = -1/0,

which is another indeterminate form. We can apply l'Hospital's Rule again by taking the derivative of the numerator and denominator with respect to θ:

lim θ→π/2 (-cos(θ))/(−2sin(2θ)) = lim θ→π/2 sin(θ)/(4cos(2θ))

Now we can substitute π/2 into the expression:

lim θ→π/2 sin(θ)/(4cos(2θ)) = sin(π/2)/(4cos(2π/2)) = 1/4.

Therefore, the limit is 1/4.

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Answer:

62.1156924

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

Calculate 256 to the power of \frac{3}{4} and get 64.

Answer:

x= 6

x= 1

Step-by-step explanation:

First we must factor the equation by finding two numbers which when multiplied equal 6, and when added equal -7

-6 * -1 = 6 and -6 - 1 = 7, so our numbers are -6 and -1.

We will then write this factored form as (x - 6)(x - 1)=0

Because of the zero product property (anything multiplied by zero will equal zero), we know that either x - 6 equals zero, or x - 1 equals zero.

This means there will be two solutions.

First, we will do x - 6 = 0. We can simply move the 6 to the other side by adding 6 to both sides. This gets x = 6.

Then, we will do x - 1 = 0. By adding 1 to both sides, we will get x = 1

So finally, we know that x = 6 and x = 1

The average speed at which the canoe traveled toward the lighthouse is approximately 17.2 feet per minute.

A is the front of the canoe

B is the position of the observer in the lighthouse

AB is the distance between the front of the canoe and the observer

θ1 is the angle of depression at 5:00

θ2 is the angle of depression at 5:05

h is the height of the front of the canoe above the water (1.3 feet)

We want to find the speed at which the canoe is traveling toward the lighthouse, which we'll call x feet per minute.

Using trigonometry, we can find the following relationships:

tan(θ1) = h / AB          (1)

tan(θ2) = h / (AB + 5x)   (2)

We can rearrange equation (1) to solve for AB:

AB = h / tan(θ1)          (3)

Substituting equation (3) into equation (2), we get:

tan(θ2) = h / (h / tan(θ1) + 5x)

tan(θ2) = tan(θ1) / (1 + 5x * tan(θ1) / h)   (4)

We can solve equation (4) for x:

x = (tan(θ1) / (tan(θ2) - tan(θ1))) * h / 5   (5)

Now we just need to plug in the values we know:

θ1 = 6.5°

θ2 = 48.7° (since θ2 = θ1 + 42.2°)

h = 1.3 feet

Plugging these into equation (5), we get:

x = (tan(6.5°) / (tan(48.7°) - tan(6.5°))) * 1.3 / 5

x ≈ 17.2 ft/min

Therefore, the average speed at which the canoe traveled toward the lighthouse is approximately 17.2 feet per minute.

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[tex]\textit{volume of a rectangular prism}\\\\ V=Lwh ~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=150\\ w=120\\ V=288000 \end{cases}\implies 288000=(150)(120)h \\\\\\ \cfrac{288000}{(150)(120)}=h\implies 16=h[/tex]

Answer:

  A.  The graph of function g is the graph of function f shifted 6 units up.

Step-by-step explanation:

You want to know how the graph of g(x) = f(x) +6 differs from the graph of f(x).

Adding 6 to the function value will cause the y-coordinate of the point on the graph to be increased by 6. When the y-coordinate is increased, the point moves up.

The graph of g(x) = f(x) +6 is the graph of function f shifted 6 units up, choice A.

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