3cm
7 cm
2 cm
Surface area of the prism

The length of the third side of the triangle is 10.7 feet.

Patricia is building a garden in her backyard that is shaped like a triangle. She has already built two sides of the garden  and they have length of 6 feet and 7 feet.

She wants to find the length of the third side. The angles between the the built sides is 110 degrees.

Therefore, let's find the third sides using the included angle and the two known sides.

using cosine rules,

c² = a² + b² - 2ab cos C

c² = 6² + 7² - 2(6)(7) cos 110

c² = 36 + 49 - 84 cos 110°

c² = 85 - 84(-0.34202014332)

c² = 85 + 28.7296920394

c = √113.729

c = 10.6643799632

c = 10.7 feet

Therefore,

third side of the triangle = 10.7 feet

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Answer:

A) oblique hexagonal prism

Step-by-step explanation:

Answer:

right hexagonal prism

Step-by-step explanation:

as seen on the Image below the left one is a right hexagonal prism and the right one is a oblique hexagonal prism.

Answer: 6.5

Step-by-step explanation:

26/4 = 6.5 hours

Answer:

- angle T is congruent to angle U (given)

- NS is congruent to SH (given)

- angle TSN is congruent to USH (vertical angles are congruent)

So triangle TNS is congruent to triangle UHS by AAS.

Answer:

3.14 (24 square) (2.5)

Step-by-step explanation:

3.14 24 square 2.5

X radius squared X height???

Answer:

32

Step-by-step explanation:

in the word problem “256 chairs in the cafeteria. this is 8 times the chairs in the library.” Which means 8 times the number of chairs in the library equals the number of chairs in the cafeteria.

L = library

8 x L = 256

to find L divided 256 by 8

256/8 = 32

L = 32

Check the answer

8 x 32 = 256

The equation for contribution for each student is 185.5/14 = 13.25.

Price of new easel= $129

Set of blank canvases = $ 46

Sales tax = $ 10.50

So, the total amount is

= 129 + 46 + 10.5

= 185.5

Then, each student contribute

= 185.5 / 14

= 13.25

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1. The width of the pen must be greater than or equal to the sum of the diameters of the two circular food containers, which is equal to 2x + 2x = 4x:

2. The width of the pen must also be less than or equal to the length of the pen, which is 10 feet:

3. The radii of the gravel bases must be greater than or equal to the radii of the food containers, which is equal to x:

4. The radii of the gravel bases must also be less than or equal to half the width of the pen, which is equal to y/2:

System of inequalities that can be used to determine the width of the pen, y, and the radii of the gravel bases, x, is:

Answer:

Step-by-step explanation:

The sum of the diameters of the gravel bases cannot exceed the width of the pen, so 2⁢x+2⁢x≤y. Rewrite this to get y≥4⁢x as the first inequality in the system.Next, to write the expression for the cost of the fencing, find the perimeter of the rectangle and multiply the perimeter by the cost per foot of fencing. The pen is a rectangle, so the perimeter is 2⁢(10)+2⁢(y), or 20+2⁢y. Multiply the cost ($4.00 per foot) by the perimeter to get 4⁢(20+2⁢y).Now write an expression for the gravel bases for the circular food containers. Because A=π⁢r2 and the cost of the gravel is $2.00 per square foot, multiply the cost of the material by the sum of these areas to get 2⁢(π⁢x2)+2⁢(π⁢x2).The total cost must be less than or equal to $150, so we can say that 4⁢(20+2⁢y)+2⁢(π⁢x2)+2⁢(π⁢x2)≤150. Finally, simplify and solve for y.80+8⁢y+2⁢π⁢x2+2⁢π⁢x2≤15080+8⁢y+4⁢π⁢x2≤1508⁢y≤70−4⁢π⁢x2y≤8.75−0.5⁢π⁢x2So, this is the system.

y≥4⁢x

y≤8.75−0.5⁢π⁢x2

Answer: Part A) 3,141.59 Part B) 75.40

Step-by-step explanation:

Sorry if this is wrong.

Answer:

2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2

B is the correct answer.

The breadth and error margin of the confidence interval will rise when the confidence level is raised from 95% to 98%.

We are more certain that the genuine population mean falls inside the interval if the confidence level is larger. The range of feasible values for the population means will be broader since we need to widen the interval in order to reach this higher degree of confidence.

Since the margin of error equals half of the interval's breadth, it is directly proportional to the interval's width. The margin of error will therefore expand as the confidence level does as well.

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Answer:

15,136 km

Step-by-step explanation:

Im not 100% sure but everyone meses up sometimes/

Answer:

5x + 3y = - 15

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, - 5) ← 2 points on the line

m = [tex]\frac{-5-0}{0-(-3)}[/tex] = [tex]\frac{-5}{0+3}[/tex] = - [tex]\frac{5}{3}[/tex]

the line crosses the y- axis at (0, - 5 ) ⇒ c = - 5

y = - [tex]\frac{5}{3}[/tex] x - 5 ← in slope- intercept form

multiply through by 3 to clear the fraction

3y = - 5x - 15 ( add 5x to both sides )

5x + 3y = - 15 ← in standard form

The  null hypothesis and the alterative hypothesis are [tex]H_0[/tex] : [tex]\mu[/tex] > 1220

[tex]H_\alpha[/tex]: [tex]\mu[/tex] ≤ 1220.

The standardized test statistic is 1.725.

We have,

[tex]\mu[/tex] > 1220,

α = 0.03

[tex]\sigma[/tex] = 202.17

X = 1249.88

n= 300

a) According to the claim and the sample statistics, the null hypothesis and the alterative hypothesis are given by:

[tex]H_0[/tex] : [tex]\mu[/tex] > 1220

[tex]H_\alpha[/tex]: [tex]\mu[/tex] ≤ 1220

b) The standardized test statistic is

=| [tex](\mu[/tex] - X) / ([tex]\sigma[/tex] / √n)|

= |( 1220 - 1249.88) / (202.17/√300)|

= |(-29.88)/ 17.320|

= |-1.725|

= 1.725

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The rule of the function table is,

⇒ y = 1/2x

Now, We have to given that;

Table is shown in image.

Let two points on the table is, (24, 12) and (12, 6)

Hence, We get;

The equation for table is,

y - 12 = (6 - 12) / (12 - 24) (x - 24)

y - 12 = - 6/-12 (x - 24)

y - 12 = 1/2 (x - 24)

y - 12 = 1/2x - 12

y = 1/2x

Thus, The rule of the function table is,

⇒ y = 1/2x

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Answer:

Step-by-step explanation:

The required vertical distance from the top of the slide to the bottom of the pool is 43.8 feet.

We can use trigonometry to solve this problem. Let's call the vertical distance from the top of the slide to the bottom of the pool "h" (in feet). We can use the angle of depression (45°) to find the horizontal distance from the top of the slide to the bottom of the pool. Since the slide has a constant slope, the angle between the slide and the ground is also 45°. It implies that the vertical height is equal to the horizontal projection of the slide.

Apply Pythagorean theorem,
45² = h² + h²
h = 45/√2
h = 31.8

Now, as mentioned that depth of the pool is 12 feet so, the total vertical height is given as,
= h + 12
= 31.8 + 12
= 43.8 feet

Thus, the required vertical distance from the top of the slide to the bottom of the pool is 43.8 feet.

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For 3 personal training session both gym cost same.

We have,

At Silver gym, membership is $25 per month and personal training sessions are $30 each.

At Fit Factor, membership is $65 per month, the and personal training sessions are $20 each.

let the number of personal session be x.

So, 25+ 30x = 65 + 20x

30x - 20x = 65 - 25

10x = 30

x= 3 sessions

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The class that contains the 80 th percentile is d) 32-34.

First, find the total frequency of the income :

Total frequency = 2 + 11 + 8 + 5 + 4 = 30

The position of the number at the 80 th percentile would then be :

= 30 x 80 %

= 24 th position

The cumulative frequency of :

26 - 28 =  2

28  - 30 : 2 + 11 = 13

30 - 32 : 13 + 8 = 21

This then means that the 24 th position is in the next interval of 32 - 34.

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Answer:

0.38 degrees.

Step-by-step explanation:

C = 2π(53) = 106π km

The train is traveling at a speed of 44 km/h, which is equivalent to (44/60) km/min since there are 60 minutes in an hour.

d = (44/60) km/min

θ = (d / C) x 360°

θ = [(44/60) / (106π)] x 360°

θ ≈ 0.38°

Therefore, the angle through which the train turns in 1 minute is approximately 0.38 degrees.

Answer:

√(6 + 9 +12) = √27 = 3√3

√(-6 + 9 + 12) = √15 = √3√5

√(6 - 9 + 12) = √9 = 3

√(6 + 9 - 12) = √3

(1/4)(3√3)(√3√5)(3)(√3)

= (1/4)(27√3)(√5) = (27√15)/4 = 26.1

Answer:correct answer is 26.1

Step-by-step explanation:

Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is given by:

A = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter, which is half the perimeter of the triangle:

s = (a + b + c) / 2

In this case, the side lengths are a = 6, b = 9, and c = 12. Therefore, the semiperimeter is:

s = (6 + 9 + 12) / 2 = 27 / 2

Using Heron's formula, we can now calculate the area of the triangle:

The probability that you will get a 15-inch monitor = 1/3

We know that probability of event is the ratio of number of possible outcomes of event A and the total number of outcomes.

Let us assume that event A = you will get a 15-inch monitor

The number of favourable outcomes for event A are 2

So, n(A) = 2

The sample space for this experiment would be,

n(S) = 6

Using the definition of probability, the required proabability would be,

P(A) = n(A) / n(S)

P(A) = 2/6

P(A) = 1/3

Therefore, the required probability = 1/3

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The likelihood that they will choose to work in an animal shelter for each of the six options they choose is around 0.2214 or 22.14%

The probability is given as,

P = (Favorable event) / (Total event)

The likelihood of choosing an opportunity at an animal shelter is 7/9. If each chance is equally likely to be chosen, the likelihood of choosing six in a row from an animal shelter may be estimated by multiplying the likelihood of choosing one opportunity by itself six times:

P = (7/9) x (7/9) x (7/9) x (7/9)

P = (7/9)⁶

P = 0.2214 or 22.14%

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[tex]\sin^2(\theta)+\cos^2(\theta)=1\hspace{9em} \begin{array}{llll} \textit{Symmetry Identities} \\\\ \sin(-\theta )=-\sin(\theta) \\\\ \cos(-\theta )=\cos(\theta ) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\cot(-x)\cos(-x)+\sin(-x)\implies \cfrac{\cos(-x)}{\sin(-x)}\cos(-x)+\sin(-x) \\\\\\ \cfrac{\cos(x)}{-\sin(x)}\cos(x)+[-\sin(x)]\implies \cfrac{-\cos^2(x)}{\sin(x)}-\sin(x) \\\\\\ \cfrac{-\cos^2(x)-\sin^2(x)}{\sin(x)}\implies \cfrac{-( ~~ \cos^2(x)+\sin^2(x) ~~ )}{\sin(x)} \\\\\\ \cfrac{-( ~~ 1 ~~ )}{\sin(x)}\implies -\cfrac{1}{\sin(x)}\implies -\csc(x)[/tex]

The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

We have the 4 functions as shown in the image attached.

The y - intercept is the point where the graph intercepts the y - axis.

Function [1] -

y = 4 + 2x

y - intercept is 4

Function [2] -

y = 5ˣ + 1

y - intercept is 2.

Function [3] -

the y-intercept is 1.

Function [4] -

the y - intercept is at -1.

Therefore, the greatest y-intercept is of function -

f(x) = 2x + 4

and the least y-intercept is of the function shown in graph [4] or function [4].

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Answer:

Carlos puts $3 into his bank account and it grows by 50% each year

f(x)=4^x+1

(The Table)

(The Graph)

The proportion Max can use to find how many quarts of lemonade is 2 gallons divided by 4 quarts per gallon equals 8 quarts.

Max can use the following proportion to calculate how many quarts of lemonade he made:

1 gallon equals 4 quarts

Max can calculate the number of quarts by multiplying 2 by 4 because he made 2 gallons of lemonade:

2 gallons divided by 4 quarts per gallon equals 8 quarts

As a result, Max created 8 pints of lemonade.

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The total weight of all the cantaloupes that weigh more than 2 1 / 2 pounds is 8 2 / 4 lb ​.

As shown on the line plot, the number of cantaloupes with a higher mass than 2 1 / 2 pounds are those which have a weight of 2 3 / 4 pounds.

There are enough of them that when they are added up, we get the sum of 8 2 / 4 lb​ as the total mass of the cantaloupes. This can also be written in decimals as 8. 5 lb.

In conclusion, option D. is correct.

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[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_5(x-7)=2\implies 5^{\log_5(x-7)}=5^2\implies x-7=5^2 \\\\\\ x-7=25\implies x=32[/tex]

Answer:

Step-by-step explanation:

1. Get mileage per gallon by dividing miles traveled by gallons used

[tex]\frac{125}{5} = 25 mpg\\[/tex]

2. Divide miles you want to travel by the mileage per gallon you got on the first step

[tex]\frac{400}{25} = 16 gallons[/tex]

The circumference of the lollipop is 12.57 inches.

Circumference is the measurement of the distance around the outer edge of a closed curve, particularly a circle. It is the total length of the curve that makes up the boundary of the circle.

The circumference of the circle is given by the formula;

Circumference = 2 × π × radius

where π (pi) is the mathematical constant approximately equal to 3.14159265359...

Given that the radius of the round lollipop is 2 inches, we can substitute this value into the formula;

Circumference = 2 × π × 2

Using the approximate value of π as 3.14159265359..., we can calculate the circumference;

Circumference = 2 × 3.141592 × 2

Circumference ≈ 12.56

Therefore, the circumference of the lollipop is approximately 12.57 inches.

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