3. Use the image to answer the following questions.
will brainiest if correct. try ur best!









(a) The angle pitch of a roof is safest when measuring between 18° – 27°. According to these guidelines, is the roof pictured in the image safe? (Note:

(b) What is length of the roof line (segment PR)? Round answer to the nearest tenth of a foot and show all your work.


Answer:

3/12, or 1/4 is the probability that it is blue.

What is probability?

Probability = number of successes / total number of outcomes

Total marbels in bag = 4+ 3 + 5 = 12  

A total of 12 marbles are in the bag.

3 blue marbles are in the bag.

Therefore, the probability of picking a blue is 3/12, or 1/4.

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The given trigonometric function consists of trigonometric values of common angles.

The values that represent the solution to [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex], x ∈ [0, 2·π) are; [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].

The given function is:  [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex]

Where; x ∈ [0, 2·π).

We have; cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B).

Which gives:

So, we obtain:
[tex]\frac{\sqrt{2} }{2} .cosx=\frac{\sqrt{2} }{2}.sinx-\frac{\sqrt{2} }{2} .sinx=0\\cosx=0\\cos\frac{\pi }{2} =0[/tex]

Therefore, the possible solutions (x-values) to cos x = 0 are:

[tex]0[/tex] ≤ [tex]\frac{n.\pi }{2}[/tex] ≤ [tex]2.\pi[/tex]

Where, n = 1, 3, 5, .., x ∈ [0, 2·π)

We get:  [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].

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For given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.

For given question,

We have been given a power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex]

We need to find the radius of convergence of the power series.

We use ratio test to find the radius of convergence of the power series.

Let [tex]a_n=\frac{(-1)^nx^n}{2^n}[/tex]

[tex]\Rightarrow a_{n+1}=\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}[/tex]

Consider,

[tex]\lim_{n \to \infty}|\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}}{ \frac{(-1)^nx^n}{2^n} } |\\\\=\lim_{n \to \infty} |\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}\times \frac{2^n}{(-1)^nx^n} |\\\\=\lim_{n \to \infty} |\frac{(-1)x}{2} |\\\\=\lim_{n \to \infty}|\frac{-x}{2} |\\\\=\frac{x}{2}[/tex]

By Ratio test, given power series converges at [tex]|\frac{x}{2} | < 1[/tex]

⇒ |x| < 2

So, the radius of convergence is 2.

Therefore, for given power series [tex]\sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}[/tex] the radius of convergence is 2.

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Answer:

-2

Step-by-step explanation:

See attachment

Answer:

 29.9 cm³

Step-by-step explanation:

You want to know the volume represented by 1/3 of a cone that is 7 cm high and has a radius of 3.5 cm.

The volume of a cone is given by ...

  V = 1/3πr²h

The volume of the cone of interest is ...

  V = 1/3π(3.5 cm)²(7 cm) ≈ 89.797 cm³

1/3 of the volume is the amount of water that sloshed out of the cone. That volume is ...

  1/3(89.797 cm³) ≈ 29.9 cm³

They sloshed out about 29.9 cm³ before they drank the water.

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[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

▪ [tex] \sf{Area\text{ ABCD=}\frac{1}{2}\times AC\times BD}[/tex]

▪ [tex] \sf{Area = 72 yd^2}[/tex]

▪ [tex] \sf{BD = 6yd}[/tex]

[tex]\leadsto[/tex] Substitute the values:

[tex]\longrightarrow \sf{72 = \dfrac{1}{2} \times AC \times 16}[/tex]

[tex]\leadsto[/tex] Solve for AC:

[tex]\longrightarrow \sf{72=8\times AC}[/tex]

[tex]\longrightarrow \sf{ \dfrac{72}{8}=\dfrac{8\times AC}{8}}[/tex]

[tex]\longrightarrow \sf{AC=9}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\large \bm{AC= \: 9 yd}[/tex]

BD = 16 yd

Area of ABCD = 72 yd²

AC = ?

Area of rhombus, using diagonal:

[tex] \frac{1}{2} \times d1 \times d2[/tex]

Therefore:

[tex] \frac{1}{2} \times 16 \times ac = 72[/tex]

Then:

[tex] \frac{16ac}{2} = 72[/tex]

Cross multiply the above into:

[tex]16ac \times 1 = 72 \times 2 = 144 \\ 16ac = 144[/tex]

Divide by the coefficient of AC:

[tex] \frac{16ac}{16} = \frac{144}{16} [/tex]

Final answer is 9 yd

Based on the fact that the number of points scored are consecutive numbers, the number of points scored by Lewis is D. 18 points.

Lewis is the player who scored the least amount of points as they are first in the order.

To find the total number of points scored in the game therefore, you need to assume Lewis's points based on the options, and then sum up the three numbers above it to see if they add up to 78 points.

If Lewis scored 19 points as the lowest then the total points would be:

= 19 + 20 + 21 + 22

= 82 points

If Lewis scored 20 points, the total points would be:

= 20 + 21 + 22 + 23

= 86 points

Lewis therefore scored less than 19 points.

If Lewis scored 18 points, the total is:

= 18 + 19 + 20 + 21

= 78 points

Lewis therefore scored 18 points.

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Answer:

D 34.8

Step-by-step explanation:

[tex]\frac{31+36+28+52+27}{5}[/tex]

(C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.

To determine which expression represents a cubic expression:

Therefore, (C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.

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The complete question is given below:

Choose the expression that represents a cubic expression.

(A) −7x + 14

(B) 7x2 − 5x + 6

(C) 8x3 − 7x2 − 6x + 5

(D) 9x4 + 8x3 − 6x2 − 2x + 11

The distance from the center of the ellipse to where the spots are located will be 2 feet.

What is Distance?

The distance from the center of the ellipse to where the spots are located will be -

= 5 - 3

= 2 feet.

Therefore, the distance from the center of the ellipse is 2 feet.

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Answer:

6 2/5 hrs or   6.4 hours total

Step-by-step explanation:

In two hours, Bob completes  2/10  = 1/5 of the job

           Ellen completes  2/ 8   = 1/4  

Find amount left

   1 - 1/5 -1/4 =  1 - 4/20 - 5/20 = 11/20 left

Ellen will need   8hrs * 11/20 = 88/20 = 4 2/5 hours to finish the job

2 hours to start + 4 2/5 hours to finish = 6 2/5 hours total

Answer:

x = 1

Step-by-step explanation:

No matter what y is, x will always be 1.

(1,-4)

(1,-3)

(1,-2)

(1,0)

(1,1)

(1,2) and so on and so on.

Answer:

x+40

Step-by-step explanation:

Let's say the the "number" is x.

"Forty more than a number" would be x+40

[tex]\Large\texttt{Answer}[/tex]

[tex]\bold{40+n}[/tex]

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]

[tex]\Large\texttt{Process}[/tex]

⇨ Letting n be the number

[tex]\bold n[/tex]

⇨ Add 40 to n (40 more)

[tex]\bold{40+n}[/tex] (or n+40; you can swap these numbers, they'll still add up to the same amount)

Hope that helped

The key features of the above given functions are correctly matched to their corresponding definition.

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The probability of selecting an ace or a heart when one card is drawn from 52 cards is 1/52.

Given that there are 52 cards in which there are 13 cards each for spades,clubs,hearts and diamonds.

We are required to find the probability of getting an ace or a heart when one card is drawn from 52 cards.

Probability is basically the chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative. The probability can be calculated through following formula:

Probability=Number of items/total number of items.

Number of hearts=13

Number of ace=4

Probability of getting an ace or a heart when one card is drawn=P(X=heart)*P(X=ace)

=13/52 * 4/52

=52/(52*52)

=1/52

Hence the probability of getting an ace or heart when one card is drawn from standard deck of cards is 1/52.

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Using the normal distribution, the probability that a worker selected at random makes between $500 and $550 is: 2.15%.

The z-score of a measure X of a normally distributed variable with mean mu and standard deviation sigma is given by:

Z = (X - mu)/sigma

The mean and the standard deviation are given as follows:

mu = 400, sigma = 50

The probability is the p-value of Z when X = 550 subtracted by the p-value of Z when X = 500, hence:

X = 550:

Z = (X - mu)/sigma

Z = (550 - 400)/50

Z = 3

Z = 3 has a p-value of 0.9987.

X = 500:

Z = (X - mu)/sigma

Z = (500 - 400)/50

Z = 2

Z = 2 has a p-value of 0.9772.

0.9987 - 0.9772 = 0.0215 = 2.15% probability.

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The length of line segment AB by observation if the diagram in the task content is; 14.

It follows from the task content that the line segment MN can be considered as parallel to line segment AB. This follows from the fact that the vertices of triangle MNO are midpoints of the line segments of triangle ABC.

Consequently, it can be concluded that line segment AB is twice the length of line segment MN and hence, BC = 2 × 7 = 14.

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The apothem is 15 inches, the perimeter is calculated to be 99.41 while the area is given as 745.59

The side of the octagon is given by x inches

the interior side of the angles can be gotten by:

8-2 * 180 / 8 sides

= 135

We have to find the value of the angles

<abc = 180 - 135 = 45 degree

<acb = 180 - 135 = 45 degrees

x² = 2AB²

AB = x/√2

30 =  x/√2 + x +  x/√2

x = 30 / 1 + √2

The apothem = 30 / 2

= 15

perimeter = 8x

= 8(30 / 1 + √2)

= 99.4 inches

area = 0.5 x 15 x 99.4

= 745.59

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The vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).

The vertex of a parabola exists as the point at the intersection of the parabola and its line of symmetry. The vertex of the parabola exists as the minimum point on the graph for a positive right-handed parabola.

Given the equation of parabola exists [tex]$x^{2}=8 y$[/tex].

[tex]$\mathrm{y}=x^{2} / 8[/tex]

General vertex form for any given parabola exists [tex]$\mathrm{y}=\mathrm{a}(x-a)^{2}+\mathrm{b}$[/tex]

where (a, b) exists the coordinates of the vertex.

For this function it exists [tex]$\mathrm{y}=1 / 8(x-0)^{2}+0$[/tex]

The vertex of the given parabola exists at (0, 0).

Therefore, the vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).

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Answer:

3

Step-by-step explanation:

f(x)-g(x)=3-cos(x)

when u limit it

u have

3-cos180

which is 3-0

3

Assuming that the variable h is the same for each figure, the figures from the least to the greatest is:

The value of h is the same for all the shape so assume the value of h is 2 units.

The volume of a cylinder is:

= πr²h

First cylinder area:

= 22/7 x 3 x 2

= 56.54867 units

The second cylinder area:

= 22/7 x 6 x 2

= 226.19467 units

The volume of a cone is:

= πr²h/3

First cone volume:

= 22/7 x 3 x 2/3

= 18.84956 units

Second cone volume:

= 22/7 x 6 x 2/3

= 75.39822 units

The order is therefore:

Cone with radius of 3 units < Cylinder with radius of 3 units < Cone with radius of 6 units < Cylinder with radius of 6 units

In conclusion, the shapes with the larger radius of 6 units will have more volume.

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We know

In a function

x represents the input and y represents output

So

x is time

So

f(30) represents distance traveled in 30mins

keeping in mind that the points are A(-8 , 6) and C(2 , 5), so

[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{6})\qquad C(\stackrel{x_2}{2}~,~\stackrel{y_2}{5})~\hspace{8em} \frac{2}{5}\textit{ of the way from A to C} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{2}-\stackrel{x_1}{(-8)}~~,~~ \stackrel{y_2}{5}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AC}}}{\left( 10 ~~,~~ -1 \right)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\left( \stackrel{x_1}{-8}~~+~~\frac{2}{5}(10)~~,~~\stackrel{y_1}{6}~~+~~\frac{2}{5}(-1) \right)\implies \left(-8+4~~,~~6-\frac{2}{5} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill B\left(-4~~,~~5\frac{3}{5} \right)~\hfill[/tex]

When calculating a nation’s digital power, the term that is used to refer to the demonstrated capabilities of a nation-state in cyber offense or defense is Cyberwarfare.

Cyberwarfare  can be regarded as the use of cyber attacks against a nation-state so as to produce significant harm.

It should be noted that Cyber Warfare is set of actions  which is been carried out by  nation or organization so as to be able to launch an attack on institutions' computer network systems.

The interests or reasons for cyberwarfares based on the Cybersecurity as well as Infrastructure Security Agency are;

In order to achieve the goals behind the cyberwarfare programs, it is usually designed to focus on spectrum of objectives which will bring harm to national interests.

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The area of the circle A and B is 86.54 inches and 124.62 mm

According to the statement

we have given that the radius of the circle A and b and we have to find the area of the given circle.

So, we know that the

The area enclosed by a circle of radius r is πr².

So, For area of the circle

For condition A :

diameter = 10.5 inches

then radius = 5.25

Area = πr²

Area = 3.14*27.56

Area = 86.54 inches

Now, For condition B :

radius = 6.3 mm

Area = πr²

Area = 3.14*39.69

Area = 124.62mm

So, The area of the circle A and B is 86.54 inches and 124.62 mm

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Answer:

y = (3/4)x + 1/2

Step-by-step explanation:

the slope-intercept form is in general

y = ax + b

with a being the slope, and b the y-intercept (the y-value when x = 0).

because we got the slope and a point we can start with the point-slope form and then transform the equation.

the point-slope form is in general

y - y1 = a(x - x1)

a is again the slope (the same value), and (x1, y1) is a point on the line.

so,

y - 2 = 3/4 × (x - 2) = (3/4)x - 3/2

y = (3/4)x - 3/2 + 2 = (3/4)x - 3/2 + 4/2 = (3/4)x + 1/2

Answer:

ANSWER:  mix 120 ml of 35% acid solution with 60 ml of 65% acid                      solution to obtain 180 ml 0f 45% acid solution

Step-by-step explanation:

If x = number of ml of 35% acid solution and 60 = number of ml of 65% acid solution, then x + 60 = number of ml of the mixture.

Acid content of first ingredient + acid content of second ingredient = acid content of the mixture

So, 0.35x + 0.65(60) = 0.45(x + 60)

    0.35x + 39 = 0.45x + 27

                12 = 0.10x

               120 = x

Answer:

Yes, they are proportional.

Step-by-step explanation:

The ratio for Veronica's trail mix is 3:7

The ratio for Casey's trail mix is 27:63 <--- Simplify this number

27:63 simplified is 3:7, which means these ratios are proportional.

hope this helps :)

Answer: The gas would not have remained liquid

Step-by-step explanation:

Since the freezing point of gasoline starts at -40°F, and the temperature that day was -49°F, we can conclude that the gasoline would not have remained liquid