isabella is building a fort.The base is 78 inches wide by 92 inches long. what is the area of the base in square inches show your work

The measure of the angle BAM is approximately 40.894°.

In this problem we proceed to draw the figure representing the entire figure and labeling all known lengths, both from statement and derived from Pythagorean theorem. Since the angle BAM is part of a right triangle, then we can apply the following trigonometric function:

[tex]\tan \theta = \frac{BM}{AB}[/tex]

[tex]\tan \theta = \frac{\frac{\sqrt{3}}{2}\cdot x }{x}[/tex]

[tex]\tan \theta = \frac{\sqrt{3}}{2}[/tex]

θ ≈ 40.894°

The measure of the angle BAM is approximately 40.894°.

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Using proportions, the expression for the final amount is:

150(1+d).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

For this problem, we have that:

Hence the equivalent expression is:

120 x 1.25 x (1 + d) = 150(1+d).

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The number of months until the insect population reaches 40 thousand is 14.29 months and the limiting factor on the insect population as time progresses is 250 thousands.

Given that population P(t) (in thousands) of insects in t months after being transplanted is P(t)=(50(1+0.05t))/(2+0.01t).

(a) Firstly, we will find the number of months until the insect population reaches 40 thousand by equating the given population expression with 40, we get

P(t)=40

(50(1+0.05t))/(2+0.01t)=40

Cross multiply both sides, we get

50(1+0.05t)=40(2+0.01t)

Apply the distributive property a(b+c)=ab+ac, we get

50+2.5t=80+0.4t

Subtract 0.4t and 50 from both sides, we get

50+2.5t-0.4t-50=80+0.4t-0.4t-50

2.1t=30

Divide both sides with 2.1, we get

t=14.29 months

(b) Now, we will find the limiting factor on the insect population as time progresses by taking limit on both sides with t→∞, we get

[tex]\begin{aligned}\lim_{t \rightarrow \infty}P(t)&=\lim_{t \rightarrow \infty}\frac{50(1+0.05t)}{2+0.01t}\\ &=\lim_{t \rightarrow \infty}\frac{50(\frac{1}{t}+0.05)}{\frac{2}{t}+0.01}\\ &=50\times \frac{0.05}{0.01}\\ &=250\end[/tex]

(c) Further, we will sketch the graph of the function using the window 0≤t≤700 and 0≤p(t)≤700 as shown in the figure.

Hence, when the population P(t) (in thousands) of insects in t months after being transplanted by P(t)=(50(1+0.05t))/(2+0.01t) then the number of months until the insect population reaches 40 thousand 14.29 months and the limiting factor on the insect population is 250 thousand and the graph is shown in the figure.

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The point of intersection of both graphs will have the coordinate (5, 9).

We are given the functions;

f(x) = x + 4

g(x) = -2x + 19

Now, the point of intersection of both graphs is when both functions are equal which is at f(x) = g(x). Thus;

x + 4 = -2x + 19

x + 2x = 19 - 4

3x = 15

x = 15/3

x = 5

Thus;

f(x) = 5 + 4 = 9

g(x) = -2(5) + 19 = 9

Thus, the point of intersection of both graphs will have the coordinate (5, 9)

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Convert [tex]-1+i[/tex] to polar form.

[tex]z = -1 + i \implies \begin{cases}|z| = \sqrt{(-1)^2 + 1^2} = \sqrt2 \\\\ \arg(z) = \pi + \tan^{-1}\left(\dfrac1{-1}\right) = \dfrac{3\pi}4 \end{cases}[/tex]

By de Moivre's theorem,

[tex]\left(-1+i\right)^7 = \left(\sqrt2 \, e^{i\,\frac{3\pi}4}\right)^7 \\\\ ~~~~~~~~ = \left(\sqrt2\right)^7 e^{i\,\frac{21\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \, e^{-i\,\frac{3\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \left(\cos\left(\dfrac{3\pi}4\right) - i \sin\left(\dfrac{3\pi}4\right)\right) \\\\ ~~~~~~~~ = 8\sqrt2 \left(-\dfrac1{\sqrt2} - \dfrac1{\sqrt2}\,i\right) \\\\ ~~~~~~~~ = -8 (1 + i)[/tex]

QED

The substance's half - life is 7 days

The formula for finding the half - life is given as;

Half - life = [tex]\frac{0. 693}{k}[/tex]

The k value given is 0.1027

Half - life = [tex]\frac{0. 693}{0.1027}[/tex]

Half - life = 6. 75

Half - life = 7 days in the nearest tenth

Thus, the substance's half - life is 7 days

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The value of x from the given expression is -2

The formula for calculating the slope of a line is expressed as:

Slope = y2-y1/x2-x1

Given the following parameters

m = 1

(x1, y1) = (0, 2)

(x2, y2) = (x, 0)

Substitute

1 = x-0/0-2

1 = x/-2

x = -2

Hence the value of x from the given expression is -2

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Answer:

m∠B > m∠C > m∠A

Step-by-step explanation:

The angle opposite the largest side in a triangle is the largest, and the angle opposite the shortest side is the smallest.

The answer is x=21 the explanation is on the picture above I hope I helped

If the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.

Speed is the distance covered by an object in a certain time period. It is also known as velocity. The formula of speed is as follows:

Speed=Distance/ Time.

We have been given that the speed of stream is 7miles per hour.

Let v be the speed of the boat, and t the time to travel

98=t*(7+v) (1)

49=t(v-7) (2)

(1)+(2) => 2tv=147

7t+(49+7t)=98

14t+49=98

14t=49

t=49/14

t=7/2

Put the value of t in equation 1 to get the value of v:

98=t(7+v)

98=7/2(7+v)

196/7=7+v

28=7+v

v=28-7

v=21

Hence if the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.

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Answer: sin(58) = 0.848, cos(26) = 0.898, and tan(63) = 1.962

Step-by-step explanation:

The greatest common factor of the expression is 4m⁴.

GCF simply means the greatest common factor.

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

Hence,

56m⁵

68m⁴

The greatest common factor of the expression  is the largest positive expression that divides evenly into all numbers with zero .

Hence, the greatest common factor is 4m⁴

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Ray has the incorrect reasoning because he incorrectly select the sine  function when he should have utilized the tangent.

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The height of the ray can be found using trigonometric ratios.

Therefore,

tan 30 = opposite / adjacent

where

opposite side = height

adjacent side = 35 inches

Therefore,

tan 30° =  height / 35

cross multiply

height = 35 tan 30°

height = 20.2072594216

height = 20.21 inches

Therefore, Ray has the incorrect reasoning because he incorrectly select the sine  function when he should have utilized the tangent.

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Answer:

1. Ray

2. Sine

3. Tangent

Step-by-step explanation:

Plato/Edmentum

Answer:

D.

Step-by-step explanation:

the suggested relation can be described as y=15x. Then the correct answer is D) Yes, the points are on the line that passes through the origin.

Answer:

[tex]tan(30) = \frac{5}{b} [/tex]

Step-by-step explanation:

Trigonometric Ratios.

To solve for b, we check the parameters that are given in the triangle.

If we're considering 30°, we can see that the opposite is given as 5cm and the adjacent is b.

Applying:

[tex]tan \alpha = \frac{oppsite}{adjacent} \\ \\ tan \: (30) = \frac{5}{b} [/tex]

Answer:

a

Step-by-step explanation:

just did the quiz!!!!

The probabilities in each of the given categories are; A) 51.33%; B) 51.33% C) 30.33% D) 30.33%

The number of ways to select 2 out of 25 is; 25C2 = 25! / (23! * 2!)

= 25*24/2

= 300

(A) Probability of selecting 1 male and 1 female:

[(11C1) * (14C1)]/300 = [11!/(10! * 1!)] * [(14!/(12! * 2!))

= 51.33%

(B)  Probability of selecting 1 female and 1 male:

[(14C1) * (11C1)]/300 = 51.33%

(C)   Probability that 2 females are selected is;

(14C2)/300 = 30.33%

D) Probability that no males are selected is;

P(no males) = (11C0 * 14C2 )/300 = 30.33%

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From the number line, the values which completes the sum in the table are:

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

From the table of values (see attachment), the values on the number line are represented as follows:

a + b = a + b

R = -1 - 2

R = -3.

a + b = a + b

S = -4 + 1

S = -3.

a + b = a + b

T = -6 - 3

T = -9.

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The limit happens to be the derivative of [tex]2^x[/tex] at [tex]x=0[/tex]:

[tex]\displaystyle f'(c) = \lim_{x\to c}\frac{f(x)-f(c)}{x-c} \implies \lim_{x\to0} \frac{2^x - 1}x = (2^x)'\bigg|_{x=0} = \ln(2)\,2^x \bigg|_{x=0} = \boxed{\ln(2)}[/tex]

[tex] \frac{1}{4} x + 1 = 32 \\ \frac{1}{4} x = 32 - 1 \\ \frac{1}{4} x = 31 \\ x = 31 \times 4 = 124[/tex]

The answer is 124.

Answer: 178 ft^3

Step-by-step explanation:

A cylinder has the formula V=pi radius ^2 height

A cone has the formula V= 1/3 pi radius ^2 height

So 1/3 of the volume of the cylinder is the volume of a cone

1/3 of 534 = 178 ft^3

The solution values in order from smallest to largest are;

let

(x - 5)-2 = 14

-2x + 10 = 14

-2x = 14 - 10

-2x = 4

x = 4/-2

x = -2

4x - 5 = -8

4x = -8 + 5

4x = -3

x = -3/4

x = -0.75

(x + 3) / 5 = -2

x + 3 = -2(5)

x + 3 = -10

x = -10 - 3

x = -13

1/2x + 4 = -1

1/2x = -1 - 4

1/2x = -5

x = -5 ÷ 1/2

= -5×2/1

x = -10

x + 2 = 6/-4

-4(x + 2) = 6

-4x - 8 = 6

-4x = 6 + 8

-4x = 14

x = 14/-4

x = -3.5

Therefore, the smallest value is -13 and the largest value is -0.75.

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Answer:

100

Step-by-step explanation:

Forming algebraic equations and solving:

Let the number of boys originally  at the stop = 'x'

Let the number of girls originally at the stop = 'y'

25  girls get on the first bus.

⇒ The number of girls now at the stop = y -25

Ratio of boys to girls:

        [tex]\sf \dfrac{x}{y -25}= \dfrac{3}{2}\\\\Cross \ multiply,\\\\2x = 3*(y- 25)\\\\2x = 3y - 3*25\\\\2x = 3y - 75 ------[/tex](I)

15 boys get on the second bus.

Now, the number of boys at the stop = x - 15

Number of girls at the stop = y - 25

Ratio of boys to girls,

     [tex]\sf \dfrac{x - 15}{y -25} = \dfrac{1}{1}\\\\Cross \ multiply, \\\\x - 15 = y -25\\\\[/tex]

             x = y -25 + 15

             x = y - 10

Plugin x = y - 10 in equation (I)

          2*(y-10) = 3y -75

          2y - 20  = 3y -75

                -20 = 3y - 75 - 2y

                -20 = y -75

         -20 +75 = y

                 [tex]\sf \boxed{\bf y = 55}[/tex]

Plugin y = 55 in equation (I)

       x = 55 -10

        [tex]\sf \boxed{\bf x = 45}[/tex]

Number of students originally at the stop = x + y

                                                                     = 55 + 45

                                                                     = 100

The exponential growth function is P(t) = 6.38 million x (1.0238^t).

The population of the city in 2018 is 7.35 million.

The year the population would be 9 million is 14.46 years.

The doubling time is 29.12 years.

FV = P (1 + r)^n

6.38 million x (1.0238^t)

Population in 2018 = 6.38 million x (1.0238^6) = 7.35 million

Number of years when population would be 9 million : (In FV / PV) / r

(In 9 / 6.38) / 0.0238 = 14.46 years

Doubling time = In 2 / 0.0238 = 29.12 years

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Answer:

Step-by-step explanation:

According to the picture, the angles with measure of 65° and x are included between two parallel pairs of lines.

It makes them equal:

y is the exterior angle of the triangle with two remote interior angles with measure of 40° and 65°.

As per definition of the exterior angle its measure is same as the sum of remote interior angles:

Answer: 0.18

Step-by-step explanation:

The probability of the event P(A and B) is equal to 0.18.

The correct option is (C).

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Probability has been introduced in Arithmetic to forecast how likely occurrences are to happen.

As per the given data:

We are given the probability of two events:

P(A) = 0.60 and P(B) = 0.30

We are also given that A and B are independent events.

To find the probability of P(A and B):

The term and is equivalent to the term intersection.

P(A and B) = P(A∩B)

For any 2 independent events A and B the probability P(A∩B) is given by:

= P(A) × P(B)

By substituting the given values in the question

= 0.60 × 0.30

= 0.18

The probability of the event P(A and B) is equal to 0.18.

Hence, The probability of the event P(A and B) is equal to 0.18.

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Answer:12

Step-by-step explanation:

Peter's age = x

John's age = y

y=2x

after 8 years = y+8=y+x+2

=(y-y)+8-2=x

=6=x

y=2(6)=12

Step-by-step explanation:

b1) Any line parallel to the x-axis is horizontal. If we look at the graph of a horizontal line, we see that for any x-value you give, the y-value will be the same. In this case, the y-value is -1. Hence, the equation for the line is [tex]y=-1[/tex], as y will be -1 no matter the x.

The gradient for a horizontal line is 0, as the "rise" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would have 0 on the top, which makes the whole fraction 0.

b2) Any line parallel to the y-axis is vertical. If we look at the graph of a vertical line, we see that for any y-value, the x-value will be the same. In this case, the x-value is -1. Hence, the equation for the line is [tex]x=-1[/tex], as x will be -1 no matter the y.

The gradient for a vertical line is undefined, as the "run" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would be dividing by 0, which is undefined.

Using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df is of Tc = 2.1098.

It is found using a calculator, with two inputs, which are given by:

In this problem, the inputs are given as follows:

Hence, using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df, using the stated two-tailed test, is of Tc = 2.1098.

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1598 cm square is the area of the container.

According to the statement

we have given that the container is rectangular prism

And Length of rectangular prism is 34cm

Width of rectangular prism is 17 cm

Height of rectangular prism is 20 cm

we use the below written formula to find the surface area

Surface area formula A=(wl+hl+hw)

To find the surface area of the container.

Substitute the values of Length, width and height in the formula then

A=(wl+hl+hw)

A=((17)(34)+(20)(34)+(20)(17))

After solving the values

A=(578+680+340)

A= 1598

So, 1598 cm square is the area of the container.

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Answer:

The small piece is 6 yards and the large piece is 8 yards.

Step-by-step explanation:

Let x  = small

Let y = large

x + y = 14       3y = 4x

3y = 4x  Divide both sides of the equation by 3 to solve for y

y = [tex]\frac{4}{3}[/tex] x  Plug [tex]\frac{4}{3}[/tex] x in for y in the first equation above.

x + y = 14

x + [tex]\frac{4}{3}[/tex] x = 14  x and 1 x mean the same thing.  Another name for 1 is [tex]\frac{3}{3}[/tex]

[tex]\frac{3}{3}[/tex]x + [tex]\frac{4}{3}[/tex]x = 14

[tex]\frac{7}{3}[/tex]x = 14  Multiple both sides by [tex]\frac{3}{7}[/tex] to solve for x

([tex]\frac{3}{7}[/tex])([tex]\frac{7}{3}[/tex]x) = 14([tex]\frac{3}{7}[/tex]) you can write 14 as [tex]\frac{14}{1}[/tex]([tex]\frac{3}{7}[/tex]) = [tex]\frac{42}{7}[/tex]= 6

x = 6

If x = 6, then y must be 8 because 6 + 8 = 14