Write 2.154 × 10∧5 in decimal form.

The slope of a line that is parallel to y=5x+3 is 5x.

Two lines must have the same slope to be parallel to each other.

the height of the pentagonal pyramid is 5. 70 meters

The formula for determining the volume of a regular pentagonal pyramid is given as;

V=5/12tan(54°)ha^2

Where

We have the volume to be;

volume = 82. 5 cubic centers

height = h

a = 5m

Substitute the values

[tex]82. 5 = \frac{5}{12}[/tex] × [tex]tan 54[/tex] × [tex]h[/tex] ×[tex]5^2[/tex]

[tex]82. 5 = 0. 42[/tex] × [tex]1. 3764[/tex] × [tex]25[/tex] × [tex]h[/tex]

Make 'h' subject of formula

[tex]h = \frac{82. 5}{14. 45}[/tex]

h = 5. 70 meters

The height of the pentagonal pyramid is 5. 70 meters

Thus, the height of the pentagonal pyramid is 5. 70 meters

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Answer:

a = 3

b = -9

c = -3

d = 22

e = 49 - 9

f = a^2 -3

Step-by-step explanation:

Please no more questions :(

Answer:

AG = 17 m

AD = 25 m

GD = ?

AD = AG + GD

GD = AD - AG

= 25 - 17

= 8 m

the answer to your question is 8m

The ratio of cos Z is cos Z = 3 / 5

A right triangle has one angle of the triangle as 90 degrees.

The sides of the right triangle can be found using trigonometric ratios.

Therefore,

sin ∅ = opposite / hypotenuse

sin Z = 3 / 5

Using Pythagoras theorem,

c² = a² + b²

5² - 3² = b²

b² = 25  - 9

b² = 16

b = √16

b = 4

Hence,

P + A = 90 degrees (complementary angles)

Therefore,

sin P = cos Z

cos Z = 3 / 5

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The probability that it will rain on exactly one of the three days they are there is 0.375.

Given that Hiking Club plans to go camping in a State park where the probability of rain on any given day is 50%.

The binomial distribution is used when there are exactly two outcomes of a trial that are mutually exclusive.

Use binomial probability:

P = ⁿCʳ pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

and p is the probability of success.

probability of rain on any given day =p =0.50

total number of ways,n=3

let X is number of days with rain out of 3 days

So, [tex]X\sim Bin(3,0.50)[/tex]

P(x=X)=ⁿCₓpˣ(1-p)ⁿ⁻ˣ

P(x=1)=³C₁(0.50)¹(1-0.50)³⁻¹

P(x=1)=3×0.50×(0.5)²

P(x=1)=1.5×0.25

P(x=1)=0.375

Hence, the probability that it will rain on exactly one of the three days they are there where the probability of rain on any given day is 50% is 0.375.

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The amplitude of function f(x)=cos(2x) is 1 and the period is 2.

Given that the function of x is f(x)=cos(2x).

We are required to find the value of amplitude and period of function f(x) which is given in the question.

Amplitude basically refers to maximum displacement from the equilibrium that an object in periodic motion show. It is a product analytics platform or term that helps businesses to track visitors with the help of collaborative analytics.

Period is basically the time interval between two waves. A function  that repeats its values at regular intervals or periods is known as periodic function.

The amplitude of f(x)=cos(2x) is 1 because the highest value that cos Θ can give 1. We can also see in graph that the value of cos 2x is going to 1 and starts decreasing again.

The period of f(x) is 2. From the graph we can say that the vertical distance between upper point and lower point is 2.

Hence the amplitude of function f(x)=cos(2x) is 1 and the period is 2.

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Answer:

5

Explanation:

Look at the number line and count the number of increments needed to get from point A to B.

5 (units) is the answer

Step-by-step explanation:

-2 is point A

3 is point B

Find the absolute value then add

|-2| + |3| = 5

There's our answer, 5! Or the second choice

The percentages for each outcome are given as follows:

a) 34.4%.

b) 29.4%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

For this problem, we already have the percentages, hence we just combine them.

For item a, he can be late in two ways, one that happens 24.4% of the time(waking up late), and the other 10%(stuck in traffic), hence the percentage is of 34.4%, as 24.4% + 10% = 34.4%.

For item b, the percentage stuck in traffic is of 5%, hence the percentage that he will be late is 24.4% + 5% = 29.4%.

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Answer:

[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]

Step-by-step explanation:

We are given the trigonometric equation of:

[tex]\displaystyle{\sin 4x = \dfrac{\sqrt{3}}{2}}[/tex]

Let u = 4x then:

[tex]\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}[/tex]

Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).

[tex]\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]

Convert u-term back to 4x:

[tex]\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]

Divide both sides by 4:

[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]

The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.

Therefore:

[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]

Answer:

Step-by-step explanation:

Option C.

Step-by-step explanation:

Initial number of clients = 18

Number of Increase per week = 4

We need to use an arithmetic sequence to write a function.

So, the required arithmetic sequence for four weeks is

18, 22, 26, 30

Here, first term is 18 and common difference is 4. The range is  [18,30].

The explicit formula of n arithmetic sequence is

where, a is first term and d is common difference.

Substitute a=18 and d=4 in the above formula.

The function notation is

The function is f(x)=4x+14 and the range is  18 ≤ y ≤ 30.

Therefore, the correct option is C.

He needs to run with approximately 6429 for a distance of 9 km

The given parameters are:

Length of stride = 1.4 m

Distance for marathon = 9 km

The number of strides needed is then calculated as:

Number of stride = Distance for marathon/Length of stride

Substitute the known values in the above equation

Number of stride = 9km/1.4m

Convert km to m

Number of stride = 9000m/1.4m

Evaluate the quotient

Number of stride = 6428.57143

Approximate the estimate

Number of stride = 6429

Hence, he needs to run with approximately 6429 for a distance of 9 km

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Answer:

True

Step-by-step explanation:

Plotting the point of any linear equation on a graph gives a straight line

Answer:

A

Step-by-step explanation:

The parallelogram is the length times the height.  The height is 8 and the length is 12 - 2 - 2 or 8.

8x8 = 64

The small rectangle is 12 x 2 or 24

64 + 24 = 88

The value of 8,590 − 4,586 is half the value of 2 x (8,590 − 4,586).

An equation is an expression that shows the relationship between two or more numbers and variables. The basic operations performed on an equation are addition, subtraction, multiplication and division.

The value of 8,590 − 4,586 = 4004

Half the value of 2 x (8,590 − 4,586) = (1/2) of 2 x (8,590 − 4,586) = 4004

The value of 8,590 − 4,586 is half the value of 2 x (8,590 − 4,586).

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Answer:

1.05

Step-by-step explanation:

Because 30% of 70 is [tex]30\% \times 70 = \frac{30}{100} \times 70 = 0.3 \times 70 = 21[/tex], so the question becomes "21 is what percent of 2000?"

To answer this, we can solve for [tex]x[/tex] in the equation [tex]21 = x\% \times 2000[/tex], which is:

[tex]21 = x\% \times 2000\\21 = \frac{x}{100} \times 2000\\21 = 20x\\x=\frac{21}{20}=1.05[/tex]

So the answer is 1.05 percent.

Answer:

Step-by-step explanation:

<E = <T                                Given

M is the midpoint of TE      Given

TM = ME                               Definition of a  midpoint

<TMI = <RME                        Property of Vertically Opposite Angles

ΔTMI = ΔRME                       ASA = ASA

MI = ME                                 Corresponding parts of Congruent triangles                                    are Congruent

answer:                              reasoning:

<E = <T                                given

M is the midpoint of TE      given

TM = ME                               definition of a  midpoint

<TMI = <RME                        property of Vertically Opposite Angles

ΔTMI = ΔRME                       ASA = ASA

MI = ME                                 corresponding parts of congruent triangles                                    are Congruent

hope this helps!

Step-by-step explanation:

y = -f(x)

so, everything is mirrored around the x-axis.

what was below the x-axis, is now above the x-axis, what was above is now below. and what was on the x-axis, is still on the x-axis.

pick the corner points of f(x), their x-values stay the same, their y-values flip the sign. the points on the x-axis (y = 0) stay the same of course.

and then connect the points, so that the curve is upside-down to the original.

The area of the circle is 78.5 square yards and the circumference of the circle is 31.4  yards

The radius of the circle is given as:

r = 5 yard

The area is calculated using

A = pi r^2

Substitute the known values in the above equation

A =3.14 * 5^2

Evaluate the exponent

A =3.14 * 25

Evaluate the product

A =78.5

Hence, the area of the circle is 78.5 square yards

The radius of the circle is given as:

r = 5 yard

The circumference is calculated using

C = 2pi r

Substitute the known values in the above equation

C =2 * 3.14 * 5

Evaluate the product

C = 31.4

Hence, the circumference of the circle is 31.4  yards

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The expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰

From the question, we are to determine the expression that represents the number of reams of paper the company produced during the second year

From the given information,

During the first year of operation,

The company produced 8.4 × 10⁹ reams of paper

And

During the second year,

the company produced 5.6 times the number of reams of paper that it produced during the first year.

Thus,

The number of reams of paper the company produced during the second year = 5.6 × 8.4 × 10⁹ reams of paper

The number of reams of paper the company produced during the second year = 47.04 × 10⁹ reams of paper

= 4.704 × 10¹ × 10⁹ reams of paper

= 4.704 × 10¹⁰ reams of paper

Hence, the expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰

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Comparing A and B we find the value of the variables as

x = radius

Centre (-2,0)

Radius 2

The sketch of the image is attached below

Generally, the equation for is mathematically given as

x = -4 cos -(i)

Multiply -(i) both sides by & we

x^2= -4xcos\theta

We know that and

x= x cos\theta

y = rsino

x² + y² = x² (cos²∅ + sin²∅).

x² + y² = x² ....sin² ∅ + cos 2∅=1

so, putting rates in (ii) we get

x²+y² = -4x

x²+4²  +4 + y²=4

(2 + 2)² + y² =4

The rectangular form of

x = -4cos∅  is (x + 2)² + y² = 4 ---- A

We can see that A is a graph of circles. The general equation of a circle is

= (x-h)² + (y)² = x² ----B

where (h, k) = centre

Comparing A and B we find

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Answer:

[tex]\sqrt[3]{192} x^{\frac{3}{5} }y^{\frac{3}{8} }[/tex]

Step-by-step explanation:

You have to simplify all of the terms individually

[tex]\sqrt[3]{192} = 5.769[/tex]

Since that isn't a whole number, it doesn't simplify

Use the root to exponent rule for the variables

[tex]\sqrt[3]{x^{5} } =x^{\frac{3}{5} }[/tex]

[tex]\sqrt[3]{y^{8} } =y^{\frac{3}{8} }[/tex]

Then put them all together to get

[tex]\sqrt[3]{192} x^{\frac{3}{5} }y^{\frac{3}{8} }[/tex]

Make sure the variables aren't under the root when you give your answer

I hope this helps!

pls mark brainliest

Answer:

(x+1)(x-2)(x-1)(x-1+2¡) multiply all together

Step-by-step explanation:

(x+1)(x-2)(x-1)(x-1+2¡)

multiply all together u have your answer

Answer:

  305 °F

Step-by-step explanation:

The core temperature of the object after 4 hours can be found using an exponential decay formula to model the decay of the difference between core temperature and ambient.

The solution to the differential equation described by Newton's law of cooling is the exponential equation ...

  y = ab^t +c

where 'a' is the initial core temperature difference from ambient, 'b' is the decay factor of that difference in 1 unit of time period t. 'c' is the ambient temperature.

For this problem, the ambient temperature is c=80, and the differences of interest are ...

  a = 1200 -80 = 1120

  b = (830 -80)/1120 = 75/112

Using these values in the model gives ...

  y = 1120(75/112)^t +80 . . . . . . where y(t) is the core temperature at time t

Note that units of time are hours.

We want y when t=4.

  y = 1120(75/112)^4 +80 ≈ 1120(0.20108) +80 ≈ 305.212

The core temperature after 4 hours is about 305 °F.

__

Additional comment

The differential equation will have a solution of the form ...

  [tex]T-T_R=(T_0-T_R)e^{kt}[/tex]

where k = ln(75/112) ≈ -0.40101

In the above, we defined b = e^k = 75/112. Accuracy with this fraction can be better than using a truncated value of k.

The function in terms of the time (t) is t=d/r and the value of the time (t) for the given values is 5.

An equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:

a= the slope

b=constant term that represents the y-intercept.

For the given example: a=2 and b=7.

In the exercise is asked the equation for the time (t) in the function of the distance (d) and the rate (r).

Thus, if d=rt, we will have t= d/r

Replacing the variables for the given values for finding t. The question gives:

distance (d) =40

rate (r) = 8

Thus, you will have t= 40/8. Then, t=5

Therefore, the answer is the fourth option.

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The slope of the graph is 1 / 5.

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

Slope describes the steepness of a line. The slope of any line remains constant along the line.

Therefore,

slope  = y₂ - y₁ / x₂ - x₁

Hence, let's take two coordinates in the graph,

(2, 2)(7, 3)

x₁ =  2

x₂ = 7

y₁ = 2

y₂ = 3

Therefore,

slope = 3 - 2 / 7 - 2

slope = 1 / 5

Therefore, the slope of the graph is 1 / 5.

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Answer: 105

Step-by-step explanation:

105 * .2 = 21 :)

Check the picture below, so the ball's path is pretty much like so, and it reaches its hightest at its vertex, so

[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ f(t)=80t-16t^2\implies f(t)=-16t^2+80t+0 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+80}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 80}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (80)^2}{4(-16)}\right) \implies \left( - \cfrac{ 80 }{ -32 }~~,~~0 - \cfrac{ 6400 }{ -64 } \right) \\\\\\ \left( \cfrac{5}{2}~~,~~100 \right)\implies \underset{~\hfill feet ~~ }{\stackrel{seconds\qquad }{\left( 2\frac{1}{2}~~,~~100 \right)}}[/tex]