An exponential growth function has a base that is____one?
Please help

Answer: $10,000

Step-by-step explanation:

Given the following :

Profit if economy remains strong = $30,000

Profit if economy grows at moderate pace = $10, 000

Loss if economy goes into recession = $30,000

Probability that economy will remain strong = 20% = 0.2

probability the economy will grow at a moderate pace = 70% = 0.7

probability the economy will slip into recession = 10% = 0.1

Expected value = sum of (x * p(x))

Here expected value equals;

Strong economy profit = $30,000 * 0.2 = $6000

Moderate economy profit = $10,000 * 0.7 = $7000

Loss on Recession = $30,000 * 0.1 = $3000

Expected profit = $(6000 + 7000 - 3000)

Expected profit = $10,000

Answer:

140 poles

Step-by-step explanation:

1. Convert to the same unit. Either meters to kilometers or kilometers to meters, so you can complete the computation.

2. Divide 0.06 by 8.4 (8.4/0.06 = 140).

3. 140 poles can be placed on the 8.4 km road when separated by 60 m or 0.06 km.

Answer:

false!

Step-by-step explanation:

i just answered true and it was false. so false is correct!

The statement that the horizontal cross-sectional shapes of the given prism are all congruent is false.

Prisms are three-dimensional shapes that have its two ends to be parallel and congruent

The given prism is a trapezoidal prism.

For the horizontal sectional shapes given prism to be congruent, the prism must be cut through the middle

Since the prism can be divided at any point, then the given statement is false

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Answer:

5

Step-by-step explanation:

Due to the direction the line is facing it can be concluded that its slope is positive.

You need two definite points on the line to find the slope.

(x¹,y¹) ( x²,y²)

Points (5,20) (0, -5)

Slope = (y² - y¹) ÷ (x² - x¹)

= (-5 - 20) ÷ (0 -5)

= (-25) ÷ (-5)

= 5

Have a great day!

Answer:

C. The hypotenuse is [tex]\sqrt{2}[/tex] times as long as either leg.

Step-by-step explanation:

The hypotenuse is square root 2 times as long as the sides is a true statement.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have to find the true statement about an isosceles right triangle.

Let us use pythagoras theorem to find this

h²=a²+b²

In this case since its an isosceles right triangle, a and b most be the same.

Let's say that the measure of the sides that are equal is x and the hypotenuse is h.

Pythagoras tells us the following:

h²=x²+x²

h²=2x²

Take square root on both sides

h=√2x

Hence, the hypotenuse is square root 2 times as long as the sides

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Answer:

2) 30, 70, 80

Step-by-step explanation:

Well there has to be 3 angles that all add up to 180°.

1)

100+130+130

=360

2)

30+70+80

= 180

3)

25+3+35

=63

4)

45 + 105 + 120

=150

150+120

270

Answer:

A. They are the same.

Step-by-step explanation:

The sine of any acute angle is equal to its cosine.

Answer:

16

Step-by-step explanation:

Well first we need to plug in 10 for g and 6 for h.

2/5(10) + 3(6) - 6

4 + 18 - 6

22 - 6

16

Thus,

the answer is 16.

Hipe this helps :)

Answer:

16

Step-by-step explanation:

We are given the expression:

2/5g+ 3h - 6

We know that g=10 and h=6. Therefore, we can substitute 10 and 6 into the expression and solve according to PEMDAS( Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

2/5(10)+3(6)-6

First, multiply 2/5 and 10

4+ 3(6)-6

Next, multiply 3 and 6

4+18-6

Next, add 4 and 18

22-6

Finally, subtract 6 from 22

16

2/5g + 3h - 6 when g=10 and h= 6 is 16.

Answer:

The first way to prove that the diagonals of a rectangle are congruent is to show that triangle ABC is congruent to triangle DCB

Here is what is given: Rectangle ABCD

Here is what you need to prove: segment AC ≅ segment BD

Since ABCD is a rectangle, it is also a parallelogram.

Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent.

Answer:

241 mm^2.

Step-by-step explanation:

There are 10 mm in a cm so there are 10*10 = 100 mm^2 in  a cm^2.

So the answer is 2.41 * 100 = 241 mm^2.

Answer:

241mm²

Step-by-step explanation:

If 10mm = 1cm,

then 100mm² = 1cm²

2.41 × 100 = 241mm²

Answer:

[tex] csc (R) = \frac{13}{12} [/tex]

Step-by-step explanation:

Formula for any given angle (Ѳ) is given as csc Ѳ = length of hypotenuse side//length of opposite side. It is the inverse of sin Ѳ.

In the right triangle given above, the opposite length = 24, while the length of the hypotenuse = 26

Thus,

[tex] csc (R) = \frac{hypotenuse}{opposite} [/tex]

[tex] csc (R) = \frac{26}{24} [/tex]

[tex] csc (R) = \frac{26}{24} [/tex]

[tex] csc (R) = \frac{13}{12} [/tex]

Question:

Find the value of the letter in each of the following and give reasons for the steps involved:

1 2 A

+ 6 A B =

A 0 9

Answer:

128 + 681 =  809

Step-by-step explanation:

Here, let's use the general form of numbers where any  letter must represent one value and each digit must be represented by just one letter.

Take the following:

A = 8

B = 1

Thus, A +B = 8 + 1 = 9

Also add:

8 + 2 = 10

In general form, tens digit is zero and the 1 is carried over.

I.e, A = 1 + 6 + 1 = 8

We can now see that,

A = 8

B = 1

Therefore,

1 2 A

+ 6 A B =

A 0 9

Will be written as:

128 + 681 =  809

Answer:  

Rectangular pyramid  8 edges

Rectangular prism    12 edges

Triangular Prism   9 edges

Triangular Pyramid  6 edges

Step-by-step explanation: Faces connected at edges

Rectangular pyramid    1 Base  and 4  slanted  triangular sides

Rectangular prism    2 top and bottom bases and 4 sides

Triangular Prism   2 top and bottom triangular bases 3 rectangular sides

Triangular Pyramid    1 triangular base, 3 slanted triangular sides

The matching is as follow:

Rectangular pyramid:  8 edges

Rectangular prism:  12 edges

Triangular Prism: 9 edges

Triangular Pyramid: 6 edges

A pyramid is a triangular-sided, single-polygonal base, three-dimensional polyhedron-shaped construction. A prism is a three-dimensional polyhedron with rectangular sides that are perpendicular to the base and two polygonal bases.

Rectangular pyramid have one Base and 4 slanted triangular sides

Rectangular prism have 2 top and bottom bases and 4 sides

Triangular Prism have 2 top and bottom triangular bases 3 rectangular sides.

Triangular Pyramid have 1 triangular base, 3 slanted triangular sides.

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Answer: No solution

Step-by-step explanation: If you are doing the Unit Test on edge2020 then D No solution is the answer.

Answer:

the answer is no "solution"

Unit Test on Edge 2023

Answer:

The answer is A.

Step-by-step explanation:

So we have the two equations:

[tex]3x+y=1\\y+4=5x[/tex]

To make a substitution of the second equation into the first equation, we need to isolate the y variable in the second equation. Thus:

[tex]y+4=5x\\y=5x-4[/tex]

Now, we can substitute this into the first equation. Therefore:

[tex]3x+y=1\\3x+(5x-4)=1\\3x+5x-4=1[/tex]

Answer:

The answer is

Step-by-step explanation:

The distance between two points is found by using the formula

[tex] \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } [/tex]

Where (x1 , y1) and ( x2 , y2) are the points

The distance between (-6, -2) and (0, -1) is

[tex] \sqrt{ {( - 6 - 0)}^{2} + {( - 2 + 1)}^{2} } \\ \\ = \sqrt{ {( - 6})^{2} + {( - 1)}^{2} } \\ \\ = \sqrt{36 + 1} \\ \\ = \sqrt{37} \: units[/tex]

Hope this helps you

Answer: √37 units

hope that helped!

Step-by-step explanation:

Notice how you get the same value each time when you divide the cost by the number of downhill rides

Moreover when the downhill rides grow by 2 the total cost grows by 5

so we can state :

To complet the chart we can use the proportionaliyu relation:

so 20 goes with 50

same method:

so 25 goes with 62.5

Answer:

3x+3y and distributive property

Step-by-step explanation:

It is given that

Gretchen buys three bags of apples = 3X

Hayley buys three bunches of bananas = 3Y

As it is also mentioned that it first it is multiplied and then it is added

So, the expression for determining the total number of fruit pieces is

3X + 3Y

And, this expression denotes the distributive property in which we multiplied the each variable and then added it

Answer:

x = -5.

Step-by-step explanation:

The solutions of the equation is when the two functions intersect. That is at (-5, 5.5), so where x = -5.

Hope this helps!

Answer:

x = -5

Step-by-step explanation:

f(x) = g(x) has more than one solution, because they intersect at two points.

The question asks for one solution of f(x) = g(x).

One point where they intersect is at (-5, 5.5), as shown in the graph.

(x , y)

x = -5, y = 5.5

Answer:

C.  6√5

Step-by-step explanation:

√20 +√80= √4*5 + √16*5 = 2√5 + 4√5 = 6√5

Answer:

The length of a side of the pool is 12 m²

Step-by-step explanation:

Let the area of the square plot be A. Since it is a square plot of 35 m side, its area is A = 35² = 1225 m².

Let A' be the area of the lawn. Since the area of the lawn is 1081 m², A' = 1081 m².

Now the area of the pool is the difference in area between the area of the square plot and the area of the lawn. So, let A'' be the area of the square swimming pool.

So, A'' = A - A'

A'' = 1225 m² - 1081 m²

A'' = 144 m².

Since the swimming pool is a square, the length of its side, L is thus

L = √A''

L = √144 m²

L = 12 m

So, the length of a side of the pool is 12 m.

Answer:

Height of the kite = 86.60 meter (Approx)

Step-by-step explanation:

The angle of elevation to see a kite from a stone lying to the ground is 60 degrees. If a thread is tied with a kite and a stone, then that thread is 100 meters long, find the height of the kite.

Given:

Length of thread = 100 meter

Angle of elevation = 60°

Find:

Height of the kite.

Computation:

Using trigonometry application:

Height of the kite / Length of thread = Sin 60°

Height of the kite / 100 = √3 / 2

Height of the kite = [√3 / 2]100

Height of the kite = 50√3

Height of the kite = 86.60 meter (Approx)

Answer:

O g(x) is shifted 4 units left and 6 units down from f(x).

Step-by-step explanation:

O g(x) is shifted 4 units left and 6 units down from f(x).

The graph of g(x) is shifted 4 units to the left and 6 units down from f(x).

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

Given functions are,

g(x) = 1/(x + 4) - 6

f(x) = 1/x

Here when a function f(x) changes to f(x + k) when it is translated k units left.

Here 1/x changes to 1/(x + 4).

So g(x) is shifted 4 units left.

Similarly a function f(x) changes to f(x) - k, if it is translated k units down.

So g(x) also shifted 6 units down.

Hence the correct option is D.

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Answer:

$ 5.65

Step-by-step explanation:

let the cost of a pencil and a ruler be $p and $r respectively.

4p +r= 1 -----(1)

6p +3r= 2.10

divide by 3 throughout:

2p +r= 0.70 -----(2)

Q: 3p +13r= ?

(1) -(2):

(4p +r) -(2p +r)= 1 -0.70

4p +r -2p -r= 0.30 (expand)

2p= 0.30 (simplify)

p= 0.30 ÷2 (÷2 on both sides)

p= 0.15

subst. into (1):

4(0.15) +r= 1

r +0.60= 1

r= 1 -0.60

r= 0.40

cost of three pencils and thirteen rulers

= 3p + 13r

= 3(0.15) + 13(0.40)

= 0.45 + 5.20

= $5.65

Answer:

1) 3x + 44

2) 2y - 8

3) x - 6

15) 5 7/8

16) 6 1/3

17) 3 7/9

Step-by-step explanation:

1) 49 + 4 - 5 - 4 + 3x = 3x + 44

2) -y - 5 + y + 2(y) - 3 = 2y - 8

3) 4x - 3 - 3(x + 1) = 4x - 3 - 3x - 3 = x - 6

15) 7 1/4 - 1 3/8 = 7 2/8 - 1 3/8 = 6 10/8 - 1 3/8 = 5 7/8

16) 9 - 2 2/3 = 8 3/3 - 2 2/3 = 6 1/3

17) 10 1/3 - 6 5/9 = 10 3/9 - 6 5/9 = 9 12/9 - 6 5/9 = 3 7/9

Answer:

2x + 3y < 17

Step-by-step explanation:

Let x be 2-pointers and y be 3-pointers. You're trying to prove that he failed to both tie OR break the record, so he has to have under 17 points total. Knowing our x and y values, just plug it into an inequality equation, and you have your answer.

Answer:

Step-by-step explanation:

To find Angle X we use sine

sin∅ = opposite/ hypotenuse

From the question

WY is the opposite

WX is the hypotenuse

So we have

sin X = WY/ WX

sin X = 6/7

X = sin-¹ 6/7

X = 58.99

X = 59° to the nearest tenth

Hope this helps you

Answer:

x=arcsine (6/7) = 58.98 degrees

Step-by-step explanation:

Performing a trigonometrical function. We can find the value of the angle:

1) sin x =6/7

x=arcsine (6/7)

x= 58.98º

Answer:

The angles are

∠A = 90°, ∠B = 26.56°, ∠C = 63.43°

Step-by-step explanation:

We have that the angles of a vector are given as follows;

[tex]cos\left ( \theta \right ) = \dfrac{\mathbf{a\cdot b}}{\left | \mathbf{a} \right |\left | \mathbf{b} \right |}[/tex]

Whereby the vertices are represented as

A= (2, 5, 0), B = (4, 11, 0), C = (-1, 6, 0),

AB =(4, 11, 0) - (2, 5, 0) = (2, 6, 0) ,  BA = (-2, -6, 0)

BC = (-1, 6, 0) - (4, 11, 0) = (-5, -5, 0), CB = (5, 5, 0)

AC = (-1, 6, 0) - (2, 5, 0) = (-3, 1, 0), CA = (3, -1, 0)

θ₁ = AB·AC

a·c = a₁c₁ + a₂c₂ + a₃c₃ = 2×(-3) + 6×1 = 0

Therefore, θ₁ = 90°

BA·BC = (-2)×(-5) + (-6)×(-5) = 40

[tex]{\left | \mathbf{}BA \right |\left | \mathbf{}BC \right |}[/tex] = (√((-2)² + (-6)²)) × (√((-5)² + (-5)²)) = 44.72

cos(θ₂) = 40/44.72 = 0.894

cos⁻¹(0.894) =θ₂= 26.56°

CA·CB = 5×3 + 5×(-1) = 10

[tex]{\left | \mathbf{}CA \right |\left | \mathbf{}CB \right |}[/tex] = (√((3)² + (-1)²)) × (√((5)² + (5)²)) = 22.36

10/22.36 = 0.447

cos(θ₃) = 0.447

θ₃ = cos⁻¹(0.447) = 63.43°.

Answer:

A, E, F, G

Step-by-step explanation:

The picture below represents a parabolic arc.

An example can be an object being thrown up in the air then then coming back down.

Answer:

24

Step-by-step explanation:

30/100=x/80

cross multiply:

100x=2400

divide by 100:

x=24

Not quite sure how you want me to explain the other way step by step... Hope this helps!

80*.3=24