Rewrite the given equation so there is a single power of 5,000 on each side. Then, set the exponents equal to each other. Which equation shows the result?

Answer:

-3

Step-by-step explanation:

the number in front of the variable is the coefficient

Answer:

8/15

Step-by-step explanation:

To start off you want both of the fractions to have the same denominator so you will change 2/5 into 6/15 and 2/3 into 10/15.

Than you figure out a number in between being 7, 8, or 9 and divide it by fifteen. Which ever one equals 0.533. (Which in this case is 8) is the numerator to the fraction.

Answer: The teacher's age increases the mean.

Step-by-step explanation:

14.2 + 27 = 41.2 years

41.2/2 = 20.6 years

20.6 years > 14.2 years

Adding the 27-year-old teacher to the student book club, which has a current mean age of 14.2 years, will increase the mean age of the club.

When a 27-year-old teacher is invited to join the book club with an average age of 14.2 years, the teacher's age will increase the mean (average) age of the club members. This occurs because the mean age is calculated by adding all of the ages together and dividing by the total number of individuals in the group. Adding a number that is significantly higher than the current mean will raise the overall total, which, when divided by the new total number of individuals, will result in a higher average age than 14.2 years. We do not have the exact number of original club members, so we cannot calculate the new mean exactly, but we can confidently say the mean age will increase due to the addition of the 27-year-old teacher's age.

Answer:

x+8y

Step-by-step explanation:

add them all together

Answer: passing through three intersecting edges

Step-by-step explanation:

To create a triangle by slicing a cube, D. pass the slicing plane through three intersecting edges, such as AB, FE, and DH, to intersect the cube and form a triangular cross-section.

To slice through a cube such that the figure formed by the intersecting plane is a triangle, you would need to follow option D, passing through three intersecting edges. Imagine the cube has vertices labeled A to H, with ABCD and EFGH being the top and bottom faces respectively, and the vertical edges connecting the corresponding vertices of these two faces.

By slicing through edge AB, edge FE, and edge DH, you would create a plane that intersects the cube in such a way that the section of the cube cut by this plane is a triangle with vertices at the points where the plane cuts through the edges AB, FE, and DH.

Answer:

-3x^3+7y^2+9y

Step-by-step explanation:

y - y² + 4y + 7y² – 3 x3 + y² + 4y​

Combine Like Terms:

=y+−y2+4y+7y2+−3x3+y2+4y

=(−3x3)+(−y2+7y2+y2)+(y+4y+4y)

=−3x3+7y2+9y

Answer:

8

Step-by-step explanation:

                                  aₙ = 2ⁿ⁻¹

a₅ = 2⁴⁻¹ =2³=8

Answer:

15

Step-by-step explanation:

using the 3 : 4 : 5 triangle triple:

we see that this triangle follows the same ratio

9:12 = 3:4, so the hypotenuse = 5*3 = 15

ANSWER: 15

Answer:

D

Step-by-step explanation:

In this problem, we are adding the two equations and we want to get rid of y. To do this, we want one positive y and one negative y with the same coefficient  because when we add the equations they will cancel each other out. The coefficient of the first equation's y is 4, so we want the second to be -4. The coefficient of the second equation's y is -2, and if we want it to be -4 we multiply it by -4/-2= 2, which is D. Once you do that you will get 4y and -4y in the first and second equations respectively and then you can add them to eliminate y!

Step-by-step explanation:

If y = - 5

Then put value of y

5x + 4(-5) = - 20

5x - 20 = - 20

5x = - 20 + 20

5x = 0

x = 0

Answer:

x = 0

y = -5

Step-by-step explanation:

Since you already have the value of y, all you need to do is plug it into the equation, like so:

5x + 4y = -20

5x + 4(-5) = -20

5x - 20 = -20

Add 20 to both sides:

5x - 20 = -20

    + 20  + 20

___________

5x = 0

Finally, divide both sides by 5:

5x = 0

x = 0

So now you have, x = 0 and y = -5

Answer:

1:The base of the rectangular pyramid shown has an area of 50 square inches

2:A triangular face with a base of 10 inches has an area of 28 square inches

3:A triangular face with a base of 5 inches has an area of 17.75 square inches

4:The total surface area of the pyramid is 141.5  square inches.

Step-by-step explanation

Answer:

1.6 km

Step-by-step explanation:

subtract 2.5 from 4.1

Answer:

[tex]-15.5+8\frac{1}{5} -1.6-20.4+15.5[/tex]

13.8 feet left to asaend to the surface

Step-by-step explanation:

Answer:

221.8°

hope this helps:)

Answer:

i believe its 132

Step-by-step explanation: you need to multiply the two numbers together to find the area.

The area of plywood = 30 feet²

A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length.

The perimeter of a rectangle is defined as the total distance covered by the outer boundary of the rectangle. It is measured in unit length. The formula of perimeter is given by:

Perimeter, P = 2 (Length + Width)

The area of the rectangle is the area covered by its outer boundaries. It is equal to the product of length and width.

The formula of area of rectangle is:

Area = Length × Width unit²

Given,

Length of the plywood (L) = 6 feet

Perimeter of Plywood (P)=  22 feet

Area of Plywood = ?

Perimeter = 2(Length + Width)

22 feet = 2 (6feet +  Width)

Width (W) = (22 /2 - 6) feet

Width (W) = (11 - 6) feet

Width (W) = 5 feet

Area of the plywood (A) = Length × Width

Area = 6feet × 5feet

Area = 30 feet²

Hence, Area of the plywood (A) = 30 feet²

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Answer:

[tex]\dfrac{1}{18}[/tex]

Step-by-step explanation:

Number of Headband Types=3

P(Reese will  choose a blue headband)=1/3

Number of Types of Necklace=2

P(Reese will  choose a  silver  necklace)=1/2

Number of Types of Earrings=3

P(Reese will  choose a  silver earrings)=1/3

In Probability Theory,

P(A AND B)=P(A) X P(B)

Therefore, the probability that Reese will  choose a blue headband, a silver  necklace, and a silver pair of earrings

[tex]=\dfrac{1}{3}X \dfrac{1}{2}X\dfrac{1}{3}\\\\=\dfrac{1}{18}[/tex]

Answer:

3.04m

Step-by-step explanation:

Time taken to swing the rope = 3.5s

Length of the rope = L

T = 2π√(L / 9.8)

3.5 = 2π√(L / 9.8)

take the square of both sides

(3.5)² =[2π√(L/9.8)]²

12.25 = 39.48 × (L / 9.8)

12.25 = 39.48L / 9.8

39.48L = 12.25 × 9.8

39.48L = 120.05

L = 120.05 / 39.48

L = 3.04m

The length of the rope is 3.04m

Answer:

Step-by-step explanation:

3.0meters

If [tex]\(y = \log_b(x)\)[/tex], then [tex]\(b^y = x\)[/tex] is the equivalent exponential form.

The logarithmic equation [tex]\(y = \log_b(x)\)[/tex] is equivalent to the exponential form [tex]\(b^y = x\)[/tex]. These two forms are related by the definition of logarithms.

In the logarithmic form [tex]\(y = \log_b(x)\)[/tex], [tex]\(b\)[/tex] is the base of the logarithm, [tex]\(x\)[/tex] is the argument of the logarithm, and [tex]\(y\)[/tex] is the exponent to which the base [tex]\(b\)[/tex] must be raised to obtain [tex]\(x\)[/tex].

In the exponential form [tex]\(b^y = x\)[/tex], [tex]\(b\)[/tex] is the base, [tex]\(y\)[/tex] is the exponent, and [tex]\(x\)[/tex] is the result of raising the base [tex]\(b\)[/tex] to the power of [tex]\(y\)[/tex].

So, if [tex]\(y = \log_b(x)\)[/tex], then [tex]\(b^y = x\)[/tex] is the equivalent exponential form.

The probable question may be:

"What is the exponential form equivalent to the logarithmic equation [tex]\(y = \log_b(x)\)[/tex], where [tex]\(b\)[/tex] is the base of the logarithm, [tex]\(x\)[/tex] is the argument, and [tex]\(y\)[/tex] is the exponent? Provide the expression in the form [tex]\(b^y = x\)[/tex]."

The equation [tex]\(y = \log_b^x\)[/tex] can be represented in exponential form as [tex]\(b^y = x\).[/tex]

When dealing with logarithms and exponential functions, there exists an inverse relationship between them. The logarithm is the inverse of the exponential function, and vice versa. In the given equation [tex]\(y = \log_b^x\),[/tex] the logarithm is in base \(b\) with an exponent of \(x\). To rewrite this equation in exponential form, we need to switch from logarithmic notation to exponential notation.

In exponential form, the base[tex](\(b\))[/tex]is raised to the power of the logarithm ((y)), resulting in [tex]\(b^y\).[/tex] The result of this exponential expression is the value (x\), which is the argument of the logarithm. This transformation showcases the fundamental relationship between logarithms and exponentials, demonstrating that they are different representations of the same mathematical concept.

Expressing the equation as[tex]\(b^y = x\)[/tex]in exponential form clarifies how the logarithmic statement[tex](\(y = \log_b^x\))[/tex] translates into an equivalent exponential form. It emphasizes the reciprocal relationship between logarithms and exponentials, providing a clear understanding of how these forms interrelate in mathematics.

This transformation from logarithmic to exponential form serves to simplify expressions, solve equations, and understand the fundamental connection between logarithms and exponentials in mathematical operations.

"".

Answer:

130

Step-by-step explanation:

The measurement of arc BC is 130°.

Step-by-step explanation:

Given :  circle with origin O, with two line segments AC and BD which are also diameters.

Measurement of arc AB = (3 x -70)° =

Measurement of arc DC= (x +10)° = ∠3

To find : Measurement of arc BC = ∠2 =?

Solution:

Let angle subtended by the arc AC = ∠1 = (3 x -70)°

Let angle subtended by the arc BD = ∠2

Let angle subtended by the arc DC = ∠3  = ( x + 10)°

Let angle subtended by the arc AD = ∠4

AC and BD are intersecting each other at O.

So, ∠1 = ∠3  (vertically opposite angles)..[1]

∠2 = ∠4 (vertically opposite angles)..[2]

(3 x -70)° =  (x +10)° (from [1])

3x - x = 10 + 70

∠1 = ∠3 = (x +10)° =  (40 +10)° = 50°

∠1 + ∠2 + ∠3 + ∠4 = 360°

50° + ∠2 + 50° + ∠2= 360° (from [2])

2∠2 = 360° -50° - 50°

2∠2 = 260°

∠2 = 260° ÷ 2

∠2 = 130°

The measurement of arc BC is 130°.

The measurement of arc BC is 130°.

A circle with origin O, with two line segments AC and BD which are also diameters.

Measurement of arc AB = (3 x -70)° =

Measurement of arc DC= (x +10)° = ∠3

Measurement of arc BC = ∠2 =?

Let angle subtended by the arc AC = ∠1 = (3 x -70)°

Let angle subtended by the arc BD = ∠2

Let angle subtended by the arc DC = ∠3  = ( x + 10)°

Let angle subtended by the arc AD = ∠4

AC and BD are intersecting each other at O.

So, ∠1 = ∠3  (vertically opposite angles)..[1]

∠2 = ∠4 (vertically opposite angles)..[2]

(3 x -70)° =  (x +10)° (from [1])

3x - x = 10 + 70

The circumference of the circle is 360 degrees the circle.

∠1 = ∠3 = (x +10)° = (40 +10)° = 50°

∠1 + ∠2 + ∠3 + ∠4 = 360°

50° + ∠2 + 50° + ∠2= 360° (from [2])

2∠2 = 360° -50° - 50°

2∠2 = 260°

∠2 = 260° ÷ 2

∠2 = 130°

The measurement of arc BC is 130°.

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Answer:

D. -6.

Step-by-step explanation:

The inverse is the number when added to 6  results in 0.

So it is 0 - 6 = -6.   (6 + -6 = 0)

Answer: x+6

Step-by-step explanation:

6 more than (+) x

Answer:

Below in bold.

Step-by-step explanation:

(a) The angles in a triangle add up to 180 degrees, so:

x + x + 2 + 6x + 10  = 180

8x + 12 = 180

8x = 168

x = 168/8 = 21 degrees.

(b)  Angle B = x + 2

= 21 + 2 = 23 degrees.

Answer:

Step-by-step explanation:

Volume=(pi)(radius^2)(height)

Volume=(pi)(5^2)(12)

V=(pi)(25)(12)

V=(pi)(300)

Answer: 300 pi

Step-by-step explanation:

on edge

By setting up an equation and solving for the number of students in the eighth grade class, we find that there must be 174 students to meet the requirement of 75 people including 17 parent chaperones.

To find the number of students in the eighth grade class for the trip to Washington DC, let's use the information provided that 1/3 of the class plus 17 parent chaperones are just enough to satisfy the requirement of 75 people for the trip. We can set up an equation to solve for the total number of students (S) in the class:

1/3 * S + 17 = 75

First, subtract 17 from both sides of the equation:

1/3 * S = 75 - 17

1/3 * S = 58

Then, multiply both sides by 3 to find the total number of students (S):

S = 58 * 3

S = 174

Thus, there must be 174 students in the eighth grade class.

Answer:

Unimodal Skewed

Step-by-step explanation:

The best describes the shape of this distribution is E. Bimodal skewed

If a histogram has one hump, it is unimodal; if it has two humps, it is bimodal; and if it has many humps, it is multimodal.

If a histogram is not symmetric, this will refer to as skewed.

It is positively skewed if the upper tail is longer than the lower tail.

It can have multiple peaks or be bimodal (two peaks) (or many peaks).

But a single distribution with two peaks characterizes a bimodal distribution.

This will appear as two separate bell curve shapes contained within two normal distributions on a graph that is displayed side by side.

We are given graph has 2 humps, we can conclude that the given distribution is Bimodal skewed.

Therefore, the given distribution is (E) Bimodal skewed as the distribution has 2 humps.

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Answer:

C. 5.2 cm

Step-by-step explanation:

Arc length formula:

[tex] s = \dfrac{n}{360^\circ} 2 \pi r [/tex]

where s = arc length

n = central angle of arc

r = radius of circle

diamter = d = 10 cm

r = d/2 = 10 cm/2 = 5 cm

n = 60 deg

[tex] s = \dfrac{n}{360^\circ} 2 \pi r [/tex]

[tex] s = \dfrac{60^\circ}{360^\circ} 2 \times 3.14159 \times 5 ~cm [/tex]

[tex] s = 5.2~cm [/tex]

Answer: 5.2 cm

Answer:

6

Step-by-step explanation:

The mode of a set of data values is the value that appears most often. ^ appers 4 times.

Answer:

B. 17.6

Step-by-step explanation:

asdasdasdasdasd

Answer:

6.169

-1.009= 5.1 48

Step-by-step explanation:

I did it backwards

Answer:

Top = 6.157 bottom =5.148

Step-by-step explanation: