which expression is equivalent to 2(5)^4

==============================================

Work Shown:

T = tens digit

U = units digit (aka ones digit)

A number like 27 is really 20+7 = 2*10 + 7*1 = 10*2 + 1*7. We have 2 in the tens digit and 7 in the units digit. So 27 can be written in the form 10T + U where T = 2 and U = 7. Reversing the digits gives 72, so T = 7 and U = 2 now. Clearly the difference between the digits 7 and 2 is not 1, so 27 or 72 is not the answer (as it's just an example).

-----------------------

Let T be larger than U. This doesn't work if T = U.

Because T is larger, saying "The difference between the digits is 1" means T - U = 1. We can isolate T to get T = U+1. We'll use this later.

-----------------------

If T > U, then the original number 10T+U reverses to the new number 10U+T and it becomes smaller. We are told that it becomes 5/6 of what it used to be.

So,

new number = (5/6)*(old number)

10U + T = (5/6)(10T + U)

6(10U + T) = 5(10T + U)

60U + 6T = 50T + 5U

60U + 6(U+1) = 50(U+1) + 5U ... plug in T = U+1

60U + 6U + 6 = 50U + 50 + 5U

66U + 6 = 55U + 50

66U - 55U = 50-6

11U = 44

U = 44/11

U = 4 is the units digit of the original number

T = U+1

T = 4+1

T = 5 is the tens digit of the original number

The original number is therefore 10T + U = 10*5+4 = 54.

We see the difference in their digits is T-U = 5-4 = 1

The reverse of 54 is 45. The number 45 is 5/6 of 54

45 = (5/6)*54

Answer:

A. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

Step-by-step explanation:

The only thing that has changed is that x^2 is multiplied by 5.

If the x^2 is multiplied by a constant that has an absolute value less than 1, the parabola will undergo a vertical compression.

If the x^2 is multiplied by a constant that has an absolute value more than 1, the parabola will undergo a vertical stretch.

Since the absolute value of 5 is more than 1, A. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

Hope this helps!

Answer:

26

Step-by-step explanation:

Because You have to just do the perimeter by counting the sides

Answer: x=5

Step-by-step explanation:

[tex]\frac{2}{14} =\frac{x}{35}[/tex]

[tex]\frac{x}{35}=\frac{2}{14}[/tex]

simplify

[tex]\frac{x}{35}=\frac{1}{7}[/tex]

multiply 35 on both sides

[tex]\frac{35x}{35}=\frac{1\cdot \:35}{7}[/tex]

[tex]\frac{1}{7} \cdot 35=5[/tex]

x=5

Answer:

  (-3/70)a

Step-by-step explanation:

Solving for ?, we have ...

  70? +3a = 0 . . . . . subtract (7a +3)

  ? +(3/70)a = 0 . . . . divide by 70

  ? = -(3/70)a . . . . . . subtract 3/70a

The missing factor is (-3/70)a.

Answer:

17) x = 11, -8

18) exact form: x = + 2 sqaure root 6/ 3 + 2

I hope this helps :)

Answer:

8677

Notice that all the numbers in the sequence are divisible by 3 except 8677.

The sum of the digits must be divisible by 3.

8+6+7+7= 2+8 =10

10 isn't divisible by 3.

Answer:

The highest possible value of b would be 750.

Step-by-step explanation:

If you graph the two equations, you'll get two crossing lines, and because y is supposed to be either equal to or less, the answer is going to be at the shaded area at the bottom.

Equate the two equations to solve them with algebra.

-15x+3000=5x

add 15x to both sides

3000=20x

divide by twenty, you get

150=x

Plug that in to both equations, you'll get y=750, which is the highest possible value of b, (aka y cuz it's on the y axis).

=======================================================

Explanation:

The distribution is perfectly symmetrical about the center 6. Notice how the left side is a mirror copy of the right side, due to the heights being the same. Because of this, the mean, median and mode are all the same value and that is 6. The mode is equal to 6 as this is the most frequent value.

The longer way to do this problem is to add up each value shown. We have four copies of '2', six copies of '3', and so on. The total sum you would get is 372. Divide this over 62 because there are 62 smaller green squares. The final result is the mean of 6.

The number closest to the mean of the given distribution is 6. Therefore, option A is the correct answer.

In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).

From the given histogram,

Number         Frequency

    2                      4

    3                      6

    4                      7

    5                      9

    6                     10

    7                      9

    8                      7

    9                      6

   10                      4

Here, the mean = [2(4)+3(6)+4(7)+5(9)+6(10)+7(9)+8(7)+9(6)+10(4)]/[4+6+7+9+10+9+7+6+4]

= [8+18+28+45+60+63+56+54+40]/62

= 372/62

= 6

Therefore, option A is the correct answer.

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Answer:

Step-by-step explanation:

<A and <B are corresponding angles

< A = < B

plugging the values

[tex]7x + 24 = 3x + 92[/tex]

Move variable to L.H.S and change its sign

[tex]7x - 3x + 24 = 92[/tex]

Move constant to R.H.S and change its sign

[tex]7x - 3x = 92 - 24[/tex]

Calculate

[tex]4x = 68[/tex]

Divide both sides of the equation by 4

[tex] \frac{4x}{4} = \frac{68}{4} [/tex]

Calculate

[tex]x = 17[/tex]

Replacing value

<A = [tex]7x + 24[/tex]

[tex] = 7 \times 17 + 24[/tex]

[tex] = 119 + 24[/tex]

[tex] = 143[/tex]

hope this helps...

Answer:

a) T(0) = 18035, D = 35, so formula is T(n) = 18035 + 35n

b) T(0) = 3800, D = 300, so formula is T(n) = 3800 + 300n

c) T(0) = 17200, D = 1100, so formula is T(n) = 17200 + 1100n

Step-by-step explanation:

They are all arithmetic progressions (AP) with a common difference, i.e. all differences of one term from the subsequent term are identical.

The general formula is

T(n) = T(0)+n*D

where

n = the term number

T(n) = nth term (considering the first term to be the zeroth term.

D = common difference

a) T(0) = 18035, D = 35, so formula is T(n) = 18035 + 35n

b) T(0) = 3800, D = 300, so formula is T(n) = 3800 + 300n

c) T(0) = 17200, D = 1100, so formula is T(n) = 17200 + 1100n

Answer:

[tex]{m}^{2} +7m + 28 = 0[/tex]

Step-by-step explanation:

Given that,

[tex]m = {x}^{2} + 3[/tex]

We know that,

[tex] {x}^{2} = m- 3[/tex]

Now look at the sum

[tex]( {x}^{2} + 3) ^{2} + 7 {x}^{2} + 21 = - 10 \\ [/tex]

[tex]( {x}^{2} + 3) ^{2} + 7 {x}^{2} + 21 = - 10 \\ {m}^{2} + 7 \times m- 3 + 21 = - 10 \\ {m}^{2} +7m + 18= - 10 \\ {m}^{2} + 7m + 18+ 10 = 0 \\ {m}^{2} + 7m + 28 = 0[/tex]

Answer:

Step-by-step explanation:

First we must find the missing number, for that we apply a simple rule of three:

3. 4

27 ------ x

x = 27 (4) / 3 = 36

Now we just do the sum:

27 + 36 = 63

Answer:

Sum = 63

[tex]\boxed{ x = 36}[/tex]

Step-by-step explanation:

3 : 4

It says that the 1st part (3) is 27

27 : x (We've to find the major)

Creating a proportion:

=> 3 : 4 = 27 : x

Product of Means = Product of Extremes

=> 3 * x = 27 * 4

=> 3x = 108

Dividing both sides by 3

=> x = 36

The sum of both is 27+36 = 63

Answer:

Compare algebraic relationships in a situation.

The half-life [tex]t_{1/2}[/tex] is the amount of time it takes for some quantity [tex]N_0[/tex] of carbon-14 to decay to half the original amount, or [tex]N=\frac{N_0}2[/tex].

In terms of the formula, it's the time such that

[tex]\dfrac{N_0}2=N_0e^{-kt_{1/2}}[/tex]

and we can divide both sides by the original amount to get

[tex]\dfrac12=e^{-kt_{1/2}}[/tex]

We want to find the time [tex]t[/tex] it takes for 57%, or 0.57, of the original amount to remain. This means we solve for [tex]t[/tex] in

[tex]0.57N_0=N_0e^{-kt}[/tex]

or

[tex]0.57=e^{-kt}[/tex]

We're given [tex]k=0.0001[/tex]; plug this in and solve for [tex]t[/tex]:

[tex]0.57=e^{-kt}\implies\ln0.57=-kt\implies t=-\dfrac{\ln0.57}k\approx\boxed{5621\,\mathrm{years}}[/tex]

You would assume that in this figure, the number of colored sections with which are not colored with respect to a " touching " colored section, would be half of the total colored sections. However that is not the case, the sections are not alternating as they still meet at a common point. After all, it notes no two touching sections, not adjacent sections. Their is no equation to calculate this requirement with respect to the total number of sections.

Let's say that we take one triangle as the starting. This triangle will be the start of a chain of other triangles that have no two touching sections, specifically 7 triangles. If a square were to be this starting shape, there are 5 shapes that have no touching sections, 3 being a square, the other two triangles. This is presumably a lower value as a square occupies two times as much space, but it also depends on the positioning. Therefore, the least number of colored sections you can color in the sections meeting the given requirement, is 5 sections for this first figure.

Respectively the solution for this second figure is 5 sections as well.

Answer:

False, we need to take the positive and negative square root of 49

Step-by-step explanation:

(x+2)^2 = 49

Take the square root of each side

sqrt((x+2)^2) = ±sqrt(49)

x+2 = ±7

Answer:

x = -5

y = -5

Step-by-step explanation:

-8y+9x = -5; 8y+7x = -75

Add the two equations together to eliminate y

-8y+9x = -5

8y+7x = -75

----------------------

0y + 16x = -80

Divide each side by 16

16x/16 = -80/16

x = -5

Now find y

8y+7x = -75

8y+7(-5) = -75

8y-35 = -75

Add 35 to each side

8y = -40

Divide by 8

8y/8 = -40/8

y = -5

Answer:

[tex]\boxed{x=-5}\\ \boxed{y=-5}[/tex]

Step-by-step explanation:

-8y + 9x = -5

8y + 7x = -75

Add the equations (eliminating the y-variable).

16x = -80

Divide both sides by 16.

[tex]\frac{16x}{16}[/tex] = [tex]\frac{-80}{16}[/tex]

x = -5

Plug x as -5 in the first equation to find y.

-8y + 9(-5) = -5

-8y +-45 = -5

Add 40 to both sides.

-8y = 40

Divide both sides by -8.

[tex]\frac{-8y}{-8}[/tex] = [tex]\frac{40}{-8}[/tex]

y = -5

Answer: C) 144

Step-by-step explanation:

The area of a pyramid can be found via lwh/3

(9*8*6)/3 = area

72*6/3 = area

432/3 = area

144 = area

Hope it helps <3

This is not the question, the correct question is:

A humanities professor assigns letter grades on a test according to the following scheme. A: Top 6% of scores B: Scores below the top 6% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 7% F: Bottom 7% of scores.

Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.

Answer:  The numerical limits for grade B is 81 and 92

Step-by-step explanation:

Given that

mean Ж = 79

Standard deviation S = 8.4

B: Scores below the top 6% and above the bottom 59%

To find the numerical value for Grade B

Below the top bottom 6% ( 0.06) is

p ( X < Ж ) = 1 - 0.06

p ( X < Ж ) = 0.94

therefore

P( (X - ц)/S < (X - Ж) / S)) = 0.94

(X - 79) / 8.4 = 1.5548 ( from normal distribution table )

X - 79 = 13.0603

X = 13.0603 + 79

X = 92.06 ≈ 92 ( nearest whole number)

Above bottom 59% ( 0.59) is

p ( X < Ж ) = 0.59

therefore

P( (X - ц)/S < (X - Ж) / S)) = 0.59

(X - 79) / 8.4 = 0.2275 ( from normal distribution table )

X - 79 = 1.9114

X = 1.9114 + 79

X = 80.91 ≈ 81 ( nearest whole number)

So the numerical limits for grade B is 81 and 92

Answer:

Hey there!

In total, there are 360 degrees. If there are 40 staff members, then each member has 360/40=9 degrees.

Hope this helps :)

Answer:

9 degrees

Step-by-step explanation:

There are 360 degrees in a circle

There are 40 people

360 / 40 = 9

Each person gets 9 degrees

Answer:

14

Step-by-step explanation:

I attached a picture and I hope this helps ;) ❤❤❤

Answer:

The third number is 14

Step-by-step explanation:

To find the average of 3 numbers add the three numbers and divide by 3

Let x be the third number

( 45+16+x) /3 = 25

Multiply each side by 3

( 45+16+x) /3 *3 = 25*3

( 45+16+x) = 75

Combine like terms

61+x = 75

Subtract 61 from each side

61+x-61 = 75-61

x = 14

Answer:

  2

Step-by-step explanation:

Polygons on either side of a common edge need to be colored differently, so 2 colors are needed, as a minimum. Polygons of the same shape do not share an edge, so all can be colored the same color.

Answer: square 105

Step-by-step explanation: Confirming answer

A radical expression is an expression containing a square root, mostly a square root.

The value of √3.√5.√7 in radical form is √105.

A radical expression is an expression containing a square root, mostly a square root.

We have,

√3.√5.√7

We can multiply the numbers together.

= √(3 x 5 x 7 )

= √(15 x 7)

= √105

Thus the value of √3.√5.√7 in radical form is  √105.

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Answer:

Step-by-step explanation:

Selling price =  $210

percentage increase = 5 %

Increased amount = 5% of 210

                              = 0.05 * 210

                               = $ 10.5

New selling price = 210 + 10.5  = $ 220.50

Answer:

Step-by-step explanation:

The authors use of figurative language gives the reader a better visualization of how the creature looked.

Answer:

The answer is A,B,D

Step-by-step explanation:

I took the test

Answer:

d

Step-by-step explanation:

a1 is 14

Given that a1 is 14, you can see that each next number in the sequence is larger than the previous one by 4, so an= an-1+4

Answer:

6

Step-by-step explanation:

The Fundamental theorem of Algebra states that a polynomial of degree n has n roots. These can be real, complex or both.

f(x) = 2[tex]x^{6}[/tex] - 3x³ + 1 - 2[tex]x^{5}[/tex] ← is a polynomial of degree 6

Thus the maximum number of real roots is 6

Answer:

b.79

Step-by-step explanation:

if you look at the graph it shows its right below 80

The 79 customers are predicted to use a card to pay on a day when 90 customers pay by cash option (B) is correct.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have a line of best fits:

y = 0.755x + 11.339

Plug x = 90

y =0.755(90) + 11.339

y = 67.95 + 11.339

y = 79.28 ≈ 79

Thus, the 79 customers are predicted to use a card to pay on a day when 90 customers pay by cash option (B) is correct.

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