Mathematics College

Which of the following shows the correct evaluation for the exponential expression 6 over 7 to the power of 2?

6 over 7 plus 2 equals 2 and 6 over 7
6 over 7 times 2 equals 12 over 7 which equals 1 and 5 over 7
6 over 7 times 6 over 7 equals 36 over 49
6 over 7 divided by 2 equals 6 over 14

Answers

Answer 1
For this case we have the following expression:
 6 over 7 to the power of 2
 (6/7) ^ 2
 By power properties we can rewrite the expression as:
 (6/7) * (6/7)
 Calculating we have:
 (6/7) * (6/7) = 36/49
 Answer:
 6 over 7 times 6 over 7 equals 36 over 49

Related Questions

ΔABC and ΔXYZ are similar triangles. If BC = x + 7, AC = x + 6, YZ = 4 − x, and XZ = 3 − x, find the value of x.

Answers

Since these triangles are similar, we have proportional sides. We can write that [tex] \frac{x+7}{4-x} = \frac{x+6}{3-x} [/tex]. Solving it, we find that x=-1.5

Answer:

-3/2 or -1.5

Step-by-step explanation:

-3/2 = -1.5

BC = -1.5 + 7 = 5.5

AC = -1.5 + 6 = 4.5

YZ = 4 - (-1.5) = 5.5

XZ = 3 - (-1.5) = 4.5

Which of the points listed is the same distance from the y-axis as the point (−1.5, 6)?

Answers

the complete question in the attached figure

we know that
the distance from a point to line (y-axis) is the perpendicular line against y-axis, which is the absolute value of x-coordinates

in this problem
the point (−1.5, 6)
the absolute value of x-coordinates is 1.5
hence 
the distance is 1.5

therefore

the answer is
the option B) the point (1.5,-3)

it took a ball 1 minute to roll 90 feet. what was ths balls average rate of speed in feet per second

Answers

1.5 ft per second. 

Divide the 90 by 60. 

Ben runs around the track at a pace of 1 lap every 80 seconds. Sally runs on the track in the opposite direction. The two meet every 30 seconds. How long does it take Sally to run each lap around the track?

Answers

48 seconds, Consider what happens between one time that Ben and Sally meet and the next. During this period Ben runs 30 (seconds)/80 (seconds/lap) = 3/8 of a lap. So Sally runs 5/8 lap in the same time. Her speed is therefore 5/8 (laps)/ 30(seconds) which amounts to 1 (lap)/ 48 (seconds).

please help me answer these!!!

Answers

You don't have to look very far in either case. Both answers are "a".

1. Checking selection "a",
  265 =? 35 +20*7 = 35 +140 = 175
  a (7, 265) is NOT a solution

2. Checking selection "a",
  18 =? 5*4 -2 = 20 -2 = 18
  a (4, 18) IS a solution

What is the area of the figure?

Answers

see attached picture:

Paisley needs 32 in of ribbon for a hair bow. The ribbon is sold by centimeters. Givin that 1 in = 2.54 centimeters, how many centimeters of ribbon does she need.

Work Pls
Thx

Answers

32 inches ⇒ ? centimeters

Multiply 32 inches by 2.54 centimeters to find how many centimeters of ribbon Paisley needs.
(32)(2.54) = 81.28

Paisley needs 81.28 centimeters of ribbon for the hair bow.

John likes 400 but not 300; he likes 100 but not 99; he likes 3600 but not 3700. Which does he like?
o 900
o 1000
o 1100
o 1200

Answers

the answer is d 1200 because you can divide it by 4

A cyclist rides a bicycle with a wheel radius of 0.500 m across campus. a piece of plastic on the front rim makes a clicking sound every time it passes through the fork. if the cyclist counts 320 clicks between her apartment and the cafeteria, how far has she traveled? (a) 0.50 km (b) 1.5 km (c) 1.0 km (d) 0.80 km (e) 1.8 km

Answers

we know that
circumference=2*pi*r
for r=0.50 m
circumference=2*pi*0.50-----> pi m

1 click correspond to a length of--------> pi meter
 320 click---------------> x
x=320*pi-----> x=1005.31 meters-------> 1 km

the answer is
the option (c) 1.0 km

A package of three compact discs cost $24.96. How much does each disc cost?

Answers

Price divided by number of discs
24.96/3 =8.32
Each disc costs $8.32. This is because $24.96 (total cost) divided by 3(amount of discs) is $8.32.

Question 11 Unsaved
Find the domain, period, range, and amplitude of the cosine function.

y = -6cos4x


Answers

For this case we have the following function:
 y = -6cos4x
 The function is defined for all values of x, therefore, the domain is:
 (-inf, inf)
 The range of the function is:
 For x = 0
 y = -6cos (4 (0))
 y = -6cos (0)
 y = -6 (1)
 y = -6
 For x = pi / 4
 y = -6cos (4 (pi / 4))
 y = -6cos (pi)
 y = -6 (-1)
 y = 6
 The range of the function is:
 [-6, 6]
 The amplitude of the function is:
 6
 Answer:
 Domain: (-inf, inf)
 Range: [-6, 6]
 Amplitude: 6

The probabilities for four different simple events are given. Of the four, which is MOST LIKELY to occur?


A. 0.5


B. 0.9


C. 0.35


D. 0.0100

Answers

im not 100% sure but i would say c
the one that is most probable is the one that  is most likely to happen, ie the one that is closes to having a 100% chance of happening

100%=1 so the number closes to 1 is the most likely
we can't have a probility of more than 1 so we can say that the greatest number is most likely


if we rank the numbers we get
0.9>0.5>0.35>0.00100

so the answer is B. 0.9 which is equivilent to an 90% chance of the event occuring

Suppose that the demand equation for a certain item is 1p+1x2−160=0. evaluate the elasticity at 65:

Answers

Price elasticity is defined as [tex]\frac{\Delta(quantity)}{\Delta(price)}[/tex].

Here, the question has omitted to define variables, so we will ASSUME
p=price
x=variable,
and we're given
p+x^2-160=0

We calculate
[tex]\delta{x}/\delta{p}[/tex] by implicit differentiation with respect to p:
1+2x (dx/dp)=0
=>
E(x)=(dx/dp)=-1/(2x)

Therefore the price elasticity at x=65 is
E(65)=1/(2*65) =-1/130 (approximately -0.00769)

The required value of elasticity at x = 65 is -0.007.

Given that,

The demand equation for a certain item is [tex]1p + 1x^{2} -160 = 0[/tex].

We have to determine,

The value of elasticity at 65.

According to the question,

The price elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price.

Therefore,

Price of elasticity = [tex]\frac{dp}{dx}[/tex]

Calculate change by differentiation with respect to p:

[tex]\dfrac{d(p+x^{2} -160)}{dx}\\\\1 + 2x\frac{dp}{dx} = 0\\[/tex]

Then,

[tex]E(x) = \frac{dp}{dx} = \frac{-1}{2x}[/tex]

Therefore, The elasticity at x = 65 is ,

[tex]E(65) = \frac{-1}{2(65)} = -0.007[/tex]

Hence, The required value of elasticity at x = 65 is -0.007.

For more information about Elasticity click the link given below.

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given that ABCD= PQRS, find AD

A.3
B.5
C.6
D.10

Answers

Given that the two polygons are congruent then,
AD=SP
plugging in the values we obtain:
3m-9=2m-4
solving for m we get:
3m-2m=-4+9
m=5
thus the value of AD will be:
AD=3m-9=3(5)-9=15-9=6

The answer is AD=6

Calculate the taxes based on the following taxable income amounts
I really need help on this fast please!
I need the estimated taxes for each problem at the bottom is the table needed.

1) income of 90,714.00
2) income of 63,036.00
3) income of 220,596.00
4) income of 166,904.00
5) income of 220,770.00
6) income of 97,266.00
7) income of 207,264.00
8) income of 479,956.00
9) income of 511,195.00
10) income of 511,104.00
11) income of 212,817.00
12) income of 435,045.00
13) income of 655,952.00
14) income of 739,334.00
15) income of 322,335.00


Income range Taxes
From To Tax rate. Plus
0.00 8,925.00 10.0%.
8925.00 36,250.00 15.0% 892.50
36,250.00 87,850.00 25.0% 5,437.50
87,850.00 183,250.00 28.0% 21,962.50
183,250.00 398,350.00 33.0% 51,310.00
398,350.00 400,000.00 35.0%. 131,455.50
400,000.000 - 39.6%. 140.000.00

Answers

1.) Taxable income is 22,764.42 (income 90,714 less range which is more than 87,850 but less than 183,250 = 2,864 multiply to its corresponding tax rate of 28% = 801.92 plus its corresponding amount of 21,962.50 = 22,764.42)

2.) Taxable income is 12,140.75

3.) Taxable income is 63,634.18

4.) Taxable income is 44,097.62

5.) Taxable income is 63,691.60

6.) Taxable income is 24,598.98

7.) Taxable income is 59,234.62

8.) Taxable income is 171,662.58

9.) Taxable income is 184,033.22

10.) Taxable income is 183,997.18

11.) Taxable income is 61,067.11

12.) Taxable income is 153,877.82

13.) Taxable income is 241,356.99

14.) Taxable income is 274,376.26

15.) Taxable income is 97,208.05

Note: Use the "from" amount as the basis, so if the income is 10,000 then you'll deduct 8,925 (basis) from 10,000 (since 10,000 is more than 8,925 but less than 36,250)

A test has forty questions worth 100 points.The test consists of True/False questions worth 3 points each and multiple choice questions worth 2 points each. How many multiple choice questions are on the test?

Answers

20 multiple choice questions

Answer:

20 multiple choice questions

Step-by-step explanation:

I hope this help you out

the circumference of an Oreo is 6.28 inches what is the area of the top cookie?

Answers

The area is equal to 1

The circumference of an Oreo is 6.28 inches what is the area of the top cookie?

Solution:

Circumference= 6.28 inches

The formula of circle =2πr

So, 2πr=6.28

2*3.14*r=6.28

6.28r=6.28

To find the value of r, Let us divide by 6.28 on both sides

6.28 r /6.28 =6.28/6.28

r=1

Area of circle=πr²

=π1²

=π

=3.14 inches²

Area of the top cookie=3.14 inches²

One aluminum can weights 1/25 pound. If your school starts a recycling drive how many cans will your school need to collect to recycle one ton?

Answers

Hello!

First you have to find how many cans make a pound

1/25 * 25 = 1

It takes 25 cans to get to 1 pound

There are 2000 pounds in a ton

Multiply the amount of cans to make a pound by the amount of pounds in a ton

25 * 2000 = 50000

The answer is 50,000 aluminum cans

Hope this helps!

5-2i and 7+6i find the midpoint

Answers

That would be (5, -2) and (7, 6) on complex plane. You can use midpoint formula 

So that would be ((5+7) / 2, (-2+6) / 2) = (6, 2)

So then answer would be 6+2i
Final answer:

The midpoint between the complex numbers 5-2i and 7+6i is 6 + 2i.

Explanation:

To find the midpoint between two complex numbers, we can use the formula:

Midpoint = (Re(z1) + Re(z2))/2 + (Im(z1) + Im(z2))/2i

Applying the formula to the given complex numbers 5-2i and 7+6i, we have:

Midpoint = (5 + 7)/2 + (-2 + 6)/2i
Midpoint = 12/2 + 4/2i
Midpoint = 6 + 2i

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What is the value of y?



11.6 ft
12.5 ft
16.5 ft
17.5 ft

Answers

we know that

in the triangle BCD
 cos C=8/14
C=arc cos (8/14)-----> C=55.15°

sin C=BD/14---------> BD=14*sin 55.15------> BD=11.49 ft

in the triangle ABC
180=∡A+∡B+∡C
∡A=180-(90+55.15)-----> ∡A=34.85°

tan A=BD/y-------> y=BD/tan A-----> y=11.49/tan 34.85----> y=16.50 ft

the answer is
y=16.50 ft
To solve the exercise shown in the picture attached, you must apply the following proccedure:

 1. First, you must apply the Pythagorean Theorem to calculate the heigth of the triangle, as below:

 a^2=b^2+c^2
 b=√(a^2-c^2)
 b=√(14)^2-(8)^2
 b=√132
 b=11.48

 2. Now, you must calculate the angle ∠BC, as below:

 Sin(α)^-1=opposite/hypotenuse
 Sin(BC)^-1=8/14
 ∠BC=34.84°

 3. Therefore, the angle ∠BA is:
 ∠BA=90°-34.84°
 ∠BA=55.15°

 4. Then, you have:

 Tan(55.15°)=y/11.48
 y=16.48

If a bank has total deposits of $7,700 and reserves of $2,100: instructions: round to the nearest whole number. (a) what is its current reserve ratio? % (b) how large is its loan portfolio (outstanding loans)? %

Answers

a.What is the total amount of deposits?_Deposits= ($2,000 – $500)/.20 =$7,500

b.What is the total amount of loans? _Loans = $7,500 - $2,000 = $5,500_

Q10 Q2.) Find the standard form of the equation of the parabola satisfying the given conditions.

Answers

To  solve this problem you must apply the proccedure shown below:

 1. You have that the standard form of the equation of the parabola must satisfy the following conditions given in the exercise above:

 Focus: (-1,4) and Directrix: y=2

 2. Therefore you have:

 √(x0-(-1))²+(y0-4)²=|y0-2|
 (x0+1)²+(y0-4)²=(y0-2)²

 3. When you simplify the expression above and clear y0, you obtain:

 y0=y

 y=1/4(x²+2x+13)
 y=(x²/4)+(x/2)+(13/4)

 Therefore, the answer is: y=(x²/4)+(x/2)+(13/4)

a band that will be the opening act for a concert charges a $700.00 flat fee as well as 16% of all ticket profits from ticket sales. if the band earned $1,200, how much was made in total ticket sales for the show?

Answers

The band earned $1,200.

1. Subtract the flat fee 1,200-700 =500
2. 500 is what just the band made. Divide that by .16 (16%) to get the total ticket amount... 500 divided by .16 = 3,125

The total ticket amount was $3,125.

A video posted on the internet is becoming very popular,and the total number of views is increasing by 40% every hour if the video currently has 38,000 views how many views will it have in 2 hours

Answers

Final answer:

The video with an initial 38,000 views will have approximately 74,480 views in 2 hours when it is increasing by 40% every hour.

Explanation:

To calculate the number of views a video will have in 2 hours if it is increasing by 40% every hour, we will use the formula for percentage growth. Initially, the video has 38,000 views. After one hour, the views will be increased by 40%, and after two hours, this new amount will again be increased by 40%. The formula for calculating the number of views after each hour is:

Views after n hours = Initial views × [tex](1 + growth rate)^n[/tex]

Where:

Initial views = 38,000

Growth rate = 40% = 0.40 (as a decimal)

n = number of hours

After 1 hour:

Views after 1 hour = 38,000 × (1 + 0.40)^1

Views after 1 hour = 38,000 × 1.40 = 53,200

After the second hour, we will use the number of views from the first hour to calculate the increase:

Views after 2 hours = 53,200 × [tex](1 + 0.40)^1[/tex]

Views after 2 hours = 53,200 × 1.40 = 74,480

Therefore, the video will have approximately 74,480 views in 2 hours.

what is the equation for horizontal line through the point (0,3)?

Answers

Your equation will be y = 3.

The y-intercept is three and there is no slope.

Hope this helps!

the cost of internet access at a cafe is a function of time the cost for 8, 25, and 40 minutes are shown write the equation in slope-intercept form that represents the function then find the cost of surfing the web at the cafe for one hour

Answers

Answer:

?

Step-by-step explanation:

Where is the graph?

hey can you please help me posted picture of question

Answers

Answer:
f⁻¹(x) = [tex] \frac{x+6}{7} [/tex]

Explanation:
To get the inverse of a function, we will follow these steps:
1- replace f(x) with y
2- swap the x and y variables
3- solve for y
replace y with f⁻¹(x)

Applying this to the given as follows:
f(x) = 7x - 6

Step 1: replace f(x) with y:
y = 7x - 6

Step 2: swap the x and y variables:
x = 7y - 6

Step 3: solve for y:
7y = x + 6
y = [tex] \frac{x+6}{7} [/tex]

Step 4: replace y with f⁻¹(x):
f⁻¹(x) = [tex] \frac{x+6}{7} [/tex]

Hope this helps :)

What is the letter ƒ in mathematics?

Answers

The letter f usually indicates that the equation is a function in the notation f(x). 

Example: f(x) = x + 1

It is a fancier/more proper replacement for the variable 'y'. The same is used for the letter g as in g(x) and h as in h(x). 

OR

It could just be a regular ole variable

Example: f + 1 = 7, solve for f




The letter f usually indicates that the equation is a function in the notation f(x). 


Example: f(x) = x + 1


It is a fancier/more proper replacement for the variable 'y'. The same is used for the letter g as in g(x) and h as in h(x). 


OR


It could just be a regular ole variable


Example: f + 1 = 7, solve for f


The current size of an image on Samuel's computer is shown below: A rectangle is shown. The length of the rectangle is labeled as length equal to 8 inches and the width is labeled as width equal to 10 inches. What are the dimensions of the image at fraction 1 over 2 times its current size

Answers

Length is equal to 4 and width is equal to 5. 

You can just divide each by 2. 

Answer:

The length and the width of image is  4 inches and 5 inches respectively

Step-by-step explanation:

Given : Length of rectangle is 8 inches

          Width of rectangle is 10 inches

To Find: What are the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size

Solution:

Length of rectangle is 8 inches

Since we are given that the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size

So, Length of image = [tex]\frac{1}{2} \times 8 = 4[/tex]

Thus the length of image is 4 inches.

Width of rectangle is 10 inches

Since we are given that the dimensions of the image at fraction [tex]\frac{1}{2}[/tex] times its current size

So, width of image = [tex]\frac{1}{2} \times 10 = 5[/tex]

Thus the width of image is 5 inches.

Hence the length and the width of image is  4 inches and 5 inches respectively.

Which of the following is the prime factored form of the lowest common denominator of?
A.2 x 2 x 2 x 3
B.2 x 4 x 2 x 3
C.8 x 6
D.2 x 12

Answers

A is the prime factored form of the lowest common denominator

2 x 2 x 2 x 3 factored form is the prime factored form.

What is a prime number?

"A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers."

The given factored forms are:

A. 2 x 2 x 2 x 3

Here, all the numbers are prime numbers.

Therefore, this factored form is the prime factored form.

B. 2 x 4 x 2 x 3

Here, all the numbers are not prime numbers.

Therefore, this factored form is not the prime factored form.

C. 8 x 6

Here, not a single number is prime number.

Therefore, this factored form is not the prime factored form.

D. 2 x 12

Here, all the numbers are not prime numbers.

Therefore, this factored form is not the prime factored form.

Learn more about prime number here: https://brainly.com/question/10454590

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