Mathematics High School

In which expression should the exponents be multiplied?
a. (5^3)-4
b. (1/3)^4*(1/3)^7
c. 3^7/3^15
d. 4^5*4^2

Answers

Answer 1
If we have the same base, we can do this:
(1/3)^4*(1/3)*7 = (1/3)^(4+7) = (1/3)^11
3^7/3^15 = (3^7)*(3*(-15)) = 3^(7 + (-15)) = 3^(-8) = 1/(3^8)
4^5*4^2 = 4^(5+2) = 4^7
Answer 2

Option b is the correct answer. Exponents should be multiplied in the expression (1/3)^4*(1/3)^7, resulting in (1/3)^11.

The expression where the exponents should be multiplied is Option b. (1/3)^4*(1/3)^7. This is because when you multiply two expressions that have the same base, you add their exponents. In this case, you have the base (1/3) raised to the 4th power and then to the 7th power, so you add the exponents 4 + 7, which equals 11. Therefore, (1/3)^4*(1/3)^7 simplifies to (1/3)^11.

Another case where you multiply exponents would be when raising a power to another power, like in (5^3)^4. Here the exponents 3 and 4 are multiplied, resulting in (5^12).

Related Questions


A bag contains 30 red tiles, 15 green tiles, and 5 yellow tiles. One tile is drawn and then replaced. Then a second tile is drawn. What is the probability that the first tile is yellow and the second tile is green?
A.
1%
B.
3%
C.
6%
D.
18%

Answers

Allright we know that the total number of tiles is 50 so we can assume that if you pick the first tile and its yellow ther is a (5/50) chance to pick it up and then REPLACED meaning that it is put back so you have still 50 tiles to choose from, if then you choose a green tile you have a (15/50) chance of picking it up

(5/50)*(15/50)=0.03 YOU HAVE A 3 PERCENT CHANCE!!!:D
^This is to calculate the probability of picking it in that order)^

1. Evaluate 6.314 - 9.77.

3.456
-3.464
-3.456
-16.084

2. Evaluate -5.118 - (-4.1).

-9.218
-1.018
1.018
9.218

3. Find the value of x + y for x = 75.9 and y = 2.65.

10.24
102.4
78.55
79.55

4. Find the value of -x + y for x = 75.9 and y = 2.65.

-78.55
78.55
73.25
-73.25

Answers

Evaluate 6.314 - 9.77.

3.456
-3.464
-3.456 ☆
-16.084

2. Evaluate -5.118 - (-4.1).

-9.218
-1.018 ☆
1.018
9.218

3. Find the value of x + y for x = 75.9 and y = 2.65.

10.24
102.4
78.55 ☆
79.55

4. Find the value of -x + y for x = 75.9 and y = 2.65.

-78.55
78.55
73.25
-73.25☆

Answer:

1. -3.456

2. -1.018

3. 78.55

4. -73.25

Step-by-step explanation:

In Algebra, the following notations have to be considered.

Algebra is a branch of mathematics that deals with the computation of numbers irrespective of the signs involved.

- × - = +

+ × - = -

- × + = -

+ × + = +

Therefore,

1. 6.314 - 9.77 = -3.456

2.  -5.118 - (-4.1) =  -5.118 + 4.1 = -1.018

3. x + y for x = 75.9 and y = 2.65.

This requires substitution

75.9 + 2.65 = 78.55

4. -x + y for x = 75.9 and y = 2.65

= -75.9 + 2.65

= -73.25

If BC=5.3, CD=8.8, and AD= 14.3, find AB to the nearest tenth.

Answers

The picture above shows us that triangle ABC and triangle ACD are similar triangles by showing us that then have congruent angles. This tells us that each side of the triangle is bigger/smaller than the other triangle by the same factor. To find this out, we use two corresponding sides of the two triangles. In this case, two corresponding lengths that are given to us are BC and CD. If we divide CD by BC, this tell us that triangle ACD is approximately 5/3 bigger than triangle ABC. Using this, we can figure out the length of AB. We simply take 14.3 and divide it by 5/3. We divide because we are trying to mind the magnitude of the length of the smaller triangle. If we were looking for the length of the larger triangle, we would have multiplied. After dividing 14.2 by 5/3, we find that the length of AB is about 8.6.

Step-by-step explanation:

8.6 is the answer to the equation

The sum of two numbers is 54 . the smaller number is 12 less than the larger number. what are the numbers?

Answers

Let x=one number and x+12= the other number.  Together the numbers=54.  Set up the equation:  x+x+12=54;  Combine the variables;  2x+12=54;  Subtract 12 from both sides of the equation;  2x=42; Divide both sides of the equation by 2;  x=21 is one number and 21+12=33 is the other number.  Check:  2(21) +12=54;  42+12=54;  54=54.

The teen club had a cupcake sale. they started with 126 cupcakes. they sold 2/3 of their cupcakes in the morning. how many were left for them to sell in the afternoon?

Answers

126 ÷ 3= 42
42×2= 84 (number of cupcakes sold)
126-84= 42 (number of cupcakes left)

The rate of inflation is 3% . The cost of an item in future years can be found by iterating the function c(x) = 1.03x. Find the cost of a $1500 refrigerator in three years if the rate of inflation remains consistent .


********PLEASE HELP********

Answers

This is the concept of business mathematics, given an inflation rate of 3%, that has modeled the price of items using the function c(x)=1.03x, the cost of the refrigerator in 3 years will be as follows;
cost after 1 year:
c(1)=1.03*1500
=1545
cost after 2 years
c(2)=1.03*1545
=1591.35
the cost after 3 years will be:
c(3)=1.03*1591.35
=$1,639.09

20 POINTS, PLEASE HELP ASAP!!!!

Answers

Question b)

17 minutes ⇒ 1 revolution = 2π
1 minute ⇒ 2π/17

Angle of rotation is 2π/17 per minute

Question c)

The period of the rotation is 2π/17 

The wheel starts rotating from the height of 5 meters from the ground and the maximum height is 125 meter from the ground.
The amplitude is 125 - 5 = 120 ÷ 2 = 60

The midline of the rotation is at 125 - 5= 120 ÷2 = 60 + 5 = 65 (this is the location of the centre of the wheel). This value is a shift of 65 from the zero midlines (which in this case would be the ground)

Question C

The movement of the wheel can be described as starting from 0° then reaching its peak at 180° and come back to its original position as it stops and it makes a complete circular turn 360°.

If we sketch this on a graph, we will obtain a curve of -cos(x)

We need to apply the period, the amplitude and the shift produced by this rotation into the equation [tex]y = -cos(x)[/tex]

The period is [tex] \frac{2 \pi }{7} [/tex] ⇒ [tex]f(t)=-cos( \frac{2 \pi }{7}t) [/tex]
The amplitude of 60 ⇒ [tex]f(t)=-60cos( \frac{2 \pi }{7}t) [/tex]
The shift of the midline by 65 units upwards ⇒ [tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]

The final equation is
[tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]

and the graph is shown in the third picture below

PLEASE HELP ^^^^^^^^^^^^

Answers

Let's work this problem out:

Step one:4(-2) = -8, right?

Step two:  3(-7) = -21, right? 

Step 3: So, -8 + (21) = 13,right? 

Your answer would be: 13 (option B.)

solve the equation by completing the square. round to the nearest hundredth if necessary. x^2-6x=20

Answers

x^2 - 6x = 20
x^2 - 6x + 9 = 20 + 9
(x - 3)^2 = 29
x - 3 = (+-) sqrt 29
x = 3 (+-) sqrt 29
x = 3 (+-) 5.39

x = 3 + 5.39 = 8.39 <=
x = 3 - 5.39 = - 2.39 <=
x^2-6x+(b/2)^2=20+(b/2)^2
x^2-6x+(6/2)^2=20+(6/2)^2
x^2-6x+(3)^2=20+(3)^2
x^2-6x+9=20+9
(x-3)^2=29
x-3=5.38 or -5.38
x=5.38+3 or -5.38+3
x=8.38 or -2.38




























From 75 campsites to 120 campsites

Answers

subtract 75 from 120

120-75 =45 more campsites

Write the equation in exponential form.

Answers

the answer is D. ( btw,the picture quality sucks,try cropping it)

At a sandwich shop they offer 3 kinds of bread, 5 kinds of meat, and 3 kinds of cheese. Each type of sandwich has a combination of exactly 3 ingredients: 1 bread, 1 meat, and 1 cheese. How many types of sandwiches are possible?

Answers

Final answer:

The sandwich shop could yield a total of 45 types of sandwiches based on the three categories provided; namely, bread, meat, and cheese. According to the counting principle in mathematics, you multiply the amount of options available from each category to get the total combinations possible.

Explanation:

In the scenario described, to determine the possible number of sandwiches, we need to analyze the provided combinations. We have 3 types of bread, 5 kinds of meat, and 3 kinds of cheese. Each sandwich exactly contains one item from each category.

To find out all possible sandwich combinations, we multiply the number of choices in each category. This is known as the counting principle.

So, the formula would be:
Number of sandwich combinations = Types of Bread * Types of Meat * Types of Cheese

Plugging the given numbers into this formula, we get:
Number of sandwich combinations = 3 * 5 * 3 = 45

So, there are 45 possible sandwich combinations available in this sandwich shop.

Learn more about Counting Principle here:

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Someone help me please !!!

Answers

Answer:

1. 10

2. 12

3. Sqrt 130

4. Sqrt 45

Step-by-step explanation:

To find the missing side of a right triangle, use the Pythagorean Theorem. The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the legs with a being the smallest and c is the hypotenuse.

1. a=6, b=8, c=?

[tex]6^2+8^2=c^2\\36+64=c^2\\100=c^2\\10=c[/tex]

2. a=5, b=?, c=13

[tex]5^2+b^2=13^2\\25+b^2=169\\169-25=b^2\\144=b^2\\12=b[/tex]

3. a=7, b=9, c=?

[tex]7^2+9^2=c^2\\49+81=c^2\\130=c^2\\\sqrt{130}=c[/tex]

4. a=2, b=?, c=7

[tex]2^2+b^2=7^2\\4+b^2=49\\49-4=b^2\\45=b^2\\\sqrt{45}=b[/tex]

Evaluate 9 - b when b = 8

Answers

9 - b = ?
9 - 8 = 1
So, your answer is 1. Hope this helps, please mark brainliest and have an amazing day!

Equations are expressions separated by an equal sign. The value of the expression 9-b is b is 8 is given as 1

Equations and expressions

Equations are expressions separated by an equal sign

Given the expression  9 - b

If b = 8, we will have to substitute the value of 8 into the expression to have:

f(b) = 9 - b

f(8) = 9 - 8

f(8) = 1

Hence the value of the expression 9-b is b is 8 is given as 1

Learn more on function and values here: https://brainly.com/question/2284360

In two or more complete sentences describe how to determine the appropriate model for the set of data, (0,2), (2,3), (5,4), (10,5).

Answers

When you have a set of data points and you want to get a model out of it, you do data fitting. The first thing to do is plot the points using a scatter plot type of chart as shown in the picture. I used MS Excel as a tool for data fitting. On the left side of the picture, I used linear fitting. Then, it gives you the linear equation y=0.2907x + 2.2643. It has a correlation coefficient, R^2, of 0.9595. This measures how good your data fits the model equation. The closer it is to 1, the better. However, it is rare to get 1 because that is very ideal. A R^2 of 0.9595 is very satisfactory already. But if you want an even better model, the right side of the picture shows data fitting on a quadratic equation with an equation of y=0.0209x^2 +0.506x+2.0232 with R^2 of 0.9992.

Answer:

The closer this value is to 1 or -1, the better the fit. For linear, the correlation coefficient R2=.96.  For quadratic, the R2=.99.  For exponential, the R2=.91.  This means quadratic is the best fit, very good actually since .99 is very close to 1.

Step-by-step explanation:

What is the precise definition of an angle? question 1 options:?

Answers

In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?

Answers

52/2 = 26 ounces of cereal in 1 box
26 * 5 = 130 ounces of cereal in 5 boxes

Answer:

If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?

Step-by-step explanation:

If we have 52 ounces in 2 boxes, in 1 box we have: 52/2 = 26 ounces.

If we have 5 boxes and 26 ounces in each, we have: 5 x 26 = 130 ounces in total.

Outside a home there is a keypad that will open the garage if the correct four digit code is entered.? How many codes are possible?

Answers

Assume that none of the digits on the keypad are repeated. This means that we have 10 digits: 0,1,2,3,4,5,6,7,8,9.

The number of ways to arrange 10 distinct digits is
10! = 10*9*8*7*6*5*4*3*2*1 = 3,628,800

Answer: 3,628,800
That is 3 million, 628 thousand, and 800.
Final answer:

There are 10,000 possible codes that can be entered into the keypad to open the garage.

Explanation:

The number of possible codes is determined by the number of choices for each digit of the code. In this case, there are 10 possible choices for each digit (0-9). Since there are 4 digits in the code, we can multiply the number of choices for each digit together to find the total number of possible codes: 10 x 10 x 10 x 10 = 10,000. Therefore, there are 10,000 possible codes that can be entered into the keypad to open the garage.

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Find the product.

(n + 7)(n - 2)

n² - 5n - 14
n² + 5n - 14
n² - 5n + 14

Answers

The answer is n^2 + 5n - 14.


[tex](n+7)(n-2)\\\\n*n+(-2)*n+7*n+7*(-2)\\\\n^{2}-2n+7n-14\\\\n^{2}+5n-14[/tex]
(n+7)(n-2)
=n•n+(-2)•n+7•n+7•(-2)
=n²-2n+7n-14
=n²+5n-14. In conclusion, the product of (n+7) and (n-2) or (n+7)(n-2)=n²+5n-14. Hope it help!

5/14 divided by 3/4, what's the answer

Answers

Rule:  (a/b)/(c/d)=(a/b)*(d/c)

(5/14)/(3/4)

(5/14)(4/3)

(5*4)/(14*3)

20/42

10/21
Answer: 10/21 or 0.47619...

This can be calculated by finding the reciprocal of 3/4, which is 4/3.
 
Next, you multiply 5/14 by 4/3. To multiply fractions, you multiply the two numerators and set it as the new numerator and multiply the two denominators and set it as the new denominator.

5 * 4 = 20
14 * 3 = 42

To simplify, you can divide each by 2 since it goes into both values.

20/2 = 10
42/2 = 21

Answer: 10/21

Rectangular prisms A and B are similar.
The edge of prism B is 3 times that of prism A. How many times the volume of prism A is the volume of prism B?

Answers

27 times smaller or 1/27 because 3^3 equals to 27.
[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{let's say the edge of A is \underline{k} long, then B's is \underline{3k}} \\\\\\ \cfrac{A}{B}\qquad \cfrac{k}{3k}\implies \cfrac{1}{3}\implies \cfrac{s}{s}\qquad thus \\\\\\ \cfrac{A}{B}\qquad \cfrac{1}{3}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{1}{3}=\sqrt[3]{\cfrac{s^3}{s^3}}\implies \left( \cfrac{1}{3} \right)^3=\cfrac{s^3}{s^3}\implies \cfrac{1^3}{3^3}=\cfrac{s^3}{s^3} \\\\\\ \cfrac{1}{27}=\cfrac{s^3}{s^3}[/tex]

My sister is 15 years older than i am. the sum of our ages is 41. find our ages

Answers

x = you, and y = ur sis

x + y = 41
y = x + 15

x + (x + 15) = 41
2x + 15 = 41
2x = 41 - 15
2x = 26
x = 26/2
x = 13 <== u r 13

y = x + 15
y = 13 + 15
y = 28 <== ur sis

Twenty times the square of a non-zero number is equal to 15 times the number

Answers

i think that the answer is 5

20x^2 = 15x
20x^2 - 15x = 0
5x(4x - 3) = 0 
5x = 0, x =0
4x -3 = 0, x = 3/4

answer
non-zero number is 3/4

Find the area of the triangle

Answers

The area of a triangle is equal to bh/2.
The base here is 8 and the height is 3.
8*3=24
24/2=12
The answer is B, 12 yd^2

To the nearest square unit, what is the area of the shaded region?

Answers

Since the diagram is a regular octagon, it can form 8 of the same triangles.
The area of one triangle= 1/2 x 15 x 18.11
=135.825
The area of the octagon = 135.825 x 8
= 1086.6
The area of shaded region will be the area of the octagon minus the square
The area of the shaded region = 1086.5-(15x15)
=861.6
Answer will be C as you need to round off to three significant figures
First we need to distribute it in parts of
2 trapezium
1 rectangle 
These reading are for shaded region
Each side of octagone is 15 as it is regular
The height of octagone=18.11 x 2=36.22 this is one side of trapezium
and the other is 15  as it is regular
the height of trapezium=10.61 from the whole horizontal length is equal to vertical as it is regular octagone 
then we need to subtract this horizontal length by 15 which is one of the side =36.22-15=21.22 then divide it by 2 so that can get height of each trapezium =10.61
so the area of each trapezium= 0.5 x (36.22+15) x 10.61=271.7
And of two are= 271.7 x 2 =543.4
The area of triangle = 15 x 21.22 ( this is not the area of rectangle shown it is the area of rectangle which is above it and part of shaded region.
=318.3 
Area of shaded region = 543.44 + 318 3 =861.7=862 to nearest whole number
SO ANSWER IS C THAT IS 862 square units

HELP QUICK!!!
An ellipse has foci F1(9, 0) and F2(11, 6), and the point (1, 6) is on the ellipse. Identify the constant sum for the ellipse.
a 20
b 10
c 0
d 100

Answers

The first step is to find the distance from the given point to each of the two foci as follows:
Distance D1:
(D1)^2 = (9-1)^2 + (0-6)^2 = 100
D1 = 10
Distance D2:
(D2)^2 = (11-1)^2 + (6-6)^2 = 100
D2 = 10

The constant sum is the summation of the two distances as follows:
constant sum = D1 + D2 = 10 + 10 = 20

The correct choice is:
a) 20

Answer:   20

Step-by-step explanation:

Two numbers are in the ratio of 3 to 4. If nine is subtracted from each, they are in the ratio of 3 to 5. Find the numbers.

Answers

12:16= 3:4 when simplified
12-9=3
16-9=5
When subtracting 9 from each the new ratio is 3:5

Hope this helps!

Webassign find the area of the region bounded by the parabola y = x2, the tangent line to this parabola at the point (6, 36), and the x-axis.

Answers

first find the tangent line

dy/dx=2x
at x=6, the slope is 2(6)=12
so
use point slope form
y-y1=m(x-x1)
point is (6,36)
so
y-36=12(x-6)
y-36=12x-72
y=12x-36

alright, so we know they intersect at x=6
and y=12x-36 is below y=x^2

so we do [tex] \int\limits^6_0 {x^2} \, dx - \int\limits^6_0 {12x-36} \, dx = \int\limits^6_0 {x^2-(12x-36)} \, dx = \int\limits^6_0 {x^2-12x+36} \, dx =[/tex]
[tex][\frac{x^3}{3}-6x^2+36x]\limits^6_0=(\frac{6^3}{3}-6(6)^2+36(6))-(0)=\frac{216}{3}-216+216=[/tex] [tex]72+0=72[/tex]

the area under the curve bounded by the lines and the x axis is 72 square units

Please help me !!!!!!!!

Answers

It's C the missing side is 9 units long so since cosine is adjacent divided by hypotenuse it would be 9/41
41^2 - 40^2 = 1681 - 1600 = 81

side xy = square root 81 = 9

cosine(X) = Adj / Hypo
cosine(X) = 9/41
answer
C. 9/41

A and b are complementary angles find a and b a=3/4x-13 b=3x-17

Answers

3/4x-13+3x-17=90

3 3/4x-30=90

3 3/4x = 120

x=32

A=11
B=79
Other Questions
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