Answers
The answer is follows,
[tex]-3^5[/tex] = -243
[tex](-3)^5[/tex] = -243
[tex]\left(-3^5\right)[/tex] = -243
[tex]-\left(-3\right)^5[/tex] = 243
An exponent is a number or letter written above and to the right of the base of a mathematical expression.
What is meant by exponent?The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. An exponent is a number that is superscripted over another number. In other words, it denotes that the base has been raised to a certain level of power. Other names for the exponent include index and power. If m is a positive number and n is its exponent, the expression mn denotes that m has been multiplied by itself n times. Power is defined in mathematics as a base number raised to the exponent, where the base number is the factor multiplied by itself and the exponent is the number of times the same base number is multiplied.To learn more about exponent, refer to:
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Related Questions
Estimate by rounding each number to the nearest ten. Then find the difference.32.76 - 22.168An estimation of the difference isThe exact difference is
Answers
ANSWER
EXPLANATION
First let us find the actual difference:
32.76 -
The cheerleading team has won ¾ of their competitions. If the team competes in 16 competitions, how many did they win?
Answers
The cheerleading team won 12 out of 16 competitions. Your answer is 12.
Marbel surveyed 55 people to find out their favorite types of music the results shown in the bar graph
Answers
To find the correct option, we need to find, first, the rate of the population that chose each type of music. Then, when we sum the rates of the types in the correct answer, it should result in 40%.
The rate of population for each type of music is given by the number of peaple that chose this type, divided by the total amount of people (55):
Country: 15/55
Jazz: 12/55
Opera: 10/55
Roch: 18/55
In the first option, we have:
Country and Opera
a. Write a formula for the perimeter P of the square.Type your answer into the box below.b. Write a formula for the area A of the square,Type your formula into the box below.
Answers
a. The formula for the perimeter of a square is P=4L, where L is the length of it's sides.
b. The formula for the area of a square is A=LxL=L^2, where L is the length of it's sides.
Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ less than 128.
Answers
The probability that the IQ is less than 128 is 0.91924
How to determine the probability?The given parameters about the distribution are
Mean value of the set of data, μ = 100Standard deviation value of the set of data σ = 20IQ value, x = 128The z-score of the data value is calculated as
z = (x - μ)/σ
Substitute the given parameters in the above equation
z = (128 - 100)/20
Evaluate
z = 1.4
The probability that the IQ is less than 128 is then calculated as:
P(x < 128) = P(z < 1.4)
From the z table of probabilities, we have;
P(x < 128) = 0.91924
Hence, the probability is 0.91924
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Ruben purchases a violin that is on sale for a total price of$1,250, which includes tax and all other fees. He makes aninitial payment of $300 in cash and puts the remainder on hisnew credit card. He makes no other purchases on the card andpays off the credit card balance with 9 monthly payments of$150. What is the difference between the total amount Rubenpays for the violin, including the initial payment and the creditcard payments, and the sale price of the violin?
Answers
Given:
Actual price of a violin is $1,250
Credit card monthly payment as $150.
Initial payment is $300.
[tex]\text{Total money paid by Ruben for violin=300+(150}\times9)[/tex][tex]\text{Total money paid by Ruben for violin=300+}1350[/tex][tex]\text{Total money paid by Ruben for violin= \$1650}[/tex]The difference between the total amount Ruben pays for the violin, including the initial payment and the credit card payments, and the sale price of the violin:
[tex]\text{Diffference amount=1650-1250}[/tex][tex]\text{Diffference amount= \$400}[/tex]Difference amount is $400.
if one face of a cubr has a area of 6.75 square inches, what is the surface of the entire cube.
Answers
The surface area of the entire cube is 40.5 square inches
Here, we want to get the surface area of a cube given the measure of the area of one of the faces
Looking at the net of a cube, we can identify six identical and equal-dimension faces
So to get the total surface area of the cube, we have to multiply the surface area of one of the faces by 6
Mathematically, that would be;
[tex]6.75\text{ }\times\text{ 6 = 40.5}[/tex]you get charged $12.50 for each movie you buy on amazon prime.Somehow you accidentally spent $87.50 on movies last month. How many movies did you buy
Answers
You buy seven movies from Amazon Prime which is determined by the division operation.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.
For example 4/2 = 2
A movie ticket costs $12.50 which is given in the question
Last month, $87.50 was spent on Amazon Prime.
Your total movie expenditure is
⇒ 87.50/12.50
Apply the division operation to get
⇒ 7.
As a result, you buy seven movies from Amazon Prime.
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The dimensions of a tennis court are 27 feet by 78 feet. The dimensions of a ping pong table are 9 feet by 5 feet. Is a tennis court a dilation of a ping pong table? Explain why or why not.
Correctly answer yes or no (4 points)
Provide a clear and logical explanation (6 points)
Answers
No, The ratios are not equal tennis court is not a dilation of the table.
Given,
The dimensions of a tennis court are 27 feet by 78 feet.
The dimensions of a ping pong table are 9 feet by 5 feet.
To check the:
Is a tennis court a dilation of a ping pong table?
Now, According to the question:
For Tennis Court :
Dimensions is 27feet by 78feet
For Ping Pong Table:
Dimensions is 9 feet by 5 feet
To check that:
27/5 = 27/5 (Take lengths of tennis court and ping pong table )
78/9 = 26/3 (Take breadths of tennis court and ping pong table )
∴ 27/3 ≠ 26/3
Since, No, The ratios are not equal tennis court is not a dilation of the table.
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Multiply. Stars and restrictions on the variable. Simplify the rational expression.
Answers
Given,
The expression is:
[tex]\frac{x^2+2x-8}{x^2+4x-12}\times\frac{5x+30}{x+5}[/tex]Required:
The simplified rational expression.
Simplifying the expression,
[tex]\begin{gathered} \frac{x^2+2x-8}{x^2+4x-12}\times\frac{5x+30}{x+5}=\frac{x^2+4x-2x-8}{x^2+6x-2x-12}\times\frac{5x+30}{x+5} \\ =\frac{x(x+4)-2(x+4)}{x(x+6)-2(x+6)}\times\frac{5(x+6)}{x+5} \\ =\frac{(x+4)(x-2)}{(x+6)(x-2)}\times\frac{5(x+6)}{x+5} \\ =\frac{(x+4)}{1}\times\frac{5}{x+5} \\ =\frac{5(x+4)}{x+5} \\ =\frac{5x+20}{x+5} \end{gathered}[/tex]Hence, the simplified rational expression is (5x+20)/(x+5).
The restriction of the expression is:
[tex]x\ne-5,\text{ 2,-6}[/tex]
Draw a model to show a 26-pack of candy bars divided equally among 7 people. Howmany candy bars will each person have?
Answers
The diagram would be:
To find how many candy bars each person will get we divide 26 by 7:
[tex]\frac{26}{7}=3\frac{5}{7}[/tex]Therefore each person will get 3 5/7 of candy bar (appoximately 3.71 candy bars)
Which table represents a linear function?
Answers
The most appropriate choice for function will be given by-
The first option is correct
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
For the first table,
Slope of function from x = 1 to x = 2
= [tex]\frac{1 - \frac{1}{2}}{2 - 1}[/tex]
=[tex]\frac{1}{2}[/tex]
Slope of function from x = 2 to x = 3
= [tex]\frac{\frac{3}{2}-1}{3 - 2}[/tex]
= [tex]\frac{1}{2}[/tex]
Slope of function from x = 3 to x = 4
= [tex]\frac{2-\frac{3}{2}}{4 - 3}[/tex]
= [tex]\frac{1}{2}[/tex]
Here the slope is same. So the function is linear
For the second table,
Slope of function from x = 1 to x = 2
= [tex]\frac{\frac{1}{2} - 1}{2 - 1}[/tex]
=[tex]-\frac{1}{2}[/tex]
Slope of function from x = 2 to x = 3
= [tex]\frac{\frac{1}{3}-\frac{1}{2}}{3 - 2}[/tex]
= [tex]-\frac{1}{6}[/tex]
Here the slope is not same. So the function is not linear
For the third table,
Slope of function from x = 1 to x = 2
= [tex]\frac{9 - 7}{2 - 1}[/tex]
= 2
Slope of function from x = 2 to x = 3
= [tex]\frac{13 - 9}{3 - 2}[/tex]
= 4
Here the slope is not same. So the function is not linear
For the Fourth table,
Slope of function from x = 1 to x = 2
= [tex]\frac{6 - 0}{2 - 1}[/tex]
=[tex]6[/tex]
Slope of function from x = 2 to x = 3
= [tex]\frac{16 - 6}{3 - 2}[/tex]
= 10
Here the slope is not same. So the function is not linear
So the first option is correct
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What is the distance between three and 11 on the number line
Answers
We need to calculate the distance between 3 and 11 on the number line:
[tex]11-3[/tex]That is, from 0 we go 11 units forward and 3 units backward, like this:
Answer: 8
Answer:
8
Step-by-step explanation:
grant is rolling a six sided number die eight times. How many possible outcomes are there?
Answers
The die has 6 faces
[tex]\begin{gathered} \text{ In n number of throws, the number outcomes is given by 6}^n \\ ^{} \end{gathered}[/tex][tex]\begin{gathered} \text{ In 8 throws, the possible outcomes will be 6}^8 \\ =1679616 \end{gathered}[/tex]
A washer and a dryer cost $935 combined. The washer costs $85 more than the dryer. What is the cost of the dryer?
Answers
Answer: $325
Step-by-step explanation:
What is the solution to this system of equations?X+ 2y = 4| 2x-2y = 5(3.-5)(3.)no solutioninfinitely many solutions
Answers
The given system of equation :
x +2y =4
2x -2y =5
On adding both equation we get
x+2y+2x-2y=4+5
3x=9
x=3
So, for y, substitute x=3
x+2y=4
3+2y=4
2y=4-3
2y=1
y=1/2
The solutions is (3,1/2)
The system of linear equation have infintely many solution if they are coincidient, i.e. slope are equal
The given expression :
x+2y =4
2y=4-x
y=(4-x)/2
y = 2-x/2
So slope is (-1/2)
The second equation : 2x-2y=5
2y=2x-5
y=(2x-5)/2
y=x-
19. What fraction of the distance from M to V is MD?
Answers
Answer:the point is located on MV
Step-by-step explanation:
The Coordinates of D (0,-3/4)
TRIG ANALYSIS- THE LAW OF SINES- THE AMBIGUOUS CASERecall that your triangle should be set up so that angside b, and angle C is opposite side c.PLEASE HELP. WILL MARK BRAINLIEST
Answers
The sine law is described by the equation
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]1) Given angle C, length of side b, and length of side c, we are looking for the value of angle B. The angle B can be computed using
[tex]\begin{gathered} \frac{\sin B}{b}=\frac{\sin C}{c} \\ \sin B=\frac{b}{c}\sin C \end{gathered}[/tex]Substitute the values on the equation above and solve, we get
[tex]\begin{gathered} \sin B=\frac{34}{31}\sin (65)=0.994 \\ B=\sin ^{-1}(0.994) \\ B=83.7 \end{gathered}[/tex]Thus, angle B is equal to 83.7 degrees.
2) Given angle B, length of side a, and length of side b, we are looking for the value of angle A. The angle A can be computed using
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b} \\ \sin A=\frac{a}{b}\sin B \end{gathered}[/tex]Substitute the values on the equation above and solve, we get
[tex]\begin{gathered} \sin A=\frac{10}{5}\sin (126)=1.62 \\ A=\sin ^{-1}(1.62)=Error_{} \end{gathered}[/tex]There are no valid measurements for angle A on this solution.
3) Given angle C, length of side c, and length of side b, we are looking for the value of angle B. The angle B can be computed using
[tex]\begin{gathered} \frac{\sin B}{b}=\frac{\sin C}{c} \\ \sin B=\frac{b}{c}\sin C \end{gathered}[/tex]Substitute the values on the equation above and solve, we get
[tex]\begin{gathered} \sin B=\frac{22}{24}\sin (22)=0.3728 \\ B=\sin ^{-1}(0.3728)=21.9 \end{gathered}[/tex]Thus, angle B is equal to 21.9 degrees.
4. Given angle A, length of side c, and length of side a, we are looking for the value of angle C. The angle C can be computed using
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \sin C=\frac{c}{a}\sin A \end{gathered}[/tex]Substitute the values on the equation above and solve, we get
[tex]\begin{gathered} \sin C=\frac{34}{32}\sin (64)=0.955_{} \\ C=\sin ^{-1}(0.955)=72.74 \end{gathered}[/tex]Thus, angle C is equal to 72.74 degrees.
5. Given angle A, length of side c, and length of side a, we are looking for the value of angle C. The angle C can be computed using
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \sin C=\frac{c}{a}\sin A \end{gathered}[/tex]Substitute the values on the equation above and solve, we get
[tex]\begin{gathered} \sin C=\frac{9}{17}\sin (127)=0.4228 \\ C=\sin ^{-1}(0.4228)=25.0 \end{gathered}[/tex]Thus, angle C is equal to 25.0 degrees.
help me with the 17 pls just give me the answer
Answers
Solution
Evaluate each function below for the given equation
17.
[tex]f(x)=11x-9[/tex]f(2) is when the value of x = 2
[tex]\begin{gathered} f(x)=11x-9 \\ f(2)=11(2)-9 \\ f(2)=22-9 \\ f(2)=13 \end{gathered}[/tex]18.
[tex]g(x)=-4(g+2)\text{ for g\lparen5\rparen}[/tex]g(5) is when the value of x = 5
[tex]\begin{gathered} g(x)=-4(g+2) \\ g(x)=-4g-8 \\ g+4g=-8 \\ 5g=-8 \\ g=-\frac{8}{5} \end{gathered}[/tex]19.
[tex]f(x)=3+2(-x)[/tex]
f(-1) is when the value of x = -1
[tex]\begin{gathered} f(x)=3+2(-x)\text{ for x = -1} \\ f(-1)=3+2(-(-1)) \\ f(-1)=3+2 \\ =5 \end{gathered}[/tex]Find the orthogonal trajectories of the family of curves. y^2=6KX^3
Answers
The orthogonal trajectories of the family of curves y² = 6Kx³ will be [tex]y = \sqrt{6(C-\frac{x^2}{4}}[/tex]
What is the orthogonal trajectory?
An orthogonal trajectory of a family of curves is any curve that forms right angles with each member of the family. The curve does not always have to cross each member of the family.
It is given that,
y² = 6Kx³
Differentiate both sides we get,
[tex]\rm 2y = 6k(3x^2) \frac{dy}{dx} \\\\ \frac{dy}{dx} =\frac{2y}{18Kx^2}[/tex]
Substitute the value of K as
[tex]\rm K = \frac{y^2}{6x^3}[/tex]
[tex]\frac{2y}{18(\frac{y^2}{6x^3})x^2} = \frac{dy}{dx} \\\\ \frac{dy}{dx} = \frac{2x}{3y}[/tex]
Consider the negative reciprocal to find the perpendicular slope.
[tex]\frac{-3y}{2x} =\frac{dy}{dx} \\\\ - \int {\frac{1}{2x} \ dx = \int \frac{1}{3y} dy \\\\[/tex]
[tex]-\frac{x^2}{4}+C = \frac{y^2}{6}[/tex]
Simplify,
[tex]\rm 6(-\frac{x^2}{4}+C)= y^2 \\\\ y = \sqrt{6(C-\frac{x^2}{4}}[/tex]
Thus, the orthogonal trajectories of the family of curves y² = 6Kx³ will be [tex]y = \sqrt{6(C-\frac{x^2}{4}}[/tex]
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price. Find the sale price. There are 252 students on the student council at West High School. If there are 700 students enrolled, what percent are on the student council?
Answers
We have in total 700 students
252 students are on the students council
700 is 100%
252 is x
x represents the percentage of the student's council, in order to calculate x we need to do the next operation
[tex]x=\frac{252\cdot1}{700}=0.36[/tex]252 is the 36%
the percent of students that are on the student council is 36%
Is y = 2x² a linear or nonlinear function? Please explain.
Answers
A linear function has the form:
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept, bot constants.
As we see, the exponent of variable x is 1 for a linear function.
So, since the exponent in the given function y = 2x² is 2, this function is a nonlinear function.
In fact, it is a quadratic function.
A candy company has decided to sell candy in a new package that is shaped like a triangular prism in order to calculate the volume of the package, the area of the base must be determined.If the base of the package is equilateral triangle with sides 10 centimeters (cm) long, what is the area of the base?
Answers
Using the formula for the area of the equilateral triangle, we have:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}a^2 \\ A=\frac{\sqrt[]{3}}{4}(10)^2cm^2\text{ (Replacing)} \\ A=\frac{\sqrt[]{3}}{4}(100)^{}cm^2\text{ (Raising 10 to the power of 2)} \\ A=25\sqrt[]{3}\text{ }cm^2\text{(Dividing 100 by 4}) \\ A=43.3\text{ }cm^2\text{ (Multiplying 25 by }\sqrt[]{3}) \\ \text{The answer is 43.3 cm}^2 \end{gathered}[/tex]If 9x - 3 = 4, what does 9x - 2 = ?
Answers
it is given that
9x - 3 = 4
then we can write this
9x - (2+1) = 4
9x - 2 -1 =4
9x - 2 = 4 +1
9x - 2 = 5
so the answer is 5
Enter the equation of the circle with the given center and radlus. Center: (0,5); radius: 8 The equation of the circle is
Answers
The equation of the circle with the given data is given as,
where,
[tex]centeris(x_1,y_1\text{) and radius is r}[/tex][tex]\begin{gathered} (x-x_1)^2+(y-y_1)^2=r^2 \\ (x-0)^2+(y-5)^2=8^2 \\ x^2+(y-5)^2=64 \end{gathered}[/tex]How do i fill the boundaries for each class? how do i draw a histogram to illustrate this information ? how can i calculate the median age of the population?
Answers
Given:
The tabular representation of the data is given.
Required:
Histogram and Median of the given data.
Explanation:
The histogram of the given data is calculated as follows:
Figure 1
The median of the given set of data is calculated as,
Answer:
Thus figure 1 represents the histogram of the given data. The median of the given set of data is 27.7353.
convert 450 m/s to m/h
Answers
1,620,000 m/h
1) To convert 450 m/s we can set out the following:
[tex]\frac{450}{1s}\text{ }\times3600s=1,620,000[/tex]Since 1 hour is equivalent to 3600s then we can simply multiply by 3600 once the unit meter remains the same. m/s to m/h
2) Hence, the answer is 1,620,000 m/h
In a bag of Jolly Ranchers, the ratio of blue to red is 3 to 4. If I have a TOTAL of 56 Jolly Ranchers, how many of them are blue?
Answers
Answer:
24
Step-by-step explanation:
If ratio of blue to red is 3:4 or in fraction terms 3/4 then the ratio of blue to all Jolly ranchers = 3/(3+4) = 3/7
Since there are a total of 56, the number of blue ones = 56 x 3/7 = 24
Answer:
24
Step-by-step explanation:
Based on the given conditions, formulate: 56 x 3 divided by (3 + 4)
Calculate the product or quotient: 168/3+4
Calculate the sum or difference:168/7
Cross out the common factor:24
get the result:24
Answer: 24
The measure of <1 is greater than 97° and at most 115°. Graph the possible values of x.
Answers
Step-by-step explanation:
it help with work
Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:
o Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50)
o Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50)
What is Val’s margin of error, rounded to the nearest whole number? (The formula is 1.96 (std dev) /
Answers
If the average weight calculated by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.
Given that average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows.
We are required to find the margin of error of Val's data.
Margin of error is the difference between the actual data and the calculated data.
Margin of error=1.96*σ/[tex]\sqrt{n}[/tex]
In our case σ=50 and n is 100.
Margin of error=1.96*50/[tex]\sqrt{100}[/tex]
=1.96*50/10
=1.96*5
=9.80
Hence if the average weight calculated by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.
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