1. Copy and complete: To multiply two powers with the same base, ? their exponents.

2. Give an example of an expression you could simplify using the quotient of powers property.

Find the product or quotient. Write your answer using exponents.
3. 4².4⁹ 4. 5³.5⁸ 5. 6₇.6 6. 7³.7⁴.7²

In 720 ways the letters of the word 'SEMESTER' be arranged such that at least two vowels are together.

Arrangement in probability

Given that:

In SEMESTER there are 8 letters.

Which include 3 vowels (E) and 5 consonants (S, M, T , R )

Take 3 vowels as one letter, we have 6 letters

arranged in 6[tex]p_{6}[/tex] = 6! ways E can be taken together in 1! ways

Number of words = 6! × 1!

                             = 6 × 5 × 4 × 3 × 2 × 1

                             = 720 ways

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The new yearly salary will be $31,694.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Employee c is paid an hourly rate of 13.25 per hour and works 2,080 hours per year.

And, The employee was just promoted and received a 15% raise.

Now,

Since, Employee c is paid an hourly rate of 13.25 per hour and works 2,080 hours per year.

And, The employee was just promoted and received a 15% raise.

Hence, The salary for 13.25 hours = 13.25 × 2080

                                                     = $27,560

And, The employee was just promoted and received a 15% raise.

Hence, The new salary = $27,560 + 15% of 27,560

                                    = 27,560 + 4134

                                    = $31,694

Thus, The new salary = $31,694

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Answer:

25,456

Step-by-step explanation:

   592                       2 x 3 = 6       9 x 3 = 27 (You put the 7 in the tens place)

x     43                     (And add 2 to the hundreds after multiplication)

______             5 x 3 = 15    15 + 2= 17    (So you add 1 to the thousand place)

   1776                                      Which would be 1776

2368

Now we do the same thing but with 4 this time, and we wont use the ones place because were putting the numbers in the tens place to start with since it's 40                        2 x 4 = 8 (Goes in tens place)

          9 x 4 = 36 (6 goes in hundreds place and 3 to thousands place)

5 x 4 = 20       (So 2 goes into the ten thousands place, and 3 to thousands place)

                                                     So it would be 2368

To find the amount of the down payment, we need to multiply the cost of the home by the down payment percentage: $90,000 * 8.8% = $7,920.

This means that the total amount that will need to be borrowed from the bank is $90,000 - $7,920 = $82,080.

The mortgage amount will be $82,080. This is the amount that will need to be borrowed from the bank after the down payment of $7,920 is paid. The down payment is calculated by multiplying the cost of the home by the required down payment percentage: $90,000 * 8.8% = $7,920. The mortgage amount is then calculated by subtracting the down payment from the cost of the home: $90,000 - $7,920 = $82,080.

In the accompanying proof, the reason (5) is SAS theorem.

In the given question,

Given: AB || DC

AB=DC

Prove: m∠DAC = m∠BCA

The statement used to prove this conditions are:

Statement                        Reason

AB || DC                            (1) Using the Quadrilateral Rule

AB=DC                             (2) Opposite sides are equal

m∠BAC = m∠DCA           (3) Alternate interior angles Theorem

AC=AC                              (4) Common Side

∆ADC≅∆CBA                   (5) SAS Theorem

m∠DAC = m∠BCA            (6) Alternate interior angles Theorem

We have to explain in the accompanying proof, what is reason (5).

So, in the accompanying proof, the reason (5) is SAS theorem.

In the proving we first prove one side equal, then angle equal and at last again one side equal.

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Answer:

Step-by-step explanation:

SolutionFinal answers are given below.

Back-up Theory and Details of calculations follow at the end.

Part (a)

Estimate of the slope for the least-squares regression line = - 0.0073  Answer 1

InterpretationFor every increase of 1 pound in car’s weight, the fuel efficiency would reduce by 0.0073 mpg.  Answer 2

Part (b)

Correlation coefficient, r = - 0.9438  Answer 3

Interpretation An r-value of - 0.9438 indicates that there is a strong inverse linear relation between car’s weight and fuel efficiency.

Negative sign implies that as car’s weight increases, the fuel efficiency would come down.Answer 4

Part (c) The estimated regression equation is: Fuel efficiency = 45.4705 – 0.0073 x car’s weight. Substituting car’s weight = 2684 in the above equation, the estimated fuel efficiency = 25.83.So, residual = 24.5 – 25.84 = - 1.23.

Thus, Residual for a car weighing 2684 pounds and having an average fuel efficiency of 24.5 mpg= - 1.23 Answer 5

Part (d)

Substituting fuel efficiency = 20.2 in the above regression equation, the estimated car’s weight = 3461Estimate of the weight of a car whose fuel efficiency is 20.2 mpg = 3461 pounds Answer 6

The pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers is number line.

What is meant by pedagogical tool?

In math, pedagogical tool refers designed to convey important lessons and allow people to improve their understanding of a problem or undertaking.

Here we need to find the research recommends that teachers use the following pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers.

While we looking into the given question, here we need to find the tool that is used to find the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers that is none other than number line because it uses the visual representation of the number that gives better understanding of number.

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Answer:

40 donuts

10 Coffees

Step-by-step explanation:

d+c=40

4d+6c=180

-4d-4c=-160

+4d +6c +180

2C=20

C=10

d+10=40

d=30

Answer: 16 hours

Step-by-step explanation:

       We will write a system of equations to help us solve. Let x be equal to the number of hours worked at the college bookstore, and y be equal to the number of hours worked at Papa Gino's.

       First, we will write an equation for the money earned. Then, we will write one for the hours worked.

8.25x + 9.25y = 247

x + y = 28

       Now, we will will substitute the second equation into the first and solve for the hours worked at Papa Gino's last week, equal to y.

x + y = 28 ➜ x = -y + 28

8.25x + 9.25y = 247

8.25(-y + 28) + 9.25y = 247

-8.25y + 231 + 9.25y = 247

y + 231 = 247

y = 16

         Rosemary worked 16 hours at Papa Gino's last week.

a) The minimum number of hikers that could have walked between 6 miles and 17 miles is of: 9.

b) The maximum number of hikers that could have walked between 6 miles and 17 miles is of: 19.

The amounts are obtained by the frequency table given in the image, which shows the number of times that each range was observed.

The minimum number in the desired range will be obtained when:

Hence the minimum number is of 9, which is the number of people in the range 10-15.

The maximum number in the desired range will be obtained when:

Then the maximum number is calculate as follows:

2 + 9 + 8 = 19 hikers.

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All of the points along the y-axis are located in the region of the coordinate plane that is equally distant from the coordinates a(-3 2) and b(3, 2).

The x-axis, a horizontal number line, and the y-axis, a vertical number line, cross to create a coordinate plane. The coordinate plane's origin is where the two axes—plural for "axes"—vertically intersect.

Each point on a coordinate plane will have an x coordinate and a y coordinate, which are stated as (x, y). For instance, the coordinate (3,2) has a y-coordinate of 2, an x-coordinate of 3, and a coordinate in between.

Here,

Given: K(3, -2) and (x, 6).

Thus ,distance between points K and L is 10 units.

Thus,

=> 10 = [tex]\sqrt{(3-x)^{2}-(-2-6)^{2} }[/tex]

=> 10 = [tex]\sqrt{9+x^{2} -6x+64\\[/tex]

=> 100 = 73 +[tex]x^{2}[/tex] -6x

=> 27 =[tex]x^{2}[/tex] -6x

=>[tex]x^{2}[/tex]-6x-27=0

=>x(x-9)+3(x-9)

=>x=-3 , x=9

Thus, x comes out to be x =-3.

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The approximate number of bricks he will use for the entire building is; 1596 bricks

We are given that;

- Tim is building a brick wall that will be 4 feet high and 57 feet long.

- It takes 7 bricks to build 1 square foot of the wall.

The area of the building is gotten by applying the area of a rectangle which is;

Area of building = Length * Width

Thus;

Area = 4 * 57

Area = 228 square foot

Now, we are told that it takes 7 bricks to build one square foot of wall. Thus;

Number of bricks required here is;

N = 228 * 7

N = 1596 bricks

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The complete question is;

Tim is building a brick wall that will be 4 feet

high and 57 feet long. It takes 7 brick to build 1 square foot of wall

(Area = Length x Width)

Approximately how many bricks will he use for the entire building?

When a die is loaded so that the probability of one side appears twice as often as the other five, the number "1" will be the most frequent result when the die is rolled.

When a die is loaded so that one side appears twice as often as the other five, the number that comes up most often when the die is rolled is "1". This is because the loaded die has an unequal probability of rolling each number, with one side being twice as likely to come up as any of the other five sides. This means that the chances of rolling this particular number are twice as great as the chances of rolling any of the other five numbers. For this reason, the number "1" will be the most frequent result when the die is rolled.The probability of rolling the number "1" is 2/7, while the probability of rolling any of the other five numbers is 1/7. Therefore, the number "1" is twice as likely to come up as any of the other five numbers when the die is rolled.

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a) The relative extrema of the function h(x)=cos((2π/3)x) on the interval [0, 2] are given as follows:

b) The absolute extremas of the function h(x)=cos((2π/3)x) on the interval [0, 2] are given as follows:

Relative extrema are all the turning points on the graph of a function, which are the points in which the derivative of the function is zero, hence the function behavior's may change from increasing to decreasing or vice versa.

From the graph given by the image at the end of the answer, the extremas of the function are given as follows:

These are also the absolute extremas, as there are only one minimum extrema and one maximum.

If there were multiple extremas, we would have that:

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The equations that are correct are a = 1/2(-2b + 2c -d) and c = a + b + d/2. The correct options are  C. c = a + b + d/2 and D. a = 1/2(-2b + 2c -d)

From the question, we are to solve the equation for each variable

The given equation is

a + b = c - d/2

Solving for a

a + b = c - d/2

a = -b + c -d/2

Multiply through by 2

2a = -2b + 2c -d

By multiplying both sides by 1/2, this can be written as

a = 1/2(-2b + 2c -d)

Solving for b

a + b = c - d/2

b = -a + c - d/2

Multiply through by 2

2b = -2a + 2c - d

By multiplying both sides by 1/2, this can be written as

b = 1/2(-2a + 2c - d)

Solving for c

a + b = c - d/2

a + b + d/2 = c

Therefore,

c = a + b + d/2

Solving for d

a + b = c - d/2

Multiply through by 2

2a + 2b = 2c - d

d = 2c  - 2a - 2b

d = -2a - 2b + 2c

Hence, a = 1/2(-2b + 2c -d) and c = a + b + d/2  are correct

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Answer:

Area = (60 + n) * 60 = 3600 + 60n

Step-by-step explanation:

The length of the land is 60 + n feet. The area of the land is the product of the length and width, so the equation representing the area of the land is:

Area = (60 + n) * 60 = 3600 + 60n

This equation represents the area of the land in square feet.

Positive coefficients show that the event is more probable at that predictor level than it is at the factor's reference level. Positive coefficients show that the event is more likely to occur at the reference level than at that level of the predictor.

Positive coefficients indicate that the event is more likely to occur at that predictor level than it is at the reference level for the factor.

Positive coefficients indicate that the event has a higher probability of happening at the reference level than at the predictor level.

The correlation coefficient (r2) is a statistic that expresses how closely two variables' movements are related to one another.

To determine the linear relationship between two variables, the Pearson product-moment correlation, the most popular correlation coefficient, is used.

However, this correlation value might not necessarily be a reliable indicator of reliance in a non-linear connection.

Hence, Positive coefficients show that the event is more probable at that predictor level than it is at the factor's reference level.

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Answer: [tex]\frac{5}{k}[/tex]

Step-by-step explanation:

        To write an algebraic expression that represents this situation, we need to know that a quotient will involve division.

        We will write the quotient of 5 and a number, k. also written as 5 divided by k, as;

       [tex]\displaystyle \frac{5}{k}[/tex]

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The algebraic expression is - [tex]\frac{5}{k}[/tex]

If one number is divided by another number, the answer obtained is called the quotient.

In mathematics, a number that divides another number is called a divisor.

The number which is to be divided by the divisor is called a dividend.

In arithmetic, if we divide one integer by another, the 'leftover' portion is called the remainder.

In this case, 5 is the dividend, and k is the divisor, which is representing an unknown number.

We can not get an actual number, but we can use an algebraic equation to express the quotient as follows:

The quotient of 5 and k = [tex]\frac{5}{k}[/tex]

The algebraic expression is - [tex]\frac{5}{k}[/tex]

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Answer:

They're asking you to plug in the x values for x. for example the first x in the table is "-6" so you will replace the x in 1/3(-6)^2 and the Y answer would be 12.

1/3 x (-6)^2 which is 36.

1/3 x 36= 12.

and you'll basically do that for each value. I hope that helps.

James owns on owns only 5 percent of the business capital.

We should know that percentage deals with number of ratios as a fraction of 100

James = $10,000

One partner = $10,000

Other two partners = ($90,000+90,000)=$180,000

Total capital invested = $)10000+10000+90000+90000)

Total investment = $200,000

James proportion= [tex]\frac{10,000}{200,000} *\frac{100}{1}[/tex]

Simplifying this to have James percentage of investment as 5 percent

James =5%

In conclusion James has only 5% of the business investment

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A 90% confidence interval places the true mean normal body temperature between 98.14269 and 98.35577.

library(UsingR)

attach(normtemp)

print(normtemp)

hist(normtemp$temperature)

shapiro.test(normtemp$temperature)

qqnorm(normtemp$temperature)

qqline(normtemp$temperature)

We can observe that the data follows a normal distribution from the histogram and q plot.

The points in the q plot fall on a straight line and correspond to a normal distribution.

P-value = 0.2332, P>0.05, from the Shapiro test

hence, we fail to reject null htpothesis.

On accepting the null hypothesis we get to know that the data follows normal distribution.

The output for the given code will be ,

data: normtemp$temperature

t = 1527.9, df = 129, p-value < 2.2e-16

alternative hypothesis: true mean ≠0

90 percent confidence interval:

98.14269 98.35577

sample estimates:

mean of x

98.24923

Therefore , we can conclude that ,

The true mean normal body temperature is believed to be between 98.14269 and 98.35577 with a 90% confidence interval.

98.6 is not included in the 90% confidence interval.

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Answer: C. 1 unit down. 2 units to the right

Step-by-step explanation:

The greater unit rate of the two functions is 2. The greater y-intercept of two functions is 6.

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

From the given table, (0, 5) and (5, 15)

Here, slope(m)=(y2-y1)/(x2-x1) =(15-5)/(5-0)

= 10/5

= 2

Substitute m=2, (x, y)=(0, 5) in y=mx+c, we get

5=2(0)+c

c=5

Substitute m=2, c=5 in y=mx+c, we get

y=2x+5 --------(I)

From the graph, (-4, 0) and (0, 6)

Here, slope(m)=(6-0)/(0+4)

= 3/2

= 1.5

Substitute m=1.5, (x, y)=(0, 6) in y=mx+c, we get

6=1.5(0)+c

c=6

Substitute m=1.5, c=6 in y=mx+c, we get

y=1.5x+6 --------(II)

Therefore, the greater unit rate of the two functions is 2. The greater y-intercept of two functions is 6.

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Answer: >

i might be wrong tho

Step-by-step explanation:

x=(-12,0)

y=(0,6)

m=6/-12

m=-1/2

slope is positive

m=1/2

y=1/2x+6

shade is to the right

y>1/2x+6

C₁₂H₁₂BrO₁N₁ is the molecular formula  that fits the following data A hydrocarbon \left(C_{x} H_{y}\right)(CxHy) with a molecular ion peak at m/z = 66.

An analytical technique used to measure the mass to charge ratio of the ions is known as mass spectrometry. This is one of the best technique used to analyse the structure of a molecule.  It is used in a a lot of applications such as carbon dating, food contamination detection, isotope detection, protein identification etc.

We have given that,

molecular ion at 265 m/z

another ion seen at 267 m/z

their ratio is 1:1

C₁₃H₉Cl₂ON₁ in this in here Cl have two isotopes that are

36 and 37 but   m/z is not equal to 265

in here C₁₂H₁₂BrO₁N₁  Br have  two isotopes

Br-79,  Br-81 and  m/z equals to 256 and 257

so the molecular formula is therefore  C₁₂H₁₂BrO₁N₁

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On solving the provided question the equation of line  segment is [tex]3y = x+11 OR y = 1/3x + 11/3[/tex]

An equation in algebra is a condition on a variable. Only for a certain value of the variable does it satisfy. This indicates that the equation 2x - 5 = 13 can only be met when x = 9. Polynomial equations and linear equations are two significant kinds of equations that are taken into account in algebra. One-variable polynomial equations can be expressed as P(x) = 0, where P is a polynomial and ax + b = 0 is the standard form for linear equations. Here, the variables a and b are used.

Let y=m x + c be the slope intercept form of the equation.

Here, the slope m and the y-intercept c are unknown.

What is known is that this goes through (x 1, y 1) and (x 2, y 2), two coordinate pairs.

Consequently, we have three equations.

[tex]y=mx+c.........1\\ y1=mx1+c....2\\ y2=mx2+c ......3[/tex]

now let's delete m and c using these.

subtracting (2) from (1), we get [tex](y-y1)=m(x-x1) ......(4)[/tex]

and subtracting (2) from (3), we get[tex](y-2-y1)=m(x2-x1) ......(5)[/tex]

[tex]\frac{y-y1}{y2-y1} = \frac{x-x1}{x2-x1} \\\\\frac{y-3}{4-3} = \frac{x+2}{1+2} \\\\y-3 = \frac{x+2}{3}\\ 3y-9 = x+2\\3y = x+11\\OR\\y = 1/3x + 11/3[/tex]

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The interest rate on this loan will be 5%.

Given that Eileen takes a student loan of 10,000 with simple interest to pay back after 10 years. If the estimated payment is 22,000.

The interest on the loan will be:

= $22000 - $11000

= $11000

The interest rate on this loan will be:

Rate = Interest / Principal × Time

Rate = 11000 / (22000 × 10)

Rate = 11000 / 220000

Rate = 5%

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The choice that is the total amount for the 3 items is C. $98.97.

The amount of money that Kayla have left after the purchase is A. $11.03.

From the information, Kayla saves $110 to purchase a new outfit. She decides to buy a skirt for $29.65, a sweater for $38.32, and a purse for $31.00.

The cost of the items will be:

= Skirt + Sweater + Purse

= $29.65 - $38.32 + $31.00

= $98.97

The amount of money that Kayla have left after the purchase is:

= $110 - $98.97

= $11.03

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Answer:

c and a

Step-by-step explanation:

If n is zero, Player A has one coin and Player B has none. B will always have 0 heads. There is a 50% chance that Player A has one head, and a 50% probability that Player A also has one head.

If they had the same number of coins, they would most likely obtain the same number of heads, and each person has an equal chance of getting more heads than the other player (the chance is less than 1/2).

If we give player A one more coin than player B, player A has a 50% probability of winning (if that extra coin comes out heads) which is the sample space.

There is a 50% probability that the coin will not provide an advantage (it come out tails). As a result, player A has a 50% probability of getting more heads than player B which is the required outcome.

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur. An event's probability is a number between 0 and 1, where 0 indicates impossibility and 1 represents certainty.

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