Sabrina has designed a rectangular painting that measures 65 feet in length and 30 feet in width. Alfred has also designed a rectangular painting, but it measures x feet shorter on each side. When x = 3, what is the area of Alfred's painting?

All of the sides of a cube are equal, then, the volume is given by the cube of the length of any side.

We need to find the biggest cubic value smaller than 80.

The largest cube has volume 64 cubic units, and the sides are 4 units long.

The simplified expression is  d/ c⁴.

To simplify the expression cd³ c⁻⁵ x d⁻², we can combine the variables with the same base (c and d) by adding their exponents:

Using the property of exponents as

When multiplying two exponential expressions with the same base, you can add the exponents. This can be expressed as follows:

aᵇ x aⁿ= aᵇ⁺ⁿ

When dividing two exponential expressions with the same base, you can subtract the exponents. This can be expressed as follows:

aᵇ / aⁿ= aᵇ⁻ⁿ

So, cd³ c⁻⁵ x d⁻²

= c¹⁻⁵ x d³⁻²

= c⁻⁴ x d¹

= dc⁻⁴

Again from the property of exponents

a⁻ᵇ = 1/aᵇ

So,  dc⁻⁴

= d/ c⁴

Therefore, the simplified expression is  d/ c⁴.

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Answer:

\(Median = 15.80\)

\(Mode = 15.20\ \&\ 15.25\)

\(IQR = 2.35\)

Step-by-step explanation:

Given

\(15.60,\ 18.75,\ 14.60,\ 15.80,\ 14.35,\)

\(13.90,\ 17.50,\ 17.55,\ 13.80,\ 14.20,\)

\(19.05,\ 15.35,\ 15.20,\ 19.45,\ 15.95,\)

\(16.50,\ 16.30,\ 15.25,\ 15.05,\ 19.10,\)

\(15.20,\ 16.22,\ 17.75,\ 18.40,\ 15.25.\)

Solving (a): The median and the mode

First, we sort the data.

\(13.80,\ 13.90,\ 14.20,\ 14.35,\ 14.60,\ 15.05,\ 15.20,\ 15.20,\ 15.25,\ 15.25,\)

\(15.35,\ 15.60,\ 15.80,\ 15.95,\ 16.22,\ 16.30,\ 16.50,\ 17.50,\ 17.55,\ 17.75,\)

\(18.40,\ 18.75,\ 19.05,\ 19.10,\ 19.45.\)

The median position is:

\(Median = \frac{n + 1}{2}th\)

\(Median = \frac{25 + 1}{2}\)

\(Median = \frac{26}{2}\)

\(Median = 13th\)

The 13th item is: 15.80

Hence:

\(Median = 15.80\)

The modes are:

\(Mode = 15.20\ \&\ 15.25\) --- they both have frequency of 2 while others occur once

Solving (b): The interquartile range

This is calculated as:

\(IQR = Q_3 - Q_1\)

Since the median is at the 13th position, Q1 is:

\(Q_1 = \frac{1 + 13}{2}th\)

\(Q_1 = \frac{14}{2}th\)

\(Q_1 = 7th\)

The 7th item is: 15.20

\(Q_1 = 15.20\)

Similarly, Q3 is:

\(Q_3 = \frac{13+n}{2}\)

\(Q_3 = \frac{13+25}{2}\)

\(Q_3 = \frac{38}{2}\)

\(Q_3 = 19th\)

The 7th item is: 17.55

So:

\(Q_3 = 17.55\)

Hence,

\(IQR = 17.55 - 15.20\)

\(IQR = 2.35\)

Answer:

8/20

Step-by-step explanation:

Answer:

The answer is: 10^5=100'000

Answer:

Step-by-step explanation:

15+5x=20x

   -5x  -5x  => Subtract 5x from each side

You get

15 = 15x

Divide both sides by 15

1=x

Answer:11

Step-by-step explanation:

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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The product of the given fractions is 224/61.

To calculate the product of the given fractions, let's simplify and cancel out any common factors.

We have:

(4/5) x (5/7) x (7/9) x (9/11) x (11/13) x (13/15) x (15/17) x (17/19) x (19/21) x (21/23) x (23/25) x (25/27) x (27/28) x (29/37) x (31/35) x (33/33) x (35/31) x (37/29)

Starting from the numerator and denominator of the first fraction, we observe the following cancellations:

5 in the numerator and denominator cancel out.

7 in the numerator and denominator cancel out.

9 in the numerator and denominator cancel out.

11 in the numerator and denominator cancel out.

13 in the numerator and denominator cancel out.

15 in the numerator and denominator cancel out.

17 in the numerator and denominator cancel out.

19 in the numerator and denominator cancel out.

21 in the numerator and denominator cancel out.

23 in the numerator and denominator cancel out.

25 in the numerator and denominator cancel out.

27 in the numerator and denominator cancel out.

Now, let's multiply the remaining fractions:

(4/1) x (1/28) x (29/37) x (31/1) x (1/35) x (37/29)

This simplifies to:

(4 x 1 x 29 x 31 x 37) / (1 x 28 x 37 x 29 x 35)

Simplifying further:

(4 x 29 x 31) / (28 x 35)

We can calculate this to get the final result:

(4 x 29 x 31) / (28 x 35) = 3584 / 980 = 224 / 61.

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The probability that the second card is also a spade is 4/17. (option A).

Probability is used to determine the extent to which it is likely that a random event would happen. The chances that the event would happen has a probability value that lies between 0 and 1.

In a deck of playing cards, there are 13 spades. After the first card is dealt, the number of spades and the number of playing cards would decline by 1. There would now be 12 spades and 51 playing cards.

Probability that the second card is a spade = number of spades / number of playing cards

Probability that the second card is a spade = 12 / 51

Probability that the second card is a spade = 4 / 17

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Answer:

The answer is 12

Step-by-step explanation:

You are correct in solving the equation.

Remember, when you divide by a fraction, you multiply by the reciprocal. So ultimately, the equation would be

6*2

which would then equal 12

Answer:

To verify the answer with a model, you could show

✔ 6

circles.

Each circle would be divided into

✔ 2

equal parts.

✔ 12

parts would be shaded.

Step-by-step explanation:

The angles x and 148° are vertical angles and si the measure of the vertical angle x is equal to 148°.

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

The angles 148° and x form vertical angles, so x = 148°

Therefore, since the angles x and 148° are vertical angles and and vertically opposite angles are equal, then the measure of the vertical angle x is equal to 148°.

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Answer: A

Step-by-step explanation: bc

Step-by-step explanation:

I didn't understand your question exactly but

eight less than a number b is :

8 < b

Answer:

x-8

Step-by-step explanation:

First, you have to assign a variable = x

Eight less than a number is x-8

Eight less is -8

Then a number is a variable

Have a good day and stay safe!

Answer: 3x - 2

Step-by-step explanation:

First to solve this, we need to know some basic information such as:

1. (-) × (-) = +

2. (+) × (-) = -

3. (+) × (+) = +

Therefore, 6x-(3x+2)​

= 6x - 3x - 2

= 3x - 2

The answer to the question after removing the bracket will be 3x - 2.

Answer:

Step-by-step explanation:

A ) Let p be the probability of getting affected . Probability of not getting affected be q

p = .3 , q = .7

If n be the member of family , probability that x children will be affected will be given by the expression

p(x) = ⁿCₓ pˣqⁿ⁻ˣ

n = 2 , x=2

p(2) = ²C₂ .3².7²⁻²

= 1 x .09 x 1 = .09

B )

p(1) = ²C₁ .3¹.7²⁻¹

=  2 x .3 x .7

= .42

C ) x = 0

p (0) = ²C₀ .3⁰.7²⁻⁰

=  1 x 1 x .49

= .49

D ) Let A be the probability that older child is affected and B be the probability that younger child is affected

P( A /B ) = P(A∩B) / P(B )

= .09 / .42

= .214

1. ask all the students in your math class - Convenience Sampling 2. choosing every 5th person on a list - Systematic Sampling. 3. pulling 50 names from a hat - Random Sampling.

In statistics, sampling is the process of choosing a portion of people or facts from a bigger group in order to estimate population characteristics. To collect data that is representative of the majority while reducing bias and mistakes, sampling is used. Various sampling techniques can be employed depending on the study, the size of the population, and the resources at hand. Simple random sampling, stratified sampling, cluster sampling, and systematic sampling are a few popular sampling techniques.

1. ask all the students in your math class - Convenience Sampling

2. choosing every 5th person on a list - Systematic Sampling.

3. pulling 50 names from a hat - Random Sampling.

4. randomly select two tables in the cafeteria and survey all the people at those two tables - Cluster Sampling.

5. dividing the population by Gender, and choosing 30 p - Stratified Sampling.

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Answer: 18(a)-89=217

Step-by-step explanation:

If a = 17 then you substitute/replace the a with the 17. Making 18(a) into 18(17). 18(17)= 306 - 89 = 217.

Hope this helped.

Answer:217

Step-by-step explanation:

putting the value of a in the equation.

18×17-89= 217

Joan delivered more than twice as many large loads of firewood as small loads on 2 of the last 10 days, which is option B.

In mathematics, a graph is a collection of vertices or nodes, along with edges or arcs, that connect pairs of these nodes. A graph can be used to represent a variety of mathematical and real-world phenomena, including social networks, transportation networks, and the structure of molecules.

To find the number of days Joan delivered more than twice as many large loads of firewood as small loads, we need to check each coordinate in the given set of points and see if the y-coordinate (large loads) is greater than twice the x-coordinate (small loads) multiplied by 2. Mathematically, we can write this as y > 2x.

Checking each coordinate, we have:

(1,4): y = 4, 2x = 2, y is not greater than 2x

(1,6): y = 6, 2x = 2, y is greater than 2x

(2,6): y = 6, 2x = 4, y is not greater than 2x

(3,5): y = 5, 2x = 6, y is not greater than 2x

(3,6): y = 6, 2x = 6, y is not greater than 2x

(3,8): y = 8, 2x = 6, y is greater than 2x

(4,4): y = 4, 2x = 8, y is not greater than 2x

(5,2): y = 2, 2x = 10, y is not greater than 2x

(6,3): y = 3, 2x = 12, y is not greater than 2x

(7,5): y = 5, 2x = 14, y is not greater than 2x

Thus, Joan delivered more than twice as many large loads of firewood as small loads on 2 of the last 10 days, which is option B.

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That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.

Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.

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The conversion of 2 liters into millimeters from the information regarding the muffins is 2000ml.

From the information, we are told to convert 2 litres into ml. This will be:

= 1000 × 2

= 2000ml

The number of eggs that will be bought to make 500 muffins will be:

= 500 × 2

= 1000 eggs.

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Answer:

Place the copies of rectangle over the plane without any gaps.

Step-by-step explanation:

Tiling is a technique to cover two dimensional region with copies of same shapes. There should be no gap in the area or region. Tiling helps to fill out the area completely. The copies of rectangle are placed on the area that is to be tiled to cover the area.

Answer:

Estimation and Confidence Intervals

Step-by-step explanation:

Just found it on a math website basically.

9514 1404 393

Answer:

  84 in

Step-by-step explanation:

The Pythagorean theorem is used to find the length 'b'.

  b^2 +12^2 = 37^2

  b = √(37^2 -12^2) = √1225 = 35

Then the perimeter is the sum of side lengths:

  P = a + b + c = 12 + 35 + 37

  P = 84 . . . inches

Answer:

in triangle

b=√(37²-12²)=35

perimeter of the triangle.=sum of all side

=37+12+35=84in

The number of small rooms reserved is 4.

The number of large rooms reserved is 8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Small rooms are denoted as S.

Large rooms are denoted as L.

Now,

We will make two equations.
L = 2S _____(1)

8L + 6S = 88 ______(2)

Putting (1) in (2) we get,

8L + 6S = 88

8 x (2S) + 6S = 88

16S + 6S = 88

22S = 88

S = 88/22

S = 8/2

S = 4

Now,

Putting S = 4 in (1) we get,

L = 2 x 4

L = 8

Thus,

The number of small rooms and large rooms reserved is 4 and 8.

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Answer:

( x + 5 )^2 + ( y - 3 )^2 = 2^2

Step-by-step explanation:

The equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2.

We know that h=-5 and k=3, so we just need to solve for r.

To do that, we need to envision the circle on a graph. If the edge of the circle touches the horizontal line y=1, how many units is it between the edge of the circle and the middle of the circle?

The middle of the circle is at y=3, and the edge is at y=1, so there are 2 units between the edge and the middle. Which means r=2.

so, ( x + 5 )^2 + ( y - 3 )^2 = 2^2.

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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The tip Maria would leave today is $1,89.

The first step is to determine the rate of the tip. In order to determine the rate, divide the tip on the lunch yesterday by the cost of the lunch yesterday.

Division is the process used to part a number into equal groups using another number. Division is used to determine the quotient of a number. The sign used to represent division is ÷.

Rate of the tip = tip / cost of the lunch

1.26 / 8.49 = 0.14841

The tip Maria would pay today today can be determined by multiplying the rate of the tip by the cost of the lunch today.

Tip paid today = cost of the lunch today x rate of tip

12.75 x 0.14841 = $1.89

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Answer: 2. They are congruent angles.

Step-by-step explanation:

      Angle 1 and angle 3 are vertical angles. In other words, they are "opposite" each other.

     Vertical angle pairs are congruent angles, meaning the answer to this question is;

              2. They are congruent angles.

Answer: They are congruent angles.

Step-by-step explanation: Complementary means the two angles equal 90°, supplementary angles are next to each other and equal 180° together, and it's obviously not a right angle, (angle that equals 90°) so we know they are congruent angles (this means that they are the same)

hope this helps!

please give brainliest!

Answer:

Step-by-step explanation:

the answer is 0.01

The base of the exponential form  is 10 and the power is -2 therefore the answer is 0.01 if the power was 2 the answer would have been 100

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