Use matrices A, B, C, and D. Find each scalar product, sum, or difference.

A-2B

The frequency distribution is calculated below

The dataset is given as

32,22,19,18,43,42,40,43,18,21,31,26,22,25,47,40,26,32,34,22,35,38,34,41,36,25,22,45,48,26,28,38,35,19,47,28,26,35,38,35.

To construct a frequency distribution using class intervals, we calculate the class width as follows:

Class width = Range / Number of intervals

So, we have

Class width = (48 - 18)/5 = 6

Now we can construct the frequency distribution table:

Class Interval Frequency

18 - 23            9

24 - 29            8

30 - 35            9

36 - 41             7

42 - 47            6

48 - 53             1

The class mark for each class can be calculated as:

Class mark = (Lower limit + Upper limit) / 2

For the class boundaries, we use the following formula

Lower boundary = Lower limit - 0.5

Upper boundary = Upper limit + 0.5

For the cumulative frequency of the distribution, we need to add up the frequencies of each class and all the preceding classes.

Lastly, for the relative frequency we divide each frequency by the total frequency (40)

Using the above as a guide, we have

Interval Frequency   Boundaries Mark CF

18 - 23            9              17.5 - 23.5        20.5        9

24 - 29            8             23.5 - 29.5       26.5        17

30 - 35            9              29.5 - 35.5      32.5        26

36 - 41             7              35.5 - 41.5        38.5       33

42 - 47            6              41.5 - 47.5         44.5       39

48 - 53             1              47.5 - 53.5        50.5       40

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F1 = 1167.35N and F2 = 1932.65N are the contact support forces on the beam

For the torques, let the axis be at support 2 and consider torques and the counterclockwise rotation is positive.

Let m = mass of athlete and M = mass of beam.

Thus, the equilibrium of torques will be:

Mg(1.96) - mg(0.54m) - F1(3.92) = 0

Substitute the values and solve for F1:

(250 * 10 * 1.96) - (60 * 10 * 0.54) - 3.92F1 = 0

3.92F1 = 4900 - 324

3.92F1 = 4576

F1 = 1167.35N

Note: The weight of the beam is acting at the center and the distance from center to axis at support 2 is 1.96m.

Balancing forces in the vertical direction, we have:

F1 + F2 - Mg − mg = 0

1167.35 + F2 - (250 * 10) − (60 * 10) = 0

1167.35 + F2 - 2500 - 600 = 0

F2 = 1932.65N

Note: upward forces (supports) are positive and downward forces are negative.

Thus, the contact support forces on the beam are F1 = 1167.35N and F2 = 1932.65N.

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The value of x for the given expression is x = 7 and x = 3.

A mathematical expression with the form ax² + bx + c, where a, b, and c are constants and x is a variable, is known as a quadratic expression. The graph of a quadratic expression can be represented by a U-shaped parabola. The y-intercept of the parabola is determined by the constant term c, whereas the coefficient a decides whether the parabola opens up or down.

The given expression is:

1.5x² - 15x + 31.5x = 0

The quadratic formula is given as:

x = -b ± √b² - 4ac / 2a

x = 15 ± √(15)² - 4(1.5)(31.5) / 2(1.5)

x = 15 ± 6 / 3

x = 15 + 6 / 3 and x = 15 - 6/3

x = 7 and x = 3

Hence, the value of x for the given expression is x = 7 and x = 3.

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The LCD we can use to simplify the equation is (2-r)(2+r) = 4 - r².

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

1. We can use the formula:

distance = rate × time

For the upstream journey:

distance = 4 miles

rate = 2 - r (since Dara is paddling against the current)

time = 4/(2-r) hours

For the downstream journey:

distance = 4 miles

rate = 2 + r (since Dara is paddling with the current)

time = 4/(2+r) hours

We can fill in the table as follows:

                       Distance (mi)    Avg Speed (mph)    Time (h)

With Current:            4                     2+r                    (4)/(2+r)

Against Current:       4                    2-r                       (4)/(2-r)

2. We know that the total time for the round trip is 6 hours:

4/(2-r) + 4/(2+r) = 6

3. Multiplying both sides by the LCD (2-r)(2+r), we get:

4(2+r) + 4(2-r) = 6(2-r)(2+r)

Simplifying, we get:

8 = 12 - 2r²

Rearranging, we get:

r² = 2

Taking the square root of both sides, we get:

r = ±√2

Since the current is flowing in one direction, we take the positive square root:

r = √2 ≈ 1.41 miles per hour

The LCD we can use to simplify the equation is (2-r)(2+r) = 4 - r².

4. To the nearest hundredth, the rate of the current is approximately 1.41 miles per hour, which is option B: About 1.15 miles per hour (rounded to two decimal places).

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hi

im pretty sure the answer is:

y= -x+4

The choice in the blank to make the statement true will be D. between $17 and $30)

Revenue = Price per book × Number of books sold = (745 - 30P) b

Since the store needs to sell at least 235 books, we have:

Revenue ≥ 235 × Price per book = 235(745 - 30P)

Simplifying this inequality, we get:

745b - 30Pb ≥ 235 × 745

P ≤ (745/30) - (235/b)

Since we want to find the minimum profit per book sold, we need to maximize the value of (235/b). The maximum value of (235/b) occurs when b is minimized

If we assume that the cost per book is constant, then the profit per book sold will increase as the price per book increases. Therefore, we can say that the minimum profit per book sold that would enable the store to sell at least 235 books is greater than $17.

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Answer:

25%

Step-by-step explanation:

$30-$24 =$6

$6×100

________ =25 percent

24

3.5

you plug in 1 in the x spot then solve

3.5 (1)

which then equals 3.5

that means that's what Y equals

The equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)

A relation is a function if it has only One y-value for each x-value.

A general form of a rational function is:

f(x) = (ax + b) / (cx + d)

To translate this function left 2 units, we need to replace x with x + 2. This gives us:

f(x + 2) = (a(x + 2) + b) / (c(x + 2) + d)

To shift this function up 1 unit, we need to add 1 to the numerator. This gives us:

f(x + 2) = (a(x + 2) + b + 1) / (c(x + 2) + d)

Therefore, the equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)

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The proof of |x−6|+x>3 is shown below.

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have  |x−6|+x>3.

Now, opening the absolute value

|x−6|+x>3

-(x- 6) + x >3

-x + 6 +x > 3

6 > 3

Thus, |x−6|+x>3 has been proved.

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The cοοrdinates οf the image if triangle ABC is A′(0, 1), B′(8, 1), C′(4, 5).

A triangle is a clοsed, twο-dimensiοnal geοmetric figure with three straight sides and three angles. It is οne οf the basic shapes in geοmetry.

A triangle is a pοlygοn with three edges and three vertices. It belοngs tο the basic geοmetric shapes. A triangle with vertices A, B, and C is knοwn as triangle ABC. Any three pοints in Euclidean geοmetry that are nοt cοllinear result in a distinct triangle and a distinct plane.

The cοοrdinates οf the image if triangle ABC is translated 8 units tο the right are:

A′(0, 1), B′(8, 1), C′(4, 5).

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Answer:

The inequality that represents the given statement is:

12 + w ≥ 45

Step-by-step explanation:

Answer: To find the distance between two points on a grid, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the coordinates of the middle school are (-5, 3), and the coordinates of the library are (2, 3). So we have:

distance = sqrt((2 - (-5))^2 + (3 - 3)^2)

distance = sqrt((2 + 5)^2 + 0^2)

distance = sqrt(7^2)

distance = 7

Therefore, the library is 7 miles away from the middle school.

Step-by-step explanation:

Answer:

Step-by-step explanation:

midpoint of AC

[tex]x=\frac{1-1}{2} =0\\y=\frac{4-4}{2} =0\\mid ~point~of~AC=(0,0)[/tex]

midpoint of BD

[tex]x=\frac{4-4}{2} =0\\y=\frac{-1+1}{2} =0\\midpoint ~of~BD=(0,0)[/tex]

so diagonals bisect each other.

The linear function that models the scatter plot is given as follows:

y = 7/8x + 6.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For the equation in this problem, we have that:

Hence the option that satisfies the sign of the slope and the intercept is given as follows:

y = 7/8x + 6.

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1) If the sales of McDonald's for one year is $650,000 and increasing at 4% annually (exponential growth), their sales after 5 years will be $790,824.

2) If the population of a school is 800 students and is increasing at a rate of 2% per year (exponential growth), after 6 years, the population will be 901.

3) With 70 northern sea otters growing at a rate of 18% annually (exponential growth), after 4 years, the population will be 136.

4) If the annual sales for a furniture stores are $375,000 and increasing (exponential growth) at a rate of 6.75% each year, the sales after 9 years will be $675,060.

5) If the population of Indiana showed an annual growth rate of 0.6% (exponential growth) and their population in 1999 was 273,000, the population in 2007 will be 286,383.

Exponential growth refers to the consistent increase in quantity over time and at a constant growth rate.

Exponential growths are modeled using the exponential growth function y = a(1+r)^t.

1. McDonalds:

y= a(1+r)^t

Where a = $650,000

r = 0.04 (4%)

t = 5 years

Sales after 5 years, y= a(1+r)^t

= $650,000 (1.04)^5

= $650,000 × 1.2166529

= $790,824

2) School Population:

Current population = 800

Annual increasing rate = 2%

a = 800

r = 2%

t = 6 years

Population after 6 years, y= a(1+r)^t

= 800(1.02)^6

=901

3) Northern Sea Otters:

a = 70

r = 18% or 0.18

t = 4 years

Population after 6 years, y= a(1+r)^t

= 70(1.18)^4

= 136

4) Furniture Stores:

a = $375,000

r = 6.75% or 0.0675

t = 9 years

Sales after 9 years, y = a(1+r)^t

= 375,000(1.0675)^9

= $675,060

5) Indiana Population:

a = 273,000

r = 0.6% or 0.006

t = 8 years (2007 - 1999)

Population after 8 years, y = a(1+r)^t

= 273,000(1.006)^8

= 286,383

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The loan's simple interest rate when the loan of $2,300 is taken will be 40.17%.

Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,

The formula for interest is written as,

I = (PRT)/100

The value of the principal is $2,300 and the amount generated in six months is $2,762. Then the percentage rate is calculated as,

($2,762 - $2,300) = [$2,300 x r x (6/12)] / 100

46,200 = 1,150r

r = 40.17%

The loan's simple interest rate when the loan of $2,300 is taken will be 40.17%.

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The domain and the range of h(n) are the set of whole numbers

Given that

h(n) is the number of houses

The possible values of n and h(n) are whole numbers

So, we have

Based on the patterns in the sequence, we have

h(n) = n

So, we have

h(5) = 5

h(11) = 11

In (b), we have

h(n) = n

Given that

s(n) is the number of segments

Based on the patterns in the sequence, we have

s(n) = 2n

So, we have

s(4) = 8

s(7) = 14

Above, we have

s(n) = 2n

The above equation is a proportional equation

This means that

The growth pattern of s(n) is linear, with a constant rate of change

Above, we have

s(n) = 2n

Hence, the explicit of s(n) is s(n) = 2n

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The area of the circular flower bed is approximately 78.54 square feet.

The circular flower bed's 10 foot diameter corresponds to a radius of 5 feet, or half the diameter. The area and circumference of the circular flower bed can be determined using the following data:

Circumference:

The formula for calculating a circle's circumference is:

C = 2πr

where the mathematical constant is roughly equivalent to 3.14159 and r is the circle's radius.

Using the values we were provided as replacements, we obtain:

C = 2π(5) \sC = 10π

We may calculate a rough estimate of the circumference using a calculator:

C ≈ 31.42 feet

As a result, the flower bed's circumference is approximately 31.42 feet.

Area:

The area of a circle is determined using the following formula:

A = πr²

Using the values we were provided as replacements, we obtain:

A = π(5)² \sA = 25π

We can calculate the area's value using a calculator as follows:

A area of 78.54 square feet.

Thus, the circumference of the flower bed is about 78.54 square feet.

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Therefore, 20 overs are bowled if 120 balls are bowled in cricket.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

If 6 balls are bowled in one over, then the number of overs can be determined by dividing the total number of balls by 6.

So, if 120 balls are bowled, the number of overs is:

Number of overs = 120 balls ÷ 6 balls/over

= 20 overs

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Answer:

To find the integer that describes the change in temperature, we can divide the total temperature drop by the number of hours:

32 ÷ 4 = 8

Therefore, the temperature dropped by 8 degrees Fahrenheit each hour. The integer that describes the change is -8, since the temperature decreased.

Answer: To find the integer that describes the change in temperature, we need to divide the total change in temperature (32° F) by the number of hours over which the temperature dropped (4 hours). This will give us the amount that the temperature dropped by each hour.

So, dividing 32 by 4, we get:

32 ÷ 4 = 8

Therefore, the temperature dropped by 8 degrees Fahrenheit each hour.

Step-by-step explanation:

Answer:

Chef will have 15 pieces of butter.

Step-by-step explanation:

Chef has 3 blocks of butter,

weight of each block = 1 pound

she cuts each block into fifth pieces,

3 / 1/5 = 15 pieces

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According to the solving Sam will spend $585.00 of the money he collects on cleaning materials.

%, a relative figure signifying hundredths of any amount. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage. Mathematical percentile is a related topic.

Sam collects $150.00 each day for 6 days, so the total amount he collects is:

$150.00/day x 6 days = $900.00

The shelter will use 35% of the money he collects to buy pet food. To find out how much money will be used to buy pet food, we can multiply the total amount Sam collects by 35% (or 0.35):

$900.00 x 0.35 = $315.00

So, $315.00 of the money that Sam collects will be used to buy pet food. To find out how much money will be used to buy cleaning supplies, we can subtract the amount used to buy pet food from the total amount collected:

$900.00 - $315.00 = $585.00

$585.00 of the money that Sam collects will be used to buy cleaning supplies.

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The optimal strategy would be to fit several models to the data using equation mathematical software or tools, and then assess the goodness of fit using statistical metrics like R-squared or Mean Squared Error.

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

The following exponential model could be a good fit for the data in the image:

[tex]f(x) = 7.5 * e^(0.1x) (0.1x)[/tex]

The data is assumed to develop exponentially with a base of e in this model, with a growth rate of 10% for each unit increase in x.

It is crucial to remember that this is only one potential model and that other exponential models with other parameters could also be able to satisfactorily match the data. The optimal strategy would be to fit several models to the data using mathematical software or tools, and then assess the goodness of fit using statistical metrics like R-squared or Mean Squared Error.

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The central angles for each category are approximately: Red: 100°, Blue: 150°, Green: 50° and Purple: 60°

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

To find the central angle of each category, we first need to calculate the total number of people:

Total = 20 + 30 + 10 + 12 = 72

Next, we can calculate the percentage of people who prefer each color:

Red: 20/72 = 0.278, or 27.8%

Blue: 30/72 = 0.417, or 41.7%

Green: 10/72 = 0.139, or 13.9%

Purple: 12/72 = 0.167, or 16.7%

To find the central angle for each category, we can multiply the percentage by 360°:

Red: 0.278 × 360° = 100.08°

Blue: 0.417 × 360° = 150.12°

Green: 0.139 × 360° = 50.04°

Purple: 0.167 × 360° = 60.48°

Therefore, the central angles for each category are approximately:

Red: 100°, Blue: 150°, Green: 50° and Purple: 60°

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Gregor scored 65 points on the Stats exam.

We can use the formula for calculating z-score:

z = (x - μ) / σ

Where

We are given that the population mean (μ) is 75 and the population standard deviation (σ) is 5.

We are also given that Gregor's z-score (z) is -2.

We can plug these values into the formula and solve for x:

-2 = (x - 75) / 5

Multiplying both sides by 5, we get:

-10 = x - 75

Adding 75 to both sides, we get:

x = 65

Hence, the score is 65 points

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Answer:
2. Total Hours= 38+5 = 43

Step-by-step explanation:

2. Wage at Normal rate80 *38 = 3040
Extra Sum of Money then Normal wage 3640-3040 = 600

Overtime rate 80*1.5= 120
Overtime hours 600/120=5

3. (a) 210/3 = 70km/hr
        140/(2.75*) = 50.91 km/hr
         *2.75= 2+ (45/60)
 

We can simplify this expression by multiplying the cube roots together:

³√5 × ³√5 × ³√5 = ³√(5 × 5 × 5)

Simplifying the product inside the cube root, we get:

³√(125)

Therefore, the cube root of 5 × 5 × 5 is equal to:

³√5׳√5׳√5 = ³√125 = 5