The mean mass of 8 men is 82.4 kg. What is the total mass of the 8 men?

To find the area of an obtuse triangle you have to multiply the base of the triangle by the vertical height and divide the result by 2 following the formula:

The base of the triangle is b= 7 miles and the height is h= 8 miles, using these lengths calculate the area as follows:

The area of the triangle is 28 square miles.

• Given that Martha baked 332 muffins,

• 332 / 12 = 27.67 boxes

• If she sold each box for $ 6 ; it will be

27*6 = $162

0.67 * 6 = 4.02

Total 162+4.02 = 166.02≈ $166

• She will make $166, ,

The polynomial function of least degree with only real coefficients will be;  y = x³ - 8 · x² + 22 · x - 20.

Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics.

The statement indicates that the polynomial has  real coefficients having zeros 3 and 1 - 32 and a lead coefficient of 1.

By algebra of quadratic equations, equations with real coefficients with complex roots are α + i β and α - i β. Then we get;

y = 1 · (x - 3) · (x - 3 - i) · (x - 3 + i)

y = (x - 3) · [x² - 3 · x - i · x - 3 · x + i · x + (3 + i) · (3 - i)]

y = (x - 3) · (x² - 6 · x + 9 - i²)

y = (x - 3) · (x² - 6 · x + 10)

y = x³ - 6 · x² + 10 · x - 2 · x² + 12 · x - 20

y = x³ - 8 · x² + 22 · x - 20

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Answer:

[tex]p(x)=x^3-5x^2+16x-30[/tex]

Step-by-step explanation:

Given information:

For any complex number  [tex]z = a+bi[/tex] , the complex conjugate of the number is defined as  [tex]z^*=a-bi[/tex].  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if p(x) is a polynomial with real coefficients, and (1 - 3i) is a root of p(x)=0, then its complex conjugate (1 + 3i) is also a root of p(x)=0.

Therefore, the polynomial in factored form is:

[tex]p(x)=a(x-3)(x-(1-3i))(x-(1+3i))[/tex]

As the leading coefficient is 1, then a = 1:

[tex]p(x)=(x-3)(x-(1-3i))(x-(1+3i))[/tex]

Expand the polynomial:

[tex]\implies p(x)=(x-3)(x-(1-3i))(x-(1+3i))[/tex]

[tex]\implies p(x)=(x-3)(x-1+3i)(x-1-3i)[/tex]

[tex]\implies p(x)=(x-3)(x^2-x-3xi-x+1+3i+3ix-3i-9i^2)[/tex]

[tex]\implies p(x)=(x-3)(x^2-x-x-3xi+3ix+1+3i-3i-9i^2)[/tex]

[tex]\implies p(x)=(x-3)(x^2-2x+1-9(-1))[/tex]

[tex]\implies p(x)=(x-3)(x^2-2x+10)[/tex]

[tex]\implies p(x)=x^3-2x^2+10x-3x^2+6x-30[/tex]

[tex]\implies p(x)=x^3-2x^2-3x^2+10x+6x-30[/tex]

[tex]\implies p(x)=x^3-5x^2+16x-30[/tex]

SOLUTION:

Step 1:

In this question, we have the following:

Step 2:

The details of the solution are as follows:

Parallelogram:

a) Two pairs of parallel sides: Yes

b) Only one pair of parallel sides: NO

c) Four right angles: NO

d) All sides congruentnt: NO

Rectangles:

a) Two pairs of parallel sides: Yes

b) Only one pair of parallel sides: NO

c) Four right angles: Yes

d) All sides congruentnt: NO

Trapezoid:

a) Two pairs of parallel sides: NO

b) Only one pair of parallel sides: NO

c) Four right angles: NO

d) All sides congruentnt: NO

Given:

The equation is given as,

The interval is given as,

The objective is to find the average rate of change.

Explanation:

The general formula to find the average rate of change is,

On plugging the function in the equation (1),

On further solving the above equation,

Hence, the average rate of change is 3.

Answer:

Explanation:

Part 1:4(5c + 3) and 9c + 7

The answer is NO.

Part 2: 10f – 10 and 2(8f - 5)

The answer is NO.

Part 3: 12g + 21 and 3(4g + 7)

Part 4: 6(4) – 6) and 24 - 36

Answer:

x = - [tex]\frac{5}{2}[/tex] , x = - [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

6x² + 23x + 20 = 0 ( factorise the left side )

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × 20 = 120 and sum = 23

the factors are + 8 and + 15

use these factors to split the x- term

6x² + 8x + 15x + 20 = 0 ( factor the first/second and third/fourth terms )

2x(3x + 4) + 5(3x + 4) = 0 ← factor out (3x + 4) from each term

(3x + 4)(2x + 5) = 0

equate each factor to zero and solve for x

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - [tex]\frac{5}{2}[/tex]

3x + 4 = 0 ⇒ 3x = - 4 ⇒ x = - [tex]\frac{4}{3}[/tex]

First, you have to locate the point (1,3)

Next, from that point, you have to locate the next one. To do that, you need the slope, which in this case is 3. So, from (1,3) you have to move 1 unit to the right and 3 units up, reaching the point (2, 6). Finally, you draw the line that passes through these two points

We need the formula that gives us the values of the sequence

where n is the value of the position

using the formula

as we can see the formula is the correct formula because we obtain the values of the sequence

The percent of increase in the cost of the perfume is 29.86%

What is percentage and how can it be calculated?
A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "%" is used to denote it. No dimension exists for percentages. Thus, it is referred to as a dimensionless number.
Mathematically,
Percent of increase = [(Final value - Initial value)/(Initial value)]×100

Given, the final value of the perfume at purchase = $41.49
Also, the initial value of the perfume as assessed = $31.95
Therefore using the formula established in the literature above,
Percentage increase = [(41.49 - 31.95)/31.95]×100 = 29.86%
Thus, the percent of increase in the cost of the perfume is 29.86%

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TheseGiven the set: {-18, -16, -14, -12, -10, -8, -6}

This is 7 numbers

Multiplies of -6 are:

This is 3 numbers

Therefore, the probability is given by:

So:

Answer: 3/7

The boy goes to school by bus for 1 3/4km, then he walks 1/3 km.

To determine the total distance he traveled you have to add both distances:

To solve this sum, add the fractions first and then add the result to the whole number:

- Add both fractions:

To add both fractions you have to express them using the same denominator first. A common multiple between the denominators "4" and "3" is "12". Multiply the first fraction by 3 and the second by 4 to express them as their equivalent fractions with denominator 12. Then proceed to add them:

The result is 13/12, as you can see the numerator is greater than the denominator, which indicates that this is an improper fraction, i.e. its value is greater than 1. You can write this fraction as a mixed number as follows:

- Solve the division:

The mixed number will have the whole number "1".

- To express the decimal value as a fraction, multiply it by 12

The result is the numerator of the fraction, and the denominator will be 12, so:

And the resulting mixed number is:

Finally, add the remaining whole number from the first sum to determine the distance between his house and the school:

The distance he traveled from home to school is 2 1/12 km.

Answer: B=3

Step-by-step explanation:

Given

P(A) = 0.52

Find

complement of P(A)

Explanation

As we know sum of probabilities is equal to one,

so ,

Final Answer

Therefore, the complement of P(A) = 0.48

The speed of the boat is given by the gradient of the line.

Given two points (x1,y1) and (x2,y2) on a graph, the gradient of the line that passes through the two points is given by

In this case,

the line passes through the points (0,0) and (2,2).

We can set (x1,x2) = (0,0) and (y1,y2) = (2,2)

Therefore,

Given that a body travels with speed, s, and in time, t, the distance travelled, d, is given by

In this case,

s = 1km/h, and t = 15hours

Therefore,

Therefore, the boat travelled a distance of 15km

The price per ticket can be calculated as follows;

The price per ticket for each is given as;

Red tickets = $0.75

Blue tickets = $0.80

Yellow tickets = $1.00

Therefore, 40 red tickets would cost

40 Red = 0.75 x 40

40 Red tickets = $30.00

Statement Problem: Mr. Bensoua buys 3 bags of Flaming Hot Cheetos for every 4 bags of Takis. He buys a total of 14 bags of chips. If the Flamin Hot Cheetos cost $2 per bag and the Takis cost $2.50 per bag, how much did Mr. Bensoua spend on all of the chips?

Solution:

When Mr. Bensoua buys 4 bags of Takis, he buys 3 bags of Flaming Hot Cheetos.

When he buys another 4 bags of Takis, he buys 3 bags of Flaming Hot Cheetos.

At the end, he buys 8 bags of Takis and 6 bags of Flaming Hot Cheetos and that makes it a total of 14 bags of chips.

The cost of Takis per bag is $2.50, the cost of 8 bags of Takis is;

The cost of Flaming Hot Cheetos per bag is $2., the cost of 6 bags of Takis is;

Hence, the total amount Mr. Bensoua spends is;

CORRECT ANSWER: $32

SOLUTION

Let the electric bill for September be x.

October's bill is $2.65 less than the September bill

This means that October's bill = x - 2.65

September + october bill = $174.65

That means that x + x - 2.65 = 174.65

Now let's find x which is september's bill

So September's bill is $88.65, now each student pays

So each student owe $29.55 for the month of September

y = (5/7)x - 13

The slope of this line is (5/7)

I a line has a slope m, then a line perpendicular would have a slope -1/m

In this case m= 5/7

So the perpendicular would be: -1/m = -7/5

Answer: -7/5

In decimal numbers: -1.4

Answer:

Is there a real question?

I can't seem to find it...

Step-by-step explanation:

Here, we want to complete the table

To do this, we consider points on the plot

From what we have;

We are told that a graph of an exponential function does not cross the x-axis and thus, y cannot be zero

When x =0, y = 1

When x = 1, y = 2

when x = 2, y = 4

The y-intercept is the value of y when x = 0; it is the point at which the graph crosses the y-axis

What we have here is that wehn x = 0, y = 1

Hence, 1 is the y-intercept

Now, let us take a look at the end behavior

We can obtain this from the graph;

As x moves towards infinity, the y value moves towards infinity too as evident from the upward curve of the graph

As x moves toward negative infinity, y moves closer to zero

Answer:

[tex] \sqrt{29} [/tex]

Answer:

3cm per day

54cm long

Explanation

Let x be yesenia's unit rate

If yesenia knits 21 centimeters of a scarf every week, then;

21 cm = 1 week (7 days)

To determine the amount for her knitting in a day, we can write;

x = 1 day

Divide both expressions

21/x = 7/1

Cross multiply

7 * x = 21

7x = 21

x = 21/7

x = 3

hence yesenia's unit rate is 3cm per day

- Recall that;

21 cm = 1 week (7 days)

Let y be the length of the scaf sfter 18 days, To get the length of the scarf, we can write;

y = 18days

Divide both resulting expressions;

21/y = 7/18

7y = 21 * 18

y = 3 * 18

y = 54cm

Hence the scarf will be 54cm longy

We are given that a cut of 6.5% is applied to a salary of $5050. To determine the amount that this amount will decrease we need to determine the product of the monthly salary by the percentage divided by 100, like this:

Solving the operations:

Therefore, the salary will decrease by $328.25.

We know that give any pair of real numbers A and B, the following statement will be true:

if, and only if

Now, if we factor a quadratic equation into two factors A and B, and use the fact we've just mentioned, we can then equal each factor to zero, solve for x and get the solutions to said quadratic equation.

Answer:

Kaitlin bought 48 yards of ribbon.

Step-by-step explanation:

Hey! Let's help you with your question here!

So, let's start by figuring out what we know and what we need to figure out. First of all, we started with $15 and ended with $4.92. We also know that the price of the ribbon is $0.21 per yard and we need to figure out how many yards of ribbon she purchased.

In order to figure this out, we first want to know the difference in the price between what we started and what we ended up with. So, we can subtract! It would look like this:

[tex]15-4.92=10.08[/tex]

So, we figured out that the difference in the price is $10.08, but how do we find out how many yards of ribbon Kaitlin bought? Well, since we know that it is $0.21 cents for a yard of ribbon, we can just take the difference in price and divide it by how much a ribbon cost for a yard of it. So it would look like this:

[tex]10.08/0.21=48[/tex]

We have a nice whole number and that's our answer! Therefore, Kaitlin bought 48 yards of ribbon.

Mathematical Way:

To do it in a more mathematical way, we can put it in the form of a formula. We know that the end total is $4.92 and the initial is $15. We also know that it's $0.21 cents per yard of ribbon but we don't know how many yards she bought. We can let the number of yards she bought represent x in the formula, so we have:

[tex]15=0.21x + 4.92[/tex]

This formula makes sense because we start with $15 at the beginning, so we want to add $4.92 from 0.21x because the end total is the remainder of how many yards Kaitlin bought. The process is essentially the same as the method above. If we were to solve the formula, it would give us the same answer:

[tex]15=0.21x+4.92[/tex]

[tex]15-4.92=0.21x[/tex] - Moving the 4.92 over to the left side, beginning to isolate x.

[tex]10.08=0.21x[/tex]  - Subtracting $4.92 from $15.

[tex]\frac{10.08}{0.21} =\frac{0.21x}{0.21}[/tex] - We divide by $0.21 to solve for x.

[tex]48=x[/tex]

And here, we get the exact same answer, 48 yards of ribbon.

Answer:

-3

Step-by-step explanation:

The slope of a line is the steepness of the line and is given by the formula below:

[tex]\boxed{\text{Slope} = \frac{y_1 - y_2}{x_1 - x_2} }[/tex], where [tex](x_1,y_1)[/tex] is the 1st coordinate while [tex](x_2,y_2)[/tex] is the 2nd coordinate

The two coordinates given are: (3, 5) and (4, 2)

Slope of line

[tex] = \frac{5 - 2}{3 - 4} [/tex]

[tex] = \frac{3}{ - 1} [/tex]

= -3

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Okay, here we heve this:

We need to combine like terms in the following equation:

The x-intercept happens when:

Therefore, the x-intercepts for that functions are:

Answ

We have a point (4,-9) it moves to (9,-14)

(4+x = 9, -9+y= -14)

x = 9-4

x = 5

y = -14 +9

y = -5

We are moving to the right 5 and down 5

We want to move the point (-9,-8) exactly the same way

(-9+5, -8-5)

(-4, -13)

(-4, -13)