8. Write the fraction from the number line that is greater than
4
but less than
5
18
3
8

10 pounds of barley should be used by the cook to mix in with the 35 quarts of the vegetable broth.

lets say we know that there is a mix of 2 pounds of barley into 7 quarts of vegetable broth, so we can say that,

2:7 is the ratio used for the mix

similarly we can say,

let the pounds of barley into 35 quarts of vegetable broth used be x

x:35 because its given that there are 35 quarts used in the vegetable soup so we need to find the value of 'x'

then, 2/7=x/35, that is pounds/quarts

then, x= 2/7 × 5

then, x = 2×5

therefore we know that x = 10

so we can say that there are 10 pounds of barley used in the mix by the cook along with the 35 quarts of vegetable broth.

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Answer: A

Step-by-step explanation:

First you add up the total prices of both cars

$67,000

Next find 8.875% of that and add to total price of both cars

Answer= $72,946.25

Answer:

Step-by-step explanation:

(a) Using de Moivre's Theorem, we have that:

z^n = cos(nθ) + i sin(nθ)

1/z^n = cos(-nθ) + i sin(-nθ)

So, we can find z^n + 1/z^n as:

z^n + 1/z^n = (cos(nθ) + i sin(nθ)) + (cos(-nθ) + i sin(-nθ)) = 2 cos(nθ)

And z^n - 1/z^n as:

z^n - 1/z^n = (cos(nθ) + i sin(nθ)) - (cos(-nθ) + i sin(-nθ)) = 2i sin(nθ)

(b) To express the equation 2z^4 - 5z^3 + 7z^2 - 5z + 2 = 0 in terms of cos(θ), we can substitute z with cos(θ) + i sin(θ):

2(cos(4θ) + i sin(4θ)) - 5(cos(3θ) + i sin(3θ)) + 7(cos(2θ) + i sin(2θ)) - 5(cos(θ) + i sin(θ)) + 2 = 0

Expanding the right hand side using the trigonometric identities, we get:

2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0

Note that the real and imaginary parts are separate, so we can simplify this equation to a real equation by equating the real and imaginary parts to 0.

(c) To solve the equation 2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0, we can use numerical methods or analytical methods such as the roots of unity.

Once the roots are found, they can be represented on an Argand diagram by plotting the real and imaginary parts of each root as a point in the complex plane. The magnitude of each point represents the magnitude of the complex number, and the argument (angle) represents the argument of the complex number.

Answer:

The area is 510 in^2.

Step-by-step explanation:

You need to find two areas. The area of the rectangle and then the area of the triangle above.

The formula for a rectangle's area is base x height. The base is 20 inches, and the height is 15 inches as shown on the side. So, you multiply 20 x 15, and the product is 300.

The formula for a triangle's height is 1/2(base x height). The 3 ft on the side is equal to 36 inches. To find the height of the triangle alone, you take the 36 inches and subtract by 15 inches, resulting in a difference of 21 inches. The base of the triangle is 20 inches, so multiply 20 x 21 = 420. Then multiply 420 by 1/2 (or divide by 2) and you get 210.

Now that we have the areas of both shapes, 210 + 300 = 510.

The area of the composite figure is 510in².

Check attached image 1.

a) For the rectangle, we have that the base is 20 inches, and that the height is 15 inches.

b) For the triangle, we see that the base is also 20 inches long, and the height must be the difference between the height of the rectangle and the total height of the composite figure.

First, convert the 3 feet to inches, because we need to have the same unit in order to make the calculations.

We know that 12 inches is 1 feet, therefore, to covert 3 feet to inches we do the following operation:

[tex]3feet*\frac{12inches}{1feet}[/tex]

The feet unit cancel out and the 3 is multiplied by 12, leaving us with the following result:

[tex]36inches[/tex]

Check attached image 2.

So the height of the triangle must  given by the following expression:

[tex]36in-15in=21in[/tex]

a) For the rectangle:

[tex]A=b*h[/tex]; where "b" is the length of the base and "h" is the height.

[tex]A=(20in)(15in)=300in^{2}.[/tex]

b) For the triangle:

[tex]A=\frac{b*h}{2} =\frac{(20in)(21in)}{2} =210in^{2} .[/tex]

So if the figured is formed by a triangle and a rectangle, the sum of the area of the 2 shaped equals the area of the composite figure. Let's add up the areas and calculate:

[tex]300in^{2} +210in^{2} =510in^{2} .[/tex]

The area of the composite figure is 510in².

Answer:

Step-by-step explanation: 34 quarts

1 Liter = approximately 1.06 quarts

so 34 x 1.06 is about 36.04 quarts

Answer: [tex]f^{-1} (x) = \sqrt{x} +1[/tex]

Step-by-step explanation:

[tex]y = x^2 - 2x + 1[/tex]

We know straight away the inverse will be a square root function. We also know that this inverse will have a restriction on the domain, (because you can only take the square root of a positive number).

So, to find the inverse, first we'll switch the x and y and solve for y:

[tex]x = y^2 - 2y +1[/tex]

[tex]x = (y-1)^2[/tex], (factor!)

±[tex]\sqrt{x} = y - 1[/tex]

So, the inverse "function" is:

[tex]f^-1(x)[/tex] = ±[tex]\sqrt{x} +1[/tex]

But theres an issue here!

If we tried graphing this, this "function" would not pass the vertical line test, so its not really a function at all!

We need to restrict the domain to only include the values that are above the x axis.

So our final inverse function is:

[tex]f^{-1} (x) = \sqrt{x} +1[/tex]

If the expression be x² - 3x - 4 then the factorize term be (x - 4)(x + 1).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

If the expression, ax³ + bx² - 5x + 2a is exactly divisible by x² - 3x - 4, then it is also divisible by both x - 4 and x + 1

If f(x) = ax³ + bx² - 5x + 2a, then f(4) = f(-1) = 0 by the factor theorem.

Hence, a(4)³ + b(4)² - 5(4) + 2a = 0 and

a(-1)³ + b(-1)² - 5(-1) + 2a = 0

⇒ so, 66a + 16b = 20 and a + b = -5

33a + 8b = 10     ...(1)

a + b = -5           ...(2)

simplifying the above (1) and (2), we get

33a + 8(-5 - a) = 10

i.e. 25a - 40 = 10

so, a = 2 ⇒ b = -7

Therefore, the function be f(x) = 2x³ - 7x² - 5x + 4

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The parameters that can help to raise the living standard are mentioned below.

Living standard is defined as the quality of housing, material comfort, and wealth experienced by an individual or group.

Given is that the standard of living is too low for many individuals in the united states.

The government can focus on the following factors -

Therefore, the parameters that can help to raise the living standard are mentioned above.

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Step-by-step explanation:

answer, verified answer

It would take Caro-line 3 hours to sketch 9 cartoon str-ips.

What is a ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

We are given that, Caro-line can sketch 6 car-toon str-ips in two hours.

And we are asked that how much time it would require for Caro-line to sketch 9 str-ips

Now let the time required be x

Hence, the ratio becomes

6/2=9/x

x= (9*2)/6

x= 3

Hence, It would take Caroline 3 hours to sketch 9 cartoon str-ips

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The possible equation of the parabola is y = (x - 5)^2 - 4

from the question, we have the following parameters that can be used in our computation:

Vertex = (5, -4)

The vertex form of a parabola is given by:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola.

We are given that the vertex of the parabola is (5,-4). Substituting these values into the vertex form, we get:

y = a(x - 5)^2 - 4

Let a = 1

So, we have

y = (x - 5)^2 - 4

Hnce, the possible equation is y = (x - 5)^2 - 4

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Answer: [tex]x-75\geq 420[/tex]

Step-by-step explanation:

... as it say...

Answer:

x -75 ⩾ 420

Step-by-step explanation:

we take away 75 from the value of X and compare it to 420 using the greater than or equal sign.

a. The possible range of values in this row is from 210 to 219, inclusive.

To see why, note that the stem value is 21, so each leaf represents a number that should be added to 21. The smallest possible value is when the leaf is 0, which gives 21 + 0 = 210. The largest possible value is when the leaf is 9, which gives 21 + 9 = 219.

b. There are 6 data values in this row.

c. The actual values in this row are 210, 211, 213, 215, 217, 219.

In statistics, a leaf is the last digit or digits of a data point in a stem-and-leaf plot. A stem-and-leaf plot is a graphical display of data that shows the distribution of values by separating each value into two parts: a stem, which consists of the leading digits of the value, and a leaf, which consists of the final digit or digits of the value. The stem values are listed in a vertical column, and the leaves are listed in a row next to the corresponding stem. This type of plot allows us to see the shape of the data and the distribution of values within it.

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Any line of the form:

y = (3/2)x + b

Is perpendicular to the given line.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is -1.

Here we want to find a line perpendicular to:

2x + 3y = 10

We can rewrite this as:

3y = 10 - 2x

y = (10/3) - (2/3)*x

Then the slope of the perpendicular line must be such that:

a*(-2/3) = -1

a = 3/2

Then any line of the form:

y = (3/2)*x + b

Is perpendicular to the given line.

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Andre borrowed 350,000 from the bank and the bank will charge him 6% interest per month. To calculate the amount he has to pay for one month of interest, we can use the following formula:

Interest = Capital * Interest rate

In this case, the capital is 350,000 and the interest rate is 6%. So, we can plug in the values:

Interest = 350,000 * 0.06

Interest = 21,000

Therefore, Andre has to pay 21,000 for one month of interest.

Answer:

B. x=5

Step-by-step explanation:

3x + 6 = 21

Subtract 6 from both sides.

3x = 15

Divide both sides by 3.

x = 5

Answer: B. X=5

Step-by-step explanation:

3x+6=21

subtract 6 on both sides

3x=15

divide by 3 on both sides

x=5

Answer:

C, I did the math

hope this helps

Answer:

Right, Isosceles

Step-by-step explanation:

The little square in the corner means its right angled, so a right triangle. This also means that it cannot be acute or obtuse.

The two hash marks shows two sides are the same. So it is isosceles. This also means it cannot be scalene or equilateral.

Answer:

Step-by-step explanation:

B

Answer:

(a) The probability distribution for the number of female students admitted can be calculated as follows:

P(0 female students) = (2C0) × (3C2) / (5C2) = (1) × (3) / (10) = 0.3

P(1 female student) = (2C1) × (3C1) / (5C2) = (2) × (3) / (10) = 0.6

P(2 female students) = (2C2) × (3C0) / (5C2) = (1) × (1) / (10) = 0.1

(b) The sampling distribution of the sample proportion of female students selected can be calculated as follows:

P(p = 0) = 0.3 (for 0 female students)

P(p = 1/2) = 0.6 (for 1 female student)

P(p = 1) = 0.1 (for 2 female students)

Note that the sampling distribution of the sample proportion is a discrete probability distribution with values of 0, 1/2, and 1, and corresponding probabilities 0.3, 0.6, and 0.1, respectively.

The exact value of cosine is 4/5

From the question, we have the following parameters that can be used in our computation:

(8,-6) be a point on the terminal side of an angle

Using the above as a guide, we have the following:

Cos(angle) = x/(√x² + y²)

In this case

x = 8 and y = -6

substitute the known values in the above equation, so, we have the following representation

Cos(angle) = 8/(√8² + (-6)²)

So, we have

Cos(angle) = 8/10

Simplify

Cos(angle) = 4/5

Hence, the value is 4/5

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The statement is true; Tests are weighed the most when determining a grade.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

Given in the question that:

Grade distribution

Quizzes, 30%

Homework 15%

Test, 30%

Classwork 25%

The total giving 100%.

A particular student scored the following;

87.9% on exams, 77.8% quiz, 90% Home work and 100%  on class participation

Calculating the percentages the student had for each

Exam total = 50 x 0.879 = 43.95% earned

Quiz = 30 x 0.778 = 23.34% earned

Home work = 15x 0.9 = 13.5% earned

Class participation = 5*1 = 5% earned

Total earned = 43.95+ 23.34 + 13.5+ 5 = 85.79%

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In the given equilateral triangle XYZ the relation which is true is WX = 2WZ. So option C is correct.

An equilateral triangle is a particular kind of triangle in which the lengths of the three sides are equal. These are a few of its main characteristics:

Congruent angles exist for all three: An equilateral triangle has 60 degrees for each angle.

The three parties all agree: The perimeter of an equilateral triangle is three times the length of any one side because each side is the same length.

For any side, the same line serves as the altitude, median, and angle bisector:

A line segment perpendicular to the other side and drawn from one vertex is the altitude. A line segment called the median is drawn from one vertex to the middle of the other side. The line segment known as the angle bisector divides the angle made up of two sides.

Given that,

The triangle XYZ,

It is known that,

All the sides in the equilateral triangle are equal,

So it can be written as,

⇒ WX = WY = XY

⇒ WY = 2WZ = 2ZY

Therefore,

⇒ WX = 2WZ

Hence, the correct relationship is WZ = 2WZ.

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Answer:

WX=2 times WZ

Step-by-step explanation:

i just took the quiz on apex

Answer:

The quotient is 3x^3 + 2x and the remainder is 0.

Step-by-step explanation:

Quotient: 3x³ + 2x

Remainder: -5

Answer:

3x^3 - 3x^2 + x - 1

x + 1 | 3x^4 + 2x^2 - 6x + 1

- (3x^4 + 3x^3)

---------------

-x^3 - 6x + 1

- (-x^3 - x^2)

-------------

-5x^2 - 6x + 1

-(-5x^2 - 5x)

------------

-x + 1

Therefore, the quotient is 3x^3 - 3x^2 + x - 1, and the remainder is -x + 1.

Answer:

they all have flat sides except for the cylinder

Step-by-step explanation:

Its okay we all are bad on some things

Answer:

2787

Step-by-step explanation:

add them all together

The option that is a factor of the function f(x) is C.

(2x - 3)

Because it becomes zero when x = 3/2.

We know that the function f(x) has zeros at x = -1/2 and x = 3/2.

And we want to see which ones of the given expressions can be a factor of the function.

If the function becomes zero at these values, then the factors need to become zero at one of these two values.

With that in mind, we can see that the correct option is C.

(2x - 3)

when x = 3/2 we get:

(2*3/2 - 3) = (3 - 3) = 0

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Answer:

15 cups

Step-by-step explanation:

So we have a ratio, butter:sugar. This ratio is given as 3:5, or 3 parts to 5 parts. Basically, every 3 cups of butter you use, you use 5 cups of sugar.

In order to calculate this, we simply need to divide the amount of butter being used by 3, and then multiply that by 5. This way, we are figuring out how much a singular "part" is in this situation, and then multiplying that by 5 for the 5 parts sugar.

9/3 = 3

3*5 = 15

Therefore, you have 15 cups of sugar.

The population at 0 hours is 1,000, at 4 hours is 1,000,024, and at 8 hours is  1,000,016.

To calculate how the number of bacteria changes over time, let's use the function provided and replace the variable t = time.

0 hours:

Population = 10^6 + (10^4)0 -(10^3)0^2

Population = 10^6 - 10^3

Population = 10^3 or 1,000

4 hours:

Population = 10^6 + (10^4)4 -(10^3)4^2

Population= 10^6 + 40,000 - 16,000

Population= 1,000,024

8 hours:

Population = 10^6 + (10^4)8 -(10^3)8^2

Population= 10^6 + 80,000 - 64,000

Population= 1,000,016

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