In a survey, the ratio of students who prefer popcorn to potato chips is 3 to 4. If the number of students surveyed who prefer popcorn is 360, how many preferred potato chips?

when we evaluate the given expression:

5*(x^2 - y)/z

in x = -3, y = 7 and z = 10 the value of the expression is 1.

Here we start with the expression:

5*(x^2 - y)/z

Where x, y, and z are called variables, meaning that can take any number we want.

And we want to evaluate this, given the values:

x = -3

y = 7

z = 10

Evaluating just means that we need to change the correspondent variables by the given numbers, if we do that in the given expression we will get:

5*( (-3)^2 - 7)/10

5*( 9 - 7)/10 = 5*(2)/10 = 10/10 = 1

So, we can see that when we evaluate the given expression in x = -3, y = 7 and z = 10 the value of the expression is 1.

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1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

Answer:

=−6x+1

Step-by-step explanation:

=3x+5+−7x+4+−2x+−8

=(3x+−7x+−2x)+(5+4+−8)

The solution is, B , is the correct answer is 10.0923.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

given that,

the equation is, 2.02 + 8.102 - 0.0297

now, we have to solve it, by addition & subtraction.

we know,

First

2.02+8.102=10.122

Then 10.122-0.0297=10.0923

i.e. we get,

2.02 + 8.102 - 0.0297

=10.122-0.0297

=10.0923.

Hence, The solution is, B , is the correct answer is 10.0923.

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To calculate the circumference of a circle, you can use the formula:

\(\displaystyle C=2\pi r\)

Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.

Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:

\(\displaystyle C=2\pi (8)\)

Simplifying the expression:

\(\displaystyle C=16\pi \)

Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.

Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The given equation is

First, we have to add 201 on each side.

The required value of points A and B is given by \(x_{A,\:B}=\frac{-12\pm \:2\sqrt{466}}{2*5}\).

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
The given equation is
y= -kx² - 4x + m
The above equation passes by points (4,-18) and (-2,30) So,
-18 = -k×4×4 - 4 × 4 + m
-18 = -16k - 16 + m
m - 16k = 2 - - - - - -(1)
Similarly,
m - 4k = 22 - - - - - - - (2)
Solving equations,
We get
k = 5/3 and m = 86/3
So the equation is given by,
y = -5/3x² - 4x + 86/3

Part (A)
Now, putting y = 0
5/3x² + 4x - 86/3 = 0
\(x_{A,\:B}=\frac{-12\pm \:2\sqrt{466}}{2*5}\)

Thus, the required value of points A and B is given by \(x_{A,\:B}=\frac{-12\pm \:2\sqrt{466}}{2*5}\).

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Answer:

Step-by-step explanation:

\(\text{The area of a circle is}\\ \\ A=\pi r^2\\ \\ \pi \approx 3.14,\ r=3ft\\ \\ A=3.14(3^2)\\ \\ A=3.14(9)\\ \\ A\approx 28.3ft^2\)

Answer: option D

Step-by-step explanation:

Given equation:

P = 6 w + 8 [eq1]

l=2w+4 [where l is length]

using eq1 we have:

6w=P-8

w=(P-8)/6

hence  option D

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The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

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Answer:

\( y = -\frac{4}{5}x + 2 \)

Step-by-step explanation:

Find slope (m) using two points (-5, 6) and (10, -6).

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6 - 6}{10 - (-5)} = \frac{-12}{15} = -\frac{4}{5} \)

m = -⅘

To find y-intercept (b), substitute x = -5, y = 6, and m = ⅘ into y = mx + b

6 = (-⅘)(-5) + b

6 = 4 + b

6 - 4 = b (subtraction property of equality)

b = 2

To write the equation, substitute m = -⅘, and b = 2 into y = mx + b

The equation of the line would be:

✅\( y = -\frac{4}{5}x + 2 \)

The equation of a line that goes through the points (-5,6) and (10,-6 in slope-intercept form is \(y = -\frac 45x + 2\)

A linear equation is an equation that have a constant rate of change or slope

From the question, we have the following ordered pairs

(x,y) = (-5,6) and (10,-6)

So, the slope (m) is then calculated as:

\(m =\frac{y_2 -y_1}{x_2 -x_1}\)

This gives

\(m =\frac{-6 - 6}{10 + 5}\)

Evaluate the differences

\(m =-\frac{12}{15}\)

Reduce the fraction

\(m =-\frac{4}{5}\)

The equation is then calculated as:

\(y = m(x -x_1) + y_1\)

So, we have:

\(y = -\frac 45(x + 5) + 6\)

Open the bracket

\(y = -\frac 45x -4 + 6\)

Evaluate the difference

\(y = -\frac 45x + 2\)

Hence, the equation in slope-intercept form is \(y = -\frac 45x + 2\)

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Answer:

x=-3

Step-by-step explanation:

You need to delete the root by ^2. First you need to leave it alone

\(\sqrt{x+7}-x=5\\\sqrt{x+7}=5-x\\(\sqrt{x+7} )^{2}=(5-x)^{2} \\x+7=25+10x+x^2\\x-10x=25+x^2-7\\-9x=18+x^2\\-x^2-9x-18=0\\-1(x^2+9x+18)=0\\x^2+9x+18=\frac{0}{-1}\\x^2+9x+18=0\\(x+6)(x+3)=0\\x+6=0 ===> x=-6\\x+3=0 ===> x=-3\\Checking\\\sqrt{-6+7}-(-6)=5===>\sqrt{1}+6=7\neq5 \\\\\sqrt{-3+7}-(-3)=5===>\sqrt{4}+3=5=5\\\\So \\x=-3\)

The value of \(m\angle2\) is \(132\) and the value of \(y\) is \(30\).

19) In this question given that,

\(m\angle1=x+10\)

\(m\angle2=3x+18\)

We have to find the value of \(m\angle2\).

As we know that the value of straight line is \(180^o\).

From the given figure we can see that

\(m\angle1+m\angle2=180^o\)

Now putting the value of \(m\angle1\) and \(m\angle2\) in the \(m\angle1+m\angle2=180^o\).

\(x+10+3x+18=180^o\)

Now simplifying the expression.

\(4x+28=180^o\)

Subtract \(28\) on both side

\(4x+28-28=180^o-28\)

\(4x=152\)

Divide by \(4\) on both side

\(\frac{4}{4}x=\frac{152}{4}\)

\(x=38\)

We have to find the value of \(m\angle2\).

As we know that \(m\angle2=3x+18\).

Now putting the value of \(x\) in the given value of \(m\angle2\).

\(m\angle2=3\times38+18\)

\(m\angle2=114+18\\\)

\(m\angle2=132\)

Hence, the value of \(m\angle2\) is \(132\).

20) In this question we have to find the value of \(y\).

As we know that the value of straight line is \(180^o\).

From the given figure we can see that

\(2y^o+(3y+30)^o=180^o\)

Now solving the expression to find the value of \(x\).

\(2y^o+3y^o+30^o=180^o\)

Simplifying the expression.

\(5y^o+30^o=180^o\)

Subtract \(30^o\) on both side

\(5y^o+30^o-30^o=180^o-30^o\)

Simplifying

\(5y^o=150^o\)

Divide by \(5\) on both side

\(\frac{5}{5}y^o=\frac{150^o}{5}\)

\(y^o=30^o\)

Hence, the value of \(y\) is \(30\).

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The english phrase "Seven less than four times a number" as an algebraic expression is 4x - 7

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

seven less than four times a number

Represent the number with x

So:

four times a number means 4x

So, we have

seven less than 4x

seven less than means - 7

So, we have

4x - 7

Hence, the english phrase as an algebraic expression is 4x - 7

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Complete question

write the english phrase as an algebraic expression. Let x represent the number

Seven less than four times a number

In a case whereby Anu was checking her emails and she casually told her friend siting next to her the ratio of unread emails in my inbox is ratio 4:1 where the total number of emails is 120  then the number of unread emails in her inbox is 96mails.

The concept that will be used here is ratio. An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

The total mails in her box is 120

The we can represent the unread mails  as 4x and read mails be 1x

This can be expressed as :

(4x+1x)=120mails

5x=120mails

x=120/5

x=24

This implies that the uread mails(4×24)

=96mails

Then the number of the read mail =(1×24)=24mails

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Answer:

The circumference of the drive wheel is 10 feet * 3.14 = 31.4 feet.

The circumference of the vat is 18 feet * 3.14 = 56.52 feet.

The total length of belt needed to go around the drive wheel and the vat is 31.4 + 56.52 = 87.92 feet.

Answer:

The equation is y = 2x² + 7x + 5

Step-by-step explanation:

In the quadratic equation y = ax² + bx + c

∵ The sum of the roots is \(\frac{-7}{2}\)

∵ The product of the roots is \(\frac{5}{2}\)

→ By using the rules above

∴ \(\frac{-b}{a}\) = \(\frac{-7}{2}\)

∴ \(\frac{c}{a}\) = \(\frac{5}{2}\)

→ Compare between them

∴ a = 2

∴ -b = -7 ⇒ divide both sides by -1

∴ b = 7

∴ c = 5

∵ The form of the quadratic function is y = ax² + bx + c

→ Substitute the values of a, b, and c in it

∴ y = 2x² + 7x + 5

∴ The equation is y = 2x² + 7x + 5

Answer:

1.92 litres

Step-by-step explanation:

1l=1000ml

1 jar=240ml=0.24l

8 jars= 240x8=1920ml=1.92l

Step-by-step explanation:

i = interest 3% for 30 years

This is a simple dynamical system for whom the the solutions are given as

\(S=R[\frac{(i+1)^n-1}{i}](i+1)\)

putting values we get

S=2000[\frac{(1.03)^{30}-1}{0.03}](1.03)

= $98005.35

withdrawal of money takes place from one year after last payment

To determine the result we use the present value formula of an annuity date

\(P = R\frac{1-(1+i)^{-n}}{i}{i+1}\)

we need to calculate R so putting the values and solving for R we get

R= $6542.2356

Answer:

Its C

Step-by-step explanation:

Let \(y=ab^x,\) as described in the problem statement. Plugging in \(x=2\) and \(x=5\) gives us the equations \(18=ab^2\) and \(60.75=ab^5.\) Since \(a,b\) are nonzero, we divide the second equation by the first to get \(\frac{27}{8}=b^3,\) which means that \(b=\frac{3}{2},\) after taking the cube root. Plugging this value for \(b\) into the first equation, we now have \(18=a(3/2)^2=\frac{9a}{4}.\) Solving gives \(a=8,\) and our desired exponential equation is \(\boxed{y=8\left(\frac{3}{2}\right)^x}.\)

(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.

To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).

Given:

f(x) = (4+x)(6+x)

g(x) = 1+x

Substituting -5 into the functions:

f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1

g(-5) = 1+(-5) = -4

Now, we can calculate (f/g)(-5):

(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4

Therefore, (f/g)(-5) equals 1/4.

Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.

To find the values that make the denominator zero, we solve the equation:

1 + x = 0

Subtracting 1 from both sides, we get:

x = -1

So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.

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Answer: y-intercept = y= -1/2x, point-slope = (y-4)=-1/2(x+8)

Step-by-step explanation:

Given that:

You know that in order for the number of girls to be significantly high, the probability must be:

In this case, you can determine that 58 girls in 100 births is a significantly high number, because:

And:

Notice that the probability for exactly 58 girls is less than 0.05.

Hence, the answer is:

The relevant probability is

so 58 girls in 100 births is a significantly high number because the relevant probability is less than 0.05.

The value of x from the logarithmic expression is 4 and -8

Logarithm are inverse of exponential function. Given the logarithmic function below;

log (X) + log (X+4)=log 32

Since positive will become multiplication, hence;

X(X+4) = 32

Expand

X^2 + 4x = 32

x^2 + 4x - 32 = 0
x^2 + 8x - 4x - 32 = 0
x(x + 8) - 4(x + 8) = 0
(x-4)(x+8) = 0
X = 4 and -8

Hence the value of x from the logarithmic expression is 4 and -8

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Answer:

WZ=4

Step-by-step explanation:

2/5=x/10

cross multiply

20=5x

x=4

Answer:

4, because 10/5 is 2, and then 2 * 2 is 4.

Answer:

bottom right

Step-by-step explanation:

It can be split in half by an axis and remain congrugent

Answer:

The first figure.

Step-by-step explanation:

Because its edges are identical

\(.\)