The names of 20 students in the class will be put in a hat. The class consists of 12 freshmen, 6 sophomores, and 2 juniors. If a sophomore was chosen there, how likely is it that another sophomore will get to play today?

Answer:

6 should be the correct answer!

Step-by-step explanation:

all of the work I did, you can ignore these:

1 x 2 = 2

2 x 2 = 4

2 x (2 - 1) = 2 x 1 = 2

2 + 4 = 6

Answer:

The answer is 6

Step-by-step explanation:

Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

9514 1404 393

Answer:

  y = 8

Step-by-step explanation:

If the variation is direct, any multiplier of the x-value will also multiply the y-value.

  old value × -1 = new value

  x: 4 × -1 = -4

  y: -8 × -1 = 8

The new value of y is 8.

The statement is given

"f varies directly as the square of x"

The mathematical model for the statement is

Here k is the constant of proportionality.

Answer:

Step-by-step explanation:

I can do this, but not the way it is set up here

3    - 4      1

-2      0     2

-1       4     -3    

Here's the solution you want. Magic squares usually include the diagonals as being equal, so naturally I assumed that this one too would require that. It is impossible, The number going in the center square has to be - 5 to neutralized the 2 and the 3. Not right. So the diagonals cannot equal 0.

Here is the solution I got for this problem

3     -1    - 2

-4    4      0

1      -3     2

Answer:A

Step-by-step explanation:

To find the rate of decay, we need to use the formula A(t) = P(0.82)^t, where A(t) is the amount after t years, P is the initial amount, and 0.82 is the decay factor.

The decay factor is equal to 1 minus the decay rate, so we can solve for the decay rate as follows:

0.82 = 1 - r

r = 1 - 0.82

r = 0.18

Therefore, the rate of decay is 18%, which corresponds to answer choice A.

Answer:

A

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

3 multiply by 5 (which is x) = 15+2

The value of function 3x + 2 at x = 5 will be 17.

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The function is,

⇒ 3x + 2

And, The value of x = 5

Now,

The value of the function 3x + 2 at x = 5 is find as;

The function is,

⇒ 3x + 2

Substitute x = 5 in above equation as;

⇒ 3x + 2

⇒ 3 × 5 + 2

⇒ 15 + 2

⇒ 17

Thus, The value of function 3x + 2 at x = 5 will be 17.

Learn more about the substitution method visit:

https://brainly.com/question/26094713

#SPJ6

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

The two angles are related in that they are supplementary angles

Supplementary angles would add tuo to 180 degrees according to the angle Theorem.

Adding the two given angles :

These angles are supplementary

The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.

Hence, the angles are related as they are supplementary angles .

Learn more on angles : https://brainly.com/question/11955149

#SPJ1

The standard form of polynomial is x^2 + 9x - 1/10

To write the equation in standard form, look at the degree of highest term and then rewrite the equation in decreasing order of degree i.e. from highest to lowest.

The given polynomial is

⇒ x^2 + 9x - 1/10

The standard form of the polynomial is

⇒ x^2 + 9x - 1/10

Learn more about polynomial here

https://brainly.com/question/15313798

#SPJ1

Answer:

Step-by-step explanation:

The system of equations with no solution is:

y + 3x = -7

4z - 2y = 10

The system of equations with exactly one solution is:

y = 6z+8

y = 6x-4

y = 3x + 2

2z-y = 5

y=-2z+8

The system of equations with infinitely many solutions is:

4z + y = 8

The sector area of the shaded portion would be 4π square centimeters if the central angle is 90 degrees.

To calculate the sector area of the shaded portion of a circle, we need to know the angle subtended by the sector at the center of the circle. Since no specific angle measure is given, let's assume that the shaded portion forms a sector with a central angle of θ degrees.

The formula to calculate the sector area is:

Sector Area = (θ/360) * π * r^2

where θ is the central angle and r is the radius of the circle.

Given that the radius of the circle is 4 cm, we can substitute the values into the formula:

Sector Area = (θ/360) * π * (4 cm)^2

Simplifying further:

Sector Area = (θ/360) * π * 16 cm^2

Now, without knowing the specific central angle measure, we cannot provide an exact numerical value for the sector area. However, we can still work with the formula and simplify it.

The sector area is directly proportional to the central angle. So, if we know the central angle in degrees, we can calculate the sector area by substituting the value of θ into the formula.

For example, if the central angle is 90 degrees, we can calculate the sector area as:

Sector Area = (90/360) * π * 16 cm^2

= (1/4) * π * 16 cm^2

= 4π cm^2

Therefore, the sector area of the shaded portion would be 4π square centimeters if the central angle is 90 degrees.

For more such questions on central angle visit:

https://brainly.com/question/29545058

#SPJ11

The answer is 1922, but round and you might get your answer.

Answer:

Meg will pay $10,596.25

Step-by-step explanation:

A=Prt

A=(8650)(.045)(5)= 1946.25

8650+1946.25=10596.25

A=$10,596.25

Answer:

10

Step-by-step explanation:

Change the fraction to a decimal:

2 1/2 = 2 + 1/2 = 2 + 0.5 = 2.5

Multiply:

4 x 2.5 = 10

10 is your answer.

~

Answer:I’m pretty sure it’s 90

Step-by-step explanation:

Answer:

tan 60=√3/t

t=√3/√3=1 is your answer

Let be "f" the number of sheet cakes that can be made using 75 cups of flour and "s" the number of sheet cakes that can be made using 75 cups of sugar.

According to the information given in the exercise, the bakery can make 1 sheet cake using 3 cups of flour and 2 cups of sugar.

Then, can set up that:

Solving for "f":

Set up the following proportion:

Solving for "s", you get:

Let be "c" the amount of cups of sugar the bakery needs to make 25 sheets cakes. You can find it as following:

Therefore, you can conclude that the amount of sugar left over will be:

The answer are:

• 25 sheet cakes.

• 25 cups of sugar will be left over.

The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.

To solve the given equations, we need to find the value of the function f(x) for specific values of x.

"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"

To find f(2), we can substitute x = 2 into the equation and solve for f(2).

Plugging in x = 2, we get:

f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)

Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.

"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"

To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).

Plugging in x = -3, we get:

f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2

Simplifying, we have:

f(-3) / 0 = 3(9) + 12 + 2

f(-3) / 0 = 27 + 12 + 2

f(-3) / 0 = 41

Additional information or context is needed to solve for f(-3).

For similar questions on denominator

https://brainly.com/question/20712359

#SPJ8

Answer: there you go :)

Car 1 consumes 30 gallons of gas.

Car 2 consumes 20 gallons of gas.

Step-by-step explanation:

Let x = gallons consumed by car 1

Let y = gallons consumed by car 2

We set up our equations:

35x+40y = 1850        eq1

x+y = 50                   eq2

Substituting eq 2 into eq 1,

35x+40(50-x) = 1850

35x+2000-40x = 1850

-5x+2000 = 1850

-5x = -150

  x = 30

Substitute value of x into eq 2.

x+y = 50

30+y = 50

     y = 20

Car 1 consumes 30 gallons of gas.

Car 2 consumes 20 gallons of gas.

\(\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=2x\\b=3\\r+1=4\Rightarrow r=3\\n=5\\T_4=\binom{5}{3}\cdot (2x)^{5-3}\cdot3^3\\T_4=\dfrac{5!}{3!2!}\cdot 4x^2\cdot27\\T_4=\dfrac{4\cdot5}{2}\cdot 4x^2\cdot27\\\\T_4=1080x^2\)

"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

To calculate the scores that are three standard deviations above and below the mean, we use the formula:

Lower limit = Mean - (Standard Deviation * 3)

Upper limit = Mean + (Standard Deviation * 3)

Given:

Mean = 269

Standard Deviation = 33

Using the formula, we can calculate the limits:

Lower limit = 269 - (33 * 3) = 269 - 99 = 170

Upper limit = 269 + (33 * 3) = 269 + 99 = 368

Therefore, the lower limit is 170 and the upper limit is 368.

To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.

Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.

For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:

Percentage = (1 - Probability) * 100

= (1 - 0.9972) * 100

= 0.0028 * 100

= 0.28%

Therefore, approximately 0.28% of the female students have scores below 302.

It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

For more questions on upper limits

https://brainly.com/question/6460579

#SPJ8

if 1 2 3 = 2

then 3 5 4 = 5

hope it helps:)

Answer:

1,560 cm²

Step-by-step explanation:

LA = (10+24+26) × 26

= 60×26

= 1,560

Answer:

4:18 and 6:27

Step-by-step explanation:

Answer:

Joe=32  Lou=40

Step-by-step explanation:

72-8=64

64/2=32

32+8=40

Joe=32

Lou=40

Hope this helped:)

Answer: So x + 2y = 0 is your answer

Step-by-step explanation:

if you look simplify all of these, you will get:

x - 2y = 0

-2y = -x

y = 1/2x  No

-x + 2y = 0

2y = x

y = 1/2x  No

x + 2y = 0

2y = -x

y = -1/2x Yes!

So x + 2y = 0 is your answer

Answer:So x + 2y = 0 is your answer

Step-by-step explanation:

if you look simplify all of these, you will get:

x - 2y = 0

-2y = -x

y = 1/2x  No

-x + 2y = 0

2y = x

y = 1/2x  No

x + 2y = 0

2y = -x

y = -1/2x Yes!

So x + 2y = 0 is your answer

Answer:

\(\begin{equation*}% \mbox{\large\( % - \left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-8\right)\)} %\end{equation*}\)

Step-by-step explanation:

sin²(x) = 1 - cos²(x)

So the expression sin²(x) + 7cosx +7 becomes

1 - cos²(x) + 7cos(x) + 7

Group like terms

\(\begin{equation*}% \mbox{\large\( %=-\cos ^2\left(x\right)+7\cos \left(x\right)+1+7 %\)} %\end{equation*}\)

\(\begin{equation*}% \mbox{\large\( %=-\cos ^2\left(x\right)+7\cos \left(x\right)+8 %\)} %\end{equation*}\)\(\begin{equation*}% \mbox{\large\( %=-\cos ^2\left(x\right)+7\cos \left(x\right)+1+7 %\)} %\end{equation*}\)\(\begin{equation*}% \mbox{\large\( %=7\cos \left(x\right)-\cos ^2\left(x\right)+8\)} %\end{equation}\)

\(\begin{equation*}% \mbox{\large\( %=-\left(\cos ^2\left(x\right)-7\cos \left(x\right)-8\right)\)} %\end{equation}\)

Let's deal with the expression in parenthesis
\(\begin{equation}% \mbox{\large\( %=\cos ^2\left(x\right)-7\cos \left(x\right)-8\)} %\end{equation}\)\(\begin{equation*}% \mbox{\large\( %=\cos ^2\left(x\right)-7\cos \left(x\right)-8)} %\end{equation}\)

\(\begin{equation*}% \mbox{\large\( %\cos^2(x) - 7\cos(x)-8\)} %\end{equation*}\\\\\)

This is of the form \(\begin{equation*}% \mbox{\large\( %ax^2 + bx + c\)} %\end{equation*}\)

with a = 1, b = -7 and c = -8

To factor this find two values u and v such that

\(\begin{equation*}% \mbox{\large\( %u\cdot v = -8, v + v = -7\)} %\end{equation*}\)

If we choose u = 1 and v = -8 we can satisfy the above relationship since
u · v = 1 (-8) = -8 and u + v = 1 +(-8) = -7

\(\displaysize {\textrm{Group\:into\:}\left(ax^2+ux\right)+\left(vx+c\right)}\)
\(\begin{equation*}% \mbox{\large\( %\left(\cos ^2\left(x\right)+\cos \left(x\right)\right)+\left(-8\cos \left(x\right)-8\right)\)} %\end{equation*}\)

\(\textrm{Factor\:out}\:\cos \left(x\right)\:\mathrm{from}\:\cos ^2\left(x\right)+\cos \left(x\right)\)

\(\begin{equation*}% \mbox{\large\( %=\cos \left(x\right)\left(\cos \left(x\right)+1\right)\)} %\end{equation*}\)

\(\textrm{Factor\:out}\:-8\:\mathrm{from}\:-8\cos \left(x\right)-8:\)

\(=-8\left(\cos \left(x\right)+1\right)\)

So
\(\begin{equation*}% \mbox{\large\( %\left(\cos ^2\left(x\right)+\cos \left(x\right)\right)+\left(-8\cos \left(x\right)-8\right)\)} %\end{equation*}\)

=  \(\begin{equation*}% \mbox{\large\( %\cos \left(x\right)\left(\cos \left(x\right)+1\right)-8\left(\cos \left(x\right)+1\right)\)} %\end{equation*}\)

\(\textrm{Factor\:out\:common\:term\:}\cos \left(x\right)+1\)
\(\begin{equation*}% \mbox{\large\( %=\left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-8\right)\)} %\end{equation*}\)

Since this was the term in the parenthesis with a leading negative sign, add the negative sign to get

\(\begin{equation*}% \mbox{\large\( %1-\cos ^2\left(x\right)+7\cos \left(x\right)+7\)} %\end{equation*}\) \(\begin{equation*}% \mbox{\large\( %= - \left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-8\right)\)} %\end{equation*}\)\(\begin{equation*}% \mbox{\large\( %= - \left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-8\right)\)} %\end{equation*}\\\)

Answer: \(\begin{equation*}% \mbox{\large\( % - \left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-8\right)\)} %\end{equation*}\)

SOLUTION

Given the information on the question tab;

Final answer:

Each dark chocolate truffle costs $3.13

The base of Triangle B is 1 inches.

Given,

Triangle A has a height of 8 inches

and base of Triangle is 2 inches

Let's Find the Area of Triangle A

We know that the formula of Area of Triangle

Area of Triangle = \(\frac{1}{2}\) × b × h

where, b is the base and h is the height of triangle.

Plug the values of base and height in above formula.

Area of Triangle A  = \(\frac{1}{2}\) × 2 × 8

Hence, Area of Triangle A is 8 sq. inches

In this question, Some part is missing that is:

Triangle A is similar to Triangle B

Now, For Triangle B is given:

Triangle B has a height of 16 inches

and, to find the base of the triangle.

We know, Area of Triangle A is 8 sq. inches.

Area of Triangle B =  \(\frac{1}{2}\) × b × h

8 =  \(\frac{1}{2}\) × b × 16

8 = 8b

b = 1 inches

Hence, The base of Triangle B is 1 inches.

Learn more about Area of Triangle at:

https://brainly.com/question/19305981

#SPJ1