If he randomly chooses two students, one at a time, what is the probability that they are both girls?

It would be $9.95 x 3

For this case we have the following system of equations:

[tex]y = -6x + 9\\y = -3x + 3[/tex]

Equating the equations we have:

[tex]-6x + 9 = -3x + 3[/tex]

Adding 3x to both sides of the equation:

[tex]-6x + 3x + 9 = 3\\-3x + 9 = 3[/tex]

Subtracting 9 from both sides of the equation:

[tex]-3x = 3-9\\-3x = -6[/tex]

Dividing between -3 on both sides of the equation:

[tex]x = \frac {-6} {- 3}\\x = 2[/tex]

We look for the value of "and":

[tex]y = -3 (2) +3\\y = -6 + 3\\y = -3[/tex]

Thus, the solution of the system is (2, -3)

Answer:

(2, -3)

Answer:

-5

Step-by-step explanation:

Sometimes f(x) can be a little confusing. You never quite know where which number goes where.

Start with the first part

f(6) means that wherever you see an x on the right you put a 6.

So do this.

f(6) = (3/2)(6) +b =

equals what

(3/2) * 6 + b = 7    That's because f(6) = 7 Now just solve it

(18)/2 + b = 7

9 + b = 7

9 - 9 + b = 7 - 9

b = - 2

================

The entire equation is

y = (3/2)x - 2

===============

What happens when you are given

f(-2)

The - 2 means that wherever you see an x, let it be - 2

f(-2) = (3/2)(-2) - 2

f(-2) = -3 - 2

f(-2) = - 5

===============

You could think of f(x) being y. You will not go wrong doing that. y = f(x)

Answer:

This situation involves a combination as the team will be the same no matter what order the students are chosen in.

There are 1402410240 possibilities for the six student team

Step-by-step explanation:

Each time a student is chosen, they cannot be chosen again, so the number of available students decreases each time that one is chosen.

[tex]36*35*34*33*32*31=1402410240[/tex]

Answer:

B. 3 spaces to the right and 4 spaces up

Step-by-step explanation:

With both coordinates positive, we know that this point (3, 4) is in Quadrant I.

B. 3 spaces to the right and 4 spaces up

  is the correct choice.

Find the product of 7 and 2/3.  When multiplying fractions, first multiply the numerators, and then multiply the denominators.

7/1*2/3

7*2=14

1*3=3

14/3 cups of lemonade

Hope this helps!!

To find the total amount of lemonade consumed by 7 people drinking 2/3 cup each, calculate the amount per person, then multiply by the number of people for the total to get 14/3 or 4 2/3 as the total lemonade consumed.

Saul threw a party for 7 people. Each person drank 2/3 cup of lemonade.

To find the total amount of lemonade consumed:

Calculate the amount of lemonade each person drank: 2/3 cup/person.

Find the total amount for all 7 people: 7 people x 2/3 cup/person = 14/3 cups.

Therefore, the total amount of lemonade consumed is 14/3 or 4 2/3 cups

Answer:

D $50

Step-by-step explanation:

50x.10=5

5+50=55

For this case we propose a rule of three:

$ 50 -------------> 100%

x -----------------> 10%

Where the variable "x" represents the amount of the tip.

[tex]x = \frac {10 * 50} {100}\\x = 5[/tex]

So, the tip was 5 dollars.

If we subtract that amount to what Matt paid at the restaurant we will have the amount of the check before the tip.[tex]55-5 = 50[/tex]

ANswer:

Option D

Answer:

  31%

Step-by-step explanation:

Of the 6101 students on financial aid, 1879 are graduates. This fraction is ...

  1879/6101 × 100% ≈ 30.798% ≈ 31%

A is the correct answer but I did do it in my head so fair warning

Answer:

The answer is 225

Step-by-step explanation:

Setup a ratio saying 150:2/3

Next divide 2/3 by 1 to see how many times it can go into it which is 1 1/2

After that multiply 1 1/2 by 150

Answer is 225.

If a yogurt is 150 calories per 2/3 cup, how many calories is a full cup?

If we know that 150 calories are in 2/3 of a cup of yogurt, we can find out how many calories are in a full cup. If there are 150 calories in 2/3 of a cup, let’s first find out how many calories are in 1/3 of a cup by dividing 150 by 2.

150 ÷ 2 = 75 calories per 1/3 of a cup.

Now, we can multiply 75 by 3 to find out how many calories are in a full cup of yogurt.

75 x 3 = 225 calories per 1 cup of yogurt.

Therefore, there are 225 calories in 1 full cup of yogurt.

Answer:

[tex]7\frac{1}{2}[/tex] pages

Step-by-step explanation:

Method 1: Working with minutes

Let us assume that, Sandra's printer can print x pages in 1 minute.

Then we can write the equation:

[tex]x:1=5:\frac{2}{3}[/tex]

We can rewrite the ratios as a fraction.

[tex]\frac{x}{1}=\frac{5}{\frac{2}{3}}[/tex]

This simplifies to

[tex]x=\frac{15}{2}[/tex]

Or

[tex]x=7\frac{1}{2}[/tex]

Method 2: Working with seconds

If 5 pages corresponds to 40 seconds, then we can write: [tex]5:40[/tex]

Let y corresponds to 60 seconds (1 minutes).

Then:

[tex]y:60=5:40[/tex]

We rewrite as fraction:

[tex]\frac{y}{60}=\frac{5}{40}[/tex]

Multiply both sides by:

[tex]y=\frac{5}{40}\times 60[/tex]

[tex]y=\frac{300}{40}[/tex]

[tex]y=\frac{15}{2}[/tex]

[tex]y=7\frac{1}{2}[/tex]

Answer:

601 square inches

Step-by-step explanation:

The wrapping is needed to cover a cubed gift box that is 9 inches high is 616 sq inches.

Calculation:-

The area of gift wrapping needed is equal to the total surface area of the box.

area of a bow =115

 ∴ side of bow =[tex]\sqrt{115}[/tex]

                       = 10.72

total surface area = 115+115+10.72+10.72

                                  =616 sq ft.

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Answer:

  60.65

Step-by-step explanation:

The Law of Cosines can help you figure this out. Call the given sides "a" and "b" and the given angle "C". Then the third side, "c" will satisfy the relation ...

  c² = a² + b² -2ab·cos(C)

  = 33² +37² -2·33·37·cos(120°) = 3679

  c = √3679 ≈ 60.65476 ≈ 60.65

The length of the third side is about 60.65 units.

Final answer:

To create a 95% confidence interval for y when x=8, we need the sample mean and the standard deviation to calculate the Error Bound for the Mean (EBM). The CI is the sample mean ± EBM. Estimating the standard deviation of y involves using the sample standard deviation as an estimate or the known population standard deviation.

Explanation:

To develop a 95% confidence interval for the expected value of y when x = 8, we first need to know the sample mean (μ) and the standard deviation of the population or an estimate from the sample (known as σ or s, respectively). When we have these statistics, we can use the normal distribution to calculate the error bound for the mean (EBM), which is the margin of error. The confidence interval (CI) is then constructed as (sample mean - EBM, sample mean + EBM).

To estimate the standard deviation of an individual value of y when x = 8, which is essentially the standard deviation of the population (σ), you need to use the sample standard deviation (s) as an estimate unless the population standard deviation is known.

Remember, the EBM for the confidence interval depends on the chosen confidence level, the standard deviation, and the size of the sample. With a higher confidence level, you get a wider interval. In practice, the confidence interval gives us a range where we expect the true population parameter lies with a certain level of confidence, acknowledging there's still a small chance the true value lies outside of this range.

Answer:

24 and 12

Step-by-step explanation:

s=2d

s+d+52+4(3)=100

Answer:

son is 24 years old and daughter is 12 years old.

Step-by-step explanation:

Let the age of son = x years and age of the daughter = y years.

Now for equations

" The son is twice as old as the daughter "

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

"After 4 years sum of all their ages will be 100."

56 + (x+4) + (y+4) = 100

x + y + 64 = 100

x + y = 100 - 64 = 36 ----------(2)

Now we substitute the values of x from equation (1) to (2)

2y + y = 36

3y    = 36

y = 12

Now from equation (1)

x = 2 × 12

x = 24 years

Therefore, son is 24 years old and daughter is 12 years old.

Answer:

45.6 degrees

Step-by-step explanation:

First of all this needs to be recognized as a right triangle problem.  The angle of depression is the angle outside the triangle that is complementary to the vertex angle (the angle at the top).  Geometrically, this angle is congruent to the base angle inside the triangle (NOT the right angle).  So we need to find the measure of the base angle to find the measure of the angle of depression since they are the same.  A 500 foot cable describes the length of the cable, which serves as our hypotenuse.  The 350 is the base length of the triangle.  What we have then is a reference angle (x), the hypotenuse (500) and the side adjacent to the angle (350).  The ratio that relates the angle to the hypotenuse and the adjacent side is the cosine.  Setting up to find our angle gives us this equation:

[tex]cos\theta=\frac{350}{500}[/tex]

You find missing angles on your calculator by hitting the 2nd button and then the trig identity you want.  We want cosine, so hit 2nd then cos and you'll get cos^-1(     on your screen.  After the parenthesis, enter your 500/350 and hit enter.  This will give you your angle measure of 45.6.  Oh yeah!!! And make sure your calculator is in degree mode for this one!

The angle of depression  from the top of a 500-foot cable that runs from a tower to a point 350 feet away is 45.6 degrees

The situation forms a right angle triangle.

The length of the cable is the hypotenuse of the triangle formed.

The distance from the tower is the adjacent side of the right angle triangle.

Therefore, using trigonometric ratio,

let

∅ = angle of depression

cos ∅ = adjacent / hypotenuse

cos ∅ = 350 / 500

∅ = cos⁻¹ 0.7

∅ = 45.5729959992

∅ = 45.6°

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Answer:

  B.  17 days

Step-by-step explanation:

We want to know how many days it took, so it is convenient to define the variable x as the number of days. Then the number of square feet is (x+269) and the total cost is ...

  124.26x +3.92(x+269) = 3233.54

  128.18x + 1054.48 = 3233.54 . . . . . . . . simplify

  128.18x = 2179.06 . . . . . . . . . . . . . . . . . . subtract 1054.48

  2179.06/128.18 = x = 17 . . . . . . . . . . . . . divide by the coefficient of x

The renovation took 17 days.

For solving the problem, we first divide the question into two equations, and then substitute and solve the equations. The renovation took around 17 days that is option B)

This is a system of equations problems in Mathematics. Let's denote the number of days as 'd' and the square footage as 'f'. According to the problem, we know that:

1. Costs of materials + Costs of labor = Total spent

2. The square footage is 269 more than the number of days. So:

We can replace 'f' from the second equation with the first one: $3.92(d + 269) + $124.26d = $3233.54. Simplifying this, we get $1052.48 + $4.93d = $3233.54, and solving for 'd', we get 'd' approximately equal to 17 days, so the answer is (B).

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Answer:

4

Step-by-step explanation:

Since perpendicular lines have negative reciprocals, we have to find out the negative reciprocal of -1/4.

To get the negative reciprocal of -1/4, we have to switch the numbers in the numerator and denominator.

That becomes 4/-1, and then we have to remove the negative, which makes the final answer 4/1.

4/1 = 4

Therefore, the negative reciprocal of -1/4 is 4.

Hope this Helps!

The slope of the red perpendicular line is 4.

Slope of a straight line is defined as the inclination of the line with respect to the coordinate axis. The slope is also measure of the tangent of angle with which the line is inclined to the axis.

If the slope of a given straight line is m then the slope of its corresponding perpendicular line will be negative reciprocal of the given slope which is -(1/m).

It is said that the lines shown below are perpendicular. Also it is mentioned that the green line has a slope of -1/4 .

As the red line is perpendicular to the green line, thus its slope is negative reciprocal of the given slope of green line.

Slope = -(-4) = 4 .

Therefore, the slope of the red perpendicular line is 4.

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The critical value for a two-tailed test of h0: β1 = 0 at α = .05 in a simple regression with 22 observations is 4.35.

A critical value can be calculated for different types of hypothesis tests. The critical value of a particular test can be interpreted from the distribution of the test statistic and the significance level.

Test of significance of linear regression between x and y.

Null hypothesis: There is no significant linear relationship between x and y.

Alternative hypothesis: There is a significant linear relationship between x and y.

Test statistic:

F0 = Mean square due to regression/  mean squared error ~ F(1, n-2)

Critical value: [tex]F_{\alpha}(1, n-2) = F_{0.05}(1,20) = 4.35[/tex]

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Answer:

$14,450

Step-by-step explanation:

y=20,000(1-0.15)^x

Hope This Helps :D

Answer:

2

Step-by-step explanation:

The equation of a horizontal line is y = c

where c is the value of the y- coordinates the line passes through

Thus y = 3 ← is the equation of a horizontal line

Answer:

$42.5

Step-by-step explanation:

Answer:

42.5

Step-by-step explanation:

The expanded algebraic expression is x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64

How to expand the algebraic expression

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

(x - 2)⁶

This is a binomial expression that can be expanded using Pascal triangle

The power of the expression is 6

At n = 6, we have the following coefficients

1   6  16  20  16  6 1

So, we have

(x - 2)⁶ = 1 * x⁶ + 6 * x⁵ * (-2) + 16 * x⁴ * (-2)² + 20 * x³ * (-2)³ + 16 * x² * (-2)⁴ + 6 * x * (-2)⁵ + 1 * (-2)⁶

Expand the exponents

(x - 2)⁶ = x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64

Hence, the expanded algebraic expression is x⁶ - 12x⁵ + 64x⁴ - 160x³ + 256x² - 192x + 64

Answer:

B, C

Step-by-step explanation:

x-intercepts are when y=0.  f(x) has two x-intercepts at (1, 0) and (5, 0).  g(x) also has two x-intercepts; (-3, 0) and (5, 0).  So the first one is false, and the second one is true.

The maximum value of f(x) is 2.  The maximum value of g(x) is 4.  So the third one is true.

The y-intercept is the value of y when x=0.  So the y-intercept of f(x) is -1, and the y-intercept of g(x) is 3.  So the fourth one is false.

The statement which is true are f(x)​ and ​g(x)​ have a common x-intercept (B) and the maximum value of ​g(x)​ is greater than the maximum value of ​f(x)​ (C).

The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the x-axis. The value of y is equal to zero at x-intercept.

The function f(x) shown in the graph has two x intercept (5,0) and (1,0). The x intercept of g(x) are (-3, 0) and (5, 0).

Similarly, the y-intercept is the point on the coordinate at which a line, curve or plane intersect with the y-axis. The value of x is equal to zero at y-intercept.

The function f(x) shown in the graph has one y intercept (0,-1). The y intercept of g(x) is (0, 3). Here the maximum value of f(x) is 2 while g(x) is 4.

Thus, the statement which is true are f(x)​ and ​g(x)​ have a common x-intercept (B) and the maximum value of ​g(x)​ is greater than the maximum value of ​f(x)​ (C).

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Answer is A) Acute due to the lengths

Answer:

A

Step-by-step explanation:

Answer:

340 units squared

Step-by-step explanation:

in the trapezoid, there is a square and an isosceles triangle

find the area of the square: 17×(23-6) =17×17 =289

find area of the triangle: 17×6 /2 =51

add the two together: 289 +51 =340

Answer:

Line MN = 23 -3 -3 = 17

Middle Area = 17 * 17 = 289

Area of BOTH Ends = 17 * 3 = 51

TOTAL Area = 289 + 51 = 340

Step-by-step explanation:

(1, 22), (3, 18), (5,14), (6, 13), (8,5)

(1, 23), (3, 18), (5,14), (6, 11), (8,7)

you plot there on a graph. do you know how to place on a graph?

if not, the line going up and down is the x-axis and the line going side to side is the y-axis,

for example (4,7) it would be (x,y)

i really hope this helps :)

Answer:

B. qualitative

Step-by-step explanation:

Answer:

x-axis

Step-by-step explanation:

The asymptote is a straight line that the curve gets closer and closer to but never touches it.

The given exponential function is [tex]f(x)=3^x[/tex].

The given graph has a horizontal asymptote,

The equation of this horizontal asymptote is y=0.

This is also refers to as the x-axis.

Therefore the asymptote is the x-axis.

[tex]\displaystyle\int_2^8g(x)\,\mathrm dx=12[/tex]

[tex]\displaystyle\int_6^8g(x)\,\mathrm dx=-3[/tex]

Use the fact that integrals are additive on their intervals. Mathematically, if [tex]c\in[a,b][/tex], then

[tex]\displaystyle\int_a^bg(x)\,\mathrm dx=\int_a^cg(x)\,\mathrm dx+\int_c^bg(x)\,\mathrm dx[/tex]

So we have

[tex]\displaystyle2\int_2^6g(x)\,\mathrm dx=2\left(\int_2^8g(x)\,\mathrm dx-\int_6^8g(x)\,\mathrm dx\right)=2(12-(-3))=30[/tex]

The value of 2 times the integral from 2 to 6 of g(x) dx is 30.

The integral from 2 to 8 of g(x) dx = 12

The integral from 6 to 8 of g(x) dx = -3

We want to find:

2 times the integral from 2 to 6 of g(x) dx.

First, we'll use the properties of integrals:

The integral from 2 to 8 of g(x) dx = The integral from 2 to 6 of g(x) dx + The integral from 6 to 8 of g(x) dx.

We know that the integral from 2 to 8 of g(x) dx is 12, and the integral from 6 to 8 of g(x) dx is -3:

12 = The integral from 2 to 6 of g(x) dx - 3.

Next, we'll isolate the integral we're interested in:

The integral from 2 to 6 of g(x) dx = 12 + 3

= 15.

Finally, we'll multiply this result by 2:

2 * 15 = 30.

So, 2 times the integral from 2 to 6 of g(x) dx is 30. The correct answer is 30.

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