Evaluate the following expression.
(-6) 2
0 -36
0 -1/36
1/36
36

Answer:

106 + 130 + 149 + 192 + 118 + 168 =

863 total students

192 + 118 + 168 = 478 sophomores

P(sophomore) = 478/863

= about .5539

The probability that a randomly chosen student was a sophomore is approximately [tex]\(0.5538\)[/tex] .

To find the probability that a randomly chosen student was a sophomore, we need to calculate the total number of students and the total number of sophomores. Then we use the probability formula:

[tex]\[ P(\text{Sophomore}) = \frac{\text{Number of Sophomores}}{\text{Total Number of Students}} \][/tex]

Step-by-Step Calculation

1. Number of Freshmen:

- A's: 106

- B's: 130

- C's: 149

Total Freshmen:

[tex]\[ 106 + 130 + 149 = 385 \][/tex]

2. Number of Sophomores:

- A's: 192

- B's: 118

- C's: 168

Total Sophomores:

[tex]\[ 192 + 118 + 168 = 478 \][/tex]

3. Total Number of Students:

[tex]\[ 385 + 478 = 863 \][/tex]

4. Probability Calculation:

[tex]\[ P(\text{Sophomore}) = \frac{478}{863} \][/tex]

Let's calculate this probability and round to 4 decimal places:

[tex]\[ P(\text{Sophomore}) \approx \frac{478}{863} \approx 0.5538 \][/tex]

Answer:

a.  domain: {0, 2, 4}, range: {2, 6, 10}

Step-by-step explanation:

The given diagram depicts a function.

Let us define function:

A function is a mapping of inputs to output.

The left ones are the input of the function while the right side values are the output of the function.

The domain of the function is the set of values that are given as input to the function while the outputs are called range.

so, in the given question

The domain is: {0,2,4} and the range is: {2,6,10}

So, Option A is correct ..

Answer:

None of the functions are even.

Step-by-step explanation:

An even function is a function that appears unchanged if reflected upon the y axis.

An example of such function is the function y = x^2, which would not appear to have been changed if we were to reflect it across the y axis.

The core property of even functions is that for any even function f(x), the following condition is always true:

[tex]f(x) = f(-x)[/tex]

Thus, if we'd like to identify whether or not a function is even, we can check if that condition is true. If it is, the function is even.

Now that we know how to identify even functions, we can apply this method to all of the given options and identify whether or not they're even.

[tex]$\begin{enum}\begin{align}\text{1) }&f(x) = x^4-x\\&f(-x)= (-x)^4-(-x)=x^4+x\\\\&\implies f(x)\neq f(-x) \textbf{ Not even!}\\\\\text{2) }&f(x)=x^2-3x+2\\&f(-x)=(-x)^2-3(-x)+2=x^2+3x+2\\\\&\implies f(x)\neq f(-x) \textbf{ Not even!}\\\\\text{3) }&f(x)=x - 2\\&f(-x)=-x-2=-(x-2)\\\\&\implies f(x)\neq f(-x) \textbf{ Not even!}\\\\\text{4) }&f(x)=x\\&f(-x)=-x\\\\&\implies f(x)\neq f(-x) \textbf{ Not even!}\end{align}\end{enum}$[/tex]

None of the functions are even.

Step-by-step explanation:

The pointl-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have

[tex]m=\dfrac{1}{3},\ (-2,\ 1)\to x_1=-2,\ y_1=1[/tex]

Substitute:

[tex]y-1=\dfrac{1}{3}(x-(-2))[/tex]

[tex]y-1=\dfrac{1}{3}(x+2)[/tex] → the point-slope form

Convert to the slope-intercept form:

[tex]y-1=\dfrac{1}{3}(x+2)[/tex]           use the distributive property

[tex]y-1=\dfrac{1}{3}x+\dfrac{2}{3}[/tex]    add 1 = 3/3 to both sides

[tex]y=\dfrac{1}{3}x+\dfrac{5}{3}[/tex] → the slope-intercept form

Convert to the standard form:

[tex]y=\dfrac{1}{3}x+\dfrac{5}{3}[/tex]       multiply both sides by 3

[tex]3y=x+5[/tex]             subtract x from both sides

[tex]-x+3y=5[/tex]         change the signs

[tex]x-3y=-5[/tex] → the standard form

Convert to the general form:

[tex]x-3y=-5[/tex]         add 5 to both sides

[tex]x-3y+5=0[/tex] → the general form

Answer:

24

Step-by-step explanation:

x + x + 1 = 49

x + x = 2x = 48

x = 48 ÷ 2 = 24

Answer:

-2

Step-by-step explanation:

given 2 points on a line (x1, yx) and (x2,y2)

the formula for slope, m  = (y2-y1) / (x2-x1)

in this case,

x1 = 4, y1 = 3, x2 = 2, y2 = 7

Hence,

m  = (7-3) / (2-4) = 4 / -2 = -2

The slope of the line that contains the points (4, 3) and (2, 7) is -2.

To estimate the slope of the line that has the points (4,3) and (2,7)

Slope formula = y₂ - y₁ / x₂ - x₁

From the question, the points given are; (4,3) and (2,7)

So,  x₁ = 4, y₁ = 3, x₂ = 2 and y₂ = 7

Slope of the line = 7 - 3 /  2- 4

   = -2

The slope of the line is -2.

therefore, the correct answer is option D. -2.

To learn more about slope equation

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The function for the reflection across the y-axis can be written as: f(x,y)=(−x,y)

To reflect a point across the y-axis, we multiply its x-coordinate by -1. This means that if a point has coordinates (x,y), its reflection across the y-axis will have coordinates (−x,y).

We can use this to define a function for the reflection across the y-axis. Let f(x,y) be the function that reflects a point across the y-axis. Then, for any point (x,y), we have:

f(x,y)=(−x,y)

In other words, f(x,y) takes a point (x,y) and returns its reflection across the y-axis.

We can also write this function in terms of components. Let x and y be the coordinates of a point. Then, the reflection of this point across the y-axis has coordinates (−x,y). Therefore, the function for the reflection across the y-axis can be written as:

f(x,y)=(−x,y)

This function takes the coordinates of a point as input and returns the coordinates of its reflection across the y-axis as output.

Answer:

Step-by-step explanation:

let : f(x) = (x²-x+1)/x+1

limf(x) = lim(x²/x) = limx = - -∞   and limf(x) =+ ∞

x → - -∞                                               x → +∞

lim/f(x)/ = ∞       .......  x = 1 is the line asymptote

limf(x)/x = 1

 x → + -∞

lim (f(x) -x ) = -1 .....so y =x -1  is the second line asymptote

x → + -∞

x → 1  

Answer:

X = 5

Step-by-step explanation

Add or subtract the like terms and take numbers in one side . Do the solution part and get your answer.

Answer:

x=5

Step-by-step explanation:

combine like terms: -2x + 6x = 4x

add eight to the other side 4x - 8 = 12 ----> 4x = 20

then divide 4x = 20 -----> x = 5

Answer:

60.3

Step-by-step explanation:

opposite = 14

adjacent = 8

Tan(B) = opposite / adjacent

Tan(B) = 14 / 8

Tan(B) = 1.75

B = tan-1(1.75)

B = 60.3

Shari did not ride the bus to work.

Answer:

Shari did not ride the bus to work.

Step-by-step explanation:

Shari rode the bus to work. What is the negation of this statement?

Negation of a statement means putting a 'not' in the sentence, to make it overall negative.

So, here, the negation of the above given sentence is -

Shari did not ride the bus to work.

Answer:

[tex]-\underbrace{4\times4\times4\times4\times4\times4\times4\times4}_{8}=-4^8[/tex]

The guy below is correct!

Answer:

y=4x-3

Step-by-step explanation:

Answer: It would be y=4x-3

Step-by-step explanation:

The format this is under is called slope intercept and we have our slope which is 4 and the Y-Intercept of -3. So the equation for this is y=mx+b and m is your slope and b is your y intercept always. Hope this helps :)

Answer:

C) 360π

Step-by-step explanation:

Note the formula for the volume of Cylinder:

V(olume) = πr²h

π = 3.14

r = radius

h = height of the cylinder

V = (3.14)(6²)(10)

Simplify. First, solve the power, then multiply

V = (3.14)(36)(10)

V = 3.14 * 360

V = 1130.97

However your answer choices all shows π, so just back track a bit.

V = 360π is your answer, or C).

~

Answer:

360π

Step-by-step explanation:

formula for finding the volume of a cylinder is

πr²h

3.14 x 6² x 10 =1130.4

you take the answer you get and divide it to the pi to get the pie answer

1130.4/3.14 = 360π

      Hope this helps and if it does mark as branliest answer thx

Answer: A. True.

Step-by-step explanation:

Considering the given figure,

Given : ∠ABD ≅ ∠CBD

In Δ ABD and Δ CBD , we have

∠ABD ≅ ∠CBD             [given]

∠A≅ ∠C ≅90°             [right angle]

BD ≅ BD                      [Reflexive property]

⇒ Δ ABD ≅ Δ CBD

⇒ AD=CD           [By CPCTC]

CPCTC is property of congruent triangle that means that Congruent parts of congruent is congruent.

Hence, the correct answer is "True".

Answer: 8

Step-by-step explanation: We are dealing with a 30 60 90 triangle which has special side lengths that I will attach.

The short leg, in this case 4, is half of the hypotenuse in 30 60 90 triangles, therefore x = 8

Answer: Last option.

Step-by-step explanation:

You need to remember the following identity:

[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

In this case, we can observe that:

[tex]\alpha=30\°\\opposite=4\\hypotenuse=x[/tex]

Now you must substitute these values into  [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for the hypotenuse. Then:

[tex]sin(30\°)=\frac{4}{x}\\\\(x)(sin(30\°))=4\\\\x=\frac{4}{sin(30\°)}\\\\x=8[/tex]

Answer:

Part a) [tex]22.95+0.43x \leq 25[/tex]

Part b) The maximum number of candy bars that you can purchase is 4

Part c) The change would be [tex]\$0.33[/tex]

Step-by-step explanation:

Part a) Write an equation representing your shopping experience and use x for the number of candy bars

Let

x -----> the number of candy bars

we know that

The inequality that represent this problem is equal to

[tex]2(3.50)+2(2.75)+10.45+0.43x \leq 25[/tex]

[tex]22.95+0.43x \leq 25[/tex]

Part b) Solve the equation to determine how many candy bars can you purchase?

[tex]22.95+0.43x \leq 25[/tex]

Solve for x

Subtract 22.95 both sides

[tex]0.43x \leq 25-22.95[/tex]

[tex]0.43x \leq 2.05[/tex]

Divide by 0.43 both sides

[tex]x \leq 2.05/0.43[/tex]

[tex]x \leq 4.8[/tex]

The maximum number of candy bars that you can purchase is 4

Part c) How much change would you have left?

If you purchase 4 candy bars

then

[tex]22.95+0.43(4)=\$24.67[/tex]

therefore

[tex]\$25-\$24.67=\$0.33[/tex]

The equation representing the shopping experience is 3.50*2 + 2.75*2 + 10.45 + 0.43x = 25. The maximum number of candy bars you can purchase is 4. You would have $1.05 in change left.

a. The equation representing your shopping experience can be written as: 3.50*2 + 2.75*2 + 10.45 + 0.43x = 25, where x represents the number of candy bars.

b. To determine how many candy bars you can purchase, we need to solve the equation for x. First, combine like terms: 7 + 5.50 + 10.45 + 0.43x = 25. Subtracting 22.95 from both sides gives 0.43x = 2.05. Dividing both sides by 0.43 gives x ≈ 4.77. Since you can't purchase a fraction of a candy bar, the maximum number of candy bars you can buy is 4.

c. To find out how much change you would have left, subtract the total cost of items from your budget. The cost of items is 3.50*2 + 2.75*2 + 10.45 = 23.95. Subtracting this from your budget of $25 gives 25 - 23.95 = $1.05 in change.

Answer:  d) No solution.

Step-by-step explanation:

Given the equation:

 [tex]\frac{3}{2}=\frac{3x}{2x}-\frac{6}{5x}[/tex]

The denominator of the fractions cannot be zero, then, the Domain is:

[tex]x\neq 0[/tex]

Simplify:

 [tex]\frac{3}{2}=\frac{3}{2}-\frac{6}{5x}[/tex]

Subtract [tex]\frac{3}{2}[/tex] from both sides of the equation. Then you get:

[tex]\frac{3}{2}-(\frac{3}{2})=\frac{3}{2}-\frac{6}{5x}-(\frac{3}{2})\\\\0=-\frac{6}{5x}[/tex]

Multiply both sides of the equation by [tex]5x[/tex] ([tex]5x \neq 0[/tex]), then:

[tex](5x)(0)=(-\frac{6}{5x})(5x)[/tex]

Since the multiplication of [tex]5x[/tex] by zero is zero, you get:

 [tex]0=-6[/tex]  (This is FALSE)

Therefore, since there is no value for the variable that makes the equation true, the equation has NO SOLUTION.

Answer:

CORRECT ANSWER IS 1/5

Step-by-step explanation:

You're right. It is D All real numbers

There are no restrictions to the value of x

The domain of the given function is "All real numbers". So, option D is correct.

The given function is f(x) = 2×[tex](\frac{1}{10})^x[/tex]

Since this function has the variable x in the exponent, this is an exponential function.

So, its inputs are of all real numbers. And the domain is {x:x ∈ R}.

Thus, option D is true.

Learn more about the domain and range of a function here:

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Answer:

4

Step-by-step explanation:

16 cups = 4 quarts

Please mark brainliest and have a great day!

Answer:

4 quarts

Step-by-step explanation:

We are given that a container of fruit punch serves 16 cups and we are to find the number of quarts that are in a container.

For this, we will use the ratio method.

We know that, 1 cup = 0.25 quarts, so:

[tex] \frac { 1 cup } { 1 6 cups } = \frac { 0 . 2 5 quarts } { x } [/tex]

[tex] x = 1 6 \times 0 . 2 5 [/tex]

[tex]x=4 quarts[/tex]

Therefore, there are 4 quarts of fruit punch in the container.

Answer:

Step-by-step explanation:

[tex]y<0.5x+2\\\\\text{Put the coordinates of the points to the inequality, and check it:}\\\\(-3,\ 2)\\2<0.5(-3)+2\\2<-1.5+2\\2<0.5\qquad\bold{FALSE}\\\\(-2,\ 1)\\1<0.5(-2)+2\\1<-1+2\\1<1\qquad\bold{FALSE}\\\\(-1,\ -2)\\-2<0.5(-1)+2\\-2<-0.5+2\\-2<1.5\qquad\bold{CORRECT}\\\\(-1,\ 2)\\2<0.5(-1)+2\\2<-0.5+2\\2<1.5\qquad\bold{FALSE}\\\\(1,\ -2)\\-2<0.5(1)+2\\-2<0.5+2\\-2<2.5\qquad\bold{CORRECT}\\\\(1,\ 2)\\2<0.5(1)+2\\2<0.5+2\\2<2.5\qquad\bold{CORRECT}[/tex]

Answer:

option is c)

Step-by-step explanation:

the answer is option is c) PCM programming device.

The device shown in the figure shows is  PCM programming device.

PCM programming device is powertrain control module which is used as the mini computer in the cars.

It is used to improve the performance of car.

It is also used to fix the negative bug in the car which can effect the performance of the car.

Answer:

I believe the answer is C. 36

Step-by-step explanation:

Because a perfect square is everything that equals the same number

Ex: all of the sides of a square is 6, you can't do that with any of the other numbers.

Hope my answer has helped you!

Answer:

frequency of females watching action movie is 99

total participants 479

joint relative frequency of females and action movie = 99/479

your answer is D: divide 99 by 479

Step-by-step explanation:

Answer:

option d is right.

Step-by-step explanation:

Given is a table showing the list of males and females who attended two different movies.

Relative frequency of attending an action movie and being a female is required

First let us find joint frequency

This is represented by 2nd row I column i.e. 99

Relative frequency is obtained by dividing 99 by total of 479

Hence option d is right.

Answer:

SD = 17.1 miles

Step-by-step explanation:

In order to find the SD we have to calculate mean first

So,

[tex]Mean = \frac{sum}{no.\ of\ items} \\=\frac{25+40+35+25+40+60+75}{7}\\ =\frac{300}{7}\\ =42.86[/tex]

Now mean will be subtracted from each value and the answers will be squared

So,

X            X-mean          (X-mean)^2

25           -17.86            318.9796

40            -2.86             8.1796

35             -7.86            61.7796

25            -17.86            318.9796

40             -2.86             8.1796

60             17.14             293.7796

75              32.14           1032.9796

So,

Sum of squares = 2042.8572

As SD is the square root of variance

so,

Variance = Sum of squares / number of data values

=2042.8572/7

=291.84

Hence,

[tex]SD = \sqrt{Variance} =\sqrt{291.84} \\=17.083\\to\ the\ nearest\ tenth\\SD=17.1\ miles[/tex]   ..

Answer:

17.1

Step-by-step explanation:

The standard deviation of the miles Henry hiked is 17.1

4 goes exactly 22.25 times. That means that it goes in 22 FULL times

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

64,800 cars

Step-by-step explanation:

45 cars times 60 = 2700 cars per hour

2700 times 24 hours = 64,800 cars per day

64,800

Basically i put into the calculator 45 times 60 then that times 24 and thats how i got 64,800.

[tex]\bf \cfrac{x}{4x+x^2}\implies \cfrac{\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(4+x)}\implies \cfrac{1}{4+x}\qquad \{x|x\in \mathbb{R}, x\ne -4\}[/tex]

if you're wondering about the restriction of x ≠ -4, is due to that would make the fraction with a denominator of 0 and thus undefined.

To simplify the expression x/4x + x^2, we combine like terms and factor out a common factor.and This simplified expression cannot be reduced further.

To simplify the expression x/4x + x^2, we need to combine like terms. First, let's simplify the fraction by finding a common denominator. The common denominator for 4x and x is 4x. Therefore, the fraction becomes x/(4x) + x^2. Next, let's combine the fractions by adding the numerators and keeping the same denominator. This gives us (x + 4x^2)/(4x). Finally, we factor out the common factor x from the numerator, resulting in x(1 + 4x)/(4x). This simplified expression cannot be reduced further.

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Answer:

case a) [tex]x^{2}=3y[/tex] ----> open up

case b) [tex]x^{2}=-10y[/tex] ----> open down

case c) [tex]y^{2}=-2x[/tex] ----> open left

case d) [tex]y^{2}=6x[/tex] ----> open right

Step-by-step explanation:

we know that

1) The general equation of a vertical parabola is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

a is a coefficient

(h,k) is the vertex

If a>0 ----> the parabola open upward and the vertex is a minimum

If a<0 ----> the parabola open downward and the vertex is a maximum

2) The general equation of a horizontal parabola is equal to

[tex]x=a(y-k)^{2}+h[/tex]

where

a is a coefficient

(h,k) is the vertex

If a>0 ----> the parabola open to the right

If a<0 ----> the parabola open to the left

Verify each case

case a) we have

[tex]x^{2}=3y[/tex]

so

[tex]y=(1/3)x^{2}[/tex]

[tex]a=(1/3)[/tex]

so

[tex]a>0[/tex]

therefore

The parabola open up

case b) we have

[tex]x^{2}=-10y[/tex]

so

[tex]y=-(1/10)x^{2}[/tex]

[tex]a=-(1/10)[/tex]

[tex]a<0[/tex]

therefore

The parabola open down

case c) we have

[tex]y^{2}=-2x[/tex]

so

[tex]x=-(1/2)y^{2}[/tex]

[tex]a=-(1/2)[/tex]

[tex]a<0[/tex]

therefore

The parabola open to the left

case d) we have

[tex]y^{2}=6x[/tex]

so

[tex]x=(1/6)y^{2}[/tex]

[tex]a=(1/6)[/tex]

[tex]a>0[/tex]

therefore

The parabola open to the right