A car goes 15 miles on a gallon of gas when it is driven at 50 miles per hour. When the car is driven at 60 miles per hour it only goes 80% as far. How many gallons of gas will it take to travel 120 miles driving at 60 miles per hour?

ANSWER

The missing probability is 0.15

EXPLANATION

From the given probability distribution table.

P(1)=0.30

P(2)=0.40

P(3)=0.15

P(4)=?

For for this to represent a probability distribution function,then the sum of all the probabilities must be equal to 1.

P(1)+P(2)+P(3)+P(4)=1

This implies that,

0.30+0.40+0.15+P(4)=1

0.85+P(4)=1

P(4)=1-0.85

P(4)=0.15

Therefore the missing probability is 0.15

Answer:

Step-by-step explanation:

[tex](f\circ f)(x)=f\bigg(f(x)\bigg)\\\\f\bigg(f(3)\bigg)\\\\\text{Calculate}\ f(3):\\\\f(3)=3^2-3=9-3=6\\\\f\bigg(f(3)\bigg)=f(6)=6^2-6=36-6=30[/tex]

Answer:

#2

Step-by-step explanation:

Step functions are functions (meaning that the x-values do not match with a y-value more than once) that increase or decrease at the same time. #1 is another type of piecewise function, while #3 is a choice to fool you.

Hope I helped and please give me brainliest!

Answer:

2

Step-by-step explanation:

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}\\(x_ {1}, y_ {1}) :( 2,2)\\(x_ {2}, y_ {2}) :( 5,5)[/tex]

Substituting the points:

[tex]d = \sqrt {(5-2) ^ 2 + (5-2) ^ 2}\\d = \sqrt {(3) ^ 2 + (3) ^ 2}\\d = \sqrt {9 + 9}\\d = \sqrt {18}\\d = 3 \sqrt {2}[/tex]

ANswer:

[tex]d = 3 \sqrt {2}[/tex]

The answer is B, if you substitute x with 0 1 or 2 the result will always be 0

ANSWER

[tex]f(x) ={x}^{3} - 3 {x}^{2} + 2x[/tex]

EXPLANATION

If the polynomial function has zeros at 0,1 and 2

Then the polynomial can be written in factored form as:

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

We expand to get,

[tex]f(x) =x({x}^{2} - 3x + 2)[/tex]

Expand further to obtain:

[tex]f(x) ={x}^{3} - 3 {x}^{2} + 2x[/tex]

The polynomial in descending powers of x is said to be in standard form .

The last choice is correct.

Answer:

One solution

Step-by-step explanation:

Expanding the equation, we get

-2w-12-6w=4w+12

Subtracting 4w from both sides, we get

-12w-12=12

Now adding 12 to both sides,

-12w=24

Solving for w, we get

w=-2

So there is only one solution to the equation.

Answer:

To the right we have 62.6 while to the left we have 49.4

Step-by-step explanation:

A normal distribution is usually symmetric with respect to the mean. The mean of the distribution is also the mode as well as the median.

The general formula for points that lie n standard deviations away from the mean on either sides of the mean is given by the formula;

mean ± n(σ)

where σ is the standard deviation of the distribution;

Two standards deviations from the mean imply that n = 2;

56 ± 2(3.3)

56 ± 6.6

To the right we have 62.6 while to the left we have 49.4

Answer:

Construct a box plot to represent the ages of the actors in a play. Step 1: Arrange the numbers in order from lowest (on the left) to highest. 24 18 30 26 24 33 32 44 25 28

Step-by-step explanation:

Actors Ages: 18, 24, 24, 25, 26, 28, 30, 32, 33, 44

Step 2: 18

Step 3: 44

Step 4: 27

Step 5: 24

Step 6: 32

Answer:

(D same size and same shape)​

Step-by-step explanation:

Congruent means the same size and shape.

Similar means the same shape, but not necessarily the same size

Answer:

The answer is : (D same size and same shape)​

Step-by-step explanation:

Two shapes or figures are called congruent, when they are identical. When the angles are equal in degrees, they are called congruent angles and when sides are congruent, this means they have the same length.Two polygons are congruent if they have the same size and shape or if their corresponding sides and angles are equal.

Therefore, option D is correct.

Answer:

Step-by-step explanation:

The domain and range of these two functions are identical.

The domain is "all real numbers."

The range is also "all real numbers."

Answer:

Domain of both given functions is the set of real numbers.

Range of both given functions is the set of real numbers.

Step-by-step explanation:

Given functions are

f(x)=5x  

And g(x)= 5x

First, we solve for f(x)

F(x)=5x

Put x=0 then we get

f(x)=0

Now , put x=1  then we get

f(x)= [tex]5\times1=5[/tex]

Put x=2 then we get

f(x)=[tex]5\times2=10[/tex]

Therefore, we can see domain of function f(x) can be set of real numbers and range of function f(x)  can be set of real numbers .Because the function is define at every value of x.

Both function are the same

Therefore , the domain of both function is same and range of both functions is same .

Hence,  the domain of  both functions is the set of real numbers and range of both functions is the set of real numbers.

Answer:

The correct answer is  last option

Cos(55) = 11/x

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = opposite side/Adjacent side

From the figure we can see a right angled triangle, with one angle is 55 degree, one side is 11 and hypotenuse is x

To find the correct trigonometric formula

Here we have adjacent side of angle 55

Cos 55 = Adjacent side/Hypotenuse

Cos 55 = 11/x

Therefore the correct answer is last option

Answer:

The measure of angle x is [tex]64.4\°[/tex]

Step-by-step explanation:

To find the measure of angle X, apply the law of cosines

The law of cosines states that

[tex]c^{2}=a^{2}+b^{2}-2(a)(b)cos(C)[/tex]

In  this problem we have

[tex]a=19\ cm[/tex]

[tex]b=25\ cm[/tex]

[tex]c=24\ cm[/tex]

[tex]C=x\°[/tex]

substitute

[tex]24^{2}=19^{2}+25^{2}-2(19)(25)cos(C)[/tex]

[tex]576=986-950cos(C)[/tex]

[tex]cos(C)=(986-576)/950[/tex]

[tex]C=arccos[(986-576)/950]=64.4\°[/tex]

Therefore

The measure of angle x is [tex]64.4\°[/tex]

Answer:

7.04 trillion = 7.04 x 10¹²

Step-by-step explanation:

Answer: 7.04 x 10^12

Step-by-step explanation:

Just took the test :)

Answer:

8%

Step-by-step explanation:

Answer:

Part 1) The x-intercept is the point (-5,0)

Par 2) The y-intercept is the point (0,-17.5)

Step-by-step explanation:

step 1

Find the x-intercept

we know that

The x-intercept is the value of x when the value of y is equal to zero

Observing the table

For x=-5, y=0

therefore

The x-intercept is the point (-5,0)

step 2

Find the equation of the line

Find the slope m

we have

(-7,7) and (-5,0)

[tex]m=(0-7)/(-5+7)\\ m=-3.5[/tex]

Find the equation of the line into point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-3.5[/tex]

point (-5,0)

substitute

[tex]y-0=-3.5(x+5)[/tex]

[tex]y=-3.5(x+5)[/tex]

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

[tex]y=-3.5(0+5)[/tex]

[tex]y=-17.5[/tex]

therefore

The y-intercept is the point (0,-17.5)

Answer:

The mean is: 85

Step-by-step explanation:

First you need to add everything up :

1 * 2 = 2

2 * 1 = 2

3 * 3 = 9

4 * 5 = 20

5 * 4 = 20

6 * 3 = 18

7 * 2 = 14

(I multiplyed them all first because i was fast than doing 4+4+4+4+4 because its the same as 4 * 5)

then add them all up 2+2+9+20+20+18+14=85

Answer:

The median is: 4

Step-by-step explanation:

Get the data in NUMERICAL ORDER (smallest to largest), then eliminate the extremes until we're at the middle. (basically chopping off the end till you get to the middle)  Therfore The answer would be 4.

Answer:

The mode would be: 4

Step-by-step explanation:

The mode is Get the data in NUMERICAL ORDER, and see which value is the most frequent (we can have more than one mode).

Answer:

25%

Step-by-step explanation:

firs you do 5 divided by 20 because there are 20 x's. this will = 0.25

0.25 = 25%

I hope I get brainiest. Sorry for taking forever. Have a nice day!

Answer: -5, and 5

Step-by-step explanation: an absolute value can only be positive. So -5 and 5 are the only answers that will give you 5.

Answer:

B and D.

Step-by-step explanation:

–15

–5

0

5

15

Absolute Value  Assignment

Finding Absolute Value

Answer:

500 Elm: Cafe

524 Elm: Grocery

538 Elm: Boutique

544 Elm: Dance studio

Step-by-step explanation:

We know that the dance studio has the highest address, so 544.

For the others let's examine the possibilities.

The boutique is between the cafe and the studio, that means the following are possible:

Boutique can be at either 524 or 538, cannot be at 500 (since cafe has to be on the its left.

Cafe can be 500 or 524, cannot be 538 since boutique has to be between cafe and studio.

The grocery is between the cafe and boutique. Meaning the grocery cannot be 500 nor 538, since it has to be in the middle of the 3 remaining businesses.  So, grocery is at 524.

Meaning the Cage is at 500 and the boutique is at 538.

Answer:

B

Step-by-step explanation:

On edge

Answer:

False

Step-by-step explanation:

The equation x = c represents the equation of a vertical line parallel to the y- axis.

The equation y = c represents the equation of a horizontal line parallel to the x- axis

In both cases c is a constant

Hence x = - 2 is not parallel to the x- axis

Answer:

c

Step-by-step explanation:

the formula is [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1}}[/tex]

When we plug that in we get [tex]\frac{-3-2}{6- (-4)} = \frac{-5}{10} = -\frac{1}{2}[/tex]

Hope this helps!

The slope of a line perpendicular to another is the negative reciprocal of the other line.

In this case, the slope of this line is just 0. It'll be better to think of it as instead of 0, something like 0/1, or 0/2, which are equivalent to 0 but work better with the explanation. I'm just going to use 0/1

Therefore, when you take the negative reciprocal of the slope of 0/1, then you end up with -1/0 as the slope of line n. When you divide by 0, the answer is always undefined. Therefore, the line has an undefined slope.

Another way to think about this is by thinking of Line m as a horizontal line. A line with a slope of 0 is just a horizontal line. Perpendicular lines are lines that meet at 90 degree angles. Therefore, the line that would meet with line m, line n, would be a vertical line. And since vertical lines have an undefined slope, line n would have an undefined slope.

Hope this helped!

Answer:

B. The mean study time of students in Class B is less than students in Class A.

Step-by-step explanation:

First step is to calculate the mean and median for both classes.

Class A: 2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5

sorted data set: 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8

total: 96

# of students: 20

Mean/average: 96 / 20 = 4.8

Median: By looking at the sorted data set, we see that the 10th value is the first 5, so median = 5

Class B: 3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6

Sorted data set: 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7

Total: 80

# students: 20

Mean/average: 80 / 20 = 4

Median: By looking at the sorted data set, we see that the 10th value is the first 4, so median = 4

So, we can see that the mean study time for group B was less than the students of class A.  Answer B.

The system of equations to represent the concession stand sales situation is 3H + 4B = 184 for the total sales, and H = B + 10 for the quantity relationship, where H is the number of hot dogs sold, and B is the number of burgers sold.

To represent this situation with a system of equations, let's denote the number of hot dogs sold as H and the number of burgers sold as B. According to the problem, hot dogs are sold at $3 each and burgers at $4 each, and the stand made $184 in total. Also, we are told that 10 more hot dogs than burgers were sold at the game.

We can create two equations to represent this scenario:

These two equations form the system that can be solved to find the number of hot dogs and burgers sold.

Answer:

y = 5x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 5, hence

y = 5x + c

The line passes through the y- axis at (0, 3) ⇒ c = 3

y = 5x + 3 ← equation of line

Answer:  [tex]h=8[/tex]

Step-by-step explanation:

To find the value of "h" you need to:

Remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Distribute the positive sign that is outside the parentheses to  eliminate the parentheses:

[tex]4h + 9 = 3 -h + 46[/tex]

Add like terms on the righ side of the equation:

 [tex]4h + 9 = -h + 49[/tex]

Add h to both sides:

[tex]4h + 9+h = -h + 49+h[/tex]

[tex]5h + 9 =49[/tex]

Subtract 9 from both sides:

[tex]5h + 9-9=49-9[/tex]

[tex]5h =40[/tex]

Divide both sides by 5:

[tex]\frac{5h}{5}=\frac{40}{5}\\\\h=8[/tex]

Answer:

AB=BC therefore ABCD is a Rhombus

Step-by-step explanation:

we have

[tex]A(0,0), B(4,5), C(8,0), D(4,-5)[/tex]

Using a graphing tool

see the attached figure

AB=BC

The figure is a flat shape with 4 equal straight sides. All sides have equal length. Opposite sides are parallel, and opposite angles are equal

therefore

The figure is a Rhombus

Answer:

360°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 4, hence

sum of interior angles = 180° × 2 = 360°

Answer:

Step-by-step explanation:

If f(x)=x²

g(x) = (3x)²

because : g(0)=0 and g(1)= (3×1)² =3 passes  through A(1;3) and O(0;0).

Answer: g(x) = 3x²

Step-by-step explanation:

Since we have given that

[tex]f(x)=x^2[/tex]

So, the function of g(x) would be

[tex]g(x)=ax^2[/tex]

since we have given that

(1,3) on g(x means (x,ax)

Here, x = 1.

So, ax = 3

which implies that a = 3.

So, g(x) would look like

[tex]g(x)=3x^2[/tex]

and the graph of g(x) is compressed.

The slope is [tex]\frac{3}{4}[/tex] and x-intercept is [tex]\frac{8}{3}[/tex] and y-intercept is -2 of the linear equation [tex]y=\frac{3}{4}x-2[/tex].

Slope intercept form is one of the forms used to calculate the equation of a straight line.

i.e. y = mx + b

Here, m= slope and y = intercept ,

We have,

[tex]y=\frac{3}{4}x-2[/tex]

Now,

Compare the given equation with the slope intercept form,

i.e.

y = mx + b

[tex]y=\frac{3}{4}x-2[/tex],

So,

Slope [tex](m)=\frac{3}{4}[/tex],

Now,

To know, the x-intercept,

put y = 0,

i.e.

[tex]0=\frac{3}{4}x-2[/tex]

⇒[tex]\frac{3}{4}x=2[/tex]

We get,

[tex]x=\frac{8}{3}[/tex],

Now,

To know, the y-intercept,

put x = 0,

i.e.

[tex]y=\frac{3}{4}*0-2[/tex]

We get,

y = -2

Hence, we can say that the slope is [tex]\frac{3}{4}[/tex] and x-intercept is [tex]\frac{8}{3}[/tex] and y-intercept is -2 of the linear equation [tex]y=\frac{3}{4}x-2[/tex].

To know more about Slope intercept forms click here

https://brainly.com/question/9682526

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Final answer:

The slope of the equation y = 3/4x - 2 is 3/4, and the y-intercept is -2.

Explanation:

The linear equation given is y = 3/4x - 2. In this equation, the coefficient of x represents the slope and the constant term represents the y-intercept. Therefore, the slope of the line is 3/4 and the y-intercept is -2. The slope indicates that for each unit increase in x, y increases by 3/4, while the y-intercept tells us that when x is 0, the value of y is -2, indicating the point at which the line crosses the y-axis.