Divide total miles driven by number of gallons of gas used.
243 miles / 9 gallons = 27 miles per gallon
324 miles / 12 gallons = 27 miles per gallon.
She can drive 27 miles on one gallon of gas.
A group of friends were working on a student film. They spent $270 on props which was 45% of their total budget. What was the total budget for their student film?
Answer:
The total budget for their student film is $600
Step-by-step explanation:
Here, we want to calculate the total budget of a group of students on a movie given the amount the spent on props.
Since we do not know this amount, we can call it x
Now, 45% of this x was the amount spent on props and it is equal to $270
Mathematically;
45/100 * x = 270
45x = 100 * 270
x = (100 * 270)/45
x = 600
A food truck sells tacos, burritos, and drinks.
Let event A = A customer buys a taco.
Let event B = A customer buys a drink.
What does P(A or B) = 0.45 mean in terms of this problem?
A. The probability that a customer buys a taco, a drink, or both is
45%.
B. Buying a taco and buying a drink are mutually exclusive events.
C. The probability that a customer buys neither a taco nor a drink is
45%.
D. The probability that a customer buys both a taco and a drink is
45%.
Answer:
The probability that a customer buys a taco, a drink, or both is 45%.
Step-by-step explanation:
apeeex
P(A or B) = 0.45 mean in terms of this problem will be the probability that a customer buys a taco, a drink, or both is 45%. Then the correct option is A.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The value of the probability of an event must lie between the interval of [0, 1].
A food truck sells tacos, burritos, and drinks.
Let event A = A customer buys a taco.
Let event B = A customer buys a drink
P(A or B) = 0.45 mean in terms of this problem will be the probability that a customer buys a taco, a drink, or both is 45%. Then the correct option is A.
More about the probability link is given below.
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Perform the indicated operation.
a/7 x b/2
a) ab
b) 9ab/14
c) ab/14
Answer:
c) ab/14
Step-by-step explanation:
[tex]\frac{a}{7} * \frac{b}{2} =\frac{ab}{14}[/tex]
multipling fractions rule is to multiply nominators and denominators separately
Solve for x. Enter the solutions from least to greatest.
x2 – X – 12 = 0
Answer:
[tex]x=-3,4[/tex]
Step-by-step explanation:
Factorise in order to reveal factors.
[tex]x^2-x-12=0\\(x-4)(x+3)=0[/tex]
The weather forecaster says that there is an 80% chance of rain today. Which statement describes the likelihood that it will rain today?
The graph of a sinusoidal function has a minimum point at (0,3)(0,3) and then intersects its midline at (5π,5)
Write the formula of the function, where x is entered in radians.
Answer: F(x) = 2*sin(x/10 +(3/2)*pi) + 5
Step-by-step explanation:
The information that we have is that:
We have a minimum at (0, 3)
the midline is at (5*pi, 5)
This is a sinusoidal function, so we can write one generic one as:
F(x) = A*sin(c*x + p) + B.
where A and B are constants, c is the frequency and p is a phase
First, the minimum of the sine function is when sin(x) = -1, and this happens at (3/2)*pi
We know that this minimum is at x = 0.
sin(c*0 + p) = -1
Then p = 3/2*pi.
So our function is:
F(x) = A*sin(c*x +(3/2)*pi) + B.
Now, we know that F(0) = 3, so:
3 = A*sin(c*0 +(3/2)*pi) + B = -A + B.
now we can use the other hint, the midpoint of the sine function is when sin(x) = 0, and this happens at x = 0 and x = pi, particularlly as we here have a phase of 3/2*pi, we should find x = 2*pi.
then:
c*5*pi + (3/2)*pi = 2*pi
c*5 + 3/2 = 2
c*5 = 2 - 3/2 = 1/2
C = 1/2*5 = 1/10
So our function is
F(x) = A*sin(x/10 +(3/2)*pi) + B
and we know that when x = 5*pi, F(5*pi) = 5, so:
5 = F(x) = A*sin(5*pi/10 +(3/2)*pi) + B
5 = B
and we aready knew that:
- A + B = 3
-A + 5 = 3
A = 5 - 3 = 2
So our equation is:
F(x) = 2*sin(x/10 +(3/2)*pi) + 5
Answer:
the correct answer is
[tex]f(x) = - 2 \cos( \frac{1}{10}x ) + 5[/tex]
PLEASE HElP ASAP 10 PTS, BRAINLEST ANSWER
Indicate the equation of the given line in standard form. Show all of your work for full credit.The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).
Answer:
is there more in the question
y=-3x+6 y=9 What is the solutions to the system of equations?
Answer:
(- 1, 9 )
Step-by-step explanation:
One of the equations gives y = 9, the y- value
To find the value of x, substitute y = - 3x + 6 , that is
- 3x + 6 = 9 ( subtract 6 from both sides )
- 3x = 3 ( divide both sides by - 3 )
x = - 1
Solution is (- 1, 9 )
A movie theater sells popcorn in bags that open to form similar prisms, as shown. The large bag has a volume of 576 cubic inches. What is the volume of the small bag?
Answer:
Can't be determined
Explanation:It can't be determined since there are two sides that you need to find out.
Answer:
432 cubic inches
Step-by-step explanation:
the ratio of the small bag to large bags side lengths is 12/16
if you want to find the small bags volume, set the ratios equal
we know the large bag is 576 cubic inches so the small bag volume is x
12/16 = x/576
cross multiply
16x= 6912
divide by 16
x= 432
The body and head of a fox measure 19 ⅘ inches, and its tail measures 10 ⅘ inches. Whatis the total length of the fox?
Answer:
The total length of the fox is 30 3/5 inches
Step-by-step explanation:
Here, we are interested in calculating the total length of a fox, given the length of its head and body and also the length of its tail.
Mathematically, the total length of the fox = length of its head and body + length of its tail
length of the head and body = 19 4/5
length of its tail = 10 4/5
Plugging these values into the equation, we have;
19 4/5 + 10 4/5
99/5 + 54/5 = (99 + 54)/5 = 153/5 = 30 3/5 inches
which expression shows the factors of 9x^ +3x-2
Answer:
[tex] \texttt{(3x+2)(3x-1)}[/tex]
Step-by-step explanation:
Factors of
[tex] 9x^2+3x-2[/tex]
[tex] 9x^2+6x-3x-2[/tex]
[tex] 3x(3x+2)-(3x+2)[/tex]
[tex] (3x+2)(3x-1)[/tex]
Joel has a summer job cutting lawns. The relationship between his profit, P , in dollars and the
number of lawns cut, n , is shown by the graph below. What type of variation is the relationship, and
what is its initial value?
Answer:
There is a direct relationship between the profit P and the number of lawns cut
The initial value is (0,-100)
Step-by-step explanation:
Firstly, we want to know the type of variation that is between the profit and the number of lawns.
Now, looking at the graph, we can see that as the number of lawns increase, there is a corresponding increase in the profit causing a sharp rise in the graph.
What this represents is that there is a direct relationship between the two quantities.
Now, we are told to get the initial value.
Looking at the plot, we can see that the number of lawns is the x axis while the profit is the y axis
The initial value is that point at which we have the graph intersecting the y-axis which is below the x-axis
This point is the point (0,-100)
This point gives the initial value of the relationship
What is the y-intercept of the graphed linear function? (0, –8) (0, –2) (0, 2) (0, 4)
Answer:
D. (0,4)
Step-by-step explanation:
show that x^2-8x+20 can be written in the form (x-a)^2+a. Where a is an integer
Answer:
(x - 4)^2 + 4
Step-by-step explanation:
x^2 - 8x + 20
= x^2 - 2*4*x + 16 + 4
= x^2 - 2*4*x + 4^2 + 4
= (x - 4)^2 + 4
= (x - a)^2 + a, with a = 4
Hope this helps!
two number pairs that belong to the function
y = –3x + 250.
Answer:
(0, 250)
(-250/3, 0)
Step-by-step explanation:
These are the intercepts and are points in the function
Answer:
(0,250)
(1,247)
Step-by-step explanation:
y = –3x + 250.
Let x = 0
y = -3(0) +250
y = 250
(0,250)
Let x = 1
y = -3(1) +250
y = -3+250
y = 247
(1,247)
Please answer CORRECTLY !!!!! Will mark brainliest !!!!!!!!!
Answer: b = -52/7 - 4a/7
20 POINTS AND BRAINLIEST !! PLEASE ANSWER THIS QUESTION !!
Answer: A
Step-by-step explanation:
it intercepts y at -3 and you can find slope using rise/run
PLEASE SEE PICTURE BELOW
Answer:
all real numbers
Step-by-step explanation:
Answer:
D, all real numbers greater than or equal to 0.
Step-by-step explanation:
The answer is D, all real numbers greater than or equal to 0
What is the general form of the equation of the line shown?
Answer:
x - y = 0
Step-by-step explanation:
The given line is y = x.
We could re-write this as x - y = 0, which is in general form.
A boy cycles at an average speed of 22 km/h . How long does it take him to travel 55 km ?
Answer:
Step-by-step explanation:
that is 55/22 = 2.5 hrs
Answer: .two and a half hours.
Step-by-step explanation:
22/1 = 55/x
22x=55
X=2.5
(6 + 3) = (4 - 5) =
Answer:
if you need to evaluate it its
Evaluate.
9=−1
however if you need to
Determine if True its False
hoped that help
Answer:
its 18, -9, 30
Step-by-step explanation:
just did it
Select the value(s) that could be the probability of an event
Answer:
what values???!!!
Step-by-step explanation:
Please help I have been stuck on this question
Evaluate: 4 + 8 / 2 * (6 + 3)
Answer:
40
Step-by-step explanation:
4 + 8 / 2 * (6 + 3)
Parentheses first
4 + 8 / 2 * (9)
Then multiply and divide from left to right
4 + 4 * (9)
4 + 36
Then add and subtract
40
Answer:
40
Step-by-step explanation:
PEMDAS
(6+3) = 9 4+8/2*(9)
8/2 = 4 4+4*(9)
4*9 = 36 4+36
36+4 = 40 40
Answer this please thanks!
Answer:
C
Step-by-step explanation:
Use the pythagorean theorem
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²
5 = c
A grazing area for animals is in the shape of
a rectangle having length 8 m and breadth
6 m. A goat is tied with a rope at one corner
of the rectangle. Find the minimum length
of the rope so that the goat can cover the
entire area for grazing.
Answer:
28m
Step-by-step explanation:
Find the perimeter
Perimeter=2(length+width)
=2(8+6). =2(14). =28m
Suzie paid a total of $324 for x tickets to a rock festival.
How much did each ticket cost?
Answer:
c(x)=324.
324 is the total price and c would be the cost of the tickets times x which is the number of tickets.
Can anybody help solve this?
There is a picture with the formula. I need to find surface area and volume.
Answer:
ok so. wheres the question
Answer:
100π and [tex]\frac{500\pi }{3}[/tex]
Step-by-step explanation:
The other picture wouldn’t attach, but the radius is 5.
Surface area = 4πr²
r= 5
4.π5²= 25.4.π = 100π
Volume = [tex]\frac{4}{3} \pi r^{3}[/tex]
r=5
[tex]\frac{4}{3} \pi 5^{3} = 125.4.\pi[/tex] = [tex]\frac{500\pi }{3}[/tex]
Hope this helps ^-^
EXERCISE
A ball is drawn randomly from a bag containing 8 red, 4 blue and 2 green identical balls. Find the probability that the ball drawn is not red.
What is the probability that a number chosen at random from the integers between 1 and 10 inclusive is either a prime or a multiple of 3?
A bag contains four red balls, five blue balls and six green balls. Three balls are drawn from the bag at random without replacement. What is the probability that all three are:
The same colour
Different colour
Answer:
1)The probability that the ball drawn is not red is 6 /14
2)Probability of getting either a prime or a multiple of 3 is 7/10
3)Probability of drawing three balls without replacement such that all three are Same colour is 0.0747
Probability of drawing three balls without replacement such that all three are different colour is 0.5
Step-by-step explanation:
1) A ball is drawn randomly from a bag containing 8 red, 4 blue and 2 green identical balls. Find the probability that the ball drawn is not red.
No. of red balls = 8
No. of blue balls = 4
No. of green balls = 2
Total no. of balls = 8+4+2=14
P(Getting red bal)=[tex]\frac{8}{14}[/tex]
P( ball drawn is not red) = [tex]1 - \frac{8}{14}=\frac{6}{14}[/tex]
So,the probability that the ball drawn is not red is 6 /14
2)What is the probability that a number chosen at random from the integers between 1 and 10 inclusive is either a prime or a multiple of 3?
Numbers : 1 ,2,3,4,5,6,7,8,9,10
Prime numbers: 2,3,5,7 = 4
Multiple of 3 = 3,6,9 =3
So, Probability of getting prime number =[tex]\frac{4}{10}[/tex]
Probability of getting multiple of 3 =[tex]\frac{3}{10}[/tex]
So, Probability of getting either a prime or a multiple of 3=[tex]\frac{4}{10}+\frac{3}{10}=\frac{7}{10}[/tex]
Hence Probability of getting either a prime or a multiple of 3 is 7/10
3)A bag contains four red balls, five blue balls and six green balls. Three balls are drawn from the bag at random without replacement. What is the probability that all three are:
The same colour
Different colour
No. of red balls = 4
No. of blue balls = 5
No. of green balls = 6
Total balls = 15
Case 1 :all three are Same colour
So, probability of drawing three balls without replacement such that all three are Same colour = [tex]\frac{4}{15} \times \frac{3}{14} \times \frac{2}{13}+\frac{5}{15} \times \frac{4}{14} \times \frac{3}{13}+\frac{6}{15} \times \frac{5}{14} \times \frac{4}{13}=0.0747[/tex]
So, probability of drawing three balls without replacement such that all three are different colour =[tex]\frac{4}{10} \times \frac{5}{9} \times \frac{6}{8}+\frac{5}{10} \times \frac{4}{9} \times \frac{6}{8}+\frac{6}{10} \times \frac{5}{9} \times \frac{4}{8}=0.5[/tex]
So,probability of drawing three balls without replacement such that all three are Same colour is 0.0747
So,probability of drawing three balls without replacement such that all three are different colour is 0.5
emergency!!!! Find the quotient and remainder when x^4 is divided by x^2 +2x -1
Answer:
quotient x² - 2x + 5
remainder (-12x+5)
Step-by-step explanation:
x² -2x +5
x² + 2x - 1 | x^4 + 0*x³ + 0*x² + 0x + 0
|-(x^4 + 2x³ - x²)
- 2x³ +x² + 0x
-(-2x³ - 4x² + 2x)
5x² - 2x + 0
-( 5x² +10x -5)
-12x + 5
x² - 2x + 5 + (-12x + 5)/(x² + 2x - 1)
The Quotient is [tex]x^{2} -2x+5[/tex] and The remainder is -12x +5
How to Solve this Problem?
This problem can be solved by following steps
According to the statement ,when x^4 is divided by x^2 +2x -1It is not possible to divide only x^4 We need more terms to make the division possible. We will add more terms such as 0*x^3+0x^2+0x+0Now it is Possible to divide by x^2 +2x -1The Quotient we get is [tex]x^{2} -2x+5[/tex]The Remainder we get is -12x+5Learn More about Quotient and remainder here
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3x/3=? I WILL MARK U BRAINLIST!!!!!
Answer:
3 x 3 =9
Step-by-step explanation:
9
Answer: x
Step-by-step explanation: When dividing 3x by 3, the 3's will cancel each other out simply leaving us with our variable, x.