Given that the delivery person works an 8-hour shift, he needs 4 gallons of gasoline in his tank.
A function is defined as the expression that relates a independent variable with a dependent variable. To evaluate a function is to substitute the value of the independent variable and then calculate the function value.
Given that the delivery person works an 8-hour shift, substitute x = 8 to the function of y.
y = f(x) = x² + 3x
y = 8² + 3(8)
y = 88
To determine the amount of gasoline needed, substitute the value of y to the function of g of y.
g = y / 22
g = 88 / 22
g = 4
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Help me in this proportion maths problems
y is inversely proportional to the square of x, here y in terms of x is 2/5.
From the given problem y is inversely proportional to the square of x.
A table of values for x and y is shown.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
From the table:
(a) As we know that, y is inversely proportional to the square of x,
Here k is proportionality constant.
y∝1/x²
y= k/x²
4=k/1²
k=4
So, y in terms of x is y=4/x²
(b) Putting the value of y=25, we get:
25=4/x²
x²=4/25
x=2/5
Therefore, y is inversely proportional to the square of x, here y in terms of x is 2/5.
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Tyrone is the supply manager of a bakery. He needs to make sure there is plenty of flour on hand for their recipes each month. The bakery begins the month with 215.4 pounds of flour. Tyrone tracks the weekly use, along with the supply delivery received in the middle of the month.
Week Weekly Flour Use (lb)
1 −5812
2 −70.6
3 75310
4 −6778
How much flour does the bakery have on hand at the end of the month? Explain how you found your answer.
The pounds of flour the bakery has at the end of the month is 92.725 lb
How much flour does the bakery have at the end of the month?The negative numbers denote when flour was used while the positive numbers denote when flour was added. The negative numbers would be subtracted while the positive numbers would be added.
For ease of computation, the mixed numbers would be converted to decimals.
-58 1/2 = -58.5
75 3/10 = 75.3
-67 7/8 = -67.875
Pounds of flour the bakery has at the end of the month: 215.4 - 58.5 - 70.6 + 75.3 - 67.875 = 92.725 lb
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Find the slope of the line that contains (1, 9) and (6, 6).
Answer:
Step-by-step explanation:
To find the slope, subtract the y values, and divide it by subtracting the x values. The order matters!
(9-6)/(1-6)=-3/5
What is the volume of this figure?
O 6,720 cm³
O 5,760 cm³
O 3,840 cm³
O I don't know.
The volume of the given figure is 5760 [tex]cm^{3}[/tex].
According to the question,
We have the following information:
We have a figure where two cuboids are joined together. So, the volume of the figure will be the sum of the volume of these cuboids.
We know that the following formula is used to find the value of cuboid:
Volume of cuboid = Length*breadth*height
Volume of larger cuboid = 40*8*12
Volume of larger cuboid = 3840 [tex]cm^{3}[/tex]
Volume of smaller cuboid = 20*8*12
Volume of smaller cuboid = 1920 [tex]cm^{3}[/tex]
Volume of the figure = 3840+1920
Volume of the figure = 5760 [tex]cm^{3}[/tex]
Hence, the correct option is B (the second option).
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Answer:
5760
Step-by-step explanation:
Find the measures of the interior angles.
Angle A:
Angle B:
Angle C:
The values of the interior angles, ( Angle A, Angle B and Angle C) of the triangles are 48°, 88° and 44° respectively.
What is interior angle?Interior angle is the inner of the two angles formed where two sides of a polygon come together.
To find the measure of each interior angle of the triangle in the diagram, first, we need to find the value of x.
Recall that: The sum of the interior angles of a triangle is equal to 180°.
Using the formula,
a+b+c = 180°............. Equation 1From the triangle,
a = 48°b = x°c = (x-44)°Substitute these values into equation 1
48+x+(x-44) = 180Solve for x
2x+4 = 1802x = 180-42x = 176x = 176/2x = 88°Therefore,
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The difference between a big shot and a little shot is that a big shot is just a little shot that kept on shooting. what do you think about this quote? answer and ill give you a lot of points 100 for free
Answer:
The quote seems to have a little to much shooting. Don’t you think?
Step-by-step explanation:
Answer:
lair lair
Step-by-step explanation:
IM GIVING BRAINLY I NEED HELP ASAPP
Answer:
C
Step-by-step explanation:
Rate change = Change in Y/ Change in Xy=mx+cand for graph, rate change is 10(10 units change in Y for every 1 unit change in X) whereas another function's rate change is 4
C= is y-intercept
and in graph its -6 whereas in function its -8, so graph has higher y-intercept
Graph: Rate of change = 10, y-intercept = -6
Function: Rate of change = 10, y-intercept = -8
A cylinder used for storing spools of thread has a radius of 2 units and a slant height of √29. What is the height of the cylinder?
PLS HELP ASAP!!(show work if can)
Height of cylinder is 5 units
Define Cylinder
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry.The volume of the slanted cylinder is V = Base area of cylinder × Height of cylinder⇒ V = (π × radius²) × h
We have given,
Slant height of cylinder = √29
Radius is = 2 units
Now, we to have to calculate the height for that we have the formula
h = √l² - r²
where, l = slant height
r = radius of the circular base
h = height of the cylinder
Now, for the sake of simplicity
h = √l² - r²
h² = l² - r²
Now, plug in the values
h² = (√29)² - 2²
h² = 29 - 4
h² = 25
h = 5
Hence, the height of cylinder is 5 units
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At a certain gas station, gas costs $2.85 a gallon. Jason paid $25.50 to fill his tank. Write and solve an equation to
find how many gallons of gas he bought?
Answer:
8.95 gallons
Step-by-step explanation:
25.50/2.85 = 8.95
Two libraries donated books to a local school. One library donated 786 books and the other
library donated 1,245 books. The school divided the books evenly among 11 classrooms.
Estimate how many books each classroom received.
Choose 1 answer:
B
200 books
Donat
50 books
The number of books each classroom received = 185
In this question, we have been given two libraries donated books to a local school. One library donated 786 books and the other library donated 1,245 books. The school divided the books evenly among 11 classrooms.
We need to find the number of books each classroom received.
Total number of books received:
786 + 1245 = 2031
The school divided the books evenly among 11 classrooms.
Let x be the number of books each classroom received.
By unitary method,
x = 2031 /11
x ≈ 185
Therefore, the number of books each classroom received = 185
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Lola’ mom walked x feet and then half that length agin how many feet did Lola’ mom walk
Total( as there is addition) feet walked by Lola is 29.25 +1.5x for the given equation.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division.
Main body:
Lola's pet turtle walked 10 feet, and then half that length again. This means that Lola's pet turtle walked:
= 10 + (1/2 × 10) = 10 + 5 = 15 feet
Lola's baby brother walked 3 feet, and then half that length again. Total length walked will be:
= 3 + (1/2 × 3) = 3 + 1.5 = 4.5 feet
Lola's hamster walked 6.5 feet, and then half that length again. Total length walked will be:
= 6.5 + (1/2 × 6.5) = 6.5 + 3.25 = 9.75
Lola's mom walked x feet, and then half that length again. Total length walked will be:
= x + (1/2 × x) = x + 0.5x = 1.5x
Total feet walked by the whole member of the family will be:
= 15 + 4.5 + 9.75 + 1.5x
= 29.25 + 1.5x
Hence Total feet walked by Lola is 29.25 +1.5x for the given equation.
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Este gráfico circular resume las especializaciones de los 450 miembros de una sororidad universitaria. El ángulo central el sector correspondiente a la especialización de ingeniería mide 50.4°. ¿Qué porcentaje de los miembros de la sororidad se especializan en ingeniería? No redondear.
Los miembros de la sororidad tiene un porcentaje de 14 % de estudiantes procedentes de la especialización de ingeniería.
¿Cuál es el porcentaje de estudiantes de la sororidad que pertenecen a la especialización de ingeniería?
El enunciado describe las características de un diagrama circula, en donde el 100 % de los miembros de la sororidad representan a los 360° del ángulo central del círculo, esto es, una revolución completa del círculo.
El porcentaje de los miembros que se especializan en ingeniería mediante la siguiente fórmula:
e = (E / 360°) × 100 %
Donde E es el ángulo asociado a la cantidad de estudiantes de la especialización de ingeniería, en grados sexagesimales.
e = (50.4° / 360°) × 100 %
e = 14 %
Los estudiantes que especializan en ingeniería corresponden a un porcentaje de 14 % de los miembros de la sororidad.
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It take an ant farm 2 day to conume 1/2 of an apple. At that rate, in how many day will the ant farm conume 2 apple?
the ant will take 8 days to consume 2 apples.
Given, an ant takes 2 days to consume 1/2 of an apple.
We have to find the number of days ant will take to consume 2 apples.
So, ant takes 2 days = consumption of 1/2 apple
ant takes 4 days = consumption of 1 apple
Consumption of 1 apple = ant takes 4 days
Consumption of 2 apples = ant takes 4×2 days
Consumption of 2 apples = ant takes 8 days
Hence, the ant will take 8 days to consume 2 apples.
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What is the value of x in the equation 3/2 (4x – 1) – 3x = 54 –(x + 2)?
A. 1/16
B. 3/16
C. 19/16
D. 3
The solution for x in the equation given as 3/2 (4x – 1) – 3x = 54 –(x + 2) is 13.375
How to determine the solution to the variable k in the expression?From the question, the algebraic expression is given as
3/2 (4x – 1) – 3x = 54 –(x + 2)
There is no constant to multiply or divide in the expression
3/2 (4x – 1) – 3x = 54 –(x + 2)
Open the brackets
So, we have
6x – 3/2 - 3x = 54 - x - 2
Collect the like term in the above equation
This gives
6x - 3x + x = 54 - 2 + 3/2
Evaluate the like term in the above equation
So, we have the following representation
4x = 53.5
Divide through by 4
x = 13.375
The above equation cannot be solved further
Hence, the solution is x = 13.375
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these researchers said the differences were statistically significant. explain what that means in context.
A statistically significant finding indicates that it is unlikely to just be explained purely by chance or random influences.
Define the term statistically significant?The notion that a set given observed data is not the result of random but can instead be linked to a specific cause is referred to as statistical significance.
A high level of statistical significance signifies that the observed link is unlikely to be coincidental.The calculation for statistical significance is prone to some inaccuracy.When researchers do not utilize precise wording when describing their findings, statistical significance could be misconstrued.Depending on the research, many sorts of significance tests are being used.Statistical significance indicates that a result is unlikely to be attributed purely by chance and random causes.
Thus, in other words, if there is no genuine effect in a research study, a statistically significant conclusion has an extremely low likelihood of occuring.
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solve the equation:x/-3.5+33=30
Answer:
x=10.5
Step-by-step explanation:
Jason is training to run in a marathon. His goal for this week is to run a minimum of 45 miles. So far this week, he has already run 10 miles. Which inequality could be used to determine the mean number of miles, m, he would need to run each day for 5 more days to achieve his goal?
The inequality that could be used to determine the mean number of miles Jason would need to run each day for 5 more days to achieve his goal is 10 + 5m ≥ 45
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Let the number of miles be given as m.
Since his goal for this week is to run a minimum of 45 miles. So far this week, he has already run 10 miles. This will be:
10 + 5m ≥ 45
This expresses the inequality.
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the time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 15 minutes. the average time necessary for 100 randomly selected students is computed. the probability the sample mean time necessary to complete the examination is less than 47.5 minutes equals approximately:
The likelihood that the sample mean time required to finish the exam will be less than 47.5 minutes is 0.566.
Given;
The average amount of time needed to finish an exam is 45 minutes, with a standard deviation of 15 minutes. The average amount of time required for 100 randomly chosen pupils is calculated.
Mean (μ) = 45
Standard deviation (σ) = 15
Here, σ/√n = 15/√100
= 1.5
To get the probability the sample mean time necessary to complete the examination is less than 47.5 minutes, we need;
P (x < 47.5) = P(z < (x-μ /σ/√n ) )
= P(z < 47.5 - 45/1.5)
= P(z < 17.5)
= 0.566
The probability the sample mean time necessary to complete the examination is less than 47.5 minutes is 0.566
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What is the answer to this question?
Answer:
0,-24,-3/4
You have to substitute the values for x and y to get the other output. When I put 0 into the equations I get back 0
at an academically challenging high school, the average gpa of a high school senior is known to be normally distributed with a variance of 0.45. a sample of 15 seniors is taken and their average gpa is found to be 2.83. assume that and . the 90% confidence interval for the population mean gpa is:
The 90% confidence interval for the population mean gpa is [2.545,3.114].
The confidence interval for population mean is:
µ ± z* . σ/√n
Where, μ is population mean, σ is standard deviation, z* is the value of z-score and n is number of samples.
The z-score value for 90% confidence interval is 1.645.
The average gpa is found to be 2.83, so μ=2.83. The variance is 0.45, it means
σ² = 0.45
σ = √0.45
σ = 0.67
The 90% confidence interval for population mean is:
2.83 ± 1.645 . 0.67/√15
[2.83 - 1.645.0.67/√15 , 2.83+1.645.0.67/√15]
[2.545 , 3.114]
Therefore, the 90% confidence interval for the population mean gpa is :
[2.545 , 3.114]
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tim and angel are working on promoting an event for a club they are in on campus. in one afternoon tim can make 4 flyers or 5 posters, and angel can make 3 flyers or 6 posters. if you were to graph angel's ppc with posters on the horizontal axis, what would be the slope of her ppc
If we graph the angel's ppc then the slope of angel's ppc will be -1.
Given, Tim and Angel are working on promoting an event for a club they are in on campus.
In one afternoon, Tim can make 4 flyers or 5 posters, and Angel can make 3 flyers or 6 posters.
we have to find the slope of the angel's ppc if we graph the angel's ppc.
As, the graph of the angel's ppc will pass through the point (3 , 6).
so, the slope = (6 - 5)/(3 - 4)
slope = 1/-1
slope = -1
Hence, if we graph the angel's ppc then the slope of angel's ppc will be -1.
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Zachary purchased a computer for $1200 on a payment plan.6 months after he purchased the computer, his balance was $420. 8 months after he purchased the computer, his balance was $160. What is an equation that models the balance y after x months?
The equation that models the balance y after x months is: y = -130x + 1200.
How to find the equation?Month Balance
0 1200
6 420
8 160
Hence,
m = (y2 - y1)/(x2 - x1)
First coordinate:
m = (420 - 1200)/(6 - 0)
m = -780 /6
m = -130
Second coordinate;
m = (160 - 420)/(8 - 6)
m = -260/2
m = -130
The formula for equation in slope intercept is
y = mx + c
where;
m = slope
c = y-intercept
So, equation is;
y = -130x + 1200
Therefore the equation is y = -130x + 1200.
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You go to the store to buy supplies for class. You want to buy a new notebook for $3 and 5
folders. The most you can spend is $10. If you buy all the same type of folders, what are the
individual folder prices you can afford?
(Algebra)
If we buy all the same type of folders, the maximum amount we can afford for an individual folder is $ 3.3
To buy : A notebook for = $ 3
number of folders required = 5
The amount of money we can spend is $ 10
The above mentioned problem is a problem of algebra because we would have to use a variable to find out the unknown value.
The individual folders price can be calculated by the equation
3x = 10
divide both sides by 3 and we will get
x = 3.3
Thus the individual folder prices we can afford is $ 3.3
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if a rectangular prism is 4 cm long, 3 cm wide and 1,5 cm high what is the volume of the prism
Answer: The volume of the prism is [tex]18^{3}[/tex]cm
Step-by-step explanation: The formula to solve for the volume of a rectangular prism is V = lwh. In this case, it's V = 4 x 3 x 1.5 therefore V = 18
Help needed immediately!!!
By reading the 2 water levels below and subtracting them, work out the volume of the gold nugget in mL
(Show working out)
Answer:
volume = 3 ml
Step-by-step explanation:
the reading on the left without the nugget is 17 ml
the reading on the right with the nugget is 20 ml
volume of nugget = 20 - 17 = 3 ml
You win 50 tickets, 12 tickets, and 16 tickets at
an arcade. You are able to buy 3 of the same item with 3 tickets left over.
How many tickets does 1 item cost?
Answer:
25
Step-by-step explanation:
First, we add 50, 12, and 16, which gives us 78. Then, we remove 3 from the answer, giving us 75. Then, divide 75 by 3.
Answer = 25.
(ps: sorry for any spelling mistakes, i dont really type answers alot)
If you are able to buy 3 of the same item with 3 tickets left over. As a result, 1 item cost 26 tickets.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, You win 50 tickets, 12 tickets, and 16 tickets at an arcade. You are able to buy 3 of the same item with 3 tickets left over.
Number of tickets won,
= 50 + 12 + 16
= 78 tickets
Number of items bought = 3 items
Let the cost of 1 item be 'x' tickets.
The cost of 3 items = 3x
By the amount, we can buy 78 tickets as,
3x = 78
x = 26
Thus, if you are able to buy 3 of the same item with 3 tickets left over. As a result, 1 item cost 26 tickets.
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What is an equation of the line that passes through the points (-2,7) and (-8,4)
Answer: y = (1/2)x + 8
Step-by-step explanation:
Slope: (4-7)/(-8--2) = (-3)/(-6) = 1/2
y = (1/2)x + b
7 = (1/2)-2 + b
7 = -1 + b
8 = b
y = (1/2)x + 8
kendra ran 12 miles in 60 minutes. if the ratio of miles to minutes is constant how many more miles can she run in 90 minutes than in 60 minutes
Answer:
it is 18 mile
Step-by-step explanation:
12mile = 60 min
x = 90 min
we cris cross the equation and
we found x=18 mile
Two similar pots have heights of 16 cm and 10 cm. The smaller pot holds 0.75 litres. Find the capacity of the larger pot.
Answer: 1,2L
Step-by-step explanation:
10 cm ------------ 0.75 L
16 cm ------------ ?
?= (16 x 0.75) : 10
?= 12 : 10
?= 1,2 L
PLEASE HELP ASAPPPPP ILL GIVE BRAINLIEST PLEASEEEEEE
Rewrite x³y + xy²
x³y +
xy(x² +5y)
xy² using a common factor.
xy(3x² +15y)
xy(x² +5y)
1x³y² (y + 5x)
Answer:
[tex] \frac{1}{6} {x}^{3} y + \frac{5}{6} x {y}^{2} \\ \frac{1}{6} xy( {x}^{2} + 5y)[/tex]
option 3 is correct