Answer:
267,168 inches
Step-by-step explanation:
If your box is a rectangular prism or a cube, the only information you need is the box's length, width, and height. You can then multiply them together to get volume. This formula is often abbreviated as V = l x w x h.
Volume = L × W × H
Where,
L means lengthW means widthH means heightVolume = 22 inches × 12 inches × 1012 inches
Volume = 267,168 inches
So, her cooler can hold 267,168 inches of ice
f(x) = 3x-1 , (f of g)(x) = x^2 , Find g(x)
Answer:
[tex]g(x)=\dfrac{x^2+1}{3}[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x-1\\(f \circ g)(x)=x^2\end{cases}[/tex]
Composite functions are when the output of one function is used as the input of another.
Therefore, the given composite function (f o g)(x) means to substitute function g(x) in place of the x in function f(x).
[tex]\begin{aligned}(f \circ g)(x) & = x^2\\f(g(x)) & = x^2\\\implies 3(g(x))-1 & = x^2\\3(g(x))-1+1 & = x^2+1\\3(g(x))&=x^2+1\\\dfrac{3(g(x))}{3}&=\dfrac{x^2+1}{3}\\\implies g(x)&=\dfrac{x^2+1}{3}\end{aligned}[/tex]
Therefore:
[tex]\boxed{g(x)=\dfrac{x^2+1}{3}}[/tex]
the volume of a cylinder closed at one end is 2136cm³.. if its height is 14cm, find its diameter
Diameter = 13.93771776 cm
Bailey, kacie, and kaiden drive a total of 50 miles to work each day. kacie drives twice as far as bailey and kaiden drive 10 miles farther than kacie. how far does each person drive?
Let Bailey drive x miles.
So, Kacie drove 2x miles.
Kaiden drove 2x + 10 miles.
According to the question,
x + 2x + 2x + 10 = 50
x = 8
Therefore, Bailey drove 8 miles and Kacie drove 16 miles, while Kaiden 36 miles.
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2. Decide whether or not each equation represents a proportional relationship. a. The remaining length (L) of 120-inch rope after x inches have been cut off: 120- x = L. EMERGENCY
Due to the fact that the line does not pass through the origin, the equation does not represent a proportionate relationship.
What is proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.
Given Data
The remaining length (L) of 120-inch rope after x inches have been cut off: 120- x = L.
The fact that
If a relationship between two variables, x and y, can be written as or, then it represents a proportionate variation.
y = kx
The line passes through the origin, and the constant of proportionality, k, is equal to the slope of the line, m.
There are
The length (L) of a 120-inch rope that is left after x inches have been removed.
There are
The dependent variable is L —->. (output variable)
The independent variable is x. (input variable)
The linear formula is
L = 120-x
Due to the fact that the line does not pass through the origin, the equation does not represent a proportionate relationship.
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help please kylie solved the following problem incorrectly
a.) In Line 1 Kylie made her error.
b.) Kylie's error is that she opened the bracket -2(x - 5) in the first line and did not change the negative sign to a positive sign as she multiplied -2 and -5 as a negative number multiplied by a negative number is a positive number.
c.) The correct solution to the problem is given by,
Given: 6x - 2(x - 5) = 22
6x - 2x + 10 = 22
4x = 22 - 10
4x = 12
x = 12/4
x = 3
Hence, the value of x is 3 and not 8.
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The cost to produce x units of wire is C = 305x +1350 , while the revenue is R = 35x. Find the interval where the product will at least break even.
The interval where the product will at least break even is [tex]$\left[\begin{array}{cc}\text { Solution: } & x \leq-5 \\ \text { Interval Notation: } & (-\infty,-5]\end{array}\right]$[/tex]
Given C= 305 x+1350C
R=60 x
To find the interval where the product will at least break even we must have [tex]$R(x) \geq c(x)$[/tex]
[tex]$\Rightarrow \quad 35 x \geq 305 x+1350$[/tex]
[tex]$$35 x \geq 305 x+1350$$[/tex]
Subtract 305 x from both sides
[tex]$$35 x-305 x \geq 305 x+1350-305 x$$[/tex]
Simplify
[tex]$$-270 x \geq 1350$$[/tex]
Multiply both sides by - 1 (reverse the inequality)
[tex]$$(-270 x)(-1) \leq 1350(-1)$$[/tex]
Simplify
[tex]$$270 x \leq-1350$$[/tex]
Divide both sides by 270
[tex]\frac{270 x}{270} \leq \frac{-1350}{270}$$[/tex]
Simplify
[tex]$$x \leq-5$$[/tex]
Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
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Jalen needs a total of $85 to buy a new play station controller. he already has $25. if he saves $13 a week, what is the least number of weeks he must work to have enough money to buy a controller? a. 3 c. 5 d. 6 2
Answer:
5
Step-by-step explanation:
he needs $85 and he has $25,
so it will be 85-25=60
that means he would need $60 more. if he saves $13 every week, it will 60÷13= 4.6 weeks or approximately 5.
Hello,May I please request help for number 13 in the uploaded picture? We are to do the following: Write the first four terms of each seequence.
To solve this question, find the 4 first terms of the sequence.
The first term is a₁
a₁ is given and a₁ = 7
The second term is a₂
Given:
[tex]a_n=a_{n-1}+5[/tex]Then, let's find a₂ using the value of a₁
[tex]\begin{gathered} a_2=a_1+5 \\ a_2=7+5 \\ a_2=12 \end{gathered}[/tex]The third term is a₃
let's find a₃ using the value of a₂
[tex]\begin{gathered} a_3=a_2+5 \\ a_3=12+5 \\ a_3=17 \end{gathered}[/tex]The fourth term is a₄
let's find a₄ using the value of a₃
[tex]\begin{gathered} a_4=a_3+5 \\ a_4=17+5 \\ a_4=22 \end{gathered}[/tex]Answer:
The four first terms are:
a₁ = 7
a₃ = 12
a₃ = 17
a₄ = 22
7. displaying sample means and their errors a researcher is investigating whether a reading intervention program improves reading comprehension for second graders. he collects a random sample of second graders and randomly assigns each second grader to participate in the reading intervention program or not participate in the program. the researcher knows that the standard deviation of the reading comprehension scores among all second graders is σ
The best plot for these results is given by:
C. Plot C.
How to verify which is the best plot for the results?The mean result for each group is given as follows:
Group 1: 36.8.Group 2: 52.4.Then we have to look at the vertical bars of each plot, and see the scores given.
For plot A, the scores are given as follows:
Group 1: 40.Group 2: 45.For plot B, the scores are given as follows:
Group 1: 22.5.Group 2: 35.For plot C, the scores are given as follows:
Group 1: 35.Group 2: 55.For plot D, the scores are given as follows:
Group 1: 20.Group 2: 45.Plot C has the closest value readings to the actual values of 36.8 and 52.4, hence it is the best option to plot the scores for each group.
What is the missing information?
The problem is missing and is given by the image at the end of the answer.
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Two motorcycle dealers sell the same motorcycle for the same original price. Dealer A advertises that the motorcycle is on sale for 7.5% off the original price. Dealer B advertises that it is reducing the motorcycle’s price by $599. When Bonnie compares the sale prices of the motorcycles in both dealers, she concludes that the sale prices are equal.
Let p represent the motorcycle’s original price.
Which equation models this situation?
The original price of the motorcycle is approximately $7,987.
Here, we are given that p represent the motorcycle’s original price.
The sale price of Dealer A will be-
7.5% less that the original price
= 92.5% of p
= 0.925p
Similarly, the sale price of dealer B will be-
$599 less than original price
= (p - 599)
Now, these two prices are equal, so we can equate the two-
0.925p = (p - 599)
0.925p = p - 599
0.925p - p = -599
-0.075p = -599
p = -599/-0.075
p = 599/0.075
p = 599000/75
p = 7,986.67
Thus, the original price of the motorcycle comes out to be approximately $7,987.
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(z+4) (z+2) (z − 1) = 0
-
Select all of the following values that make the equation true.
04
01
0-4
00
0-2
02
0-1
The Zero Product Property simply notes that if ab = 0, then either a = 0 or b = 0. The solutions exists x = -4, x = -2, x = 1.
What is meant by zero-factor rule?The zero-product property in algebra asserts that two nonzero items cannot be multiplied together to produce zero.
The Zero Product Property simply notes that if ab = 0, then either a = 0 or b = 0 (or both). A product of factors exists zero if and only if one or more of the factors exists zero.
Let the given equation be (x+4)(x+2)(x-1)=0
By using the Zero Factor Principle, we get
If ab = 0 then a = 0 or b = 0
then x + 4 = 0 or x + 2 = 0 or x - 1 = 0
Solve x + 4 = 0
⇒ x = -4
Solve x + 2 = 0
⇒ x = -2
Solve x - 1 = 0
⇒ x = 1
The solutions are x = -4, x = -2, x = 1
Therefore, the correct options exists:
b) 1
c) -4
e) -2
The complete question is:
An equation is shown below.
(x + 4)(x + 2)(x - 1) = 0
Select all of the following values that make the equation true.
a) 4
b) 1
c) -4
d) 0
e) -2
f) 2
g) -1
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Suppose a life insurance company sells a $280,000 one year term life insurance policy to a 24 year old female for $290. the probability that the female survives the year is 0.999576. compute and interpret the expected value of this policy to the insurance company
Suppose a life insurance company sells a $280,000 one year term life insurance policy to a 24 year old female for $290.Then The expected value of this policy to the insurance company is $168.76
Probability that Person doesn't die = 0.999567. Profit = Revenue - Cost; Profit = $290 - 0 = $290
Probability that Person dies = 1 - 0.999567 = 0.000433. Profit = Revenue - Cost; Profit = $290 - $280000 = -$279710
Expected Value E(X) = ∑xp(x)
E(X) = $290*(0.999567) + (-$279,710* 0.000433)
E(X) = $289.87443 - $121.11443
E(X) = $168.76
Thus, the expected value of this policy to the insurance company is $168.76
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Solve the quadratic equation.
6^{2} = 5x + 6
I would appreciate help with this, thanks in advance!
≧◠‿●‿◠≦
[tex]6 {x}^{2} - 5x - 6 = 0 \\ 6 {x}^{2} - 9x + 4x - 6 = 0 \\ (6 {x}^{2} - 9x) + (4x - 6) = 0 \\ 3x(2x - 3) + 2(2x - 3) = 0 \\ (3x + 2)(2x - 3) = 0 \\ 3x + 2 = 0 \\ \\ \\ or \\ 2x - 3 = 0 \\ x = \frac{ - 2}{3} \\ \\ or \\ \\ x = \frac{3}{2} [/tex]
I FACTORISED THE EQUATION FIRST WITH A SIMPLE METHOD OF MULTIPLYING THE COEFFICIENT OF
[tex] {x}^{2} [/tex]
and the constant number then find the factors that will give me the coefficient of x.
ATTACHED IS THE SOLUTION
Step-by-step explanation:
are you sure this is the whole information ?
because
6² = 5x + 6
is not called a quadratic equation.
it is a quadratic equation, when there is one term in x² involved.
I assume therefore, that your problem is
6x² = 5x + 6
that is then as basic quadratic equation
6x² - 5x - 6 = 0
the general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
a = 6
b = -5
c = -6
x = (5 ± sqrt((-5)² - 4×6×-6))/(2×6) =
= (5 ± sqrt(25 + 144))/12 = (5 ± sqrt(169))/12 =
= (5 ± 13)/12
x1 = (5 + 13)/12 = 18/12 = 3/2
x2 = (5 - 13)/12 = -8/12 = -2/3
so, the 2 solutions for the quadratic equation are
x = 3/2 and x = -2/3
The equation y=0.52x+157 gives the cost y of renting a car if the care is driven x
miles. Based on this equation, for every mile the car is driven the cost of increases by
how much?
If triangle ABC is congruent to triangle DEC,
angle B = 2x + 31 and angle E = 7x - 24
x = ?
In a case whereby triangle ABC is congruent to triangle DEC, angle B = 2x + 31 and angle E = 7x - 24, the X is 11.
What is the meaning of congruent triangle?It should be noted that when a Triangles are exactly the same in term of size and shape then it is congruent.
Since the angle E and angle B is the same, then we can equate it so that we can find the value of X , then this can be calculated as
(2x + 31) = (7x - 24)
The we have
(7x - 2x) = (31 +24)
The we will have
(5x) =( 55)
Then
x = 11
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2. Round the following numbers to the nearest 10 thousand:
990,201:_____________________
159,994 :____________________
Answer:
A, 9100 210 C 1520 99144 NO ES PERO BUENO MIRA AVER SI
A 10-question multiple choice test has 4 possible answers for each question. A student selects at least 6 correct answers
PLEASE HELP ME FAST
0.020 is a probability for student selects at least 6 .
What is a probability simple definition?
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.Three main categories of probability exist: Probability in theory. Scientific Probability. Probability axiomatically.There are two ways to do it. You can either interpret this as
One minus the probability that the student will guess 5 or fewer
correct answers with a probability of a correct answer being = 1/4 ⇒
0.0197277069
The probability that the student will guess 4 or fewer wrong answers
with a probability of a wrong answer being = 3/4
binomcdf (10,3/4,4)
= 0.0197277069
Either way it rounds to 0.020
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Find the cube root of 13824 by prime factorisation
Step-by-step explanation:
the set of prime numbers that, when multiplied together, give
13824:
2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3
Answer:
24
Step-by-step explanation:
which of the following expressions represents the distance between -1/4 and 3/4
The expression that represents the distance is |-1/4 - 3/4|
How to determine the distance expression?From the question, the endpoints are given as
-1/4 and 3/4
Rewrite the endpoints properly
This is done as follows
Endpoint 1 = -1/4
Endpoint 2 = 3/4
The distance expression between the endpoints is then calculated as
Distance = |Endpoint 1 - Endpoint 2 |
Substitute the known values in the above equation
So, we have the following equation
Distance = |-1/4 - 3/4|
Hence, the disance expression is |-1/4 - 3/4|
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what is the equation of the line that passes through the points (2,-2) and (3,-4)
Answer:
y + 2 = -2(x - 2) (point-slope form)
y = -2x + 2 (slope-intercept form)
2x + y = 2 (standard form)
Step-by-step explanation:
[tex]m = \frac{ - 4 - ( - 2)}{3 - 2} = - \frac{2}{1} = - 2[/tex]
[tex]y + 2 = - 2(x - 2)[/tex]
[tex]y + 2 = - 2x + 4[/tex]
[tex]y = - 2x + 2[/tex]
[tex]2x + y = 2[/tex]
Simplify the expression 2(2/5) + 2(-1/5)
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
2([tex]\frac{2}{5}[/tex] ) + 2(- [tex]\frac{1}{5}[/tex] )
= [tex]\frac{4}{5}[/tex] + (- [tex]\frac{2}{5}[/tex] )
= [tex]\frac{4}{5}[/tex] - [tex]\frac{2}{5}[/tex]
= [tex]\frac{2}{5}[/tex]
Which is the most efficient step to solve the equation 2/3n=15 ?
Group of answer choices
Multiply both sides by 2/3
Subtract 15 from both sides
Subtract 2/3 from both sides
Divide both sides by 2/3
Answer:
This is the most optimal way to resolve the problem:
Step-by-step explanation:
15/n+2 = 3n/n
15/n+2 = 3
3 (n+2) = 15
n = 5 - 2
n = 3
choose the inequality shown by this diagram
Answer: C
Step-by-step explanation:
Starting off we need to understand what the circles are in inequalities.
A closed circle means that the number on the inequality is included in the solution. An open circle means that the number in the inequality is not included in the solution. A closed circle would use [tex]\leq or \geq[/tex]. An open circle would use < or >.
So, using these processes, -2<x[tex]\leq[/tex]7 would be the answer.
A musical group wants to see who has downloaded its No. 1 hit song and find out the reasons why. Which description represents a sample?
The first 5,000 people who downloaded its No. 1 hit song
The first 5,000 people who chose not download its No. 1 hit song
All people who downloaded its No. 1 hit song
All people who did not download its No. 1 hit song
The description that represents a sample is A. The first 5,000 people who downloaded its No. 1 hit song.
What is sampling?Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.
It should be noted that all people who downloaded its No. 1 hit song represents the entire population. The sample is a subset of the population.
In conclusion, the correct option is A.
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Write an equation for each of the following phrases or word problems. Solve for the missing variable.
Three is a number divided by 6.
The mathematical sentence can be written as:
3 = x/6
And the solution is x = 18.
How to write and solve the equation?Here we have the following mathematical sentence:
"three is a number divided by 6"
If we define x as the "number", then we can write this as:
3 = x/6
So we have a simple linear equation, to solve this, we just need to multiply both sides of the equation by 6, we will get:
3*6 = (x/6)*6
18 = x
We conclude that the solution is 6.
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Hypotenuse is 13.5 the angle is 41 degrees what’s the opposite
If the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units
The length of the hypotenuse = 13.5 units
The angle = 41 degrees
Here we have to use the trigonometric function
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
tan θ = Opposite side / Adjacent side
In this question hypotenuse and angles are given and we have to find the opposite side.
sin θ= opposite side / Hypotenuse
Substitute the values in the equation
sin 41 = Opposite side / 13.5
Opposite side = sin 41×13.5
= 8.86 units
Hence, if the length of the hypotenuse is 13.5 units and angle is 41 degrees, then the length of the opposite side is 8.86 units.
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- Solve the system of equations by graphing.
y = x² - 3
x + y = -1
Answer: y=x2+3x−1
Hope this helps! :)
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.Find the side of a square whose diagonal is of the given measure.Given = 12*10^(1/2) ft.
We have to find the side of a square with a diagonal with length 12√10 ft.
We can sketch this as:
We can apply the Pythagorean theorem as:
[tex]\begin{gathered} a^2+a^2=(12\sqrt{10})^2 \\ 2a^2=12^2\cdot10 \\ 2a^2=144\cdot10 \\ a^2=\frac{144\cdot10}{2} \\ a^2=720 \\ a=\sqrt{720} \\ a=\sqrt{16\cdot9\cdot5} \\ a=4\cdot3\cdot\sqrt{5} \\ a=12\sqrt{5} \end{gathered}[/tex]Answer: the square side length is 12√5
1/2 of a birthday cake was left over from a party. The next day , it is shared among 6 people. How big a piece of the original cake did each person get
Each person gets 1/12 fraction of the original cake.
What is a fraction?
A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. A common, vulgar, or simple fraction is one that has a non-zero denominator shown below (or after) the line that separates the numerator from the denominator. Composite fractions, complicated fractions, and combined numeral fractions are examples of uncommon fractions that use numerators and denominators.
Each person gets = 1/2 x 1/6 = 1/12
Hence, each person gets 1/12 fraction of the original cake.
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The vertex of the parabloa is (-5,-2). When the x-value is -4
Answer:
the formula for the vertex is f(x)=a(x-h)²+k
so if you replace -4= a(0-5)²+-2
so a=-0.08
The formula would end up like this f(x)=-0.08(x-5)²+-2
Step-by-step explanation: