The volume that the shipping box which measure 36 inches by 24 inches by 18 inches can hold is 9 cubic feet.
What is the volume of the shipping box with the given dimensions?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Given the data in the question;
Length l = 36 in = ( 32/12 )ft = 3ftWidth w = 24 in = ( 24/12 )ft = 2ftHeight h = 18 in = ( 18/12 )ft = 1.5ftVolume V = ?Plug the given values into the formula above and solve for the volume V.
V = w × h × l
V = 2ft × 1.5ft × 3ft
V = 3ft² × 3ft
Volume V = 9ft³
Therefore, the volume of the rectangular prism is 9 cubic feet.
Option B is the correct answer.
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A friend lends you $720, which you agree to repay with 4% interest. How much will you have to repay? How much was the interest?
Answer: $16081.60
Step-by-step explanation:
1)
FV=3000(1.03)=$3090
2)
240*1.04=$249.60
3)
FV=14000(1.02)^7
FV=14000(1.1487)
FV=$16081.60
Is the package late? A shipping company claims that 90% of its shipments arrive on time.
Suppose this claim is true. If we take a random sample of 20 shipments made by the
company, what's the probability that at least 1 of them arrives late?
Using the binomial distribution, there is a 0.8784 = 87.84% probability that at least 1 of them arrives late.
Binomial distributionThe probability mass function, giving the the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters of the distribution are given as follows:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.In the context of this problem, of 20% shipments with 90% on time, the parameters are:
p = 0.9, n = 20.
The probability that all arrive on time is:
P(X = 20) = (0.9)^20 = 0.1216.
All on time and least one late are complementary events, hence the probability of at least one package arriving late is given as follows:
P(X < 20) = 1 - P(X = 10) = 1 - 0.1216 = 0.8784.
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At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 28 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon. How many fencers are expected to not use the foil as their main weapon? (Round your answer to the nearest whole number.)
Based on the percentage of fencers who said they used foil as their main weapon when surveyed, the number of fencers out of 28 fencers who would not use foil as their main weapon is 11 fencers
How to find the number of fencers?The random survey showed that in a given sample, there would be 60% of fencers who would prefer to use foil as their main weapon. This means that the percentage of fencers who would not use foil as their main weapon is:
= 1 - percentage who use foil as main weapon
= 1 - 60%
= 40%
If 28 fencers are randomly surveyed, the percentage of them who would not use foil as their main weapon would be expected to be:
= Number of fencers x Percentage who don't use foil as main weapon:
= 28 x 40%
= 11.2 fencers
= 11 fencers to the nearest whole number
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A sales representative receive a monthly salary of $1600 plus a commission of 3% of the total monthly sales. write a linear model that relates total monthly wages W to sales S
Answer:
The equation is W = 1600 + .03S
the functions f and g are defined as follows.
f (x) = -2x^3 - 3 g (x) = 2x + 4.
find f (-2) and g (-6)
Simplify your answers as much as possible.
Answer: [tex]f(-2)=13, g(-6)=-8[/tex]
Step-by-step explanation:
[tex]f(-2)=-2(-2)^3 -3=13\\\\g(-6)=2(-6)+4=-8[/tex]
The values of functions f(-2) and g(-6) are 13 and -8 respectively.
Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
It is given in the question that:-
[tex]f (x) = -2x^3 - 3[/tex]
g(x) = 2x + 4
We have to find the values of f(-2) and g(-6).
Putting x = -2 in f(x), we get,
f(-2) = [tex]-2(-2)^3 - 3[/tex] = -2*(-8) - 3 = 16 - 3 = 13
Putting x = -6 in g(x), we get,
g(-6) = 2(-6) + 4 = -12 + 4 = -8
Hence, the values of functions f(-2) and g(-6) are 13 and -8 respectively.
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Find the savings plan balance after 6 months with an APR of 8% and monthly payments of $200
The savings account balance after six months with an 8% annual percentage rate and $200 monthly contributions is $202.6.
What does a savings plan formula serve?Savings Plan Formula
The future worth of a savings or investment account in which you make regular deposits can be calculated using the formula below.
EXAMPLE 1 Assume you put $100 into a savings account each month that pays 7.3% interest that is compounded monthly.
To determine the saving plan balance after 6 month
First of all we have to calculate the growth factor
Growth factor =(1+(0.08/6)) per month
Growth factor= 1.013
Now let calculate the savings plan balance after 6 month
Saving plan balance after 6
Months =$200.00x1.0133
= $202.6
From conclusion the saving plan balance after 6 month is=$202.6
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Using the digits 1 to 9 as many times as you want, fill in the boxes to create three equivalent ratios. _ : _ = _ _ : _ = _ _ : _ _
The three equivalent ratios are given below .
What are equivalent ratios?
Ratios that can be streamlined or decreased to the same value are said to be equivalent. In other words, if one ratio can be written as a multiple of the other, then they are said to be equivalent. The ratios 1:2 and 4:8, 3:5 and 12:20, 9:4 and 18:8, and others are some examples of analogous ratios. To put it another way, two ratios are said to be equivalent if one of them can be written as the multiple of the other. Therefore, we must multiply the two values (antecedent and consequent) by the same number in order to obtain the equivalent ratio of another ratio. This approach is comparable to the approach for determining equivalent fractions.
1:9 , 99:11 , 9:11 , 1:99
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in a large bag of marbles, 20% of them are red. A child chooses 14 marbles from his bag. If the child uses the marbles at random what is a chance that the child gets less than six red marbles?
If the child uses the marbles at random what is the chance that the child gets less than six red marbles is given as 0.9561. See the calculation below.
Note that we are given the following:
p = 20% = 0.20
1 - p = 1 - 0.20 = 0.80
n = 14
Utilizing the binomial formula, we have:
P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x
P(X < 6) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)+ P(x = 4) + P(x = 5)
Plugging in the value of n, we have:
= ((14! / 0! (14)!) * 0.200 * (0.80)14 + ((14! / 1! (13)!) * 0.201 * (0.80)13 + ((14! / 2! (12)!) * 0.202 * (0.80)12 + ((14! / 3! (11)!) * 0.203 * (0.80)11 + ((14! / 4! (10)!) * 0.204 * (0.80)10 + ((14! / 5! (9)!) * 0.205 * (0.80)9
= 0.9561
As a result, the probability that the youngster would receive less than six red marbles is provided as 0.9561 if the marbles are used at random.
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What is the focus point of a parabola with this equation?
By interpreting the vertex form of the equation of parabola, the focus of the curve is equal to F(x, y) = (2, 0). (Correct choice: D)
How to determine the coordinates of the focus of a parabola
In this problem we find the equation of a parabola in standard form, which has to be rearranged into its vertex form in order to determine the coordinates of its focus.
The focus of a parabola is a point outside the curve such that the least distance from any point of the parabola and the least distance between that the point on the parabola and directrix are the same.
First, rearrange the polynomial into its vertex form by algebraic handling:
y = (1 / 8) · (x² - 4 · x - 12)
y + (1 / 8) · 16 = (1 / 8) · (x² - 4 · x - 12) + (1 / 8) · 16
y + 2 = (1 / 8) · (x² - 4 · x + 4)
y + 2 = (1 / 8) · (x - 2)²
y + 2 = [1 / (4 · 2)] · (x - 2)²
Second, determine the vertex and the distance between the vertex and the focus:
The parabola has a vertex of (h, k) = (2, - 2) and vertex-to-focus distance of 2.
Third, determine the coordinates of the focus:
F(x, y) = (h, k) + (0, p)
F(x, y) = (2, - 2) + (0, 2)
F(x, y) = (2, 0)
The focus of the parabola is equal to F(x, y) = (2, 0).
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Please help I’ll mark you as brainliest if correct!!
The set of letters in the word 'woodpecker' using the most concise method is {c, d, e, k, o, p, r, w}
Writing the elements of a setFrom the question, we are to write the set of letters of the given word.
The word is 'woodpecker'
We are to write the set using the listing (roster) method or the set builder notation.
The roster method or listing method is a way to show the elements of a set by listing the elements inside of brackets
Set builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy
The set builder notation is not a suitable method to list the elements of the given word.
The most concise method to list the elements of the given word, 'woodpecker', is the listing (roster) method.
Thus,
Using the listing (roster) method,
The set of letters of the given word is {c, d, e, k, o, p, r, w}
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ASAP!! The Brown family baked 3 pies for Thanksgiving. They made a pumpkin pie, an apple pie, and a cherry pie. They ate 0.75 of the pumpkin pie, 0.5 of the apple pie, and 0.6 of the cherry pie How many pies did the Brown family eat in all? Record your answer as a decimal number.
Answer: The Brown family ate 1.85 pies in all
Step-by-step explanation: If you think about it all you have to do is 0.75+0.5= 1.25 and then you do 1.25+ 0.6 and then get 1.85 so they ate 1.85 pies in all
Hope this helped!!!!
2. Solve the following addition problem. Remember to carry as necessary.
6 cu yd 9 cu ft
134 cu in
+ 1 cu yd 12 cu ft
200 cu in
The solution to the given addition problem is 150.6 ft^9.
Converting everything to the same unit is the simplest solution to this problem.
The conversions are:
1 cubic yard = (27 cubic feet)
1 cubic inch = (0.000578704 cubic feet)
The addition can be performed as,
(6 cu yd × 9 cu ft × 134 cu in) + (1 cu yd × 12 cu ft × 200 cu in)
= [6(27 cu ft) × 9 cu ft × 134(0.000578704 cu ft)] + [1(27 cu ft) × 12 cu ft × 200(0.000578704 cu ft)]
= 150.6 ft^9
The result of the addition is 150.6 ft^9.
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Consider the graph of the function f(x) = 2^x Which statements describe key features of function g if g(x) = f(x + 2)?
The statements that describe key features of function g if g(x) = f(x + 2) are;
a. y-intercept at (0,4)
b. domain of {x|-∞ < x < ∞}
c. horizontal asymptote of y = 0
What are the features of the Function?We are given the function f(x) = 2^(x)
We want to find the features of the function g if;
g(x) = f(x + 2)
Let us first find f(x + 2);
g(x) = f(x + 2) = 2^(x + 2)
The y-intercept is when x = 0;
g(0) = 2^(0 + 2)
g(0) = 4
Some features in a function that limit the x values are: roots, fractions, etc.
g(x) = 2^(x + 2) does not have any restricting value of x.
This means the value of x ranges from negative infinity to positive infinity.
Hence, the domain is: (-∞, ∞)
Next, calculate the horizontal asymptote.
To do this, we plot the graph of g(x) --> see attachment
Then we trace a horizontal line from the horizontal part of the curve of g(x) till it gets to the y-axis.
From the attached graph of g(x), the line touches the y-axis at y = 0
So, the horizontal asymptote is: y = 0
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The missing options are;
a. y-intercept at (0,4)
b. domain of {x|-∞ < x < ∞}
c. horizontal asymptote of y = 0
d. horizontal asymptote of y=2
e. y-intercept at (0,1)
Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
In 25 minutes Shiloh can In 10 laps around the track. Determine the number of
laps he can run
per minute.
A.
Find the constant of proportionality in this situation.
Answer:
B. Write an equation to represent the relationship.
Answer:
Shiloh can run 04 laps per minute if in 25 minutes Shiloh can run in 10 laps around the track and it is Laps per minute is simply division.
What is constant of proportionality?The ratio that is connecting two given numbers is what is known as the exact proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names that can be given for the constant of proportionality.
To represent the equation in laps per min,
L/m = 10/25
= 2/5
= 0.4 laps per minute
The constant of proportionality in this situation
10/25 = 0.4
The equation to represent the relationship.
y = 0.4x
How do you determine the proportionality constant?Identifying the same x and y variables is the first step in determining the proportionality constant. X will be the weight and Y will be the number of butter sticks in order to calculate the exact weight to stick ratio.
Then to determine the proportionality constant, we can use the constant equation k = y x.
Why is K the proportionality constant?When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.
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Help me pls with this fast!
Answer:
Step-by-step explanation:
...
Answer:
2x+9=7
Step-by-step explanation:
"Sum" means addition
"2 times a number" since the number is unknown we use a letter, since its a letter we usually don't need parentheses
"and" is usually used ror addition so another clue
"is" just means equals
Solve for x: |x − 2| + 10 = 12 (1 point)
x = 0 and x = 4
x = −4 and x = 0
x = −20 and x = 4
No solution
Answer:
x=20 and x=4
Step-by-step explanation:
pls help
what are the coordinates of Y if 5,12 is 1/3 of the way from X to Y
The coordinates of the point Y at the other endpoint is 41
How to determine the coordinates of the point Y?From the question, the given parameters are
Point X = 5The location of the point between X and Y = 12Proportion = 1/3Because there is not y coordinates in the coordinates, we can make use of only the x coordinate
So, we have the following equation
Point = Proportion * (Y - X)
Substitute the known values in the above equation
So, we have the following equation
12 = 1/3 * (Y - 5)
Multiply through the equation by 3
So, we have the following equation
36 = Y - 5
Add 5 to both sides of the equation
So, we have the following equation
Y = 41
This means that the conclusion is the coordinate of the point Y is 41
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2x-5>3 and -4x+7<-25
whats the compound inequality and how would it be graphed
Answer:
8 < x
see attached for the graph
Step-by-step explanation:
You want the compound inequality and the graph that represents the solution to the system ...
2x-5>3 and -4x+7<-25
SolutionThe first inequality has the solution ...
2x -5 > 3 . . . . . given
2x > 8 . . . . . . . add 5
x > 4 . . . . . . . divide by 2
The second inequality has the solution ...
-4x +7 < -25
-4x < -32 . . . . . . subtract 7
x > 8 . . . . . . . . divide by -4
The solution is the intersection of these solution spaces:
4 < x and 8 < x
The intersection is ...
8 < x . . . . . solution to the compound inequality
The graph is attached.
What’s the correct answer answer asap
the answers is a. bones to bones
I need help with question #8
1/4(n-6)= 1/4n-3/2
Hint: undo the fraction
1/4(n-6)=1/4n-3/2. We can say left side is equal to right side.
Given that,
1/4(n-6)=1/4n-3/2
We have to find the n value.
We have to 1st prove left side is equal to right side
We can split an equation into two parts, the left hand side and the right hand side. We refer to the LHS and RHS of the equation in abbreviated form. If the LHS and RHS are equal, then the equation is true; otherwise, the equation does not hold for at least some real number values.
First take the left side which is
1/4(n-6)
We multiply 1/4 to n-6
1/4n-1/4(6)
Now we divide 6/4
1/4n-3/2
See the right side
1/4n-3/2
Therefore,
left side is equal to right side.
1/4(n-6)=1/4n-3/2
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divide and round to the nearest hundredths place. 4.05 divided 0.07
We have the next operation
[tex]\frac{4.05}{0.07}=57.857=57.86[/tex]the result of this operation rounded to nearest hundredths place is 57.86
) Which problem below would require that you use the distributive property to help yousimplify it? Explain why the distributive property is required for that problem. What wouldyou use to simplify the other problem?2 (x+4)5+ 9(5-1)
Given the expressions:
[tex]\begin{gathered} 2(x+4) \\ 5+9\mleft(5-1\mright) \end{gathered}[/tex]You need to remember that the Distributive Property states that:
[tex]a(b\pm c)=ab\pm ac[/tex]• In order to simplify the first expression, you only need to apply the Distributive Property, because there is a number multiplying a Sum. Therefore, get:
[tex]\begin{gathered} =(2)(x)+(2)(4) \\ =2x+8 \end{gathered}[/tex]• In order to simplify the second expression, you need to follow these steps:
1. Apply the Distributive Property:
[tex]=5+(9)(5)-(9)(1)[/tex][tex]=5+45-9[/tex]2. Solve the Addition:
[tex]=41[/tex]Hence, the answers are:
• The first problem requires to use only the Distributive Property to simplify it. It is required because there is a number multiplying a Sum:
[tex]2(x+4)[/tex]Notice that the second expression can be simplified using the Distributive Property as the first step.
• The second problem can be simplified by applying the Distributive Property and then adding the numbers.
Which of the following is the correct factorization of the polynomial below?
2p²-11pq+24q²
A. (2p-4q)(p-4q)
B. (2p-4q)(p+ 4q)
C. (2p-4q)(2p² + 2q)
D. The polynomial is irreducible.
Answer:
I think it's D because it can't be factorized
What is the product of the reciprocal of 2/3, 1/8, and 5?
A. 5/12
B. 15/16
C. 2-2/5
D.9-1/10.
The answer key says (C) but I’m getting 12/5 so I’m confused
Answer:
c
Step-by-step explanation:
2-2/5=12/5
12/5=
2-2/5 is the mixed fraction for the number 12/5
well, the key and you are absolutely correct, so you're golden
[tex]\stackrel{reciprocals}{\cfrac{3}{2}\cdot \cfrac{8}{1}\cdot \cfrac{1}{5}}\implies \cfrac{3}{5}\cdot \cfrac{8}{2}\cdot \cfrac{1}{1}\implies \cfrac{3}{5}\cdot \cfrac{4}{1}\cdot \cfrac{1}{1}\implies \cfrac{12}{5}\implies \cfrac{10+2}{5} \\\\\\ \cfrac{10}{5}+\cfrac{2}{5}\implies 2+\cfrac{2}{5}\implies 2\frac{2}{5} ~~ \checkmark[/tex]
Find a smart way to compute.1 8/11 x 5/12 + 5/12 x 3/11
On simplifying the given equation, the answer is [tex]\frac{5}{6}[/tex]
How an equation can be simplified?The fundamental guidelines and procedures to simplify any statement are as follows:
By multiplying factors, remove any grouping symbols like brackets and parenthesis.
If the words contain exponents, use the exponent rule to eliminate grouping.
Add or subtract like terms to combine them.
Add the constants together.
Given,
1 8/11 x 5/12 + 5/12 x 3/11
[tex]\frac{19}{11}[/tex] × [tex]\frac{5}{12}[/tex] + [tex]\frac{5}{12}[/tex] × [tex]\frac{3}{11}[/tex]
Taking [tex]\frac{5}{11 * 12}[/tex] as a common factor,
⇒ [tex]\frac{5}{11 * 12}[/tex] ( [tex]19 + 3[/tex])
⇒ [tex]\frac{5}{11 * 12}[/tex] × 22
On simplifying,
⇒ [tex]\frac{5}{6}[/tex]
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go quick if you have a good brain
see attachment beloww.
Answer:y=21°
x=8°
Step-by-step explanation:
3y+27=90
3y=63
y=21°
x+90°+8x+18°=180°
9x+108°=180°
9x=72°
x=8°
at birth,a male baby giraffe stands almost 2 feet tall.at 3 years of age ,the male giraffe will be about three times as tallas at birth.
Answer: if you're asking how tall it will stand at 3 years of age it would be 6.
Step-by-step explanation: 2 times 3 equals 6.
Fråga 5 20 poäng A farmer wants to plant a small rectangular plot of ornamental blue corn. He has enough fencing material to enclose a space with a perimeter of 144 feet. He wants to know the dimensions of the largest rectangle that can be enclosed with 144 feet of fence. To help find them, he graphed the following equation. Area = x (72 - x) What are the dimensions of the largest area the farmer can enclose with 144 feet of fence?
The maximum dimensions is a square of sides 36 ft by 36 ft;
The maximum area is 1,296 ft^2
Here, we want to know the diemensions of the largest area the farmer can enclose within the perimeter
Mathematically, the greatest dimension that can maximize the area of the plot is the shape being a square
In other words, we need the diemnsions of both sides to be equal so as to get the area
If the dimensions are equal, we can say the length and width are represented by x
The length is thus as follows;
[tex]\begin{gathered} 4\text{ }\times\text{ x = 144} \\ 4x\text{ = 144} \\ \text{ x = 144/4} \\ x\text{ = 36 ft} \end{gathered}[/tex]The greatest possible or the maximum area is thus;
[tex]36\times36=1,296ft^2[/tex]The perimeter of a garden is 88 feet. The length is 12 feet greater than the width.
Answer:
Part 1 is B, Part 2 is D
If you want an explanation I can give one :)