Final answer:
The box fits four cubical blocks with a side of 2 cm, so its volume is four times the volume of one block, which is 32 cm³.
Explanation:
Each cubical block has a side of 2 cm, and since only four blocks fit in the box completely without any space left, we can understand that the box accommodates exactly four cubes. To find the volume of one cube, we calculate the volume of a cube which is given by side³. Since the side is 2 cm, the volume of one cube is 2 cm * 2 cm * 2 cm = 8 cm³. Therefore, the box that fits exactly four of these cubes would have a volume which is four times the volume of one cube, which is 4 * 8 cm³ = 32 cm³. Hence, the volume of the box is 32 cm³, which corresponds to option B.
there are 100 officials at the race. you read that the total cost of all the officials for one day is 20 654. how much does each official get paid per day?
Answer:
$206.54
Step-by-step explanation:
Divide the number of officials by the total days pay to get the pay for each official working the race
Jamal claims that the graph of f(x)+2 is equivalent to the graph of f(x+k).For the case where Jamals claim is correct, what must be the value of k?
A.-4
B.-1
C.1
D.2
Answer:
[tex]k=2[/tex]
Step-by-step explanation:
1) Rewriting:
[tex]f(x+k)=f(x)+2[/tex]
2) Suppose f(x)= ax (Linear function with b=0)
[tex]a(x+k)=ax+2\\a(x+k)=x+2\\ax+ak=x+2 \Rightarrow a=1\\x+k=x+2\\k=2[/tex]
3) Check the graph below
The correct option is D) 2.
Step-by-step explanation:
Given :
f(x) +2 and f(x +k)
Solution :
let, [tex]f(x) = ax[/tex] (linear function with b = 0)
so, [tex]f(x+k)=a(x + k)\;\;\;at,\; x=x+k[/tex]
Rewriting,
[tex]f(x+k)=f(x) + 2[/tex]
[tex]a(x + k) = ax +2[/tex]
[tex]k = 2 \;\;\;(at,\;a=1)[/tex]
Therefore, the correct option is D) 2.
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How do you convert minutes to hours
Easy, just do 60 seconds which equals a minute. Since we know that now simply use 60 minutes to get you to an hour. If your doing minutes to hours make sure there is a 0 at the end.
If a single six sided die is rolled, what are the odds that you will roll a number less than 5?
Choose the correct answer below.
Answer:
C) 4 : 2 Odds of rolling a number less than 5
Step-by-step explanation:
If there are 6 sides on the dice, 4 of the sides are going to be less than 5 and two of them are not.
Answer:
4:2 Odds of rolling a number less than 5.
Step-by-step explanation:
ODDS is defined as probability that event will occur divided by probability that event will not occur.
A six sided die has 6 numbers in total.
Numbers less than 5 are: 1,2,3, and 4. In total 4 numbers.Numbers NOT less than 5 are: 5 and 6. In total 2 numbers.The odds of rolling a number LESS THAN 5 is therefore:
Odds = 4:2
Last answer choice is right.
The Organic Cafe ordered 45 boxes of sugar packets. Each box contained 37 packets of sugar. How many sugar packets in total did The Organic Cafe order?
In the figure below, A shows the position of a house on the shore and B shows the position of a house on an island. To find the distance between the two houses,a surveyor measures from the house on shore to point C. An instrument is used to find
The surveyor is using a trigonometric method to calculate the distance between the two houses. They form a right triangle with points A, B and C, measure the length AC and the angle at point A or C, and then calculate the distance AB using trigonometric ratios.
Explanation:In this scenario, the surveyor is using a method resembling triangle-based methods in Mathematics, which specifically relates to trigonometry. To determine the distance between points A (house on shore) and B (house on island), the surveyor measures line AC, forms a right triangle ABC, and uses an instrument (like a theodolite) to measure one of the corners (usually angle at point A or C). With the measured length and angle, the distance AB can be calculated using trigonometric ratios (like sine, cosine, or tangent), depending upon the given scenario. For instance, if the angle at point A and length AC are known, then the distance AB can be calculated as AB = AC / cos(A), where A is the angle at point A.
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Which of the following is the graph of y= 2x2+3/4?
Compare the graph of the function, g(x)=(1)/(x-1)-3(, with the graph of its parent function. ) Which of the following options best describes the transformations undergone by g(x)? Select all that apply.
left 1
up 3
right 1
left 3
down 3
up 1
right 3
Answers:
right 1, down 3 (these two answers only)
Step-by-step explanation:
There are two transformations going on. The first of which is the horizontal or x translation (aka shifting) where the 'x' turns into 'x-1'. This moves the xy axis 1 spot to the left, giving the illusion that the graph moves 1 unit to the right.
The "-3" at the end shifts the graph down 3 units. If g(x) = f(x) - 3, then g(x) is the output of f(x) but 3 less than that, which is why it shifts down 3 units.
The function g(x) represents two transformations from its parent function f(x) = 1/x: a horizontal shift to the right by 1 unit and a vertical shift down by 3 units.
Explanation:When comparing the graph of the function g(x) = (1)/(x-1) - 3 with its parent function f(x) = 1/x, the transformations undergone by g(x) include:
The addition of -1 inside the parentheses with the independent variable x, which shifts the graph to the right by 1 unit.The subtraction of 3 from the entire expression, which translates the graph down by 3 units.These transformations can be understood with the help of given examples. For instance, adding or subtracting a number to/from the independent variable x, like f(x+1), results in a horizontal shift of the graph. Multiplying the independent variable by a number, say 2 as in f(2x), would cause a horizontal compression of the graph. In our case, since the function g(x) includes x-1, it is indicating a horizontal shift to the right, and since the -3 is subtracted from the entire function, it denotes a vertical shift downward.
If x=9 and y=−2, evaluate the following expression : 6x−8y
6(9)-8(-2)
6*9=54
8*(-2)=-16
54-16=38
38<-----
Answer:
70
Step-by-step explanation:
x=9 and y=−2, evaluate the following expression : 6x−8y
plug in
6(9) - 8(-2)
= 54 + 16
= 70
Which part of the proof does the fourth statement and reason represent?
Given: AB ≅ BC
BC ≅ EF
Prove: EG = AB + FG
It is part of the given information.
It is part of the argument.
It is the conclusion.
It is an assumption.
Answer:
Option B is correct.
Reason:It is an argument
Step-by-step explanation:
Given: [tex]AB \cong BC[/tex] and [tex]BC \cong EF[/tex]
By transitive property: a = b and b = c then, a =c
⇒[tex]AB \cong EF[/tex]
AB = EF [def of [tex]\cong[/tex] segment]
By Segment Addition Postulate states that given two points A and C, and a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation
AB + BC = AC.
Since, the line segment EG , F lies on the line segment;
then, by segment addition postulates we have;
EG = EF + FG
By substitution AB=EF
⇒ EG = AB + FG hence proved!
Since, in the fourth statement reason is: It is an argument
Answer:
B, it is an argument
Step-by-step explanation:
Solve the system of equations in three variables
We start from the third equation:
4z = 16 divide both sides by 4
z = 4Put the value of z to the second equation:
y + 4 = 5 subtract 4 from both sides
y = 1Put the values of y and z to the first equation:
3x + 2(1) - 4 = 4
3x + 2 - 4 = 4
3x - 2 = 4 add 2 to both sides
3x = 6 divide both sides by 3
x = 2Michael and Imani go out to eat for lunch. If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill?
Answer:
The bill total is $27.32
Step-by-step explanation:
how to figure out tax amount: 25.30 x .08 = $2.024
add tax to cost of meal : 25.30 + 2.024 = $27.32
To calculate the total cost of the meal including an 8% tax, multiply the cost of the meal by the tax rate and add this to the original meal cost. The tax comes to $2.02. So, the total cost of the meal, including tax, is $27.32.
Explanation:The question asks how much the total bill is for Michael and Imani when they go out to eat for lunch. The food and beverages cost $25.30 and there is an 8% meal tax. To calculate the total cost of the meal including the tax, we can multiply the cost of the meal ($25.30) by the tax rate (8%) and add this to the original cost for the meal.
First, let's convert the tax rate from a percentage to a decimal. 8% is equivalent to 0.08 as a decimal. Then, we multiply $25.30 by 0.08:
$25.30 * 0.08 = $2.02
This amount ($2.02) is the tax on the meal. To get the total cost, add this tax amount to the cost of the meal:
$25.30 + $2.02 = $27.32
So, Michael and Imani's bill, including the 8% meals tax, will be $27.32.
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Stan drove 3300m to the grocery store. The tires on his truck are 2.2m in circumference. How many rotations did each tire make on Stan's drive?
Answer:
1,500 rotations
Step-by-step explanation:
To answer this, divide 2.2 m into 3300 m. This results in 1500.
The wheels made 1,500 rotations each.
Is 3x+12-2x equivalent to x+12. Use two properties of operations to justify your answer
Answer:
Step-by-step explanation:
Commutative property: 3x+12-2x = 3x-2x+12
Substitution property: 3x-2x+12 = x+12
x+12 = x+12
Subtraction property: x-x+12 = x-x+12
Substitution property: 12 = 12
pre algebra 25=12+r r =? please show your work
[tex]25=12+r\\r=25-12\\r=13[/tex]
12 + r = 25 subtract 12 from both sides
12 - 12 + r = 25 - 12
r = 13Keiko makes 8 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Answer:
8h = pStep-by-step explanation:
So if p is the total amount paid, and h is the amount of time spent working, it'll be worked out something like this.
The amount of money she makes per hour x the amount of time spent working = the amount she is paid.
Thus making it...
8 x h = p
but in algebra expressions, we don't normally use arithmetic symbols. So if we get rid of that, we get the answer of 8h = p.
:)
If you know the answer could you help me on it
Answer:
The answer is B because the numbers in the geometric sequence are being multiplied by 2.
Solve the system by the elimination method. 2x + y - 4 = 0 2x - y - 4 = 0 When you eliminate y, what is the resulting equation? x = 0 4x = -8 4x = 8
Answer:
Option C.
Step-by-step explanation:
System of the equation consists of two equations
2x + y - 4 = 0
2x + y - 4 + 4 = 0 + 4
2x + y = 4--------(1)
and 2x - y - 4 = 0
2x - y + 4 - 4 = 0 + 4
2x - y = 4------(2)
Now we will add these equations to eliminate y.
(2x + y) + (2x - y) = (4 + 4)
(2x + 2x) + (y - y) = 8
4x = 8
Therefore, resulting equation will be 4x = 8
Option C. will be the answer.
If you are given a 4% raise and inflation is 1%, you are _____.
A you earn 3 percent more money
Step-by-step explanation:
4-1
Answer:
If you are given a 4% raise and inflation is 1%, you are making 3% more.
Step-by-step explanation:
If you are given a 4% raise and inflation is 1%, you are making 3% more.
[tex]4-1=3[/tex]
Or we can say you are making more money.
This is because you are given high percent of raise as compared to the low rate or percent of inflation, that shows you are on the positive side.
Suppose you have $30 to spend on bags of tootsie rolls that are worth $3 and bags of lollipops worth $5. If you have to use all of their money, what combinations of candy bags can they buy?
Construct a linear equation and find/explain the y-intercept, x-intercept, and slope.
Finally, if you have $45 to spend on the candy, how would that impact everything?
Answer:
see below
Step-by-step explanation:
Let x = tootsie rolls
y = lollipops
Toosie rolls are 3 dollars and lollipops are $5 and you only have 30 dollars.
3x+5y =30
To find the x intercept, set y=0 and solve for x
3x +0 = 30
3x = 30
Divide by 3
3x/3 = 30/3
x = 10
The x intercept is 10. This means if you get no lollipops, you can have ten tootsie rolls.
To find the y intercept, set x=0 and solve for y
0 +5y = 30
5y = 30
Divide by 5
5y/5 = 30/5
x = 6
The y intercept is 6. This means if you get no tootsie rolls you can have 6 lollipops.
To find the slope, solve the equation for y
3x+5y =30
Subtract 3x from each side
3x-3x+5y = -3x+30
5y = -3x+30
Divide by 5
y = -3/5 x +30/5
y = -3/5 x +6
The slope is -3/5. For every three less lollipops you get, you can have 5 more tootsie rolls.
If you have $45 dollars instead of 30, this will change the x and y intercepts, but not the slope.
3x+5y =45
To find the x intercept, set y=0 and solve for x
3x +0 = 45
3x = 45
Divide by 3
3x/3 = 45/3
x = 15
The x intercept is 15. This means if you get no lollipops, you can have 15 tootsie rolls.
To find the y intercept, set x=0 and solve for y
0 +5y = 45
5y = 45
Divide by 5
5y/5 = 45/5
x = 9
The y intercept is 9. This means if you get no tootsie rolls you can have 9 lollipops.
To find the slope, solve the equation for y
3x+5y =45
Subtract 3x from each side
3x-3x+5y = -3x+45
5y = -3x+45
Divide by 5
y = -3/5 x +45/5
y = -3/5 x +9
The slope is -3/5. For every three less lollipops you get, you can have 5 more tootsie rolls.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the inverse of the given function.
27pionts
Answer:
D. f^-1(x) = log2(x -6)4x^2 -3 . . . . x ≤ 0B. √(x^5) -3√(x^3) -18√xStep-by-step explanation:
1. When you replace f(x) by x and x by y, you have
... x = 2^y + 6
The first thing you do is subtract 6; then you take the base-2 logarithm:
... (x -6) = 2^y
... log2(x -6) = y = f^-1(x)
You know that to get the y-term by itself, you must subtract 6. Anything else you do will operate on (x-6). Only answer choice D has that sort of construction.
2. When you swap x and y and solve for y, you have ...
... x = -1/2√(y+3)
... -2x = √(y +3) . . . . . . multiply by -2
... (-2x)^2 = y +3 . . . . . square
... 4x^2 - 3 = y = f^-1(x) . . . . subtract 3
The range of f(x) is (-∞, 0], so that is the domain of f^-1(x). That is, f^-1(x) is defined for x ≤ 0.
3. The product of the two functions is ...
... (x -6)(√x)(x +3) = (√x)(x^2 -3x -18)
Every term will have a factor of √x, and the coefficients will be 1, -3, -18. Only selection B matches those conditions.
Answer:
Question One: log_2(x - 6) = y
Question Two: First blank: 4 Second blank 0
Question Three: B
Step-by-step explanation:
f(x) = 2^x + 6
y = 2^x + 6 Interchange the x and y
x = 2^y + 6 Subtract 6 from both sides
x - 6 = 2^y Take the log of both sides
log(x - 6) = log 2^y The power can be multiplied by the log of 2
log(x - 6) = y log(2) Divide by the log of 2
log(x - 6)/log(2) = y This to me is the preferred answer. It allows you to calculate what the actual number is or graph it on Desmos
The answer I have given is equivalent to using base 2 as your log, but calculating that is not always easy.
log_2(x - 6) = y
Answer: D
Problem Two
You want the inverse of y = - 1/2 sqrt(x + 3) x ≥ - 3
Note: you cannot have any number less than -3 because if you do, you will be taking the square root of -x which involves complex numbers. In addition x ≥ -3 is a domain. You have to keep that in mind when doing this question.
y = - 1/2 sqrt(x + 3) Interchange the x and yx = - 1/2 sqrt(y + 3) Multiply by - 2-2x = sqrt(y + 3) Square both sides(-2x)^2 = sqrt(y + 3)^2 4x^2 = y + 3 Subtract 3 from both sidesy = 4x^2 - 3The domain and range of this is a little harder to figure out. The range of f(x) becomes the domain of f-1(x)
The range of f(x) is 0 <=y < - infinity
So the domain of f-1(x) <= 0
Answer: The first blank is 4 and the second one is 0
Graph: the graph is given you below the question. What it shows is the f(x) and f^-1(x) are symmetrical about y = x. Most inverses are. If you want to check your work, it is best to include a graph when doing inverses.
Red OriginalBlue inverseBlack: y = xProblem Three
The best way to begin this problem is to apply the associative property of multiplication and start by rewriting the givens as x^(1/2)[(x - 6)(x + 3)]. Do what is in the square brackets first.
x^(1/2) [x^2 - 6x + 3x - 18]x^(1/2) [x^2 - 3x - 18]Now deal with the x^(1/2) which must be multiplied by all three terms in the square brackets.
x^(1/2)*x^2: x^(2 + 1/2) = x^(4/2 + 1/2) = x^(5/2)x^(1/2)*(-3x): - 3 x^(2/2 + 1/2) = - 3x^(3/2)x^(1/2)*(-18): - 18x^(1/2)Result: x^(5/2) - 3x^(3/2) - 18x^(1/2)
Answer: √(x^5) - 3√x^3 - 18√x
Answer: B
Your Food Cost s are $2,500. Your total food sales ae $17,500. What percent of your food sales do the food costs represent?
Answer:
the correct answer is 14.29%
Step-by-step explanation:
REBECA HAD 9/10 OF A YARDOF RIBBON. THEN SHE GAVE 7/20 OF A YARD OF FRIEND. HOW MUCH DOES SHE HAVE LEFT?
Answer:
She has 11/20 yds left
Step-by-step explanation:
We take what she had and subtract what she gave away
9/10 - 7/20
We need to get a common denominator of 20
9/10 *2/2 - 7/20
18/20 - 7/20
11/20
She has 11/20 yds left
Translate the word phrase into a math expression.
11 times the sum of a number and 15
11(y+15)
11+(y+15)
11y+15y
11y+15
Answer: 11(y+15)
Step-by-step explanation:
−
42
6
=
x
+
15
−
7
=
x
+
15
−
7
−
15
=
x
−
22
=
x
Complete the following sentence: Two events that are mutually exclusive...
Answer:
If two events are mutually exclusive then they cannot occur at the same time.
Step-by-step explanation:
If two events are mutually exclusive then they cannot occur at the same time.
For example: If you take a coin, the two possible outcomes on flipping a coin will be mutually exclusive as when you flip a coin, it cannot give both heads and tails at the same time.
Hence, the two mutually exclusive events cannot occur at the same time.
Russell has a collection of 1,200 pennies. Of these pennies, 25% are dated before 1980, 35% are dated from 1980 to 2000, and the rest are dated after 2000. How many pennies in Russell’s collection are dated after 2000?
Answer:
480 pennies dated after 2000.
Step-by-step explanation:
1. Pennies dated before 1980 (x) - 25%,
All pennies (1,200) - 100%.
Then
[tex]\dfrac{x}{1,200}=\dfrac{25}{100},\\ \\100x=25\cdot 1,200,\\ \\x=25\cdot 12=300.[/tex]
2. Pennies dated from 1980 to 2000 (y) - 35%,
All pennies (1,200) - 100%.
Then
[tex]\dfrac{y}{1,200}=\dfrac{35}{100},\\ \\100y=35\cdot 1,200,\\ \\y=35\cdot 12=420.[/tex]
3. Rest pennies are dated after 2000, then
[tex]1,200-300-420=480.[/tex]
Answer:
480
Step-by-step explanation:
Please help!! Only answer if you know the answer. Thank you.
ANSWER: Tim Carter's weekly pay was $282.25.
I will work on Tim Carter's weekly pay. Because he worked 50 hours, and there are 40 regular hours, he worked 10 overtime hours.
To find out his regular pay, we need to multiply his regular pay by his regular hours.
[tex]40 * 5.15 = 206[/tex]
Tim Carter makes $206 for his regular hours. To find out his overtime pay, we need to multiply his regular pay by his overtime hours, then multiply that product by 1.5.
[tex]10 * 5.15 = 51.5\\\\51.5 * 1.5 = 77.25[/tex]
Tim Carter makes $77.25 for his overtime hours. Lastly, add the regular pay and his overtime pay to get his weekly pay.
[tex]206 + 77.25 = 283.25[/tex]
Tim Carter's weekly pay was $283.25.
Answer:
Step-by-step explanation:
OT Weekly Pay
Tim Carter: 10 40x5.15= 206 5.15 x 1.5=7.725
7.725 x 10 = 77.25 206 + 77.25 = $283.25
Jesse Jones: 7.5 40x5.15= 206 5.15 x 1.5 = 7.725
7.725 x 7.5 = 57.9375 = 57.94
206 + 57.94 = $263.94
Barbara Burns: 4 40x5.15= 206 5.15x1.5 = 7.725
7.725 x 4 = 30.90 206 + 30.90 = $236.90
A car's wheels spins at 1000 revolutions per minute. The diameter of the wheels is 23 inches. You want to know how fast the car is traveling, so what is the speed?Thank you
Answer:
72,220 inches per minute
Step-by-step explanation:
A car's wheels spins at 1000 revolutions per minute. The diameter of the wheels is 23 inches.
1 revolution = [tex]2\pi[/tex] radians
[tex]\frac{theta}{tome}=\frac{1000 \ revolution}{1 \ minuite} = \frac{1000* 2\pi }{1} =\frac{2000\pi}{1 \ minute}[/tex]
Speed [tex]V= \frac{r*theta}{t}[/tex]
r is the radius , theta is the angle and t is the time
We know diameter = 23 , then radius = 23/2
Speed [tex]V= \frac{23}{2}*\frac{2000\pi}{1}[/tex]
Value of pi = 3.14
speed = 23000* 3.14= 72220 inches/ minute
Answer:
72,220 inches per minute
Step-by-step explanation:
657 passengers paid £247 each for a cruise on a small cruise ship. Estimate the amount paid by the passengers in total
Answer:
The passengers paid approximately 162500
Step-by-step explanation:
We are find how much the passengers paid
657 passengers * 247 per passenger
Round 657 to 650
Round 247 to 250
650 * 250 = 162500
The passengers paid approximately 162500
Erica babysits for 4.5 hours and is paid $27. If the people she babysits for have $34 to pay her, how long can they stay out?
Answer:
5 2/3 hours
Step-by-step explanation:
We can use a ratio to solve this problem
hours over money
4.5 hours x hours
------------- = ------------
27 dollars 34 dollars
Using cross products
4.5 * 34 = 27 * x
153 =27x
Divide each side by 27
153/27 = 27x/27
5.666666 hours