Compared with the beam, the large cube has the same volume but a smaller surface area.
What is a rectangle?It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
Given that, there are two sets of eight blocks, each with an edge measurement of 1 cm. Two blocks are placed on top of two other blocks to form a big cube. You assemble the second set into a 1-by-8-block straight beam.
Since the volume is the same.
The surface area of a cube,
=6a²
=6(2)²
=6×4
=24 cm²
The surface area of a beam,
=1 × 8
=8 cm²
Thus, compared with the beam, the large cube has the same volume but a smaller surface area.
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A cable on a fishing boat lowers a fish trap into a lake at a rate of 3 1/2 feet per second. What is the change in depth of the fish trap after 12 seconds?
Answer:
After 12 Seconds the cable would be 42 Ft down in depth
Step-by-step explanation:
3 1/2 Ft = 1 Second
3 1/2 Ft x 12 Seconds = 42Ft in Depth
The change in the depth of the fish trap after 12 second is 30 feet.
What is multiplication?The mathematical operation of multiplication is arithmetic. Additionally, it involves repeating the same forms of statements.
Example: 2 + 3 signifies that 2 is multiplied by 3 or that 3 is multiplied by 2 times.
Given, a cable on a fishing boat lowers a fish trap into a lake at a rate of 3 1/2 feet per second.
[tex]3\frac{1}{2}[/tex] = 5/2 feet per second.
To find the change in depth of the fish trap after 12 seconds:
Multiplied by 12 to the rate of feet per second.
5/2 x 12
= 30 feet
The change of rate is 30 feet per 12 second.
Therefore, the change in depth is 30 feet per 12 second.
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We are evaluating a project that costs $786,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 65,000 units per year. Price per unit is $48, variable cost per unit is $25, and fixed costs are $725,000 per year. The tax rate is 22 percent, and we require a return of 10 percent on this project.
We are evaluating a project that costs $786,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 65,000 units per year. Price per unit is $48, variable cost per unit is $25, and fixed costs are $725,000 per year. The tax rate is 22 percent, and we require a return of 10 percent on this project
The tax rate for 10% is IRR = 78%.
The Initial evaluating cost is $786000 and the
Depreciation expense per year will be = $786,000 / 8 = $98,250.
and the contribution margin per unit = $48 - $25 = $23
total units sold Projected per year = 65,000
fixed costs will be per year = $725,000
At Present the tax rate = 22%
Net cost fixed per year = -$786,000
Net Cost Fixed year 1-8 = {[($23 x 65,000) - $98,250 - $725,000] x 0.78} + $98,250 = $622,215
Net Per Variable = $2,533,471.10
Hence the answer is, The tax rate for 10% is IRR = 78%.
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QUESTION 2 1 POINT
A stock broker allocated $100,000 to an account earning 4% per year compounded continuously. If no withdrawals are
made, how much was in the account at the end of four years? Round the answer to nearest dollar.
Answer: 16,000
100,000 x 0.04 x 4
p x I x T.
A camera store develop 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls. What is the ratio of rolls with double prints to rolls develop?
A camera store develops 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls, then the ratio of rolls with double prints to rolls develop would be 5:7.
What is the ratio in mathematics?
A ratio in mathematics shows how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-total fruit ratio is 8:14.
A camera store develops 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls.
Then the ratio of rolls with double prints to develop = 1500/2100
Simplifying the above ratio we get
= 5/7
Hence, the ratio of rolls with double prints to rolls develop would be 5:7.
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I need assistance working these problem out.
Inverse [tex]f^{-1}(x) = \frac{log(x)}{log7}[/tex] and [tex]f(x) = 10^{x}[/tex].
[tex]f(x) = 7^{x}[/tex]
First, replace f(x) with f(y).
Now, [tex]y = 7^{x}[/tex] will become [tex]x = 7^{y}[/tex]
Taking log on both sides,
log(x) = y(log 7)
y = log(x)/log 7.
Similarly, [tex]f^{-1}(x) = log_{10}x[/tex]
replace f(x) with f(y).
[tex]x = f^{-1}(y) = log_{10}y[/tex]
[tex]y = 10^{x}[/tex]
Hence, [tex]f(x) = 10^{x}[/tex].
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solve each system by substitution 5x+4y=-16 y= 2x+9 what is the anwser
x=-20/13 and y=77/13 are solutions of 5x+4y=-16 and y= 2x+9
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The two equations are
5x+4y=-16 ...(1)
Five x plus 4 y equal to minus sixteen.
y= 2x+9 ...(2)
y equal to two times of x plus nine.
Substitute 2 in 1.
5x+4y=-16
5x+4(2x+9)=-16
5x+8x+36=16
13x+36-16=0
13x+20=0
13x=-20
x=-20/13=-1.53
substitute the value of x in y.
y=2(-20/13)+9
y=(-40+117)/13
y=77/13
Hence the value of x is -20/13 and y value is 77/13.
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Suppose the length and width of the rectangle are doubled. What effect would this have on the area? Justify your answer.
The area is increased by 204 ft².
What is rectangle?
A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
Initial length l= 4 ft
Initial width l= 17 ft
Area = l*w = 4*17 = 68 ft²
When length and width of the rectangle are doubled:
l=2*4=8 ft
w= 2*17= 34 ft
Area= 8*34= 272 ft²
Difference = 272 - 68 = 204 ft²
Thus, the area is increased by 204 ft².
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15. Evie added 4 stamps to her collection and then lost 9 stamps when she brought her stamp book outside. Write an equation that shows Evie's net gain or loss.
The linear equation y = x - 5 show's Evie's net loss or gain
Linear EquationLinear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.
In solving this problem, we have to write the problem in a form of linear equation.
Let;
y = The number of stamps available nowx = number of stamps she originally hady = x + 4 - 9
y = x - 5
The equation to show Evie's net gain or loss is y = x - 5
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A taxi company charges a flat fee of $5.50 plus an additional $1.50 per mile. Write an equation in slope-intercept form that represents the total cost, c, of a ride that is m miles long.
Look at the linear expression:
. 4a-4+6a-11
What are the like terms in the expression?
:
The like terms to the Linear expression: 4a-4+6a-11 is 10a - 15
What is linear expression?A Linear equations are the equations of degree 1. It is the equation for the straight line.
Collect the like terms of the expression
4a +6a -4 -11
Add the like terms
10a -15
Therefore the like terms in the linear expression is 10a -15
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I thought of a 3 digit number. Each digit i the quare of the digit to the right. What i my number?
The answer to the given question is 111.
The complete question might be as follows:
I thought of a 3 digit number. Each digit is the square of the digit to the right. What is my number?
= x*100 + y*10 + z.
Requirements:
y = z^2
x = y^2.
Now we shall start to give values to z. Let us start with zero.
If z = 0, then: y = 0^2 = 0, then: x = 0^2 = 0. Then the number would be 0*100 + 0*10 + 0 = 0. This is not a 3 digit number.If z = 1, then: y = 1^2 = 1, then: x = 1^2 = 1. Then the number would be 1*100 + 1*10 + 1 = 111. This is a 3 digit number.If z = 2, then: y = 2^2 = 4, then: x = 4^2 = 16. Then the number would be 16*100 + 4*10 + 2 = 1642. This is not a 3 digit number. This happened because the first digit (x) is not a single digit number.So, values of z which are equal or larger than 2 can be eliminated.Hence, for the question: I thought of a 3 digit number. Each digit is the square of the digit to the right. What is my number? The answer is 111, because the 3 digit number that would fit the requirements mentioned is only 111.
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PLEASE HELP! I NEED THIS BADLY! Is (x-3) a factor of 2x^3-4x^2-6?
YES OR NO?
find the remainder of 2x^3-4x^2-6
(just type the answer!)
Answer: 1. no 2. 104
Step-by-step explanation:
A manufacturing machine has a 7% defect rate. If 4 items are chosen at random, what is the probability that at least one will have a defect?.
A manufacturing machine has a 7% defect rate. If 4 items are chosen at random,
The probability of randomly choosing atleast one defective item would be 0.3043
Given the Parameters :
Defect rate = P(defect) = 0.07
Probability = required outcome / Total possible outcomes
P(atleast 1 is defective) = 1 - P(none is defective)
P(not defective) = 1 - P(defective) = 1 - 0.07 = 0.93
P(none is defective) = P(non defective)^4
P(none defective) = 0.93 × 0.93 × 0.93 × 0.93 = 0.7480
P(atleast one is defective) = 1 - 0.7480 = 0.252
Therefore, probability of atleast one defective item is 0.252.
Hence the answer is, the probability of randomly choosing atleast one defective item would be 0.3043
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in a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack. (round your answers to four decimal places.) if a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack?
The probability that the player will receive a blackjack from a player is dealt 2 cards from a standard deck of 52 well-shuffled cards is 0.0483.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
Combinations of drawing 1 ace * combinations of drawing 1 face cards / all possible 2 card combinations
4C1 * 16C1 / 52C2
4 * 16 / (52 * 51/2)
=64/1326
=.0483
When a player is dealt two cards from a standard deck of 52 properly shuffled cards, the likelihood that they will get a blackjack is 0.0483.
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-5(13d+ 11) how can i simplify this?
Answer:
-65d - 55
Step-by-step explanation:
Given expression,
→ -5(13d + 11)
Simplifying the expression,
→ -5(13d + 11)
→ (-5 × 13d) + (-5 × 11)
→ -65d + (-55)
→ -65d - 55
Thus, answer is -65d - 55.
Question 3 (2 points)
2
-2 -1
3-
1
-1+
-2+
-3
1 2 3
The function f(x)is graphed on the coordinate plane.
What is f(4)?
Enter your answer in the box.
f(4) =
The value of f(4) = 0 by the given graph.
What is graph?
Graph is diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Given graph is straight line, and the equation of line is given as
y =mx+b
where m is the slope and as we know y is dependent variable,
we can write it as
f(x)= mx +b
The coordinates are (4,0) and (0,2)
m = 2-0/0-4
m = -1/2
y = -1/2 x +b
we can see the line intersect the y-axis at 0,2
b =2
y = -1/2 x +2
at x =4
f(4) = -2+2=0
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Select the best answer for the question.
15. A basketball team's free-throw percentage (FT%) is calculated using two other statistics: their free throws attempted (FTA) and free throws made
(FTM). Which of these shows the correct formula?
O A. FT% = FT/FTM* 100%
O B. FT% = FT/FTA * 100%
O C. FT% = (FTM-FTA) * 100%
O D. FT% = (FTA-FTM)* 100%
The correct formula to represent the free throw percentage for the basketball team is given by FT% = FTM/FTA × 100%
The percentage of any quantity is measured by multiplying the ratio of the successful amount and the total amount by 100.
Here
Total number of free throws attempted = FTA (this is the total amount)
Total number of free throws made = FTM (this is the successful amount)
Required percentage = (FTM / FTA ) × 100%
Hence the required correct option is the second one:
FT% = FTM/FTA × 100%
The English word "percentage" derives from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100. It is a relationship, in other words, where the value of the whole is always taken to be 100.
Calculating a percentage in terms of 100 is known as calculating a percentage. You can determine a percentage in one of two ways:
We employ a unitary method by changing the denominator of the fraction to 100.
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The linear function f(x) is represented in the graph, and the linear function g(x) is represented in the table. Graph of linear function f of x going through negative 4 comma negative 1, negative 2 comma 0, 0 comma 1, and 4 comma 3. x g(x) −4 3 0 1 2 0 4 −1 Which of the following best compares the slopes and y-intercepts of the two functions? (1 point) The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
The correct option regarding the slope and the intercept of the linear functions is given as follows:
The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
What is the definition of a linear function?The definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope of the function, which is the rate of change of the output variable y relative to the input variable x.b is the y-intercept of the function, which is the value of y when the function crosses the y-axis, that is, when x = 0.The points that compose function f(x) are given as follows:
(0,1) and (4,3).
Hence:
The slope is of 0.5, as when x increases by 4, y increases by 2.The intercept is of 1, as when x = 0, y = 1.The points that compose function g(x) are given as follows:
(0,1) and (4,-1).
Hence the coefficients are as follows:
The slope is of -0.5, as when x increases by 4, y decreases by 2.The intercept is of 1, as when x = 0, y = 1.Hence the correct option is:
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Two buildings are 18.5 meters apart. The angles of elevation from the top of one building to the top of the other is 18 degrees. If the taller building is 15 meters tall, how tall is the shorter building?
Answer: 9m
Step-by-step explanation:
If we draw a right triangle, we can get a triangle with an angle of 18 degrees and a base of 18.5m. To get the height, we would do TOA or tan = opp / adj:
tan18 = x / 18.5
Multiply both sides by 18.5 to isolate x:
x = 18.5 * tan18
x = 6m (approximately)
This means that the taller building is 6 meters taller, so:
15m - 6m = 9m
Can anyone solve this for me?
Answer:
21.17 to 2d.p.
Step-by-step explanation:
Using Pythagoras rearrage to find b c^2-a^2 = b^2
c= hypothenuse
32^2 = 1024 and 24^2 = 576
1024 -576 = 448
[tex]\sqrt{448}[/tex] = 21.1660105
21.17 to 2d.p.
SHOW WORK FOR BRAINLIST
Answer:
Below
Step-by-step explanation:
Graph the two lines....where they intersect is the solution:
(-4,3)
OR sub in x = -4 into the first equation to find y = 3
Using your work from the first problem on Tuesday find the area of the triangle if x=3/2 and the height of the triangle was 6x+10. Help me please!!
If the height of the triangle is (6x + 10) and the base of the triangle is (3/2) the area of the triangle is 14.25 square units.
What is the area of the triangle?
The area of a triangle is the region bounded by its perimeter or its three sides.
If the height of the triangle is 'h' and the base is 'b', the area of the triangle would be
Area = 1/2 × height × base
The base of the triangle is x = 3/2.
Height of the triangle = 6x + 10 = 19.
Area of triangle = 1/2×3/2×19
= 14.25 square units.
Hence, If the height of the triangle is (6x + 10) and the base of the triangle is (3/2) the area of the triangle is 14.25 square units.
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Ariany run a farm tand that ell grape and apple. Each pound of grape ell for $3. 75 and each pound of apple ell for $4. Ariany made $251. 75 from elling a total of 64 pound of grape and apple. Determine the number of pound of grape old and the number of pound of apple old
Hence, there should be 5 pounds of apples and 7 pounds of grapes in 12 pounds.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
pound apple cost = 0.60 dollar1 pound of grapes cost = 1 dollarTotal fruits bought = 12 poundsTotal money paid = 10 dollarsTotal grapes that can be bought with 10$ = 10/1Pounds = 10Total apple that can be bought with 10$ = 10/0.6Pounds = 16.66To buy 12 pounds of fruit in 10 dollars each pound cost = 12/10= 1.2$ per poundRatio of grapes and apple in 12 pound fruits = 1/0.6= 1 : 1.6Apples in 12 pounds = 0.6×5Cost = 3$Grapes in 12 pounds = 1×7Cost = 7$Hence, there should be 5 pounds of apples and 7 pounds of grapes in 12 pounds.
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suppose that 11% of people are left-handed. if 5 people are selected at random, find the probability that exactly 2 are left- handed.
The probability that exactly 2 people are left handed if 11% people are left handed and 5 are selected at random is 100.
Probability is a method with the help of which we chose a particular object on random from many given objects.
P(E) = no of favorable outcomes/total number of outcomes
Let there are 100 people
11% are left handed = 11% of 100 = 11
5 are selected randomly.
No of favorable outcomes = 5
Total no of outcomes = 11
Hence, the probability that people selected are left handed is 5/11
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From the given percent of people are left handed and probability of exactly 2 of them are left handed from 5 selected at random is equal to 0.0853.
As given in the question,
Number of people selected at random 'n' = 5
Percent of people are left handed = 11%
Probability of success 'p' = 0.11
Probability of failure 'q' = 1- p
= 1-0.11
= 0.89
Exact number of left handed people 'x' = 2
Probability of people that are exactly left handed
= ⁿCₓ (p)ˣ(q)ⁿ⁻ˣ
=⁵C₂(0.11)²(0.89)⁵⁻²
= (5!/ (5-2)!2!) × (0.0121) × (0.704969)
= 10 × (0.0121) × (0.704969)
= 0.0853
Therefore, from the given percent of people are left handed and probability of exactly 2 of them are left handed from 5 selected at random is equal to 0.0853.
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Andy says that all rectangles with an area of 24cm² have the same perimeter
Show that Andy is wrong.
Answer:
no because area is multiplication, but perimeter is adding.
Please help hurry it is worth 12 points if you help me solve
Answer:
Since [tex]s=\frac{3}{4}ft[/tex],
27 ÷ s² = 27 ÷ [tex](\frac{3}{4})^{2}[/tex]
= 27 ÷ [tex]\frac{9}{16}[/tex]
= [tex]\frac{27}{1}[/tex] × [tex]\frac{16}{9}[/tex]
= 48
∴ Mr Grant would need to buy 48 of such square tiles.
Step-by-step explanation:
what that simply means is that the area he needs the files for is 27 ft².
as the tiles are squares, each one has an individual area of s² = 3/4 × 3/4 = 9/16 ft²
how many tiles do we need ?
as b many as how often the area of one tile fits into the total area :
27 ÷ s² = 27 / 9/16 = 27/1 / 9/16 = 27/1 × 16/9 =
= 3/1 × 16/1 = 3×16 = 48
he has to buy 48 tiles.
if electricity power failures occur according to a poisson distribution with an average of 3 failures over 4 weeks, what is the probability that there will be 4 failure during a particular week. what is e[x] are v(x)?
The probability that there will be 4 failure in particular week is 0.00622.
e(x) = 0.75 = v(x)
Given,
If electricity power failures occur according to a Poisson distribution with an average of 3 failures over 4 weeks, what is the probability that there will be 4 failures during a particular week?
To know e(x) are v(x);
From the given info,
So 3/4 failure per 4/4 weeks.
That means on average 0.75 failures per week.
The probability that there will be 4 failure in particular week,
[tex]\frac{e^{-0.75}0.75^{4}}{4!}=\frac{0.4723*0.3164}{24}=0.00622[/tex]
e(x) = Average = 0.75
Poisson distribution have mean and variance same.
So v(x) = 0.75
Hence, the probability that there will be 4 failure in particular week is 0.00622.
e(x) = 0.75 = v(x)
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100 POINTS!
PLEASE ANSWER FAST
y=8x+1 in standard form step by step
Answer: y = 8
Step-by-step explanation:
Answer: -8x+y=1
Step-by-step explanation:
Standard form is Ax+By=C
y=8x+1
Move the 8x to the other side of the equation.
y-8x=1
-8x+y=1
2 1/4 x 3 1/5 answer for the following as a fraction
Answer:
I don't know which one you needed so here you go.....
144/20 (improper fraction version)
7 4/20 (Mixed number answer.) 7 1/5 (Mixed number version simplified)
36/5 (Simplified improper fraction version)
Step-by-step explanation:
2 1/4. I'm going to multiply 4 and 2 which is 8. Then I'll do 1+8=9 so now I can put the 9 on top so it's going to look like this 9/4.
3 1/5. I'm going to multiply 5 and 3 which is 15. Then I'll do 15+1=16 so now I can put the 16 on top and it's going to look like this 16/5.
Now that we have our two numbers (numbers that are bolded), let's multiply them. So first we want to multiply the numerators so 16*9=144. So 144 is going to be the numerator to our answer.
Since we have multiplied the numerator we now multiply the denominators by each other so, 5*4=20
So our answer is going to be 144/20 (improper fraction version)
Or 7 4/20 (Mixed number answer.)
Hope this helps!!! (Please mark me brainliest)
Claudia buys 12 postcards, 12 stamps, and 1 pen. The postcards cost twice as much as the stamps. The pen costs $14.10. How much does each postcard cost? Show your work.
According to the unitary method, the cost of each postcard is $0.7.
Unitary method:
Unitary method is used to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.
Given,
Claudia buys 12 postcards, 12 stamps, and 1 pen. The postcards cost twice as much as the stamps. The pen costs $14.10.
Here we need to find the cost of the postcard.
In the given question, we have two variables, the price of the postcard and the price of the stamp, since the price for the pen is known.
And we also have the total cost of the purchase that is $14.1.
Therefore, now we have to create an equation as shown:
=> (12 x postcards) + (12 x stamps) + pen = 14.1
This equation refers the total amount spent by Claudia, but here we know that each pen costs $1.5, therefore:
When we apply the value on the equation then we get,
=> (12 x postcards) + (12 x stamps) + 1.5 = 14.1
=> (12 x postcards) + (12 x stamps) = 14.1 - 1.5
Therefore, (12 x postcards) + (12 x stamps) = 12.6
Here we also know that the postcards cost twice as much as the stamps, Then it can be written as,
postcards = 2 x stamps
By apply this value on the equation then we get the value of the stamp as,
=> (12 x (2 x stamps)) + (12 x stamps) = 12.6
=> (24 x stamps) + (12 x stamps) = 12.6
=> 36 x stamps = 12.6
Then the value of on stamp is stamps = 12.6/36
Therefore, the value of the stamps is 0.35
When we apply these values, then we get,
postcards = 2 x stamps = 2 x 0.35 = 0.7
Therefore, each postcard cost $0.7.
To know more about Unitary method here.
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