Answers
Answer:
Area of the parallelogram = 120 square units
Area of the triangle = 17.5 square units
Area of the trapezoid = 372 square units
Step-by-step explanation:
The first polygon is a parallelogram with a base of 15 units and a height of 8 units.
[tex]\begin{aligned}\sf Area\;of\;a\;parallelogram&=\sf base \times height\\&=\sf 15 \times 8\\&=\sf 120\;square\;units\end{aligned}[/tex]
Therefore, the area of the parallelogram is 120 square units.
[tex]\hrulefill[/tex]
The second polygon is a triangle with a base of 5 units and a height of 7 units.
[tex]\begin{aligned}\sf Area\;of\;a\;triangle&=\sf \dfrac{1}{2} \times base \times height\\\\&=\sf \dfrac{1}{2} \times 5 \times 7\\\\&=\sf 17.5\;square\;units\end{aligned}[/tex]
Therefore, the area of the triangle is 17.5 square units.
[tex]\hrulefill[/tex]
The third polygon is a trapezoid with bases of 7 units and 24 units, and a height of 24 units.
[tex]\begin{aligned}\sf Area\;of\;a\;trapezoid&=\sf \dfrac{sum\;of\;bases}{2} \times height\\\\&=\sf \dfrac{7+24}{2} \times 24\\\\&=\sf \dfrac{31}{2}\times 24\\\\&=\sf 372\;square\;units\end{aligned}[/tex]
Therefore, the area of the trapezoid is 372 square units.
Answer:
see below
Step-by-step explanation:
To find:-
The areas of the given shaded polygons.Answer:-
There are three polygons viz parallelogram, triangle and a trapezium. To find out the areas we can use the following formulae :-
Area of triangle :-
Area = 1/2 * base * heightArea of parallelogram:-
Area = base * perpendicular heightArea of trapezium:-
Area = 1/2 * (sum of parallel sides)*distance between the sidesNow we may use the above formulae as ,
Area of the given parallelogram:-
→ A = base * height
→ A = * 15 * 8
→ A = 120units²
Area of the given triangle:-
→ A = 1/2 * b * h
→ A = 1/2 * 5 * 7
→ A = 17.5 units²
Area of the given trapezium:-
→ A = 1/2 * sum of || sides* distance between them
→ A = 1/2 * (7+24) * 24
→ A = 12 * 31
→ A = 372 units ²
This is our required answers .
Related Questions
Charlie is playing a boardgame she is rolling two number cubes.
How many outcomes are possible?
Create an outcome chart to prove your answer
Answers
In a random sample of 892 college students in the United States, 272 say they skip at least one class per week.
Find the point estimate for the proportion parameter for this population. Write your answer as a decimal rounded to three decimal places.
O 0.305
O 0.695
O 0.272
O 0.50
4
Answers
The point estimate for the proportion parameter for this population is A)0.305.
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
In a random sample of 892 college students in the United States, 272 say they skip at least one class per week.
From the given information then,
Sample size n = 892
No of favorable outcomes (i.e successes) x=272
We know ,
The point estimate for the population parameter [tex]\hat P[/tex]=x/n.
Where n=sample size , x=number of success.
Here x = 272 ,n=892 then
The point estimate for the proportion parameter for this population then,
=> [tex]\hat p[/tex] = 272/892 = 0.305.
Hence the point estimate for the proportion parameter for this population is A)0.305.
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What was the equation of the graph below before it was shifted to the right 1
unit?
GD)-(x-1.5)-(x-1.5)
OA. G(x) = (x)3
OB. G(x) = (x-0.5)³-(x-0.5)
C. G(x) = (x-2)3-(x-2)
D. G(x) = (x-.5)³
Answers
The equation of the graph before it was shifted to the right one unit is given as follows:
B. G(x) = (x - 0.5)³ - (x - 0.5).
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The function in this problem is defined as follows:
G(x) = (x - 1.5)³ - (x - 1.5).
To remove the effect of a shift right one unit, we must shift the graph left one unit, hence the original rule is given as follows:
G(x) = (x - 1.5 + 1)³ - (x - 1.5 + 1).
G(x) = (x - 0.5)³ - (x - 0.5).
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HELP ASAP
A composite figure is represented in the image.
A four-sided shape with the base side labeled as 21.3 yards. The height is labeled 12.8 yards. A portion of the top from the perpendicular side to a right vertex is labeled 6.4 yards. A portion of the top from the perpendicular side to a left vertex is labeled 14.9 yards.
What is the total area of the figure?
272.64 yd2
231.68 yd2
190.72 yd2
136.32 yd2
Answers
The total area of the figure is 272.64 yd². Hence the correct option is (a) 272.64 yd².
The shape described in the problem is a trapezoid. The formula to calculate the area of a trapezoid is:
[tex]Area = (base1 + base2) x height / 2[/tex]
We are given the following measurements:
Base1 = 21.3 yards
Height = 12.8 yards
A portion of the top from the perpendicular side to a right vertex is labeled 6.4 yards, which is a part of the base2.
A portion of the top from the perpendicular side to a left vertex is labeled 14.9 yards, which is the remaining part of the base2.
To calculate the missing part of base2, we subtract the known parts of base2 from the total length of the top, which is:
21.3 - 6.4 - 14.9 = 0
This means that the missing part of base2 is zero, and the trapezoid becomes a rectangle. Therefore, the area of the trapezoid is equal to the area of the rectangle, which is:
Area = base x height
Area = 21.3 x 12.8
Area = 272.64 square yards
Therefore, the total area of the figure is 272.64 yd². Hence the correct option is (a) 272.64 yd².
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If a town with a population of 8,380 doubles in size every 77 years, what will the population
be 462 years from now?
Answers
It might just be 536320
Question 10
According to a study on the effects of smoking by pregnant women on rates of asthma in their
children, for expectant mothers who smoke 20 cigarettes per day, 22.7% of their children
developed asthma by the age of two in the US. A biology professor at a university would like to
test if the percentage is lower in another country. She randomly selects 341 women who only
deliver one child and smoke 20 cigarettes per day during pregnancy in that country and finds that 71 of the children
developed asthma by the age of two. In this hypothesis test,
20 points
the test statistic, z =
and the p-value =
(Round your answers to four decimal places.)
Type numbers in the boxes.
aby Part 1: 10 points
aby Part 2: 10 points
Answers
part1)Rounding to four decimal places, the test statistic is z = -1.7918. part2) Rounding to four decimal places, the p-value is p = 0.0728.
what is decimal places ?
Decimal places refer to the number of digits to the right of the decimal point in a decimal number. For example, in the decimal number 3.14159, there are 5 decimal places, with the digit 1 being in the first decimal place, the digit 4 being in the second decimal place, and so on.
In the given question,
Part 1:
To calculate the test statistic, we use the formula:
z = (p - P) / √[(P(1-P))/n]
where p is the sample proportion (71/341 = 0.2082), P is the hypothesized proportion (0.227), n is the sample size (341).
z = (0.2082 - 0.227) / √[(0.227 * 0.773)/341]
z = -1.7918
Rounding to four decimal places, the test statistic is z = -1.7918.
Part 2:
To calculate the p-value, we use a standard normal distribution table or a calculator. Since this is a two-tailed test, we calculate the area in both tails of the distribution.
Using a calculator or a standard normal distribution table, we find that the area to the left of z = -1.7918 is 0.0364. Therefore, the area in the right tail is also 0.0364.
Thus, the p-value is 2*0.0364 = 0.0728.
Rounding to four decimal places, the p-value is p = 0.0728.
Therefore, we would fail to reject the null hypothesis at the 0.05 significance level since the p-value is greater than the level of significance. We do not have enough evidence to suggest that the percentage of children who develop asthma by age two for expectant mothers who smoke 20 cigarettes per day during pregnancy is lower in this other country compared to the US.
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Madelyn is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop?
45 points
Answers
We can use the multiplication principle of counting to find the total number of possible outcomes.
Since there are 5 options on the first spinner, 6 options on the second die, and 3 options on the third spinner, there are a total of:
5 x 6 x 3 = 90
different possible outcomes.
Therefore, there are 90 different possible outcomes if Madelyn spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop.
Answer:
what is biology and types
4. If 99.7 percent of the data is between 30 and 90, then please find the mean and the standard of deviation.
b. a:
a. u:
5. If 68 percent of the data is between 42 and 58, then please find the mean and the standard of deviation.
b. a:
a. H
6. If 95 percent of the data is between 34 and 64, then please find the mean and the standard of deviation.
b. a:
a. u
Need help with this too
Answers
The mean is 49 and the standard deviation is 5.33.
What is mean?
The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.
We can use the empirical rule to solve these problems. According to the empirical rule:
About 68% of the data falls within one standard deviation of the mean.
About 95% of the data falls within two standard deviations of the mean.
About 99.7% of the data falls within three standard deviations of the mean.
a) To find the mean (u) and standard deviation (sigma) for each problem, we can use the following formulas:
u = (a + b) / 2
sigma = (b - a) / 6
where a and b are the lower and upper bounds for the data, respectively.
b) For each problem, we can use the given information to set up an equation and solve for either the mean or standard deviation.
If 68 percent of the data is between 42 and 58:
a) H: We are not given enough information to solve for the mean or standard deviation.
b) To find one of the missing values, we can use the formulas above and the given information. Since we are given that 68% of the data falls within one standard deviation of the mean, we know that:
(58 - u) / sigma = 1
Simplifying this equation, we get:
58 - u = sigma
We can also use the fact that the range of the data is 16 (from 42 to 58):
b - a = 16
58 - u - (42 - u) = 16
16 = 16u/16
Solving for the mean, we get:
u = (42 + 58) / 2
u = 50
Using the equation 58 - u = sigma, we can solve for the standard deviation:
sigma = 58 - u
sigma = 8
Therefore, the mean is 50 and the standard deviation is 8.
If 95 percent of the data is between 34 and 64:
a) u: We can find the mean using the formula:
u = (a + b) / 2
u = (34 + 64) / 2
u = 49
b) To find the standard deviation, we can use the formula:
sigma = (b - a) / 6
sigma = (64 - 34) / 6
sigma = 5.33
Therefore, the mean is 49 and the standard deviation is 5.33.
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The school athletics department is raising money for new gym equipment. To raise $7,200 by spring training, the department decides to sell T-shirts during the fall semester. Based on previous fundraising drives, the expression
–
10p+560 can be used to gauge how many shirts the department will sell depending on the price of a shirt, p.
What is the lowest shirt price the athletics department can use to raise exactly $7,200 in revenue?
Answers
-10p+560 = 7200
Subtracting 560 from both sides:
-10p = 6640
Dividing both sides by -10:
p = -664
This answer does not make sense as a price for a T-shirt. The negative value suggests that the expression does not apply for such a low price. Therefore, we can assume that the athletics department cannot sell T-shirts at such a low price.
To find the lowest possible price for a T-shirt that will raise exactly $7,200, we need to find the value of p that makes the expression equal to 7,200.
-10p+560 = 7200
Subtracting 560 from both sides:
-10p = 6640
Dividing both sides by -10:
p = -664
Again, this answer does not make sense.
Therefore, we need to try a higher price for the T-shirt. Let's try a price of $20 per shirt:
-10(20)+560 = 360
This means that for every T-shirt sold at $20, the revenue generated will be $360.
To find out how many T-shirts need to be sold to raise $7,200, we can set up an equation:
360x = 7200
Dividing both sides by 360:
x = 20
This means that the athletics department will need to sell 20 T-shirts at $20 each to raise exactly $7,200 in revenue.
Use the 2020 Federal Tax Rates for Individuals to calculate the estimated taxes for a taxable income of $63,700.
Tax rate
10%
12%
22%
24 %
32%
35%
37%
2020 Federal Tax Rates for Individuals
Taxable Income Bracket
$0 to $9875
$9876 to $40,125
$40,126 to $85,525
$85,526 to $163,300
$163,301 to $207,350
$207,351 to $518,400
$518,401 or more
Answers
The estimated taxes for a taxable income of $63,700 using the 2020 Federal Tax Rates for Individuals is $9,804.00.
How the estimated taxes are determined:The estimated taxes for an individual with a taxable income of $63,700 for the fiscal year uses the progressive tax (graduated) system of the Federal Tax Rates for Individuals, as computed below.
Taxable Income for 2020 = $63,700
2020 Federal Tax Rates for Individuals:Tax rate Taxable Income Bracket Tax Payable
10% $0 to $9875 $987.50 ($9,875 x 10%)
12% $9876 to $40,125 $3,630.00 ($30,250 x 12%)
22% $40,126 to $85,525 $5,186.50 ($23,575 x 22%)
Estimated taxes $9,804.00
Thus, an individual whose taxable income is $63,700 in 2020 is expected to pay taxes amounting to $9,804.00.
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The latin dance club needs go raise more than 178.50 to buy costumes. The club already has 35.70. which inequality shows how much money each of the 7 club number needs to raise m if each person rasises the same amount
Answers
Answer:
its on quizzes
Step-by-step explanation:
HELP ASAP 25 PONITS PLEASE HELP
Answers
Convert 3% to a decimal by doing 3/100. You should get 0.03.
Now multiply 0.03 and 44.50, you will get 1.335.
Add 1.335 to 44.50 and you will get 45.835.
The new price of the item after it was marked up is $45.835
Suppose that 17 inches of wire costs 85 cents. At the same rate, how many inches of wire can be bought for 65 cents?
Answers
Answer:
13 inches
Step-by-step explanation:
17=85
1=85/17
1=5
Now
For 65 cents,
65=nx5
65/5=n
n=13 inches
Answer: 13 inches
Step-by-step explanation:
To solve this problem you would need to make a ratio.
A Ratio can be the symbol, : , / or the word to.
In this case you would need to do the problem as shown:
17/85 = x/65
First you would need to cross multiply, then flip the equation. And should end up with something like this:
85x =1105
Then Divide both sides by 85.
85x/85 = 1105/85
Answer:
X= 13
The shape below is formed from a rectangle measuring 13 cm by 16 cm from which a rectangle of length 7.3 cm has been removed. Work out the perimeter of the shape 13 cm 5.7 cm 16 cm 7.3 cm 6.2 cm
Answers
Thus, the perimeter of the left shape when length of rectangle ABCD is reduced to 7.3 cm is found as: P = 43.4 cm.
Explain about the features of rectangle:Each vertex of a rectangle has a 90° internal angle.The total of a rectangle's internal angles is 360°.The diagonals cut each other in half.The diagonals are all the same length.A rectangle is also referred to as a parallelogram since its sides are parallel.While all parallelograms are rectangles, not all rectangles are parallelograms.Given data:
Length of rectangle ABCD 'l' = 16 cmWidth of rectangle ABCD 'w' = 13 cmRemoved length AE = 7.3 cmPerimeter = sum of all sides:
The shaded portion in the figure shows the left over rectangle:
Perimeter of EFCD = EF + FC + CD + DE
ED = FC = 16 - 7.3 = 8.7
P = 8.7 + 13 + 8.7 + 13
P = 43.4 cm.
Thus, the perimeter of the left shape when length of rectangle ABCD is reduced to 7.3 cm is found as: P = 43.4 cm.
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complete question:
The shape below is formed from a rectangle measuring 13 cm by 16 cm from which a rectangle of length 7.3 cm has been removed. Work out the perimeter of the left shape.
Three distinct, five-sided dice are rolled, and the numbers showing are recorded. How many different outcomes are possible
Answers
Answer:
Step-by-step explanation:
Each die can show one of the five possible numbers. So, the number of possible outcomes for rolling one die is 5.
Since there are three dice being rolled, the total number of possible outcomes is the product of the number of possible outcomes for each die. That is:
Number of possible outcomes = 5 x 5 x 5 = 125
Therefore, there are 125 different outcomes possible when rolling three distinct, five-sided dice.
Consider a political discussion group consisting of 10 Democrats, 9 Republicans, and 3 Independents. Suppose that
two group members are randomly selected, in succession, to attend a political convention. Find the probability of
selecting two Independents.
Answers
As a result, there is a 1/77 chance of choosing two Independents consecutively as probabilities in order to get the likelihood of choosing two Independents.
what is probability ?The chance of an event happening is gauged by probability. It is stated as a value between zero and 1, with 0 denoting that the occurrence is unlikely and 1 denoting that it is unavoidable. Typically, P stands for the likelihood of something happening A. (A). It is computed by dividing the number of positive outcomes but by total number of potential outcomes. For instance, if you flip a fair coin, the likelihood of receiving heads is 50% since there is only one positive result (heads) so out two possible possibilities (heads or tails).
given
The likelihood of choosing an Independent on the first draw is: There are 3 Independents out of a total of 10 Democrats, 9 Republicans, and 3 Independents.
P(Unrelated to the initial draw) = 3/22
P(Independent on First Draw and Second Draw) = 2/21
We must compound these probabilities in order to get the likelihood of choosing two Independents consecutively:
P(Choosing two Independents) = P(Independent on first draw) + P(Independent on second draw | Independent on first draw)
= (3/22) * (2/21)
= 6/462
= 1/77
As a result, there is a 1/77 chance of choosing two Independents consecutively as probabilities in order to get the likelihood of choosing two Independents.
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5 ) A basketball league has a single- elimination tournament that begins with 32 teams playing in 16 games. After the first game, only 16 teams remain in the tournament to play 8 games. This continues until there is a winner. How many total games were played in the tournament?
Answers
To solve this problem, we can start by noticing that each round cuts the number of teams in half. Therefore, we can create a table to see how many teams are left after each round:
Round Number of Teams
1 32
2 16
3 8
4 4
5 2
6 1
We can see that there are 6 rounds in total, and that the number of games in each round is half the number of teams. So we can calculate the number of games for each round and add them up to get the total number of games:
Round Number of Teams Number of Games
1 32 16
2 16 8
3 8 4
4 4 2
5 2 1
6 1 0
Adding up the number of games for each round, we get:
16 + 8 + 4 + 2 + 1 + 0 = 31
Therefore, a total of 31 games were played in the tournament.
What does 2y plus 5 equal
Answers
Answer:
[tex]-\frac{5}{2}[/tex] or -2.5
Step-by-step explanation:
1) [tex]2y + 5 = 0[/tex]
2) Move 5 over to the other side by subtracting
[tex]2y = -5[/tex]
3) Divide both sides by 2 so y is alone
[tex]y = -\frac{5}{2}[/tex]
Here is a graph of the function g
Use the graph to find the following.
If there is more than one answer, separate them with commas.
(a) All values at which g has a local minimum:___
(b) All local minimum values of g :___
Answers
(a) All values at which g has a local minimum: -2, 3
(b) All local minimum values of g: g(-2) ≈ -2.5, g(3) ≈ -1.5
What is the Graph?
The graph is a visual representation of the function g, which shows how the output of the function varies with the input. It plots the values of g(x) on the vertical axis against the values of x on the horizontal axis.
(a) All values at which g has a local minimum:
From the graph, it appears that there are two values at which g has a local minimum:
x = -2
x = 3
(b) All local minimum values of g:
From the graph, the local minimum value at x = -2 appears to be approximately -2.5, and the local minimum value at x = 3 appears to be approximately -1.5. So, the local minimum values of g are:
g(-2) ≈ -2.5
g(3) ≈ -1.5
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PLEASE HELP. company is going to make an oil container in the shape of a cylinder. As shown below, the container will have a height of 7m and a diameter of 8m. The container will be made from steel (including its top and bottom). If the steel costs 29$ for each square meter, how much will the steel cost in total? Use 3.14 for pi , and do not round your answer.
Answers
The container will be 7 meters high and 8 meters in diameter. Steel will be used to make the container (including its top and bottom). If a square meter of steel costs 29 dollars, the total cost of the steel will be $5,467.60.
The cylinder has a diameter of 8m and a height of 7m, which means the radius of the cylinder is 4m (half of the diameter).
The surface area of a cylinder is calculated as follows:
SA = 2πr² + 2πrh
where h is the cylinder's height and r is the radius.
Plugging in the values we get:
SA = 2 x 3.14 x 4² + 2 x 3.14 x 4 x 7
SA = 100.48 + 87.92
SA = 188.4 square meters
So, the surface area of the cylinder is 188.4 square meters.
If the steel costs $29 per square meter, then the cost of the steel for the cylinder would be:
Cost = 188.4 x $29
Cost = $5,467.60
Therefore, the cost of the steel for the cylinder would be $5,467.60.
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Round 473,615 to the nearest hundred. O A. 473,610 B. 473,000 O c. C. 473,700 D. 473,600 E. 473.100
Answers
473,615 rounded to the nearest hundred is D. 473,600.
What is number rounding?Number rounding or approximation is the adjustment of the digits (up or down) to make rough calculations easier.
The result of number rounding is an estimated value rather than a precise one.
Number rounding or approximation are useful when the precise information is not required for decision-making.
473,615 = 473,600
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I need help with this ( Q7 to Q12 )
Answers
The values of the composite function are (f + g)(x) = 2x² + 3x - 2, (f - g)(x) = -2x² + 3x - 8, (f . g)(x) = 6x³ + 4x² - 15x - 15, (f o g)(x) = 6x² + 4, (g o f)(x) = 18x² - 60x + 53, (f o g)(3) = 58
What are the values of the composite functionsTo determine the values of the composite functions, we have to evaluate or simplify each as
7. (f + g)(x) = f(x) + g(x) = (3x - 5) + (2x² + 3) = 2x² + 3x - 2
8. (f - g)(x) = f(x) - g(x) = (3x - 5) - (2x² + 3) = -2x² + 3x - 8
9. (f . g)(x) = f(x) * g(x) = (3x - 5) * (2x² + 3) = 6x³ + 4x² - 15x - 15
10. (f o g)(x) = f(g(x)) = f(2x² + 3) = 3(2x² + 3) - 5 = 6x² + 4
11. (g o f)(x) = g(f(x)) = g(3x - 5) = 2(3x - 5)² + 3 = 18x² - 60x + 53
12. (f o g)(3) = f(g(3)) = f(2(3)² + 3) = f(21) = 3(21) - 5 = 58
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Se utilizan 3/5 de la capacidad de un camión para transportar sacos de papa. Un tercio de los sacos de papas son de papas chilotas y el resto es papas pukará. El resto del cargamento se divide en partes iguales entre lechugas y zapallos
¿Qué producto ocupa más capacidad?
Answers
(3/5) * C
donde C es la capacidad total del camión.
El número de sacos de papas chilotas se puede representar como:
(1/3) * (3/5) * C = C/5
El número de sacos de papas pukará es:
(2/3) * (3/5) * C = 2C/5
El resto del cargamento se divide en partes iguales entre lechugas y zapallos. Por lo tanto, cada uno ocupa la mitad del espacio restante en el camión:
(1 - 3/5) / 2 = 1/5
Por lo tanto, la capacidad ocupada por las lechugas y los zapallos es:
(1/5) * C + (1/5) * C = 2/5 * C
En resumen, la capacidad ocupada por cada producto es:
Papas chilotas: C/5
Papas pukará: 2C/5
Lechugas y zapallos: 2/5 * C
Por lo tanto, el producto que ocupa más capacidad son las papas pukará, con 2C/5.
Can i please get help
Answers
The expression is equivalent to -4x²-3x-5
Define equationAn equation is a statement of equality between two mathematical expressions that contain variables and mathematical operations. The goal of solving an equation is to determine the value of the variable that make the equation true. For example, in the equation 2x + 5 = 11, the variable x is being multiplied by 2, added to 5, and then compared to the number 11. To solve for x, one must isolate the variable on one side of the equation by performing the same operation on both sides of the equation until the variable is alone on one side. The resulting value of x will make the equation true.
Given expression is:
-4x²+2x-5(1+x)
Solving the expression
-4x²+2x-5-5x
-4x²-3x-5
Hence, the expression is equivalent to -4x²-3x-5.
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There is a card under 30% of the chairs at a booster meeting. Finn wants to find the probability that the first card he finds will be under the third chair that he checks. He generates 10 sets of random numbers from 1 to 10. The numbers 1-3 represent a chair with a card and 4-10 represent a chair without a card. Complete the table, and find the experimental probability of the event.
Answers
The experimental probability of finding a card under the third chair is 4/10 or 2/5, which is 0.4 or 40%
How to find the experimental probability of the event?The experimental probability of finding a card is 30%. The complete table is given below:
Trial Numbers Generated Chairs Checked
1 6,5,1 No Card, No Card, Card
2 8,1 No Card, Card
3 10,1 No Card, Card
4 7,8,4,1 No Card, No Card, No Card, Card
5 9,3 No Card, Card
6 5,4,2 No Card, No Card, Card
7 3 Card
8 9,5,8,2 No Card, No Card, No Card, Card
9 7,3 No Card, Card
10 9,6,8,4,7,3 No Card, No Card, No Card, No Card, No Card, Card
The probability that the first card he finds will be under the third chair that he checks is calculated by taking the total number of trials in which the third chair had a card (3) and dividing it by the total number of trials (10).
The table can be completed by generating 10 sets of random numbers from 1 to 10 and checking the first three numbers in each set. If the first number is between 1 and 3, then the first chair has a card. If the second number is between 1 and 3, then the second chair has a card. If the third number is between 1 and 3, then the third chair has a card. If none of the first three numbers are between 1 and 3, then there are no cards in the first three chairs
Out of the 10 trials, 4 have a card under the third chair. Therefore, the experimental probability of finding a card under the third chair is 4/10 or 2/5, which is 0.4 or 40%.
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Which point on the number line represents ?
B
A
D
C
Answers
Answer:
B = 1/2
A = 1/3
D = 2/3
C = 5/6
Step-by-step explanation:
B = 3/6 = 1/2
A = 2/6 = 1/3
D = 4/6 = 2/3
C = 5/6
The diameter of a circle is 5in. Find the length of its radius.
Answers
Hope that helps
A fast-food restaurant has a cost of production C(x)=13x+132 and a revenue function R(x)=7x . When does the company start to turn a profit?
Answers
The company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
To find the point at which the company starts to turn a profit, we need to find the value of x for which the revenue is greater than the cost of production.
The revenue function is R(x) = 7x, and the cost of production is C(x) = 13x + 132.
So, we need to solve the inequality:
R(x) > C(x)
7x > 13x + 132
Subtracting 13x from both sides, we get:
-6x > 132
Dividing both sides by -6 (and flipping the inequality because we're dividing by a negative number), we get:
x < -22
Therefore, the company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.
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Square
G
(x²-8)
meters
x meters
*.
...
What expression represents the total area of the
shaded figure. Simplify your expression.
Answers
The total area of the shaded portion is (x² - 16)(x²- 1) square meters.
What is a square?Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.
Equation:The area of the outer square is (x² - 8)², and the area of the inner square is x². Therefore, the area of the shaded region can be found by subtracting the area of the inner square from the area of the outer square:
Area of shaded region = Area of outer square - Area of inner square
= (x² - 8)² - x²
Expanding the first term using the formula for the square of a binomial, we get:
Area of shaded region = (x⁴ - 16x² + 64) - x²
= x⁴ - 17x² + 64
Therefore, the expression that represents the total area of the shaded figure is x⁴ - 17x² + 64, which can be simplified by factoring:
x⁴ - 17x² + 64 = (x² - 16)(x² - 1)
So the simplified expression for the total area of the shaded figure is (x² - 16)(x²- 1).
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help?? would really appreciate it! (i highly dislike being bad at math)
Answers
Step-by-step explanation:
Put both of the equations into y = mx + b form to compare them
m = slope if they have the same slope they are parallel and do not intersect
b = y axis intercept
if m and b are equal in each of the equations , they are the same line
2x+y = 0 ======> y = - 2x + 0
2y = -4x + 6 ====> y = - 2x + 3
The both have the same slope = -2 so they are parallel
but they have different b values so they are not the same lines
No intersection means no solution : parallel lines do not intersect