Answer:
Sample mean for solution 1: 19.27; sample mean for solution 2: 10.32
Step-by-step explanation:
To find the sample mean, find the sum of the data values and divide by the sample size.
For solution 1, the sum is given by:
9.7+10.5+9.4+10.6+9.3+10.7+9.6+10.4+10.2+10.5 = 192.7
The sample size is 10; this gives us
192.7/10 = 19.27
For solution 2, the sum is given by:
10.6+10.3+10.3+10.2+10.0+10.7+10.3+10.4+10.1+10.3 = 103.2
The sample size is 10, this gives us
103.2/10 = 10.32
The sample mean for Solution 1 is 10.05 mils per minute, while the sample mean for Solution 2 is 10.32 mils per minute. These figures represent the average etch rates of each solution in the semiconductor manufacturing process. So here the sample mean should be calculated.
Explanation:To calculate the sample means of Solution 1 and Solution 2, we first sum up the etch rates of each solution, and then divide by the number of samples in each solution.
For Solution 1, the etch rates sum up to 100.5 mils per minute. Dividing this by 10 (number of samples), we get a sample mean of 10.05 mils per minute.
For Solution 2, the etch rates sum up to 103.2 mils per minute. Dividing this by 10 (number of samples), we get a sample mean of 10.32 mils per minute.
So, the sample means for Solution 1 and Solution 2 are 10.05 and 10.32 mils per minute respectively. These means are useful to compare the average efficiency of these two solutions as a part of normal distribution analysis in the semiconductor manufacturing process.
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Simplify the expression. log(1/7)
Answer:
d. [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
The given logarithm is
[tex]10^{\log(\frac{1}{7})}[/tex]
Recall that the common logarithm has a base of 10.
[tex]10^{\log(\frac{1}{7})}=10^{\log_{10}(\frac{1}{7})}[/tex]
Recall also that;[tex]p^{(\log_pa)}=a[/tex]
[tex]10^{\log(\frac{1}{7})}=10^{\log_{10}(\frac{1}{7})}=\frac{1}{7}[/tex]
Which situation describes DEPENDENT events? A) A die is rolled, the outcome is recorded, then a coin is tossed. B) A die is rolled, the outcome is recorded, then the same die is rolled again. C) A spinner is spun once, the outcome is recorded, then it is spun again. D) A card is drawn from a deck, then a second card is drawn from the same deck. Eliminate
Answer:
the answer is D
Step-by-step explanation:
Solve by using proper methods. Show your work.
Determine the principal P that must be invested at 7%, compounded monthly, so that $200,000 will be available for retirement in 15 years?
Answer:
$70,201.38
Step-by-step explanation:
To determine the principal amount, we can use the formula:
[tex]P=\dfrac{A}{(1+\frac{r}{n})^{nt}}[/tex]
A = $200,000
r = 7% or 0.07
t = 15 years
n = 12
Now let's substitute our values.
[tex]P=\dfrac{200,000}{(1+\frac{0.07}{12})^{12(15)}}[/tex]
[tex]P=\dfrac{200,000}{(1.00583333333)^{12(15)}}[/tex]
[tex]P=70,201.38[/tex]
So the principal needed to get 200,000 in 15 years is $70,201.38.
I dont understand anything
Answer:
D
Step-by-step explanation:
Answer:
The correct answer options are D and E.
Step-by-step explanation:
We are to determine whether which of the given data sets in the answer options are continuous.
For this, we need to know what a continuous data set is.
A data set which have no definite end to its value but keep on continuing.
Here, the data sets given in A, B and C have definite starting and ending points.
While D and E are continuous sets as its values are continuing.
13 ? start fraction, 13, divided by, 10, end fraction of a number is what percentage of that number?
Answer:
The percentage is [tex]130\%[/tex]
Step-by-step explanation:
Let
x-----> the number
we have
[tex]\frac{13}{10}x=1.3x[/tex]
To find the percentage multiply by 100
[tex]1.3*100=130\%[/tex]
Holly has a rectangular garden that measures 12 m wide by 14 m long. She wants to increase the area to 255 m? by increasing the width and length by the same amount. What will be the length (longer dimension) of the new garden? Enter your answer in the box.
Answer:
255 square meters
Step-by-step explanation:
Present area = 12 * 14 = 168 square meters
The area has to increase by a factor of 255 / 168 = 1.5178571429
Therefore, the width and length are increased by a factor of the
square root of 1.5178571429 = 1.2320134508
So the width becomes
12 * 1.2320134508 = 14.7841614091
and the length becomes
14 * 1.2320134508 = 17.2481883107
That's roughly 14.78 by 17.25 and the area equals
14.78 * 17.25 = 255 square meters
Answer: The answer is 17
Step-by-step explanation:
Which is true about the functional relationship shown in the graph?
Answer:
D
Step-by-step explanation:
For linear graphs, we say that the y-axis (y) is a function of the x-axis (x).
The y-axis shows earnings and the x-axis shows time worked (in hours). Thus, we can say that earnings is a function of the number of hours worked.
Looking at the answer choices, D is the correct choice.
Answer:
D
Step-by-step explanation:
I got it correct on A P E X
Determine the slope of the line that has the following coordinates: (-3, 6) (4,-2)
Answer: [tex]m=-\frac{8}{7}[/tex]
Step-by-step explanation:
To calculate the slope of the line that has the coordinates given in the problem you must use the formula shown below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given the points (-3, 6) (4,-2), when you substitute them into the eequation shown above, you obtain that the slope is the following:
[tex]m=\frac{-2-6}{4-(-3)}\\m=-\frac{8}{7}[/tex]
Answer:
[tex] - \frac { 8 } { 7 } [/tex]
Step-by-step explanation:
We are given the following two points on a line and we are to find the slope of this line:
(-3, 6) and (4,-2)
We know the formula of the slope is given by:
[tex] \frac { y_2 - y_1 } { x_2 - x_1 } [/tex]
Substituting the given coordinates in the above formula to get:
Slope = [tex] \frac { - 2 - 6 } { 4 - - 3 } = - \frac { 8 } { 7 } [/tex]
Anvi designs a game in which a player either wins or loses 4 points during each turn. Which equation represents all numbers of points(p), a player may have after his or her first turn of the game?
p = 4
p = -4
|p| = 4
|p| = -4
Will mark the brainliest answer to the first person to correctly answer it
Answer: c) | p | = 4
Step-by-step explanation:
A player wins 4 (+4) or loses 4 (-4) points so you are looking for an answer that is ±4.
| p | = 4 → p = 4, p = -4
Please answer at least one of these questions!! Please state which question you answered too. Will give brainliest!
Answer:
15. 4.9 cm
17. 6.63 cm
Step-by-step explanation:
15. A perpendicular bisector is a segment which divides another in half. Since JH is 9.8 then each of the two segments it divides into is 4.9.
17. The segments within the circle form a right angle. Triangle CRS as a right triangle must follow the Pythagorean theorem which says the square of each leg adds to the square of the hypotenuse.
a² + b² = c²
Here a is unknown, b = 10 and c = 12.
a² + 10² = 12²
a² + 100 = 144
a² = 44
a = √44 = 6.63
23 points help asap!
Find the unit price and choose the better buy.
80 oz bottle of cleaner for $13.60
70 oz bottle of cleaner for $13.30
90 oz bottle of cleaner for $18.00
60 oz bottle of cleaner for $10.80
Answer:
60
Step-by-step explanation:
ITS THE BEST ONE
an 80 oz bottle of cleaner for $13.60 is the better buy because usually it would be about $40 for that size bottle
Triangle ABC has vertices at A(–2, 3), B(–3, –6), and C(2, –1). Is triangle ABC a right triangle? If so, which angle is the right angle? No, the triangle has no right angles. Yes, the right angle is angle A. Yes, the right angle is angle B. Yes, the right angle is angle C.
Answer:
Yes, the right angle is angle C.
Step-by-step explanation:
The given triangle has vertices at A(–2, 3), B(–3, –6), and C(2, –1).
Recall the slope formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the line going through AC is
[tex]m_{AC}=\frac{-1-3}{2--2}=-1[/tex]
The slope of the line going through BC s
[tex]m_{AC}=\frac{-1--6}{2--3}=1[/tex]
The product of the slopes of AC and BC is [tex]-1\times1=-1[/tex]
This means line AC is perpendicular to BC at C.
Hence the triangle ABC is right angled at C.
Answer:
Yes, the right angle is angle C.
Step-by-step explanation:
Pete’s parents are offering to pay him a weekly allowance for doing his chores. They’ve given him two different payment options for a period of 15 weeks.
Option 1: $20 every week
Option 2: A penny in the first week, and then double the amount from the previous week in each week after that. So, 1 penny in the first week, 2 pennies in the second week, 4 pennies in the third week, and so on.
Which one is the better option for Pete? Explain why.
Find the total of each option to see which one is better.
Option 1:
$20 every week for 15 weeks = 15 x 20 = $300 total.
Option 2:
Week 1 you have 1 penny.
Week 2 you would have 1 +2 = 3 pennies.
Week 3 you would have 3 + 4 = 7 pennies.
From this we can see a pattern of 2^x - 1 where x is the number of weeks.
So in 15 weeks he would have 2^15 - 1 = 32767 pennies.
100 pennies equal $1
32767 / 100 = $327.67
The second option is better because he ends up with more money.
The quarterly returns for a group of 51 mutual funds are well modeled by a Normal model with a mean of 7.4% and a standard deviation of 3.4%. Use the 68-95-99.7 Rule to find the cutoff values that would separate the following percentages of funds, rather than using technology to find the exact values. a) the highest 50% b) the highest 16% c) the lowest 2.5% d) the middle 68% a) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.) A. xless than or equals 50% B. xgreater than or equals nothing% C. nothing%less than or equalsxless than or equals nothing% b) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.) A. xgreater than or equals nothing% B. xless than or equals nothing% C. nothing%less than or equalsxless than or equals nothing% c) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.) A. xless than or equals nothing% B. xgreater than or equals nothing% C. nothing%less than or equalsxless than or equals nothing% d) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.)
Answer:
A) x ≥ 0.074; B) x ≥ 0.108; C) x ≤ 0.006; D) 0.04 ≤ x ≤ 0.108
Step-by-step explanation:
68% of data will fall within 1 standard deviation of the mean; 95% of data will fall within 2 standard deviations of the mean; and 99.7% of data will fall within 3 standard deviations of the mean.
Breaking this down, we find that 34% of data fall from the mean to 1 standard deviation above the mean; 13.5% of data fall from 1 standard deviation above the mean to 2 standard deviations above the mean; 2.35% of data fall from 2 standard deviations above the mean to 3 standard deviations above the mean; and 0.15% of data fall above 3 standard deviations above the mean.
The same percentages apply to the standard deviations below the mean.
The highest 50% of data will fall from the mean to the end of the right tail. This means the inequality for the highest 50% will be x ≥ 0.074, the mean.
The highest 16% of data will fall from 1 standard deviation above the mean to the end of the right tail. This means the inequality for the highest 16% will be x ≥ 0.074+0.034, or x ≥ 0.108.
The lowest 2.5% of data will fall from 2 standard deviations below the mean to the end of the left tail. This means the inequality for the lowest 2.5% will be x ≤ 0.074-0.034-0.034, or x ≤ 0.066.
The middle 68% will fall from 1 standard deviation below the mean to 1 standard deviation above the mean; this means the inequality for the middle 68% will be
0.074-0.034 ≤ x ≤ 0.074+0.034, or
0.04 ≤ x ≤ 0.108
The cutoff values using the 68-95-99.7 Rule for the given mutual funds data are calculated. The highest 50% lies between 4.0% and 10.8%, the highest 16% lies between 0.6% and 14.2%, the lowest 2.5% lies between -2.8% and 17.8%, and the middle 68% lies between 4.0% and 10.8%.
Explanation:The cutoff values can be found using the 68-95-99.7 Rule, which states that approximately 68 percent of the data lies within one standard deviation of the mean, 95 percent lies within two standard deviations, and 99.7 percent lies within three standard deviations. With a mean of 7.4% and a standard deviation of 3.4%, we can determine the cutoff values:
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Find the inverse function of that problem! Please!!
Answer:
[tex]y=\frac{\sqrt{x} -8}{-2}[/tex]
Step-by-step explanation:
To find an inverse, switch x and y values in the equation. Then solve for y.
[tex]F(x) = (8-2x)^2\\x = (8-2y)^2\\\sqrt{x} = 8 - 2y\\\sqrt{x} -8 = -2y\\\frac{\sqrt{x} -8}{-2} =y[/tex]
The volume of a prism is 48 cubic centimeters. If the length is 2 centimeters and the width is 4 centimeters. What is the height?
Answer:
6
Step-by-step explanation:
volume is (lwh) since youre trying to find the height just multiply the 2 and 4 together to get 8. Then divide 8 by 48 to get your height.
upper text bottom text left text right text this is for min word req problem in picture
Replace x in the second equation with the value of x from the first one.
x = -3y
x + y = -6
-3y + y = -6
Simplify:
-2y = -6
Divide both sides by -2:
y = -6 / -2
y = 3
Now replace Y with 3 in one of the equations to solve for x:
x = -3y = -3(3) = -9
X = -9, Y = 3
(-9,3)
Match each expression to its equivalent expression with a rational denominator.
Answer: BCDA
Step-by-step explanation:
[tex]\dfrac{1}{\sqrt[4]{3x^3y^5}}\\\\\\\text{Since it is a 4th root, you need 4 on the "inside" to make 1 on the "outside"}\\=\dfrac{1}{y\sqrt[4]{3x^3y}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{1}{y\sqrt[4]{3x^3y}}\bigg(\dfrac{\sqrt[4]{3^3xy^3} }{\sqrt[4]{3^3xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{\sqrt[4]{3^3xy^3} }{y(3xy)}\\\\\\\boxed{=\dfrac{\sqrt[4]{3^3xy^3} }{3xy^2}}\quad Option\ B[/tex]
[tex]\dfrac{3}{\sqrt[4]{3^3x^{11}y^{13}}}\\\\\\\text{Since it is a 4th root, you need 4 on the "inside" to make 1 on the "outside"}\\=\dfrac{3}{x^2y^3\sqrt[4]{3^3x^3y}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{3}{x^2y^3\sqrt[4]{3^3x^3y}}\bigg(\dfrac{\sqrt[4]{3xy^3} }{\sqrt[4]{3xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{3\sqrt[4]{3xy^3} }{x^2y^3(3xy)}\\\\\\\boxed{=\dfrac{\sqrt[4]{3xy^3} }{x^3y^4}}\quad Option\ C[/tex]
[tex]\dfrac{2}{\sqrt[6]{2x^7y^5}}\\\\\\\text{Since it is a 6th root, you need 6 on the "inside" to make 1 on the "outside"}\\=\dfrac{2}{x\sqrt[6]{2xy^5}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{2}{x\sqrt[6]{2xy^5}}\bigg(\dfrac{\sqrt[6]{2^5x^5y} }{\sqrt[6]{2^5x^5y}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{2\sqrt[6]{32x^5y} }{x(2xy)}\\\\\\\boxed{=\dfrac{\sqrt[6]{32x^5y} }{x^2y}}\quad Option\ D[/tex]
[tex]\dfrac{4}{\sqrt[6]{2^5x^5y^9}}\\\\\\\text{Since it is a 6th root, you need 6 on the "inside" to make 1 on the "outside"}\\=\dfrac{4}{y\sqrt[6]{2^5x^5y^3}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{4}{y\sqrt[6]{2^5x^5y^3}}\bigg(\dfrac{\sqrt[6]{2xy^3}}{\sqrt[6]{2xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{4\sqrt[6]{2xy^3} }{y(2xy)}\\\\\\\boxed{=\dfrac{2\sqrt[6]{2xy^3} }{xy^2}}\quad Option\ A[/tex]
An elevator has a placard stating that the maximum capacity is 23252325 lblong dash—1515 passengers. So, 1515 adult male passengers can have a mean weight of up to 2325 divided by 15 equals 155 pounds.2325/15=155 pounds. If the elevator is loaded with 1515 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 155155 lb. (Assume that weights of males are normally distributed with a mean of 161 lb161 lb and a standard deviation of 31 lb31 lb.) Does this elevator appear to be safe?
Answer:
0.7734; no, it does not.
Step-by-step explanation:
To find this probability we will use a z-score. We are dealing with the probability of a sample mean being larger than a given value; this means we use the formula
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
Our x-bar in this problem is 155, as that is the sample mean we are trying to find the probability of. Our mean, μ, is 161 and our standard deviation, σ, is 31. Our sample size, n, is 15. This gives us
[tex]z=\frac{155-161}{31\div \sqrt{15}}=\frac{-6}{8.0042}=-0.75[/tex]
Using a z table, we see that the area under the curve less than this, corresponding with probability less than this value, is 0.2266. This means that the probability of the sample mean being larger than this is
1-0.2266 = 0.7734, or 77.34%.
Since there is a 77.34% chance of the passengers having a mean weight that is too heavy, this elevator is not safe.
The probability that the elevator is overloaded using the normal distribution principle is 0.7870
Given the Parameters :
Mean, μ = 161Standard deviation, σ = 31 Sample size, n = 15X = 155Using the relation :
Zscore = (xbar - μ) ÷ (σ/√(n))
Zscore = (155 - 161) ÷ (31/√15)
Zscore = - 0.796
The probability that lift is overloaded can be expressed thus :
P(Z ≥ - 0.796) = 1 - P(Z ≤ - 0.796)
Using a normal distribution table ; PP(Z ≤ - 0.796) = 0.2130
P(Z ≥ - 0.796) = 1 - 0.2130
P(Z ≥ - 0.796) = 0.7870
Therefore, the probability that weight is overloaded is 0.7870
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There are 5 4/5 cups of milk left in a carton. Write 5 4/5 as an improper fraction. Explain what the fraction represents in this situation.
Answer:
[tex]\frac{29}{5}\ cups[/tex]
Step-by-step explanation:
we have
[tex]5\frac{4}{5} \ cups[/tex]
Convert to an improper fraction
[tex]5\frac{4}{5}=\frac{5*5+4}{5}=\frac{29}{5}\ cups[/tex]
[tex]=(\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{4}{5})\ cups[/tex]
[tex]=(1+1+1+1+1+\frac{4}{5})\ cups[/tex]
The fraction represent (25/5) cups of milk plus (4/5) cups of milk left in a carton
or
The fraction represent 5 cups of milk plus (4/5) cups of milk left in a carton
5 4/5 cups of milk is equivalent to 29/5 cups when written as an improper fraction. This represents that there are a total of 29 fifths of a cup of milk in the carton.
Explanation:To convert 5 4/5 cups of milk to an improper fraction, you multiply the whole number by the denominator of the fraction and add the numerator. Here, 5 is the whole number, 4 is the numerator, and 5 is the denominator. So, you calculate (5 × 5) + 4 = 25 + 4 = 29. Therefore, 5 4/5 cups is the same as 29/5 cups of milk in improper fraction form.
In this situation, the improper fraction 29/5 represents the total number of fifths of a cup of milk in the carton. Since there are five fifths in a whole cup, and we have 5 whole cups plus an additional 4 fifths, we have a total of 29 fifths of a cup of milk.
Find the point of intersection of the lines: y = 4x + 1 and y = – 2x + 4 A. (2 , 9) B. ( 1 2, 3 ) C. (1 , 2) D. ( 1 4, 2)
Answer:
B. (1/2, 3)
Step-by-step explanation:
It is perhaps easiest to try the point values in the equations.
A — 4·2+1 = 9; -2·2 +4 ≠9 . . . . not the answer
B — 4·1/2 +1 = 3; -2·(1/2) +4 = 3 . . . . this is the answer
we need go no further since we have the answer
To find the point of intersection, solve the system of equations formed by the two lines. Substituting x=1 into either equation gives y=5. Therefore, the point of intersection is (1,5).
Explanation:To find the point of intersection of two lines, we need to solve the system of equations formed by the two lines. In this case, the equations are y = 4x + 1 and y = -2x + 4.
Setting the equations equal to each other, we have 4x + 1 = -2x + 4. Solving for x, we get x = 1.
Substituting x = 1 into either of the original equations, we find y = 4(1) + 1 = 5. Therefore, the point of intersection is (1, 5).
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Tom had $56. He bought a soda for $2 and 2 cookies for $3. Which expression correctly shows the total money Tom has left? A. $56 + (?$2) + (?$3) B $56 + (?$2) ? (?$3) C $56 ? (?$2) ? (?$3) D $56 ? (?$2) + (?$3)
C ($56) - ($2) - ($3)
Answer:
I believe it's A
Step-by-step explanation:
Sorry if wrong ;-;
Muriel has kept track of her income and expenses for the week in the spreadsheet below. How much was Muriel's restaurant bill? a. $17.66 b. $42.55 c. $6.35 d. $112.55
Answer:
The answer to this question is option B which is $42.55.
The above statement shows that Muriel has kept track of her income and also expenses for the week in the spreadsheet.
By using the spreadsheet, you can easily calculate the restaurant bill of Muriel. The Muriel’s restaurant bill is calculated as $42.55
How many 30 degree angles are in a 150 degree angle? Use repeated subtraction to solve.
150 minus 30 equals 120 but i did 150/30 and got 5
To find the number of 30 degree angles in a 150 degree angle using repeated subtraction, subtract 30 from 150 until reaching 30 and count the number of times you were able to subtract. In this case, there are four 30 degree angles in a 150 degree angle.
Explanation:To determine how many 30 degree angles are in a 150 degree angle using repeated subtraction, we start by subtracting 30 from 150 until we can no longer subtract without going negative. Each time we subtract 30, we count the number of times we were able to subtract. So, 150 - 30 = 120, 120 - 30 = 90, 90 - 30 = 60, and 60 - 30 = 30. We were able to subtract 30 four times before reaching 30, so there are four 30 degree angles in a 150 degree angle.
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A real estate broker's base salary is $18,000. She earns a 4% commission on total sales. How much must she sell to earn $55,000 total? Show your work and explain your reasoning in the space provided below.
The salary of the real estate broker = $18,000
Commission earned on total sales = 4% or 0.04
Total income earnings = $55,000
Let the total sales be = x
Equation becomes :
[tex]18000+0.04x=55000[/tex]
[tex]0.04x=55000-18000[/tex]
[tex]0.04x=37000[/tex]
[tex]x=925000[/tex]
Hence, the real estate broker must sell $925,000 worth of real estate to earn $55,000.
To earn $55,000 total, the real estate broker must sell $925,000 in total.
Explanation:To find out how much the real estate broker must sell to earn $55,000 total, we need to consider both her base salary and her commission. Let's set up an equation to solve for the total sales needed:
$18,000 + 0.04x = $55,000
Subtracting $18,000 from both sides gives:
0.04x = $37,000
Dividing both sides by 0.04 gives:
x = $925,000
Therefore, the real estate broker must sell $925,000 in total to earn $55,000.
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find the missing sides. Brainliest!!
Answer:
1. x = 28; y = 14√3
2. x = 9√2
Step-by-step explanation:
For these, it is helpful to remember that the side lengths of a 30°-60°-90° triangle have the ratio 1 : √3 : 2, and those of a 45°-45°-90° triangle have the ratio 1 : 1 : √2.
1. 14 is the shortest side, and x is the longest side, so ...
x = 2·14 = 28
y = (√3)·14 = 14√3
__
2. 18 is the longest side and x is the shortest side of this 45°-45°-90° triangle, so ...
x·√2 = 18
x = 18/√2 = 18·(√2)/2 = 9√2
Abott simplified an expression. His work is shown below.
Step 1
Step 2
Step 3
Step 4
45.5
In which step did Abott make his first mistake?
step 1
step 2
step 3
step 4
Mark this and return
Save and Exit Next Submit
Abott make his first mistake in step 2
Further explanationCalculation operations include multiply, divide, add, substract, etc.
In mathematical operations we can use the order of operation / calculation according to the principle of PEMDAS
P: Parentheses ⇒ ( ) E: Exponents (powers, square roots, etc.)⇒√,² MD: Multiplication and Division ⇒ x and : AS: Addition and Subtraction ⇒ + and -Multiplication and division or addition and subtraction are interchangeable/rank equally so the calculations/equation operations should be done from left to right
Abbot expression :
9.5 : 0.25 + + 4(0.25+0.5) + 6
Step 1 : 9.5 : 0.25 + + 4(0.75) + 6
Step 2 : 38 + 10(0.75)
Step 3 : 38 + 7.5
Step 4 : 45.5
From the Abott steps it can be concluded that the error occurred in step 2, because the number 4 must be multiplied first with the number in parentheses (ie 0.75)
The correct steps should:
step 1: Step 1: 9.5: 0.25 + 4 (0.75) + 6
Step 2: 38 + 3 + 6
Step 3: 38 + 9
Step 4: 47
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Answer:
Its B
Step-by-step explanation:
What term describes this polygon ?
Answer:
Step-by-step explanation:
The last one
I hope I helped you.
Polygons are closed figures based on a plane that are characterized by their sides and angles. Without an image or description of the polygon, it's impossible to identify the specific polygon indicated.
Explanation:In mathematics, polygons are divided based on many factors such as the number of sides, length of sides, angle measures, etc. However, without the image or description of the polygon, I can't definitively tell what polygon you're referring to. For example, a polygon could be anything from a triangle (3 sides) to a decagon (10 sides). Remember, a polygon is basically a closed figure formed by three or more sides in a plane.
Learn more about Polygon here:https://brainly.com/question/34047098
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A theater wants to build movable steps that they can use to go on and off the stage. The dimesions are 12 in, 16 in, 20 in, 6 in, and 8 in. They want the steps to have enough space inside so they can also be used to store props. How much space is inside the steps?
Answer:
The total volume of the space inside the steps is 2880 cubic inches.
Step-by-step explanation:
Given : A theater wants to build movable steps that they can use to go on and off the stage. The dimensions are 12 in, 16 in, 20 in, 6 in, and 8 in. They want the steps to have enough space inside so they can also be used to store props.
To find : How much space is inside the steps?
Solution :
According to question,
The image form of store props is a prism split into two rectangular prism.
Refer the attached figure below.
The bottom portion of the steps having dimension [tex]16\times 20\times 6 in[/tex]
The volume of the bottom portion is
[tex]V=l\times b\times h\\V=16\times 20\times 6\\V=1920 in^3[/tex]
The top part have a width of 8 inches as entire width of bottom is 16 inches.
Length is 20 inches.
Height of the steps is 6 inches as total height is 12 inches.
The volume of the top part is
[tex]V=l\times b\times h\\V=20\times 8\times 6\\V=960 in^3[/tex]
So, the total volume of the space inside the steps is
1920+960 = 2880 cubic inches.
Therefore, The total volume of the space inside the steps is 2880 cubic inches.
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. Midpoint (15, -8), endpoint (16, -3). What is the other endpoint?
Answer:
the other endpoint is [tex](14,-13)[/tex]
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
Let
[tex](x1,y1)=(16,-3)[/tex]
so
[tex](16+x2)/2=15[/tex] -----> [tex]x2=30-16=14[/tex]
[tex](-3+y2)/2=-8[/tex] -----> [tex]y2=-16+3=-13[/tex]
therefore
the other endpoint is [tex](x2,y2)=(14,-13)[/tex]