Answers
To solve this problem, we will use the following formula for the area of a trapezoid:
[tex]A=\frac{a+b}{2}h,[/tex]where a, and b are the lengths of the bases and h is the height.
Now, we are given that ( we will omit the units to simplify the calculations):
[tex]\begin{gathered} h=\frac{1}{4}(a+b), \\ h=2\frac{1}{2}. \end{gathered}[/tex]Therefore:
[tex]\frac{(a+b)}{2}=2(\frac{a+b}{4})=2h=2(2+\frac{1}{2})=4+1=5.[/tex]Substituting in the above formula, we get:
[tex]A=\frac{5}{2}\times(2\frac{1}{2}).[/tex]Simplifying the above result, we get:
[tex]A=\frac{25}{4}ft^2.[/tex]Answer:
[tex]\begin{gathered} A=\frac{1}{2}(2\frac{1}{2})(2\frac{1}{2}\cdot2) \\ =\frac{1}{2}(\frac{5}{2})(\frac{5}{2}\cdot2) \\ =\frac{50}{8}=\frac{25}{4}=6.25ft^2. \end{gathered}[/tex]Related Questions
4. Write a quadratic function given the roots (3, 0) and (-1, 0)
and the point (4, 10).
Answers
character character character
Answer the two questions in the photo for easy points ( will mark brainliest if correct )
Answers
[10] D
A counter-example is an example that shows the argument can have true premises and a false conclusion.
Option D shows someone who is good at math, but isn't an engineer. This is a counter-example.
[11] B
Similar to the previous question, options A, B, and D are all dogs. However, option C is not a dog and also has four legs. Therefore, it is a counter-example.
Vab if a = √8 and b = 2√√/2
Answers
Answer:
I will assume that 2√√/2 is actually 2[tex]\sqrt{2}[/tex]
Vab = 8
Step-by-step explanation:
ab
([tex]\sqrt{8}[/tex])*( 2[tex]\sqrt{2}[/tex])
2*[tex]\sqrt{16}[/tex]
2*4
Vab = 8
2/4 x 1/3 because i need help
Answers
Answer:
5/6
Step-by-step explanation:
Step 1: Find the GCD (greatest common denominator)
12
Step 2: multiply your factions to represent this
[tex]\frac{2x3}{4x3} = \frac{6}{12} \\[/tex] , [tex]\frac{1x4}{3x4} = \frac{4}{12}[/tex]
Step 3: add the numerators:
[tex]\frac{6}{12} + \frac{4}{12} = \frac{10}{12}[/tex]
Step 4: reduce your fraction
[tex]\frac{10}{12} = \frac{5}{6}[/tex]
Hope that helps
Fraction multiplication
2/4 x 1/3
We reduce the fraction 2/4 to its lowest expression by extracting and canceling 2.
1/2 x (1/3)
Multiply 1/2 by 1/3 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
1 x 1/2 x 3 =====> Multiply
1/6 ====> Answer
the question is in the photo! :)
Answers
Answer:
2
Step-by-step explanation:
So to get the answer we need to figure out what x is
2×2=4
so x has to be 2
Eleanor and Max used two rectangular pieces of plywood, placed end-to-end, to make a long rectangular stage for the school play. One board was 6 feet long, and the other was 5
1
2
feet long. The two pieces of plywood had equal widths. The total area of the stage was 66
1
8
square feet. What was the width of the plywood?
Answers
The width of the plywood = 23/8 ft
The two rectangular pieces of plywood had equal widths.
The length of first rectangular piece = 6 ft
The length of second rectangular piece = 5 1/2 ft = 11/2 ft
The two pieces are joined to make a single rectangular stage.
Then the total length of the stage = 6 + 11/2 = 23/2 ft
Now area of the rectangular stage = 66 1/8 = 529/8 square feet.
⇒ length x width = 529/8
⇒ 23/2 x width = 529/8
⇒ width = 529/8 x 2/23 = 23/4 ft
Let 'x' be the width of a rectangular plywood.
Then 2x = width of the stage
⇒ 2x = 23/4
⇒ x = 23/8 ft
Hence width of the plywood = 23/8 ft
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in the first week of July, a record 1,020 people went to the local swimming pool. In the second week, 100 fewer
people went to the pool than in the first week. In the third week, 135 more people went to the pool than in the second week.
In the fourth week, 137 fewer people went to the pool than in the third week. What is the percent decrease in the number of
people who went to the pool over these four weeks?
Answers
With the concepts of percentages and calculations, the percent decrease in the number of people who went to the pool over these four weeks is 10%
What is the way to solve percentages?Take the base as 100 and convert the percentage to numbers and then proceed with the same.
Now, the initial number of people in the local swimming pool is 1020, after which 100 fewer went, hence 920 people
Now, 135 people more people need to be added, thus 1055 people.
Now, 137 fewer people went, so 918 people went to the pool in the four weeks.
Therefore percent decrease = Difference/No. of people in the first week * 100
Thus, the percent decrease = 102/1020*100=10%
Hence 10% of people went less in the fourth week as compared to the first week.
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A fair number cube with the numbers 1, 2, 3, 4, 5, and 6 is rolled
a. What is the probability of getting an even number?
b. What is the probability of getting a factor of 6?
Answers
The probability of getting an even number is 1/2 while the probability of getting a factor of 6 is 1/6
How to determine the probabilities?The probability of an even number
From the question, the sample space of the number cube is given as
Space = 1, 2, 3, 4, 5, and 6
The above means that
Sample size, n = 6 ---- i.e. the number of observations
Number of even numbers, x = 3
The probability of getting an even number is then calculated as
P(Even) = Number of even numbers/Sample size
This gives
P(Even) = 3/6 = 1/2
The probability of a factor of 6
From the question, the sample space of the number cube is given as
Space = 1, 2, 3, 4, 5, and 6
The above means that
Sample size, n = 6 ---- i.e. the number of observations
Number of factor of 6, x = 1
The probability of getting a factor of 6 is then calculated as
P(factor) = Number of factor of 6/Sample size
This gives
P(factor) = 1/6
Hence, the probability is 1/2 and 1/6
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A train of length 150 metres entered a straight tunnel of length s metres. It took the entire crossing of the tunnel in a time of 15 seconds. Find the length of the tunnel if the train moves with uniform velocity equals 90 km./hr
Answers
The tunnel measures 225 meters in length.
Uniform velocity: What is it?
Velocity is the measure of how quickly an object's position changes over time and in relation to a frame of reference. A body moves across space with uniform velocity when it does so with an equal displacement per unit of time.
Velocity is equal to the product of distance and time.
It measures in m/s.
In response to the query, we are provided with the-
150m is the length of the train.
s m is the tunnel's length.
90 km/hr is the train's speed.
= 90 × 5/18 m/sec
= 25m/sec
Total distance equals (train length plus tunnel length).
[tex]Speed = \frac{Distance}{Time}[/tex]
⇒ 25 = (150 + s) / 15
⇒ 25 × 15 = 150 +s
⇒ 375 = 150 + s
⇒ 375 - 150 = s
⇒ s = 225
⇒ s = 225m
Hence, the length of the tunnel is 225 m.
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PLEASE PLEASE HELP!!!
Answers
If you are trying to find x, you would want to do tangent of 26 (trigonometry). You would get 26tan17 which equals roughly 90.84. Hope this helps.
Point C(6,-2)is dilated from the origin by scale factor r =3/4.what are the coordinates of point c
Answers
the coordinates of point c is (9/2, -3/2)
Explanation:The original coordinate = C(6, -2)
scale factor r =3/4
New coordinate (c) = scale factor × the original coordinate
c = 3/4(6, -2)
c = (3/4×6, -2×3/4)
c = (18/4, -6/4)
c = (9/2, -3/2)
Hence, the coordinates of point c is (9/2, -3/2)
Examine graphs A and B. What do you notice about the difference between the Y axis for the good graph A and the Poot graph B? How is a break shown on the Y axis of graph A
Answers
Answer:
The well-desgined graph has an appropriate scale for the y-axis. By appropriate we mean that the scale is such that all points on the graph can be discerned easily. In other words, the scale is not too wide or too narrow.
For graph A, the scale is such that the data points are at such a distance from each other that their values can be easily read off. On the other hand, for graph B, there isn't enough vertical distance between the data points for them to be easily read.
True or False
Corresponding angles must be proportional.
O True
O False
Answers
Answer:
True
Step-by-step explanation:
Matching sides of two or more polygons are titled corresponding sides,and matching angles are titled corresponding angles . If two figures are lookalike,then the measures of the corresponding angles are similar and the ratios of the lengths of the corresponding sides are proportional .
Suppose James has a credit card with a balance of $4289. Each month, the credit card company charges 5% interest. James pays off all new purchases that he makes each month without paying off the old balance or its interest. He wants to know what the balance on his credit card will be one year from now. Is this situation an example of exponential growth or exponential decay?
Answers
The balance on his credit card will be the amount of $4076.56 one year from now.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
First, we must compute James' monthly charges on his balance of 4289.
Principal = 4289
Rate = 5%
Time = 1 month = 1/12 year
Simple interest = 4289×5×1/12×100 = 17.87
The monthly charge is 17.87,
So the yearly charge would be: 12 × 17.87 = $214.44
His credit card balance one year from now = Principal - Interest
⇒ 4289 - 214.44
⇒ 4076.56
In one year, his credit card amount will be 4076.56.
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Mia made at least one mistake when
simplifying the expression below. The steps she took are shown.
Step 1:
Step 2:
Step 3:
In which step did Mia make her first mistake?
Choose one option from each drop-down menu to answer the questions
Mia made a mistake in Choose. She simplified the Choose
Choose
incorrectly She should have
Answers
Using properties of exponents, it is found that Mia's first mistake is described as follows:
Mia made a mistake in Step 3. She simplified the exponents 16 and -8 incorrectly. She should have subtracted them.
Which properties of exponents are used in this problem?When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, as follows:
3^0 x 3^(16) = 3^(0 + 16) = 3^16.
Hence the Step 1 is correct.
For the power of power rule, we keep the base and multiply the exponents, hence:
(3^(-4))² = 3^(-4 x 2) = 3^(-8).
Hence the Step 2 is correct.
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, as follows:
3^16/(3^(-8)) = 3^(16 - (-8)) = 3^(16 + 8) = 24.
Which is Mia's mistake, as she did not subtract the exponents.
What is the missing information?The steps are missing and are given by the image at the end of the answer.
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Which of the following statements is the best description of a survey?
A survey is a list of questions used to acquire customer feedback.
A survey is a study that collects data on every subject in sample.
A survey always collects categorical data.
A survey is a kind of convenience sample.
Answers
Answer:
I believe it's " a study that collects data on every subject in sample"
I need help with this for my class
Answers
but I believe that they relations are not functions because the line hits the graph at one or more spots.
Eight workers are hired to weed a field by
hand. Each is given a plot which is 9×7
meters in size. What is the total area of
the field?
Answers
Step-by-step explanation:
1.work out area of a single plot
[tex]area = 9 \times 7[/tex]
[tex]area = 63m ^{2} [/tex]
2.multiply the area by the amount of workers
[tex]total \: area = 63 \times 3[/tex]
[tex]total \: area \: = 189m ^{2} [/tex]
3x-(2x+10) for x= 7 5/13
Answers
The result of the expression 3x-(2x+10) for x = [tex]7\frac{5}{13}[/tex] is -2.61
The expression is
3x-(2x+10)
The expression is the mathematical sentence with a minimum of two variables and at least one math operation.
The value of the x = [tex]7\frac{5}{13}[/tex]
Convert the mixed fraction to the simple fraction
[tex]7\frac{5}{13}[/tex] = 96/13
Convert the simple fraction to the decimal form
96/13 = 7.39
Substitute the value of x in the given expression 3x - (2x + 10)
= 3 × 7.39 - (2×7.39 + 10)
Multiply the terms first
= 22.17 - (14.78 + 10)
= 22.17 - (24.78)
= -2.61
Hence, the result of the expression 3x-(2x+10) for x = [tex]7\frac{5}{13}[/tex] is -2.61
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prove that: [tex](a+b)^-^1.(a^-^1 +b^-^1) = (ab)^-^1[/tex]
Answers
Answer:
See below
Step-by-step explanation:
[tex]\frac{1}{a+b}[/tex] ([tex]\frac{1}{a}[/tex] + [tex]\frac{1}{b}[/tex])
[tex]\frac{1}{a+b}[/tex] ([tex]\frac{b}{ab}[/tex] + [tex]\frac{a}{ab}[/tex])
[tex]\frac{1}{a+b}[/tex] ([tex]\frac{b+a}{ab}[/tex])
[tex]\frac{(a+b)}{(a+b)(ab)}[/tex]
[tex]\frac{1}{ab}[/tex]
[tex]ab^{-1}[/tex]
the brain volumes () of 50 brains vary from a low of to a high of . use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of , assuming the estimate is accurate if it is within 15
Answers
The estimated standard deviation from the range rule is 145.5 cm3.As it is 29.8 cm3 smaller than the exact standard deviation, we consider that the estimation is not accurate enough.
Generally, brain volumes which are smaller than 921.1 cm3 can be considered significantly low and bigger than 1417.5 cm3 can be considered significantly high. Hence, brain volume of 1457.5 cm3 is bigger than the expected maximum, so it can be considered significantly high.
The calculation goes like this,
According to the range rule, the standard deviation and range, or the distance between the maximum and smallest value, are roughly inversely proportional:
[tex]s=R/4[/tex]
If we have a sample of 50 brains volumes, and they range from 910 cm3 to 1492 cm3, we can estimate the standard deviation as:
[tex]s=max-min/4[/tex]
s=1492-910/4=582/4=145.5
The exact standard deviation is 175.3 cm3.The difference is 175.3-145.5=29.8 cm3, so the estimation is not accurate enough.
The range rule of thumb states that we should anticipate a maximum value that is approximately two standard deviations above the mean and a lowest value that is approximately two standard deviations below the mean. The expected ranges are as follows given our mean volume of 1169.3 cm3 and standard deviation of 124.1 cm3:
Min= M-2s=1169.3-2*124.1=921.1
Max=M+2s=1169.3+2*124.1=1417.5
The brain capacity of 1457.5 cm3 can be regarded as significantly high because it is higher than the predicted maximum.
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Steven earns extra money babysitting. He charges $33.75 for 5 hours and $47.25 for 7 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits a
y represent the amount he charges.
The equation is y =
Answers
Answer:
y = 6.75x
Step-by-step explanation:
$33.75 ÷ 5 = $6.75
$47.25 ÷ 7 = $6.75
So we have y = 6.75x.
One-Step Inequalities MC) Solve k over negative 3.7 is less than or equal to negative 2.2 for k. k ≥ 8.14 k ≤ −8.14 k ≥ −5.9 k ≤ −5.9
Answers
Answer: k>8.14
Step-by-step explanation: just do math.
What is the slope of the line on the graph
Answers
Answer:
Slope is -2!
y= -2x
Step-by-step explanation:
Based on the 2 points given: (3, -6) (-3, 6)
PLS TELL ME ASAPPPPP
Answers
Instructions: Determine whether the graph is a correct representation of the given inequality. If there is an error, select which error is present.
Answers
The given inequality is,
[tex]y\leq-\frac{5}{2}-4[/tex]The graph of the inequality will be shown below
sk-00000y5 Cog 10) -7x+2y=18 6361-30 33 42952 read 10,000 13x+40%3D2Ax0 Swazo 7-12 - 1234-5y=1722119 ターにはまった Ax - Ay=0 いりさわさったのにーちゃん 14) 42-y=20 Solve each system by elimination. 1S) 8x-6y%3D-20 ~16x+7y%3D30 y2-2142 りたい セー Crysoe Y=24 doe 24 -2x-2y= 10 JS-04-26 とおり 2012-2010 2010年10 プラス・マトリー 7 10分 16) 6x-12y = 24 yeye 一X-6y=4 Hey-400 SK-121024 ~42-30) 224.5メートル 60-124:24 カー123) 2012 ームが2012 1348
Answers
Given:
The linear equations are,
[tex]\begin{gathered} 20x-8y-22x-16=0 \\ -22x-18y=36 \end{gathered}[/tex]The objective is to solve by elimination method.
The equations can be rearranged as,
[tex]\begin{gathered} -2x-8y=16\text{ ..}\ldots..\ldots\ldots(1) \\ -22x-18y=36\text{ ..}\ldots..\ldots\ldots(2) \end{gathered}[/tex]To solve the equation, multiply equation (1) b
If a car is traveling at 65 miles per hour, then
how far does it travel in 2 hours?
Answers
Answer:
130 miles
Step-by-step explanation:
65×2=130 So if I am driving at a rate of 65 mph then in one hour I drive 65 miles. Since it is in 2 hours I will have driven 130 miles.
Answer:
130 miles.
Step-by-step explanation:
so it said that the car is traveling 65 miles per hour and it wants to know how far it would go in 2 hours. so if 1 hour is 65 miles if we multiply it by two then we will get
65 miles = 1 hour
130 miles = 2 hours
Mr. Ridley has 4 boxes of pencils and 7 single pencils. In all, he has 79 pencils. How many
pencils are there in a box?
Answers
Answer:
18
Step-by-step explanation:
You want to know the number of pencils in a box when 7 more than 4 boxes totals 79 pencils.
SetupLet b represent the number of pencils in a box. Then the total number of pencils Mr. Ridley has is ...
4b +7 = 79
SolutionThis 2-step linear equation is solved in the usual way:
Step 1: isolate the variable term
4b +7 -7 = 79 -7 . . . . . . add the opposite of the left-side constant
4b = 72 . . . . . . . . . simplify
Step 2: isolate the variable
4b/4 = 72/4 . . . . . . . . . . divide by the coefficient of the variable
b = 18 . . . . . . . . . . simplify
There were 18 pencils in each of Mr. Ridley's pencil boxes.
Terry bought 2 shirts for $14 each, 2 pair of socks for $2.99 a pair, and a pair of slacksfor $25.00. The sales tax rate is 6.5%. How much did he pay? (Enter the dollar amountonly. Round to the nearest cent.)
Answers
Answer:
Explanation:
Terry bought 2 shirts for $14 each.
That is $28 on shirts
2 pair of socks for $2.99
That is $5.98 on socks
A pair of slacks for $25
The sales tax rate is 6.5% or 6.5/100 or 0.065
We want to know how much he paid.
Adding all the items he bought together, we have:
$28 + $5.98 + $25
= $58.98
Next, we apply the sales tax rate.
Take 6.5% of $58.98
This is: $58.98 * 0.065
= $3.83
Finally, add the sales tax with the amount we got
$58.98 + $3.83
= $62.81
He paid $62.81 in total