Answers
Hello there. To solve this question, we'll have to remember some properties about trapezoids and right triangles.
Given the following trapezoid:
We have to determine its area and perimeter.
For this, remember that:
The area of a trapezoid with bases B and b (larger and smaller, respectively) and height h can be found by the formula
[tex]A=\dfrac{(B+b)\cdot h}{2}[/tex]The perimeter is the sum of the measures of all sides of the figure.
For the perimeter, we'll use the pythagorean theorem to determine the measure of the legs of the trapezoid.
Okay. Notice that in the trapezoid, the larger base B measures 41, the smaller base measures 21 and the height is 18.
By the formula for area, we get
[tex]A=\dfrac{(41+21)\cdot18}{2}=62\cdot9=558[/tex]Now, notice we can determine a right triangle on the left:
To determine the legs of the triangle, we make
[tex]\dfrac{41-21}{2}=\dfrac{20}{2}=10[/tex]Now we have a right triangle with legs 10 and 18.
Using the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]For a triangle with legs a and b and hypotenuse c, the sum of the squares of the legs is equal to the square of the hypotenuse.
Using a = 10 and b = 18, we get
[tex]\begin{gathered} 10^2+18^2=c^2 \\ 100+324=c^2 \\ 424=c^2 \\ 4\cdot106=c^2 \\ c=2\sqrt{106} \end{gathered}[/tex]Since the other right triangle is the same, the other leg have the same measure, hence we add
[tex]\text{ Perimeter }=21+41+2\cdot2\sqrt{106}=62+4\sqrt{106}[/tex]We can approximate this value using a calculator
[tex]\text{ Perimeter }\approx103.18[/tex]
Related Questions
PLSS HELP Find a formula for the exponential function passing through the points (-3, 3/8) and (3,24)
Answers
The exponential function is of the form:
[tex]y=ab^x[/tex]Given the two points, we can plug each point into the equation and see:
1.
[tex]\begin{gathered} y=ab^x \\ \frac{3}{8}=ab^{-3} \end{gathered}[/tex]2.
[tex]\begin{gathered} y=ab^x \\ 24=ab^3 \end{gathered}[/tex]Let's divide the the 2nd equation by the 1st one:
[tex]\begin{gathered} \frac{24}{\frac{3}{8}}=\frac{ab^3}{ab^{-3}} \\ 24\times\frac{8}{3}=\frac{b^3}{b^{-3}} \\ 64=b^{3+3} \\ b^6=64 \end{gathered}[/tex]Note: we used the property of exponents, 1/a^x = a^ -x to simplify it.
Now, we can solve for b:
[tex]\begin{gathered} b^6=64 \\ b=\sqrt[6]{64} \\ b=2 \end{gathered}[/tex]The second equation, now, becomes:
[tex]\begin{gathered} 24=ab^3 \\ 24=a(2)^3 \end{gathered}[/tex]Now, we can easily find a:
[tex]\begin{gathered} 24=a(8) \\ a=\frac{24}{8} \\ a=3 \end{gathered}[/tex]We know b = 2 and a = 3.
So, the final equation will be:
[tex]\begin{gathered} y=ab^x \\ y=3(2)^x \end{gathered}[/tex]The cost in dollars of a class party is 59+13n, where n is the number of people attending. What is the cost of 44 people?
Answers
The function is:
C(n) = 59 + 13n
where n is the number of people, and C(n) is the cost of a class party.
To determine the value of C(n) where n = 44, just replace this value of n into the previous formula, and simplify the expression, just as folow:
C(44) = 59 + 13(44)
C(44) = 59 + 572
C(44) = 631
Hence, the cost for 44 people is 631 dollars.
Complete the following statements.
In general, ________% of the values in a data set lie at or below the median.
________% of the values in a data set lie at or below the third quartile (Q3).
If a sample consists of 2100 test scores, ________ of them would be at or below the second quartile (Q2).
If a sample consists of 2100 test scores, ________ of them would be at or above the first quartile (Q1).
Answers
In general, 50% of the values in a data set lie at or below the median.
75% of the values in a data set lie at or below the third quartile (Q3).
If a sample consists of 2100 test scores, 1100 of them would be at or below the second quartile (Q2).
If a sample consists of 2100 test scores, 525 of them would be at or above the first quartile (Q1).
What are quartiles?Three values called quartiles divide sorted data into four equal portions with the same amount of observations in each.
One kind of quantile is a quantile. Q1, or the lower quartile, is another name for the first quartile.
Second quartile: Also referred to as the median or Q2.
Third quartile, or the upper quartile, is also referred to as Q3.
The second quartile is 50%
Samples of 2100 test scores that are at or below at the second quartile
= 50% of 2100
= 0.5 * 2100
= 1100
The first quartile is 25%
= 0.25 * 2100
= 525
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James and Susan wish to have $10,000 available for their wedding in 2 years.
How much money should they set aside now at 6% compounded monthly in
order to reach their financial goal?
Answers
They need to set aside $8871.86
what is the area of a square with side of 14 millimeters
Answers
The formula for determining the area of a square is expressed as
Area = length^2
If the length of each side of the given square is 14 millimeters, then
Area = 14^2
Area = 196 mm^2
Find the product 54,612 x 46?
Answers
Explanation
Step 1
Multiply. as you would with whole numbers.( ignore the comma)
so
[tex]\begin{gathered} 54,612x46\rightarrow54612\cdot46=2512152 \\ \end{gathered}[/tex]Step 2
Count the total number of decimal places in your factors.
[tex]54,612\rightarrow\text{3 numbers in decimal places}[/tex]Step 3
Move the decimal point in the product one place to the left for each decimal place you counted.
so
[tex]2512152\rightarrow3\text{ places}\rightarrow2512,152[/tex]so, the answer is
[tex]2512,152[/tex]I hope this helps you
over Thanksgiving break Joshua drove from Connecticut to Ohio which is 422 Mi this trip took Jason and his family 6 hours how fast was Joshua driving be sure to round your answer to the nearest whole number
Answers
In this case the answer is very simple. .
Step 01:
Data
total distance = 422 mi
total time = 6 hours
Step 02:
[tex]\frac{total\text{ distance}}{\text{total time}}=\frac{422mi}{6\text{ hour}}\text{ = }70.33\text{ mi / hour}[/tex]The answer is:
Joshua's speed was 70 mi/hours
Which value is in the solution for the inequality 7 + 3x < 37?
Answers
the solution of the inequality will be x<10, i mean all the real numbers that are less than 10. It's because:
[tex]7+3x<37\Rightarrow3x<37-7=30\Rightarrow x<\frac{30}{3}=10[/tex]10 ex 9 10 ex 3 simplified
Answers
ANSWER
[tex]10^6[/tex]EXPLANATION
We want to simplify the fraction below:
[tex]\frac{10^9}{10^3}[/tex]When you have a fraction of powers and the numerator and denominator have the same base (e.g. 10 in this case), the power on the denominator is subtracted from the power of the numerator.
So, that is:
[tex]\begin{gathered} 10^{9-\text{ 3}} \\ =>10^6 \end{gathered}[/tex]That is the answer.
Drag the preimage to the correct location on the graph.
Quadrilateral 2 is a reflection of a quadrilateral across line m. Where is the preimage for quadrilateral 2 located and what is its orientation?
Answers
It is true that the preimage of the quadrilateral labeled 1 is reflected across line M to produce 2. The preimage for quadrilateral 2 is located at exactly below the position of quadrilateral 2 as indicated in the attached image. Its orientation is °180 the current location of image 2.
What is a preimage?Preimage refers to a collection of some input set items that are handed to a function to get some output set elements. It is the opposite of the Image. Domain = all valid independent variable values. This is the input set of a function, also known as the set of departure.
The orientation (that is angular position or attitude or bearing, or direction) of an object, such as a line, plane, or rigid body, is described in geometry as part of how it is positioned in the space it inhabits.
Hence quadrilateral 2 is 180° reflected from the preimage, given that it was reflected across line m.
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took me an hour to figure it out
Step-by-step explanation:
I need help quick please i have to turn this in tomorrow it’s 4am.
Answers
Answer:
sitting in his highchair modifies baby
You have a bag of 36 ounces of popcorn. Your friend eats 1/4 of the bag. You eat 1/3 of the bag. How many ounces did you eat? How many ounces are left?
Answers
Answer: You Eat: 12 ounces. There are 15 ounces left.
Step-by-step explanation:
36(1/4)=9 ounces
36(1/3)=12 ounces, which is how much you eat.
36-12-9=15 ounces left
Step-by-step explanation:
How many ounces did you eat?
¼+⅓=3+4/12=7/12 ounces were eaten
How many ounces are left?
36-7/12=432-7/12
=425/12
=\frac{425}{12}
=35^5/12
Erian's extended family is staying at the lake house this weekend for a family reunion. She is in charge of making homemadepancakes for the entire group. The pancake mix requires 2 cups of flour for every 10 pancakes.[a] Write a ratio to show the relationship between the number of cups of flour and the number of pancakes made.[b] Determine the value of the ratio.c Use the value of the ratio to fill in the following two multiplicative comparison statements..The number of pancakes made is.times the amount of cups of flour needed.The amount of cups of flour needed isof the number of pancakes made.(d If Erian has to make 70 pancakes, how many cups of flour will she have to use?
Answers
(a) The ratio is:
[tex]\frac{\text{ number of cups of flour}}{\text{ number of pancakes}}[/tex](b) This ratio is equal to:
[tex]\begin{gathered} \frac{\text{ number of cups of flour}}{\text{ number of pancakes}}=\frac{2}{10} \\ S\text{implifying} \\ \frac{\text{ number of cups of flour}}{\text{ number of pancakes}}=\frac{1}{5} \end{gathered}[/tex](c) Isolating "number of cups of flour":
[tex]\text{ number of cups of flour}=\frac{1}{5}\cdot\text{number of pancakes}[/tex]Isolating "number of pancakes":
[tex]5\cdot\text{ number of cups of flour}=\text{ number of pancakes}[/tex]The number of pancakes made is 5 times the amount of cups of flour needed.
The amount of cups of flour needed is 1/5 of the number of pancakes made.
(d) Substituting with "number of pancakes" = 70, we get:
[tex]\begin{gathered} \text{ number of cups of flour}=\frac{1}{5}\cdot\text{7}0 \\ \text{ number of cups of flour}=14 \end{gathered}[/tex]She will have to use 14 cups of flour
Writing rational numbers as a decimal
Answers
2. Let's convert the rational number as a decimal
[tex]-2\frac{4}{5}[/tex]The given number is a mixed number, so we need to convert it to rational.
[tex]-2\frac{4}{5}=-2+\frac{4}{5}=-\frac{6}{5}[/tex]Then: To convert -6/5 into a decimal number, divide 6 by 5:
6 divide by 5
5*1 = 5, then 6-5 = 1
6 l 5
1
--------------
6 l5
5 1
-------------
1 l 5
1
We add
2) Find the volume of a shoe box that is wide9, 15 inches, and 6 inches high.
Answers
volume of the shoe box is 1080 inches³
Explanation:2) The shoe box is rectangular prism
So we will find the volume of a rectangular prism:
Volume of rectangular prism = length × width × height
length = 15 inches
width = 9 inches
height = 6 inches
Volume = 15 × 9 ×6
Volume = 1080 inches³
Hence, the volume of the shoe box is 1080 inches³
A fashion designer makes and sells hats. The material for each had cost three dollars. The hats sell for $13.50 each. The designer spends $2121 on fixed cost: advertising, Power, water, rent . How many hats mustard designers sell to break even
Answers
The designer spends $2121 and $3 each for hat and he can sell it for $13.50 each.
If there are x number of hats, it will cost him (2121 + 3x) and he can gain 13.50x
The break even is when the cost and sales are equal.
Equating both expressions :
[tex]\begin{gathered} 2121+3x=13.50x \\ 2121=13.50x-3x \\ 2121=10.50x \\ x=\frac{2121}{10.50}=202 \end{gathered}[/tex]The answer is 202 hats
Question 3(Multiple Choice Worth 3 points)
(01.02 MC)
Joaquin wants to make his famous chocolate chip cookies to bring to his friend's birthday party. The original recipe serves 5 people and requires 1/4 a cup of butter but he needs to serve 28 people. How many cups of butter will he need?
Answers
Answer:
B
Step-by-step explanation:
Find the circumference of the circle. Round to the nearest hundredth if necessary. (Use 3.14 for a) A circle with a diameter of 18 in
Answers
Given data:
The given diameter of the circle is D=18 in.
The expression for the circumference is,
[tex]C=\pi D[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} C=\pi(18\text{ in)} \\ =56.52\text{ in} \end{gathered}[/tex]Thus, the circumference of the circle is 56.52 in.
1. Given triangle ABC, what is the length of the line segment connecting the midpoints of AC and BC?
A = (1,6)
B = (3,1)
C = (8,3)
Answers
The length of the line segment connecting the midpoints of AC and BC is 2.69 units.
We are given a triangle. The vertices of the triangle are A, B, and C. The coordinates of the vertices are A (1, 6), B (3, 1), and C (8, 3). We need to find the length of the line segment connecting the midpoints of AC and BC.
Let the midpoints of AC and BC be E and F.
The coordinates of the midpoint E are calculated below.
E = [(1 + 8)/2, (6 + 3)/2] = (4.5, 4.5)
The coordinates of the midpoint F are calculated below.
F = [(3 + 8)/2, (1 + 3)/2] = (5.5, 2)
The length of the line segment EF can be calculated by using the distance formula. Let the length of EF be represented by "L".
L = √[(4.5 - 5.5)² + (4.5 - 2)²]
L = √(1 + 6.25)
L = √7.25
L = 2.69
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I need help number 7
Answers
The population at the beginning of 1950 was 2600 thousand people.
Then it started increasing exponentially 23% every decade.
The general form of any exponential function is:
[tex]f(x)=a(b)^x[/tex]Where
a is the initial value
b is the growth/decay factor
x is the number of time periods
y is the final value after x time periods
a. To calculate the growth factor of an exponential function, you have to add the increase rate (expressed as a decimal value) to 1:
[tex]\begin{gathered} b=1+r \\ b=1+\frac{23}{100} \\ b=1.23 \end{gathered}[/tex]b. Considering the initial value a= 2600 thousand people and the growth factor b=1.23, you can express the exponential function in terms of the number of decades, d, as follows:
[tex]f(d)=2600(1.23)^d[/tex]c. Considering that the time unit is measured in decades, i.e d=1 represents 10 years
To determine the corresponding value of the variable d for 1 year, you have to divide 1 by 10
[tex]1\text{year/10years d}=\frac{1}{10}=0.1[/tex]Calculate the growth factor powered by 0.1:
[tex]\begin{gathered} b_{1year}=(1.23)^{0.1} \\ b_{1year}=1.0209\approx1.02 \end{gathered}[/tex]d. Use the factor calculated in item c
[tex]g(t)=2600(1.0209)^t[/tex]PLEASE HELP!!!! Explain in depth!!! In a geometry course, the grade is based on the average score on six tests, each worth 100 points. W. Orrier has an average of 88.5 on his first four tests. What is the lowest average he could obtain on his next two tests and still receive an A (an average of 90 or better)?
Answers
Answer:
93 marks
Step-by-step explanation:
If he has an average of 88.5 marks on the first four tests then the total score for these four tests is:
[tex]\implies 88.5 \times 4=354[/tex]
To obtain an average of at least 90 marks on each test the total number of marks needed for the six tests is:
[tex]\implies 90 \times 6=540[/tex]
So the minimum total marks he needs to obtain an A is 540.
To find the lowest average he could obtain on his next two tests to still receive an A, subtract the total for the first four tests from the total needed for the six tests and divide by two:
[tex]\implies \dfrac{540-354}{2}=\dfrac{186}{2}=93[/tex]
Therefore, he needs to score an average of at least 93 marks on his next two tests to still receive an A grade.
- Which subsets of the real number system does -2.8 belong? A.Rational and Integer.B.Irrational and Integer.C.Irrational onlyD. Rational only.
Answers
Answer:
D. Rational only.
Step-by-step explanation:
-2.8 is only rational.
It is not irrational because it is rational(decimal numbers are rational).
It is not integer because there is a decimal part.
So, the correct answer is:
D. Rational only.
In a video game, Connor scored 25% more points than Max. If c is the number of points that Connor scored and m is the number of points that Max scored. Write an equation that represents the situation.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Connor scored = c
Max scored = m
equation = ?
Step 02:
Connor scored =>>> + 25% Max scored
c = m + m * 0.25
c = m ( 1 + 0.25)
c = 1.25 m
The answer is:
c = 1.25 m
Suppose a sample of 383 Americans over 21 is drawn. Of these people, 280 don't smoke. Using the data, construct the 80% confidence interval for the population proportion of Americans over 21 who smoke. Round your answers to three decimal places.
Answers
The 80% confidence interval for the population proportion of Americans over 21 who smoke is: 0.240; 0.298.
How to find the confidence interval?First step is to find the population proportion p
Sample size = n = 383
Using this formula to find the population proportion (p)
p = x /n
Let plug in the formula
p = (383 - 280) / 383
p = 103/383
p = 0.2689
Second step is to find the Margin of error (MOE)
Value of z-score for a confidence level of 80%= 1.282
Using this formula to margin of error
MOE =( z alpha x √(p) (1-p) / n )
Let plug in the formula
MOE =( 1.282x √(0.2689)(1-.0.2689) / 383)
MOE =( 1.282 x √(0.2689)(0.7311) / 383)
MOE =( 1.282 x √0.000513297
MOE =( 1.282 x 0.0226561)
MOE = 0.02905
Third step is to find the confidence interval (CI)
Confidence interval = p ± MOE
Confidence interval = 0.2689 ± 0.02905
Confidence interval = ( 0.2689 - 0.02905) , (0.57 + 0.02905)
Confidence interval = 0.23985; 0.29795
Confidence interval = 0.240; 0.298 ( Three decimal places)
Therefore the CI is 0.240; 0.298.
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Solve the equation. 6x = 96a16b576c90d102
Answers
Answer
Option A is correct.
x = 16
Explanation
We are asked to solve the equation
6x = 96
Divide both sides by 6
(6x/6) = (96/6)
x = 16
Hope this Helps!!!
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function =ht−80t16t2. After how long will it reach its maximum height?
Answers
Can anyone help me with this a 7 more problem
Answers
We are given the following statement.
If a number is an integer, then it is either positve or negative.
In the above statement, the 1st part is the condition and the 2nd part is conclusion.
Condition = a number is an integer
Conclusion = it is either positve or negative
Therefore, the conclusion of the conditional is option B.
A number is either positive or negative.
Reflect the vector (-3,5) acrossthe x-axis.([?],[])
Answers
1) When we reflex across the x-axis we must follow this rule:
Pre-image Image
(x, y) ----------------> (x,-y)
2) Since we have a vector <-3,5> then reflecting it across the x-axis we'll have
Pre-image Image
<-3,5>---------> <-3, -5>
3) So the vector after the reflection is < -3,-5>
Identify a benchmark you can use to find an equivalent percent for eachratio. Then find the equivalent percent. (Example 1)13. Lo Benchmark: 4. Benchmark:6105.Benchmark:
Answers
The benchmark of a fraction a/b is 1/b. Then, for the given:
To find the equivalent percent: find the a/b of 100 :
6/10:
[tex]\frac{6}{10}\cdot100=60[/tex]6/10 =60%___________________
2/4:
[tex]\frac{2}{4}\cdot100=50[/tex]2/4=50%___________________
4/5:
[tex]\frac{4}{5}\cdot100=80[/tex]4/5 = 80%Quadrilateral QRST with vertices Q (1,2), R(3,4), S(5,6) and T(2,7), is dilated by a factor of 2 with the center of dilation at the origin. what are the coordinates of the quadrilateral QRST
Answers
SOLUTION
Now, since the center of dilation is at the origin, to get the new coordinates of the vertices of the quadrilateral, we will simply multiply the coordinates by a the scale factor of 2. This becomes
d
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