The diagram represents the floor of a museum. The figure is made up of a rectangle and a triangle.
What is the area of the floor?
Enter your answer in the box.
______ ft2 I'll but the link for the pic
Answers
The figure is formed of a rectangle and a triangle
The rectangle has dimensions:length=38ft and width=20ft
The triangle has dimensions:base=33ft and height=9ft
Area of rectangle=length*width of rectangle
Area of triangle=[tex] \frac{1}{2} [/tex]*base*height
Area of figure= area of rectangle + area of triangle
Area=length*width+[tex] \frac{1}{2} [/tex]*base*height
Area=38*20 + [tex] \frac{1}{2} [/tex]*33*9
Area=760+[tex] \frac{1}{2} [/tex]*297
So we have, Area=760+[tex] \frac{297}{2} [/tex]
Or, Area=760+148.5
Area=908.5
Area of the floor=908.5[tex] ft^{2} [/tex]
Related Questions
Solve the equation
3/4=y−1/5 (8)
y=
Answers
Jacobs & Johnson, an accounting firm, employs 15 accountants, of whom 9 are CPAs. If a delegation of 4 accountants is randomly selected from the firm to attend a conference, what is the probability that 4 CPAs will be selected? (Round your answer to three decimal places.)
Answers
Using the hypergeometric distribution, it is found that there is a 0.0923 = 9.23% probability that 4 CPAs will be selected.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem, there are 15 accountants, 9 are CPAs and 4 will be selected, hence N = 15, k = 9, n = 4.
The probability that 4 CPAs will be selected is P(X = 4), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,15,4,9) = \frac{C_{9,4}C_{6,0}}{C_{15,4}} = 0.0923[/tex]
0.0923 = 9.23% probability that 4 CPAs will be selected.
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determine the area of a 21ft circle
Answers
.. = (π/4)*(21 ft)^2
.. = 110.25π ft^2
.. ≈ 346.36 ft^2
The IRS has a group of 45 tax returns, 15 of which contain errors. An IRS auditor randomly selects 3 tax returns from this group. What is the probability the auditor selects none of those containing errors? Round to four decimal places.
Answers
If the auditor randomly selects 3 returns, without replacement, then
P(1)=30/45,
for the second one, there will be 29 correct returns out of 44, so
P(2)=29/44
Similarly,
P(3)=28/43
Therefore, by the multiplication rule, the probability of selecting 3 correct returns is the product
P(1)*P(2)*P(3)=30*29*28/(45*44*43)=406/1419
Answeeeeeerrrrr
0.2861
I need help I would really thank wheeler answers this for me
Answers
When a number is positive, it is greater than a negative number.
a. -4.84 > -8.48
b. 7 > -7
c. -6.5 < -5 1/2
d. -1 < 0
> is greater than
< is less than
-4.84 > -8.48
b.
7 > -7
c.
-6.5 < -5 1/2
d.
-1 < 0
Paul needs 40 pounds of 48% silver alloy to finish a collection of jewelry. How many pounds each of 45% silver alloy and 60% silver alloy should he melt together to obtain the alloy he needs
Answers
silver + silver = silver
0.45x + 0.60(40-x) = 0.48*40
----------------
45x + 60*40 - 60x = 48*40
--------
-15x = -12*40
x = (4/5)40
x = 32 lbs (amt of 45% slloy needed)
40-x = 8 lbs (amt of 60% alloy needed)
Rewrite as a simplified fraction
2.267 = ?
Answers
The decimal 2.267 is equivalent to the simplified fraction 2267/1000.
To express the decimal 2.267 as a simplified fraction, we can consider the place values of each digit. The decimal portion .267 can be written as the fraction 267/1000 since there are three decimal places. Combining this with the whole number 2, we get:
2.267 = 2 + 267/1000.
To simplify this mixed number, we first find a common denominator, which is 1000. We convert the whole number 2 to an equivalent fraction with this denominator: 2 = 2000/1000. Now, we can add the fractions:
2 + 267/1000 = 2000/1000 + 267/1000 = 2267/1000.
This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1, yielding the simplified fraction:
2267/1000.
In summary, 2.267 can be expressed as the simplified fraction 2267/1000.
The question probable may be:
Write the following 2.267 in simplified fraction.
jeffery wei received a 6 year non subsidized student loan of 30000 at an annual interest rate of 5.2%. what are jeffery’s monthly loan payments for this loan after he graduates in 4 years
Answers
Jeffery's monthly loan payments for the loan will be $515.19.
Explanation:To calculate the monthly loan payments for Jeffrey, we can use the formula for calculating the monthly payment of a loan. The formula is:
Monthly Payment = (Principal * Monthly Interest rate) / (1 - (1 + Monthly Interest rate) ^ (-n))
In this case, Jeffrey's principal is $30,000, the annual interest rate is 5.2%, and the loan term is 6 years. Since Jeffrey will graduate in 4 years, we need to adjust the loan term accordingly. The monthly interest rate can be calculated by dividing the annual interest rate by 12, and the number of monthly payments will be multiplied by 4.
Using these values in the formula, we can calculate the monthly loan payment for Jeffrey.
Monthly Payment = (30000 * 0.052/12) / (1 - (1 + 0.052/12) ^ (-24))
Monthly Payment = $515.19
what is the factor of x^2-11xy-60y?
Answers
where
a=1
b=-11
c=-60
We look for m, n such that m+n=b=-11, mn=c=-60.
It is possible to find m, n mentally, or compile a table as follows:
-1*60=-60, -1+60=59 > -11
-2*30=-60, -2+30=28 > -11
-3*20=-60, -3+20=17 > -11
-4*15=-60, -4+15=11 > -11
But 4*(-15)=-60, and 4-15=-11, exactly what we want!
So
[tex]x^2-11xy-60y^2=(x+4)(x-15)[/tex]
how much lower is Checkpoint 1 than Checkpoint 5?
checkpoint 1: -188
checkpoint 5: -57
the top of a hill rises 462 feet above Checkpoint 1. What is the altitude of the top of the hill?
checkpoint 1: -188
hill rises: 462ft
Answers
The altitude of the top of the hill is 274 feet.
To find how much lower Checkpoint 1 is than Checkpoint 5, we subtract the elevation of Checkpoint 1 from the elevation of Checkpoint 5:
Difference = Elevation at Checkpoint 5 - Elevation at Checkpoint 1
Difference = (-57) - (-188)
Now, simplify the expression:
Difference = -57 + 188
Difference = 131 feet
So, Checkpoint 1 is 131 feet lower than Checkpoint 5.
Next, to find the altitude of the top of the hill, we add the rise of the hill to the elevation at Checkpoint 1:
Altitude of the top of the hill = Elevation at Checkpoint 1 + Hill rise
Altitude = (-188) + 462
Now, calculate the sum:
Altitude = 274 feet
The altitude of the top of the hill is 274 feet.
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A prism with a base area of 3m^2 and a height of 4m^2 is dilated by a factor of 3/2 what is the volume of the dilated prism
Answers
Let u = <-6, 1>, v = <-5, 2>. Find -4u + 2v.
A) <34, -8>
B) <14, 0>
C) <14, 3>
D) <44, -12>
Answers
-4u +2v
= -4<-6, 1> +2<-5, 2>
= <(-4)(-6)+2(-5), (-4)(1) +2(2)>
= <14, 0>
The appropriate choice is ...
... B) <14, 0>
To find the result of -4u + 2v, calculate -4u and 2v separately, then add the results together to get <-34, 0>.
To find -4u + 2v, we first need to calculate -4u and 2v separately and then add them together.
Calculate -4u = -4 * <-6, 1> = <-24, -4>Calculate 2v = 2 * <-5, 2> = <-10, 4>Add -4u and 2v: <-24, -4> + <-10, 4> = <-34, 0>Therefore, the answer is: -34, 0.
Two squares are attached to the sides of a quarter circle as shown. What is the best approximation for the area of this figure? Use 3.14 to approximate pi. 178.5 mm² 215.7 mm² 231.8 mm² 278.5 mm² Two squares with sides measuring 10 mm. Both squares are connected by a quarter circle.
Answers
Answer:
the answer is D
Step-by-step explanation:
One angle of a rhombus measures 108°, and the shorter diagonal is 9 inches long. Approximately how long is the side of the rhombus? (Hint: Diagonals of a rhombus bisect the angles.) 7 in. 8 in. 11 in.
Answers
cos θ=adjacent /hypotenuse
θ=108/2=54°
adjacent = 9/2=4.5 inch
hypotenuse=length of the rhombus
thus
cos 54=9/x
x=4.5/cos 54
x=7.6558~8 inches
the answer is 8 inches
Answer:
8 in.
Step-by-step explanation:
Let's find the rhombus's length...
cosine = [tex]\frac{adjacent}{hypotenuse}[/tex]
cosine = ° = 54°
adjacent = = 4.5 in
Length of Rhombus = Hypotenuse
So...
cos54 = [tex]\frac{9}{x}[/tex]
x = [tex]\frac{4.5}{cos 54}[/tex]
x = 7.6558... about 8 inches
a parallelogram has an area of 108 square inches. The base of the parallelogram is 18 inches. Explain how you could find the height of the parallelogram, then find the height. Show your work.
Answers
A=bh
108=18h
divide both sides by 18 to find h
6=h
The height is 6 inches.
Answer:
Height=6in
Step-by-step explanation:
Took test and got it correct
Hendrick makes birdhouses every weekend. it takes him 35 minutes to make a birdhouse. write and algebric expression that shows how long it takes him to make a birdhouse
Answers
anaya drew a cylinder with a radius of 3 inches and a height of 5 inches. she also drew a cone with the same radius and height. which of the following is true?
Answers
Please help me with question 4
Answers
Answer:
A. XV
Step-by-step explanation:
The letters identifying the shortest side of ΔMNP are the last (P) and first (M) of the designator for that triangle. The corresponding side of ΔVWX will be identified by the last (X) and first (V) letters of that triangle's name. Hence the segment of interest is XV.
the digit in the __ place is the best stem value for the set of data shown above? please help
Answers
Using the mode concept, according to the stem-and-leaf plot, the missing value is of 71.
What is the mode of the data-set?It is the value that appears the most times in the data-set. When it's unique, the mode is the value that appears the most often in a data set and it can be used as a measure of central tendency, like the median and mean.
Here, we have,
In this problem, following the key format of the stem-and-leaf plot, disconsidering the missing value, the values 71 and 64 each appear 3 times.
However, the mode is 71, meaning that is should appear more times than 64, which means that the missing value is of 71.
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complete question:
This Stem-and-Leaf Plot is missing one data item. If the mode of the data set is 71, what is the value of the unknown data item?
When 1 is added to the difference between seven times a number and 9, the result is greater than 10 added to 6 times the number. Find all such numbers.
Answers
A fraction that is equal to 3/5 that has the denominator 10.
Answers
Which system of inequalities is represented by the graph?
y ≤ –x
y > –1
y ≥ –x
y < –1
y < –x
y ≥ –1
y > –x
y ≤ –1
Answers
Answer:
[tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex] are system of inequalities is represented by the graph.
Step-by-step explanation:
We are given four option and need to choose correct inequality for given graph.
In graph, we can see two line
Red line: It is horizontal solid line passing through (0,-1) and shaded region above the line.
Equation of line: y≥-1
Blue line: It is slant dotted line passing through origin and (-2,1)
Equation of line: [tex]y<-\frac{1}{2}x[/tex]
System of inequalities represented by the graph.
[tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex]
Thus, [tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex] are system of inequalities is represented by the graph.
Can someone answer B please???
Answers
150 were surveyed, possible outcomes, and 132 said they prefer dogs, favorable outcomes, 132/150 or 22/25 or 0.88, now 0.88 * 100 is just 88, namely 88% is the probability.
b)
since we know is 88%, what is 88% of 100? (88/100) * 100, 0.88 * 100, or just 88 students.
c)
18/150 or 3/25 or 0.12 namely 12%,
what's 12% of 300? (12/100) * 300, or 0.12 * 300, so just 36 students.
What do you notice about the frequency of the sine function: y=sin(x) and the frequency of the cosine function: y=cos(x) ?]
a. they have the same value
c. the value is the same as the amplitude
b. they have a zero value
d. there is no frequency value for the cosine function
Answers
Answer:
they have always the same
Step-by-step explanation:
Therefore, after plotting the points on the graph
What is the trigonometry?
Trigonometry states that the trigon means 'triangle', and the metry means 'metron' is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here given angles are:-
[tex]y=sin(x)[/tex] and [tex]y=cos(x)[/tex]
Draw the graph
Hence, after plotting the points on the graph is:-
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One class of 75 students has an average midterm score of 67 and an sd of 12. another class of 325 students has an average of 72 and an sd of 15. find the average and the sd of the combined list of 400 students. hint: this uses the sd of a long list formula.one class of 75 students has an average midterm score of 67 and an sd of 12. another class of 325 students has an average of 72 and an sd of 15. find the average and the sd of the combined list of 400 students. hint: this uses the sd of a long list formula.
Answers
- average: 71.0625
- standard deviation:
Explanation:
Let
a = average score of 325 students = 72
b = average score of 75 students = 67
S = total score of 325 students
T = total score of 75 students
u = standard deviation of the score of 325 students = 15
v = standard deviation of the score of 75 students = 12
C = average of the squares of the scores of 325 students
D = average of the squares of the scores of 75 students
The total score of 325 students is calculated as:
S = 325a
= 325(72)
S = 23,400
While the total score of 75 students is calculated in similar manner:
T = 75b
= 75(67)
T = 5,025
To get the total score of 400 students, we just add the total score of 325 students and the total score of 75 students. So, the total score of 400 students is given by
S + T = 23,400 + 5,025
S + T = 28,425
To get the average score of 400 students, we just divide the total score of 400 students by the number of students, which is 400. In terms of equation,
[tex]\text{average score of 400 students} = \frac{S + T }{400} \\ = \frac{28,425}{400} \\ \boxed{\text{average score of 400 students} = 71.0625}[/tex]
To calculate the standard deviation of the scores of 400 students, we use the following formula:
[tex]\sigma_{400} = \sqrt{\left( C + D \right) - \left( \frac{S + T}{400} \right)^2}[/tex]
where
[tex]\sigma_{400}[/tex] = standard deviation of the scores of 400 students
[tex] C + D [/tex] = average of the squares of the scores of 400 students
[tex]\frac{S + T}{400}[/tex] = average of the scores of 400 students = 71.0625
Because
C = average of the squares of the scores of 325 students
D = average of the squares of the scores of 75 students
u = standard deviation of the score of 325 students = 15
v = standard deviation of the score of 75 students = 12
a = average score of 325 students = 72
b = average score of 75 students = 67
We have the following
[tex]u^2 = C - a^2 \\ \Rightarrow \boxed{C = a^2 + u^2} [/tex] (1)
[tex]v^2 = D - b^2 \\ \Rightarrow \boxed{D = v^2 + b^2}[/tex] (2)
So, using equations (1) and (2),
[tex]C + D = (a^2 + u^2) + (v^2 + b^2) \\ = (72^2 + 15^2) + (12^2 + 67^2) \\ \boxed{C + D = 10,042}[/tex]
Hence, the standard deviation of the scores of 400 students is calculated as
[tex]\sigma_{400} = \sqrt{\left( C + D \right) - \left( \frac{S + T}{400} \right)^2} \\ = \sqrt{\left( 10,042 \right) - \left(71.0625 \right)^2} \\ \boxed{\sigma_{400} \approx 70.65 }[/tex]
The average of the combined list of 400 students is 71.9 and the standard deviation is 13.1.
Explanation:To find the average and standard deviation of the combined list of 400 students, you can use the following formulas:
Average of combined list = (Average of one class * Number of students in one class + Average of another class * Number of students in another class) / Total number of students
Standard deviation of combined list = sqrt(((SD of one class)^2 * (Number of students in one class - 1) + (SD of another class)^2 * (Number of students in another class - 1) + ((Average of one class - Average of another class)^2 * Number of students in one class * Number of students in another class)) / Total number of students)
Applying the values from the given information:
Average of combined list = (67 * 75 + 72 * 325) / 400 = 71.9
Standard deviation of combined list
= sqrt(((12^2 * 74) + (15^2 * 324) + ((67 - 72)^2 * 75 * 325)) / 400)
= 13.1
Sophia and Charlie brought potato salad to the company cookout. Sophia brought 2 quarts and Charlie brought 4 pints. How many TOTAL cups of potato salad did Sophia and Charlie bring together? (1 quart = 4 cups; 1 pint = 2 cups) A) 8 cups B) 10 cups C) 16 cups D) 20 cups
Answers
PLEASE HELP IM SO CONFUSED BY THIS
If the measure of angle ACB = 30 and the measure of angle A = 80, find the measure of angle B
A: 60
B: 110
C: 180
D: 70
Answers
m∠B = 180 - 30 - 80 = 70°
D: 70
If the measure of angle ACB = 30 and the measure of angle A = 80, the measure of angle B is 70 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
If the measure of angle ACB = 30 and the measure of angle A = 80, To find the measure of angle B
We know that the angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
∠ACB + ∠A + ∠B = 180
30 + 80 + ∠B = 180
∠B = 180 - 110
∠B = 70
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Determine the equations of the vertical and horizontal asymptotes, if any, for g(x)=x^3/(x-2)(x+1)
a. x=2,x-1
b. x=-2,y=-1
c. x=-2,x=-1
d. x=2,y=-1
Answers
So we have to study your domain:
g (x) = x ^ 3 / (x-2) (x + 1)
We see what values make the denominator is not defined:
(x-2) (x + 1) = 0
First value:
x-2 = 0
x = 2
Second value:
x + 1 = 0
x = -1
The function has two vertical asymptotes:
x = 2
x = -1
Answer:
a. x = 2, x-1
I can't seem to figure out what numbers to use to solve this equation.
Answers
The first thing you should notice is that the exponent will be less than 1, as raising 27 to any power greater than 1 will make it larger, and you're trying to figure out what makes it equal to 3, a number less than 27.
Raising a number to a fractional power is taking its nth root: [tex] 21^{1/3} [/tex] is [tex] \sqrt[3]{21} [/tex], so you'll really need to take the nth root of 27 to get 3. To figure out which root, write the number in exponential form with a base of 3:
[tex] 27^{x} [/tex] = 3
[tex] 3^{3x} [/tex] = [tex] 3^{1} [/tex]
Now, the bases are the same (they are both 3), so you can set the exponents equal to each other:
3x = 1
Divide both sides by 3 and you've isolated x:
[tex]x = \frac{1}{3} [/tex]
Answer:
[tex] 27^{1/3} = 3[/tex]
Add the opposite number of 1 1/5 to the sum of the numbers (−8 3/4 ) and (−2 5/6 ).
Answers
= -((8 +2 +1) +(45/60 +50/60 +12/60))
= -(11 +107/60)
= -(12 47/60)
= -12 47/60