Answer:
Done
Step-by-step explanation:
To solve the problem, we can use a Venn diagram to visualize the information provided in the question.
Let's draw three overlapping circles to represent the three groups of people: those who eat fruits, those who eat vegetables, and those who eat cheese.
We know that:
- 37 people eat fruits, so we write "37" in the circle representing fruits.
- 33 people eat vegetables, so we write "33" in the circle representing vegetables.
- 9 people eat both cheese and fruits, so we write "9" in the overlap between the cheese and fruits circles.
- 12 people eat both cheese and vegetables, so we write "12" in the overlap between the cheese and vegetables circles.
- 10 people eat both fruits and vegetables, so we write "10" in the overlap between the fruits and vegetables circles.
- 12 people eat only cheese, so we write "12" in the part of the cheese circle that does not overlap with the other circles.
- 3 people eat all three offerings, so we write "3" in the intersection of all three circles.
Here's what the Venn diagram looks like:
```
Cheese
+----9----+----3----+----12---+
| | Cheese | | |
| Fruits +----6----+--4 | |
| | | | |
+----10---+----3----+----8---+---+
| Vegetables |
+------------+
9 24 15
```
To find out how many people eat cheese, we add up the numbers in the cheese circle: 9 + 3 + 12 = 24. So, 24 people eat cheese.
To find out how many people do not eat any of the offerings, we need to add up the numbers in the regions that are not part of any circle: the region outside of all circles, and the region in the center of the Venn diagram. These regions add up to 9 + 15 = 24. So, 100 - 24 = 76 people do eat at least one of the offerings.
A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 7.5%, and the tax in the second city was 5%. The total hotel tax paid for the two cities was $825. How much was the hotel charge in each city before tax?
The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.
Let x be the hotel charge before tax in the first city, and y be the hotel charge before tax in the second city. Then we have:
y = x + 1500 (the hotel charge before tax in the second city was $1500 higher than in the first)
0.075x + 0.05y = 825 (the total hotel tax paid for the two cities was $825)
We can use the first equation to solve for y in terms of x:
y = x + 1500
Then we can substitute this expression for y into the second equation:
0.075x + 0.05(x + 1500) = 825
Simplifying this equation, we get:
0.075x + 0.05x + 75 = 825
0.125x = 750
x = 6000
So the hotel charge before tax in the first city was $6000. Using the first equation, we can find the hotel charge before tax in the second city:
y = x + 1500
y = 6000 + 1500
y = 7500
So the hotel charge before tax in the second city was $7500.
Therefore, the answer is: The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.
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A skyscraper casts a shadow 200 ft long. If the angle of elevation of the Sun is 38 degrees, then the height of the skyscraper is approximately _____.
A. 200 ft
B. 173.34 ft
D. 156.26 ft
The height of the skyscraper is D. 156.26 ft
How to determine the valueTo determine the height of the skyscraper, we need to consider the following trigonometric identities listed thus;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
Angle, θ = 38 degrees
The shadow casted is the adjacent side of the angle and is 200 ft
The height off the skyscraper is the opposite side
Now, using the tangent identity, we have that;
tan θ = opposite/adjacent
tan 38 = h/200
cross multiply the values, we get;
h = 200(0.7812)
Multiply the values
h = 156. 26 ft
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Peter and Joey and Tommy made $42.18 for the lemonade stand if they split the profit evenly how much will each of the boys get
express 2/5-4/y+3 as a single fraction
Answer:
To express the expression 2/5 - 4/y + 3 as a single fraction, we need to find a common denominator for the fractions involved.
The common denominator for 5 and y is 5y.
First, we'll rewrite 2/5 as an equivalent fraction with the denominator 5y:
2/5 = (2 * y)/(5 * y) = 2y/5y
Next, we'll rewrite 4/y as an equivalent fraction with the denominator 5y:
4/y = (4 * 5)/(y * 5) = 20/5y
Now, we can rewrite the expression with the common denominator 5y:
2y/5y - 20/5y + 3
Since the denominators are now the same, we can combine the numerators:
(2y - 20 + 3 * 5y)/(5y)
Simplifying further:
(2y - 20 + 15y)/(5y) = (17y - 20)/(5y)
Thus, the expression 2/5 - 4/y + 3 can be expressed as a single fraction: (17y - 20)/(5y).If m d=18 and m c = 45 what is m bc
The measure of angle BC is 27 degrees.
To find the measure of angle BC, we need to use the angle sum property of triangles. In triangle ABC, the sum of all angles is equal to 180 degrees. We know that angle ACD is a straight angle and therefore measures 180 - 45 = 135 degrees.
Additionally, we know that angle ADB is also a straight angle and therefore measures 180 - 18 = 162 degrees.
To find angle BCD, we subtract the measure of angle ACD from the measure of angle ADB, which gives us:
m BCD = m ADB - m ACD
m BCD = 162 - 135
m BCD = 27 degrees
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Simplify. 9 x (7 + 7) + 5
Answer:131
Step-by-step explanation:
Use BEDMAS
9x(7+7)+5
=9 x 14 + 5
= 126 + 5
= 131
What is the function equation for the graph below?
The function equation for the graph above include the following: B. f(x) = -[x] + 3.
What is a greatest integer function?In Mathematics and Geometry, a greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.
Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:
y = [x].
By critically observing the given graph, we can logically deduce that the parent function was reflected over the y-axis (negative slope) and it was vertically translated from the origin by 3 units up;
y = [x]
f(x) = -[x] + 3.
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Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
A. 1: √3
B. √2:√√3
C. 1: √2
D. √ √√3
DE √ √√2
F. 25: 6
It should be noted that the ratio between the lengths of the two legs is B. 1: ✓3.
It should be noted that the ratio between the lengths of the two legs will be equal to the tangent.
In this case, tan (30°) = ✓3/3
Tan (60°) = ✓3
Therefore, the ratio between the lengths of the two legs of a 30-60-90 triangle will be 1 : ✓3.
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Solve the system of equations:
3x-8y+z=8
-x+y-z = -1
x-3y = 3
X=
Y=
Z=
Step 1: Add Equation 2 and Equation 3 to eliminate z.
(-x + y - z) + (x - 3y) = -1 + 3
y - 4y = 2
-3y = 2
y = -2/3
Step 2: Substitute the value of y (-2/3) into Equation 3 to find the value of x.
x - 3(-2/3) = 3
x + 2 = 3
x = 1
Step 3: Substitute the values of x and y into Equation 1 to find the value of z.
3(1) - 8(-2/3) + z = 8
3 + 16/3 + z = 8
9/3 + 16/3 + z = 8
25/3 + z = 8
z = 8 - 25/3
z = 24/3 - 25/3
z = -1/3
Therefore, the solution to the system of equations is:
x = 1
y = -2/3
z = -1/3
HELPPP please 5 stars to the correct answer
Answer:
46.48 cm----------------------
AB and AC are perpendicular since AB is tangent to circle at point A.
BC is the hypotenuse of ΔABC and it length is:
BC = AC + 20BC = 44 + 20BC = 64Find the length of AB using Pythagorean theorem:
[tex]AB=\sqrt{BC^2-AC^2}[/tex][tex]AB=\sqrt{64^2-44^2} =\sqrt{2160} =46.48\ rounded[/tex]Use the figures below for the problems on this page.
Write the volume of each figure. Write your answers in terms of π, and
Answer:
Step-by-step explanation:
A: V = πr²h
B: V = 1/3π(2r)²(2h) = 1/3π(4r²)(2h) = 1/3π8r²h = 8/3πr²h
C: V = π(2r)²(2h) = π(4r²)(2h) = π8r²h = 8πr²h
D: V = 1/3πr²(2h) = 2/3πr²h
What is the volume of a right circular cylinder with a diameter of 10 meters and a height of 16 meters. Leave the answer in terms of π.
400π m3
1,600π m3
160π m3
1,256π m3
Answer:
400π m3
Step-by-step explanation:
V = πr^2h
V = π(5^2)(16)
V = π(25)(16)
V = 400π
Express sin L as a fraction in simplest terms
The SinL as a fraction in the simplest form is 12/13.
We are given
The side NM = 5,
The side LM = 12,
By using Pythagoras' theorem, we can say that;
NL² = NM² + LM²
Substitute the values of NM and LM;
NL² = 12² + 5²
NL = 13,
For Sin L = perpendicular side/hypotenuse side
Sin L = NM / NL,
Sin L = 12/13
Therefore, the SinL as a fraction in the simplest form is 12/13
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Qasim spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7200 feet. Qasim initially measures an angle of elevation of 16 ∘ ∘ to the plane at point � A. At some later time, he measures an angle of elevation of 38 ∘ ∘ to the plane at point � B. Find the distance the plane traveled from point � A to point � B. Round your answer to the nearest foot if necessary.
The distance from point B to point A is given as follows:
15,893 ft
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For each angle, we have that:
The position is the adjacent side.The height of 7200 feet is the opposite side.Hence the position A is obtained as follows:
tan(16º) = 7200/a
a = 7200/tangent of 16 degrees
a = 25109 ft.
The position B is obtained as follows:
tan(38º) = 7200/b
b = 7200/tangent of 38 degrees
b = 9216 ft.
Hence the distance is of:
25109 - 9216 = 15,893 ft.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The solution to a system of two linear equations is x = 3; y = 9. the following response is form the solution
1. From the origin, move 3 units right and 9 units up
2. The point of intersection of the two lines
3.Yes, if both lines are the same exact line
4. Can you have exactly two solutions to a Linear system of equations?
5. No, because lines are straight
6. Yes, if the lines are parallel
What are parallel lines?Parallel lines refers to lines that has equal slopes, such lines do no intersect each other at any point.
Hence we say that no solution is obtained in when linear equations turns out to be parallel lines.
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What is the answer?
Answer:
side AC
Step-by-step explanation:
is the opposite angle B because it is the furthest you can get on the triangle to be away from point B.
3.2 Blood groups in humans are controlled by multiple alleles. As a result, there
are four possible blood groups: A, AB, B and O. Study the graph below
which shows the percentage of people that have different blood group and
then answer the questions that follow.
Percentage of people with
different blood groups
3.2.1
3.2.2
3.2.3
60-
50
40
30
20
10-
24
49
38
A
Blood groups
10
B
3
AB
Explain what is meant by multiple alleles.
Which blood group is the least common in the human population?
Recent population statistics show that KwaZulu-Natal has a human
population of approximately 9,2 million. Calculate the number of
people who will have blood group O in KwaZulu-Natal.
9.2 million
49:100
(2)
(2)
Answer:
5.52 million people with blood group O in KwaZulu-Natal.
Step-by-step explanation:
Multiple alleles refer to the existence of more than two possible alleles (or variations) of a gene within a population. In the case of blood groups, there are multiple alleles for the gene that controls blood type, resulting in the four possible blood groups: A, AB, B, and O.
The blood group AB is the least common in the human population, with only 3% of people having this blood type.
To calculate the number of people who will have blood group O in KwaZulu-Natal, we need to multiply the total population by the percentage of people with blood group O.
9.2 million x (60/100) = 5.52 million people with blood group O in KwaZulu-Natal.
What value of x satisfies the equation −1.5x−2.7=20.1+4.5x
The value of x that satisfies the equation -1.5x - 2.7 = 20.1 + 4.5x is -3.8.
To solve this equation, we need to isolate the variable x on one side of the equation. We can do this by using basic algebraic operations, such as adding, subtracting, multiplying or dividing both sides of the equation by the same value.
The first step in solving this equation is to get rid of the constant terms on one side of the equation. We can do this by adding 2.7 to both sides of the equation:
-1.5x - 2.7 + 2.7 = 20.1 + 4.5x + 2.7
Simplifying the left-hand side of the equation, we get:
-1.5x = 20.1 + 4.5x + 2.7
Next, we can move the variable terms to the left side of the equation and the constant terms to the right side of the equation by subtracting 4.5x from both sides:
-1.5x - 4.5x = 20.1 + 2.7
Simplifying the left-hand side, we get:
-6x = 22.8
Finally, we can solve for x by dividing both sides of the equation by -6:
x = -3.8
Therefore, the value of x that satisfies the equation -1.5x - 2.7 = 20.1 + 4.5x is -3.8.
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23/100 equals what percent 23%.69%, 11.5% 46%
Answer:
23/100 equals 23%.
Answer: 23%
Step-by-step explanation: When doing these problems, remember, 100 and a 100% are the same thing, so when you have a problem like this, divide 25 by 100, then multiply by a 100.
PLS HELP HURRY Mr. Little predicts that the median of the second test’s scores will increase by 20% from the median of the first test scored. Enter mr littles prediction for the second tests median score in the response box.
Little's prediction for the second tests median score is 84
Calculating Little's prediction for the second tests median scoreFrom the question, we have the following parameters that can be used in our computation:
The dot plot
The median is the middle number on the dot plot
From the dot plot, the middle number is
Middle = 70
This means that
Median = 70
For the new prediction, we have
New median = 70 * (1 + 20%)
Evaluate
New median = 84
Hence, Little's prediction for the second tests median score is 84
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Martin is training for a marathon. His plan is to keep a consistent pace plan is to keep throughout the race. Using the data from the table, create a linear model that shows the miles Martin has run as the input, and the total time, in minutes, he has been running as the output.
Miles 5 9 20 Total Time 60 104 225
Miles is the number of miles Martin has run, and Total Time is the total time in minutes that he has been running, which is 11Miles + 5.
To create a linear model, we need to find the equation of the line that best fits the data.
We can do this by finding the slope and y-intercept of the line.
First, we need to find the slope, which is the change in y divided by the change in x.
We can choose any two points on the line to calculate the slope.
Let's use the first and second data points:
Slope = (y2 - y1) / (x2 - x1)
Slope = (104 - 60) / (9 - 5)
Slope = 44 / 4
Slope = 11
Now we can use the point-slope form of the equation of a line to find the y-intercept.
We can use the first data point:
The linear model has the form y = mx + b, where y represents the total time (in minutes), x represents the miles run, m is the slope, and b is the y-intercept.
We can use the data points to find the slope (m) as follows: m = (change in total time) / (change in miles)
Using the first two data points, (5, 60) and (9, 104):
m = (104 - 60) / (9 - 5) = 44 / 4 = 11
Now that we have the slope, we can find the y-intercept (b) using one of the data points.
Let's use (5, 60): 60 = 11 * 5 + b 60 = 55 + b b = 5
So the linear model representing Martin's pace is: y = 11x + 5 In this model, x is the miles run, and y is the total time in minutes.
y - y1 = m(x - x1)
y - 60 = 11(x - 5)
y - 60 = 11x - 55
y = 11x + 5
So the linear model that shows the miles Martin has run as the input, and the total time, in minutes, he has been running as the output is
Total Time = 11Miles + 5
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is
Integer Concepts with a Number Line - Item 30985
units to the
is 13 units to the left of 0.
Use the drop-down menus to complete the statement about -x.
of 0.
CLE
The required, -x is also 13 units from 0, but to the right of 0 instead of to the left.
The statement about -x is that it is 13 units to the right of 0. This is because the original number, which is 13 units to the left of 0, is represented by a point on the number line to the left of 0. If we negate this number to get -x, then we are reflecting it across the origin (0) to the right side of the number line. This means that the distance of -x from 0 is the same as the distance of the original number from 0, which is 13 units.
Therefore, -x is also 13 units from 0, but to the right of 0 instead of to the left.
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Solve the simultaneous Equations
y=5x-6
5xy = -7
Answer:
Solving the system of equations.
Point form: (3+√25,−3+√2),(3−√25,−3−√2)
Equation form:
x=3+√25,y=−3+√2x=3−√25,y=−3−√2
Step-by-step explanation:
Find the volume please
Answer:
6 cm³
Step-by-step explanation:
The figure is a triangular prism with a triangular base with side lengths 3 cm, 4 cm, 5 cm. The height of the prism is 1 cm.
The sides measuring 3 cm and 4 cm form a right angle.
V = BH
where B = area of the base, and
H = height of the prism.
The base is a triangle, so B = (1/2)bh,
where b = base of the triangle, and
h = height of the triangle
V = (1/2)bhH
V = (1/2)(3 cm)(4 cm)(1 cm)
V = 6 cm³
the same entries of the first row are:
The entries of the first row is 3,6. Option B
How to find the entries of the first rowTo add the entries of the first row in the two matrices, we need to first identify the first row of each matrix and then add the corresponding entries together.
Matrix A:
[1 4]
[7 1]
Matrix B:
[2 2]
[4 3]
To add the first rows of these matrices, we simply add the corresponding entries:
1+2 4+2
2 6
Hence, the entries of the first of the two matrices is 2,6
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(i) This case study is based on Magma printers, a large printing company specializing in newspaper printing. They have 10 state of the art printers in the printing area. The probability of a machine breaking down is 10%. They require at least 8 machines to be functioning in order to meet all the printing requirements for the day. Printing orders for Magma printers arrive at an average rate of 5 orders per hour. Assume these orders follow a Poisson distribution. (a) Calculate the probability that exactly 4 orders will arrive in 30 minutes? (b) Determine the probability that at least 2 orders will arrive in an hour?
(a) The probability that exactly 4 orders will arrive in 30 minutes is 0.1127
(b) The probability that at least 2 orders will arrive in an hour is 0.7586.
How to calculate the probability(a) We need to adjust λ to reflect the 30-minute time interval:
λ = 5 orders per hour * 0.5 hours = 2.5 orders in 30 minutes
Now we can plug in the numbers and calculate the probability:
P(X = 4) = ([tex]e^{2.5}[/tex]) *) [tex]2.5^{4}[/tex]/ 4! = 0.1127
(b) We can use the Poisson probability formula again, with λ = 5 orders per hour and x = 0 or 1:
P(X < 2) = P(X = 0) + P(X = 1) = 0.0404 + 0.2010 = 0.2414
Then we can subtract this from 1 to get the probability that at least 2 orders will arrive in an hour:
P(X ≥ 2) = 1 - P(X < 2) = 1 - 0.2414 = 0.7586
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Multiplication What 7 x 4 / 8
Answer:
7/2
Step-by-step explanation:
7 x 4 / 8
= 7 x 1/2
= (7 x 1)/2
= 7/2
Note
1. When you see a fraction, first simplify the numerator and denominator.
That is,
In 4/8,
4 is the numerator
8 is the denominator
4/8 = 1/2
2. Multiply number with numerator, then divide it with the denominator
7 x 1/2
7 x 1 = 7
(7 x 1)/2 = 7/2
The following table list two investment plans, A and B. Given this information, determine which investment is an ordinary annuity and the future value of the ordinary annuity after one year, given that both investments, A and B, compound interest monthly at the rate of 3.5%. Round to the nearest cent.
A 13-column table with 2 rows. Column 1 has entries A, B. Column 2 is labeled January with entries 350, blank. Column 3 is labeled February with entries 350, 350. Column 4 is labeled March with entries 350, 350. Column 5 is labeled April with entries 350, 350. Column 6 is labeled May with entries 350, 350. Column 7 is labeled June with entries 350, 350. Column 8 is labeled July with entries 350, 350. Column 9 is labeled August with entries 350, 350. Column 10 is labeled September with entries 350, 350. Column 11 is labeled October with entries 350, 350. Column 12 is labeled November with entries 350, 350. Column 13 is labeled December with entries blank, 350.
a.
Investment A is an ordinary annuity with $3,918.03 in the account after 1 year.
b.
Investment B is an ordinary annuity with $3,918.03 in the account after 1 year.
c.
Investment A is an ordinary annuity with $3,906.64 in the account after 1 year.
d.
Investment B is an ordinary annuity with $3,906.64 in the account after 1 year
Investment B is an ordinary subvention with$ 3,906.64 in the account after one time. The correct answer is option d.
To determine which investment is an ordinary subvention and the unborn value after one time, we first need to understand that an ordinary subvention is a series of equal payments made at the end of each period.
Given the table, we can see that Investment A has payments starting in January and ends in November( missing December), while Investment B starts in February and ends in December.
thus, Investment B is the ordinary subvention since the payments are made at the end of each month. Now let's calculate the unborn value of Investment B after one time
1. Convert the periodic interest rate to a yearly rate( 10.035)(1/12)- 1 ≈0.002867
2. Determine the number of payments made 11 months 3. Use the unborn value of subvention formula FV = P *(( 1 r) n- 1)/ r
Where P = yearly payment($ 350),
r = yearly interest rate(0.002867), and n = number of payments( 11) . Plug in the values
FV = 350 *(( 10.002867) 11- 1)/0.002867 ≈3906.64
So, Investment B is an ordinary subvention with$ 3,906.64 in the account after one time. The correct answer is optiond.
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What is the probability that both events occur?
Answer:
P(A and B) = P(A)P(B)
= (1/3)(1/2) = 1/6
= about .17 = about 17%
Group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together. Hint: Type the answer as one word e.g. ABC
The 6 drawings are grouped to one another
Given data ,
Let the 6 drawings into be divided into two groups of 3 drawings each
And , drawings of each group is similar to one another in some way
where Group 1: ABD
On simplifying the equation , we get
Their curves and the points are in a same order
Group 2: CEF
On simplifying the equation , we get
Their curves and points are oppositely drawn
Hence , the drawings are solved
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The complete question is attached below :
Group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together.
