Answer:
293 feet
Step-by-step explanation:
The distance the wire is attached in the tower is 200 feet
the angle between the wire and the tower is 47 degrees
The length of the wire (x) is the hypotenuse of the triangles formed
The formed triangle is a right angle triangle
For 47 degree angle the adjacent side is 200 feet and hypotenuse is x
[tex]cos(theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(47)=\frac{200}{x}[/tex]
Cross multiply it
[tex]xcos(47)= 200[/tex]
divide by cos on both sides
[tex]x=\frac{200}{cos(47)}[/tex]
x=293.25 feet
PLEASE HELP
Which system of inequalities is represented by the graph?
A. y less than or equal to-2x+4 and y greater than or equal to x-6
B. y less than or equal to2x+4 and y greater than or equal to -x -6
C. y less than or equal to 2x-4 and y greater than or equal to -x-6
D. y less than or equal to 2x+4 and y greater than or equal to -x+6
Answer:
The answer to your question is letter B
Step-by-step explanation:
Process
1.- Find two points of each line
Line A (-2, 0) (-1, 2)
Line B (-1. - 5) (-6, 0)
2.- Find the slope and equation of each line
Line A
[tex]m = \frac{2 - 0}{-1 + 2}[/tex]
[tex]m = \frac{2}{1}[/tex]
m = 2
y - 0 = 2(x + 2)
y = 2x + 4
Line B
[tex]m = \frac{0 + 5}{-6 + 1}[/tex]
[tex]m = \frac{5}{-5}[/tex]
m = -1
y - 0 = -1(x + 6)
y = -x - 6
3.- Find the inequalities
Line A, we are interesteed in the lower area of the line, so the inequality is
y ≤ 2x + 4
Line B, we are also interested in the lower area of the line so the inequality is
y ≥ - x - 6
Answer:B
Step-by-step explanation:
In triangle $ABC$, $BC = 20 \sqrt{3}$ and $\angle C = 30^\circ$. Let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. Find the length of $DE$.
Answer:
DE=10
Step-by-step explanation:
Given that in triangle ABC, $BC = 20 \sqrt{3}$ and $\angle C = 30^\circ$. Let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$,
To find length of DE
Please refer to the attachment for solution
Since perpendicular bisector we have DC = 1/2 BC = 10 sqrt 3
Using right triangle CDE, we get DE = 10
In the XY-Plane above, the circle has center (h,k) and radius 10. What is the value of k?
Answer:
k = +/- 6
Step-by-step explanation:
In the XY-Plane above, the circle has center (h,k) and radius 10. What is the value of k?
The concluding part of this question will be
Two coordinates are given, (4,0) and (20,0)
equation of a circle
([tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
We can then have two equations of the circle and solve simultaneously
([tex](4-h)^{2} +(-k)^{2} =10^{2}[/tex] .............................1
([tex](20-h)^{2} +(-k)^{2} =10^{2}[/tex] ......................................2
combining the two equation to solve
(20-h)^2 - (4-h)^2 = 0
20^2 - 40h +h^2 -4^2 + 8h -h^2 = 0
20^2 - 42 = 32h
h = 12
(4-12)^2 + (-k)^2 = 100
k^2 = 36
k = +/- 6
The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 250,000 locusts?A. 6B. 8C. 10D. 12E. 14
4 hours ago = 1,000
2 hours ago = 2,000
Now = 4,000
In 2 hours = 8,000
In 4 hours = 16,000
In 6 hours = 32,000
In 8 hours = 64,000
In 10 hours = 128,000
In 12 hours = 256,000
The answer would be D. 12 hours.
QUESTION 4 of 5: You have insurance premiums of $250 due quarterly. How much will you pay annually?
Answer:
$1000
Step-by-step explanation:
quarterly is 1/4
12/4 is 3
so every 3 months you pay $250
annually is the whole year so 250*4
Answer:
1000
Step-by-step explanation:
What is the Median for the following set of numbers? ​21 23 76 47 55 135 45 30 17
Answer:
Median = 45
Step-by-step explanation:
We are given the following data set:
21, 23, 76, 47, 55, 135, 45, 30, 17
Median is the number that divides the data into two equal parts.
Formula:
[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]
Sorted data:
17, 21, 23, 30, 45, 47, 55, 76, 135
Sample size = 9, which is odd
Median =
[tex]\dfrac{9+1}{2}^{th}\text{ term} = \dfrac{10}{2}^{th}\text{ term} = 5^{th}\text{ term}\\\\= 45[/tex]
The median of given set of numbers is 45.
Identify the monomial function described as odd or even, and indicate whether a is positive or negative.
Answer:
Case 1: As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
It is an 'odd' function with 'positive' a.
Case 2: As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
It is an 'even' function with 'negative' a.
Case 3: As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
It is an 'even' function with 'positive' a.
Case 4: As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.
It is an 'odd' function with 'negative' a.
Step-by-step explanation:
Let us consider a monomial function:
f(x) = axⁿ
Case 1:
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
This happens only if a is 'positive' and n is 'odd'. So, it is an 'odd' function with 'positive' a.
Case 2:
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
This happens only if a is 'negative' and n is 'even'. So, it is an 'even' function with 'negative' a.
Case 3:
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
This happens only if a is 'positive' and n is 'even'. So, it is an 'even' function with 'positive' a.
Case 4:
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.
This happens only if a is 'negative' and n is 'odd'. So, it is an 'odd' function with 'negative' a.
Keywords: monomial function, odd function, even function
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Identify the monomial function described as odd or even, and indicate whether a is positive or negative.
Thomas brings over 1/2 of his marble collection. He divides these marbles equally among 3 friends. What fraction of Thomas's entire marble collection did each friend get?
Answer:
Each of the three friends will get one-sixth of the Thomas's enitre marble collection.
Step-by-step explanation:
Fraction of the total marble collection brought by Thomas = [tex]\frac{1}{2}[/tex]
Now, Thomas divides these marbles equally among his three friends. So, each of the three friends will get one-third of the total marble collection brought by Thomas.
Fraction of total marble collection got by each friend = [tex]\frac{1}{3} \;of\;fraction\;of\;total\;marble\;collection\;brought\;by\;Thomas[/tex]
= [tex]\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}[/tex]
∴ Each of the three friends of Thomas will get one-sixth of his entire collection of marbles.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of fish caught during a fishing tournament b. The number of textbook authors now sitting at a computer c. The political party affiliation of adults in the United States d. The square footage of a house e. The number of free dash throw attempts before the first shot is made f. The weight of a Upper T dash bone steak
Answer:
a. Discrete
b. Discrete
c. Not a random variable
d. Continuous
e. Discrete
f. Continuous
Step-by-step explanation:
The discrete random variable is countable while continuous random variable is measurable.
a. The number of fish caught is a discrete random variable because these are countable.
b. The number of text book authors are also countable so it is a discrete random variable.
c. The political party affiliation of adults is not a random variable because the political party affiliation depends on person's interest and it cannot be randomly assigned to person. Also random variable is the numerical outcome of random experiment whereas political affiliation is the categorical variable that results in non numerical responses such as Democrat, Republicans etc.
d. The square footage of a house is measurable and so it is a continuous random variable.
e. The number of free dash throw attempts are countable so it is a discrete random variable
f. The weight of Upper T dash bone steak is measurable and so it is a continuous random variable.
The number of fish caught during a fishing tournament is a discrete random variable, while the square footage of a house is a continuous random variable. The other examples are not random variables.
Explanation:a. The number of fish caught during a fishing tournament is a discrete random variable. The values of the variable are obtained by counting the number of fish caught.
b. The number of textbook authors now sitting at a computer is not a random variable. It is a fixed number and does not vary.
c. The political party affiliation of adults in the United States is not a random variable. It can be determined by surveying adults or analyzing existing data.
d. The square footage of a house is a continuous random variable. The values of the variable are obtained by measuring the size of the house.
e. The number of free-throw attempts before the first shot is made is a discrete random variable. The values of the variable are obtained by counting the number of attempts.
f. The weight of an Upper T-bone steak is a continuous random variable. The values of the variable are obtained by measuring the weight of the steak.
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average rate of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
A. 0.5< t < 0.75
B. 1.75< t < 2.0
C. 2.0 < t < 2.5
D. 2.5 < t < 3.0
E. 3 < t < 3.5
Answer:
C. 2.0 < t < 2.5
Step-by-step explanation:
Diameter of track (D) = 2 miles, Average rate (A) = 3 miles per hour
A = distance/ time
time (t) = distance/A
distance around the track (circumference) = πD = 3.142 × 2 miles = 6.284 miles
t = 6.284miles/3miles/hour = 2.1 hour
Therefore, 2.0 < t < 2.5
A baby was born and then began to gain weight at a rate of 1.5 pounds per month. After 4 months, the baby's weight was 16 pounds. Write an equation for the function W ( t ) , W(t), representing weight, in pounds, of the newborn baby t t months after birth.
Answer:
w=1.5t+12
Step-by-step explanation:
that's the right answer
The equation for the function W(t) representing the weight of the newborn baby t months after birth is W(t) = 16 + 1.5t
To solve this problem
We can make use of the given data.
The infant gained weight at a pace of 1.5 pounds each month, reaching 16 pounds at the end of 4 months. With this knowledge, the equation can be written as follows:
W(t) = Initial weight + (Rate of weight gain per month) * (Number of months)
W(t) = 16 + (1.5 * t)
So, the equation for the function W(t) representing the weight of the newborn baby t months after birth is W(t) = 16 + 1.5t
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A 85cm snowman melts and loses 3cm in height for every hour the sun shine and the sun shine only 6.5 hours a day. How many days will it take for the snowman to melt
Answer:
Step-by-step explanation:
The initial height of the snowman is 85 cm. snowman melts and loses 3cm in height for every hour the sun shine and the sun shine only 6.5 hours a day. This means that the height that the snowman loses in a day would be
3 × 6.5 = 19.5 cm
Therefore, in a day, the snowman loses 19.5 cm in height. Therefore,
the number of days that it will take the snowman to melt would be
85/19.5 = 4.36 days
if the sum of the interior angles of a regular n-gon is 900 degrees, then n=what?
Answer:
n=7
Step-by-step explanation:
let n be number of sides.
(n-2)180=900
n-2=900/180=5
n=5+2=7
A number consists of two digits whose sum is 12. If 16 is added to the number, then one of the digits is four times the value of the other. What is the number?
Answer: The number is 12.
Step-by-step explanation:
Since we have given that
Sum of two digits = 12
Let the one's digit be 'x'
Let the ten's digit be '12-x'
So, Original number would be
[tex]x+10(12-x)\\\\=x+120-10x\\\\=-9x+120[/tex]
If 16 is added to the number, then one of the digit is four times the value of the other.
According to question, we get that
[tex]-9x+120+16\\\\=-9x+136[/tex]
so, the one's digit be 'x'.
Let the ten's digit be '4x'.
so, New number would be
[tex]10x+4x=14x[/tex]
According to question, it becomes,
[tex]14x=-9x+136\\\\14x+9x=136\\\\23x=136\\\\x=\dfrac{136}{23}=12[/tex]
So, the number would be
[tex]-9x+120=-9\times 12+120=-108+120=12[/tex]
Hence, the number is 12.
Answer:
66
Step-by-step explanation:
Brute force:
2 digit numbers that has sum of 12:
39, 48, 57, 66
Add 16 to the numbers:
55, 64, 73, 82
Find the number that shows a digit is 4 times the value of other:
82 (2x4 =8)
PLEASE HELP WITH QUESTION!!!!!
Find the sum of the series:
The sum of the given series [tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] is 130.
Step-by-step explanation:
The sum of series need to be found is [tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] .
Apply sum rule,
[tex]\sum x_n+y_n=\sum x_n+\sum y_n[/tex]
[tex]\sum _{a=1}^{10}\:\left(2a+2\right).[/tex] =[tex]\sum 2a+\sum 2[/tex].
Apply the constant multiplication rule,
[tex]\sum c\cdot a_n=c\cdot \sum a_n[/tex] .
[tex]\sum 2\cdot a=2\cdot \sum a[/tex].
[tex]\sum _{a=1}^{10}n[/tex] = 1+2+3+4+5+6+7+8+9+10.
[tex]\sum _{a=1}^{10}n[/tex] = 55.
[tex]\sum 2\cdot a[/tex]=2×55.
[tex]\sum 2\cdot a [/tex]=110.
To find [tex]\sum _{a=1}^{10}2[/tex],
Apply sum rule, [tex]\sum _{k=1}^n\:a\:=\:a\cdot n[/tex] ,
[tex]\sum _{a=1}^{10}2[/tex] =2×10.
[tex]\sum _{a=1}^{10}2[/tex] = 20.
[tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] = 110+20.
[tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] =130.
In how many ways can 8 people be seated in a row if there are no restrictions on the seating arrangement?
persons A and B must sit next to each other?
there are 4 men and 4 women and no 2 men or 2 women can sit next to each other?
there are 5 men and they must sit next to one another?
there are 4 married couples and each couple must sit together?
Answer:
a ) P₈ = 40320
b) P = 576
c) P = 1440
d) P = 24
Step-by-step explanation:
a ) 8 people sitting in a row without restrictions
simple Total ways = P₈ = 8!
P₈ = 8*7*6*5*4*3*2*1
P₈ = 40320
b) There are 4 men and 4 women and no two men or 2 women can sit next to each other
Let letters e women and numbers be men we have something like this
1 a 2 b 3 c 4 d
So we have the permutations of the four digits (men)
P₄ = 4!
P₄ = 4*3*2*1 = 24
And the permutations of the 4 women too equal to 24
Then total ways of sitting in a row in this case is
P = 24*24 = 576
c) There are 5 men and they have to sit next to each other
In this case we have 2 groups:
Group 1 5 men Group 2 3 women
We have two groups and the ways are
group men first group of women second 1 way
group of women first group of men second 2 way
Permutations within men group
P₅ = 5! = 5*4*3*2*1
P₅ = 120
Permutations within the women group
P₃ = 3! = 3*2*1
P₃ = 6
Total ways case c) T = 6*120*2 =
P(c) = 1440
d) There are four couples and each couple must be together
P₄ = 4! = 4*3*2*1
P₄ = 24
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
Final answer:
When a positive integer x, which leaves a remainder of 5 when divided by 9, is multiplied by 3, the remainder when 3x is divided by 9 is 6.
Explanation:
When the positive integer x is divided by 9, the remainder is 5. To determine the remainder when 3x is divided by 9, we should remember that when two positive numbers multiply, the result has a positive sign. So multiplying x by 3, we get 3x. The initial information tells us that x = 9n + 5 for some integer n. Thus, 3x equals 3(9n + 5), which simplifies to 27n + 15. This expression can be further broken down as 27n + 9 + 6, which is the same as 9(3n + 1) + 6. Therefore, when 3x is divided by 9, it is the same as dividing this expression by 9, which leaves us with a remainder of 6. Hence, the remainder when 3x is divided by 9 is 6.
On a final exam, 75 percent of a class had scores that were greater than 70, and 60 percent of the class had scores that were less than 85. What percent of the class had scores that were greater than 70 but less than 85 ?
Answer:
The answer is 35.
35% of the class had scores that were greater than 70 but less than 85.
Step-by-step explanation:
Let's assume the number of students in the class =100
If 75% of the class scored greater than 70, then, it means 25% (100-75) of the scores were less than or equal to 70
In other words, 25 scores were less than or equal to 70.
If 60% of the class had scores that were less than 85, then, it means 40%(100-60) of the scores were greater than or equal to 85
Therefore, of the 100 scores, 25 scores were LESS THAN OR EQUAL to 70, and 40 scores were GREATER THAN OR EQUAL to 85.
We've now accounted for 65 (25+40) scores, which means the remaining 35 (100-65) scores must be between 70 and 85.
Answer:
The answer is 35.
35% of the class had scores that were greater than 70 but less than 85.
Step-by-step explanation:
Let's assume the number of students in the class =100
If 75% of the class scored greater than 70, then, it means 25% (100-75) of the scores were less than or equal to 70
In other words, 25 scores were less than or equal to 70.
If 60% of the class had scores that were less than 85, then, it means 40%(100-60) of the scores were greater than or equal to 85
Therefore, of the 100 scores, 25 scores were LESS THAN OR EQUAL to 70, and 40 scores were GREATER THAN OR EQUAL to 85.
We've now accounted for 65 (25+40) scores, which means the remaining 35 (100-65) scores must be between 70
A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
A. 22B. 33C. 55D. 77E. 88
Answer:
B. 33
Step-by-step explanation:
Let the number of Fuji trees be F, the number of gala be G and the total number of trees be x.
10% cross pollinated, this means 1/10 cross pollinated or 0.1x
Number of Fuji plus cross pollinated is 187.
And cross pollinated is 3/4 of total or let’s say 0.75 of total which is 0.75x
Now, adding 0.1x + 0.75x would equal 187
0.85x = 187
x = 187/0.85 = 220 trees
The total number of trees is 220.
The number of gala trees is thus 220 - 187 = 33 trees
John wants to pay off a $2,100 bill in the next 13 months. What is the approximate amount that he will have to set aside each month to reach his goal?
$154
$167
$162
$187
Answer:the approximate amount that he will have to set aside each month to reach his goal is $162
Step-by-step explanation:
Total amount of bill that John wants to pay off js $2,100. $2,100 bill in the next 13 months. To determine the amount that he will have to set aside each month to reach his goal, we would divide the total bill by the number of months. It becomes
2100/13 = 161.538
The approximate amount is $162
Answer:
$162
Step-by-step explanation:
$2,100/13
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the _____.
a. variance
b. standard error
c. residual
d. predicted interval
Answer:
Option C. Residual
Step-by-step explanation:
Residuals are defined as:
Residual is the error that are not explained by the regression line.It is defined as the difference between observed value of dependent variable and the predicted variable.Residual = Observed value - Predicted value[tex]e = y_{\text{observed}}- \hat{y}[/tex], where e is the residual.Residuals are the unexplained differences.Thus,
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residuals.
Option C. Residual
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residual.
The following information should be considered:
Residual should be the error i.e. not described by the regression line. It shows the difference between the observed value and the predicted value.Therefore we can conclude that option c is correct.
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Make a Venn Diagram from the following information to answer below question?25 students played soccer 4 boys played soccer and baseball 3 girls played soccer and baseball 10 boys played baseball 4 girls played baseball 9 students played tennis 3 boys played soccer and tennis 3 girls played soccer and tennis 3 boys played baseball and tennis 1 girl played baseball and tennis 1 boy played all three sports 1 girl played all three sports How many students played soccer, but not baseball or tennis?
To find the number of students who played soccer but not baseball or tennis, we need to analyze the given information and use the formula A = (A ∩ B) + (A ∩ C) + (A - A ∩ B ∩ C). Substituting the given values, we find that 32 students played soccer but not baseball or tennis.
Explanation:To determine how many students played soccer but not baseball or tennis, we need to analyze the information given in the Venn diagram provided. Let's label the regions of the Venn diagram:
A represents the set of students who played soccer.
B represents the set of students who played baseball.
C represents the set of students who played tennis.
From the given information, we know that:
A = 25A ∩ B = 4A ∩ C = 3B = 10B ∩ C = 4C = 9A ∩ B ∩ C = 1To find the number of students who played soccer but not baseball or tennis, we need to calculate the value of A without the intersection of the other sets. Using the formula:
A = (A ∩ B) + (A ∩ C) + (A - A ∩ B ∩ C),
we can substitute the given values:
A = 4 + 3 + (25 - 1)
A = 32
Therefore, 32 students played soccer but not baseball or tennis.
Allison works for a computer software company. She earns \$225$225dollar sign, 225 per week plus \$25$25dollar sign, 25 for each software package that she sells that week. If she wants to earn at least \$400$400dollar sign, 400 this week, what is the minimum number of software packages that she must sell this week?
Answer:
7 software packages
Step-by-step explanation:
Given,
Signing amount = $ 225,
Additional amount for each software package = $ 25
Thus, the total amount for x software packages = signing amount + additional amount for x packages
= 225 + 25x
If total amount ≥ $ 400
225 + 25x ≥ 400
25x ≥ 400 - 225
25x ≥ 175
[tex]\implies x \geq \frac{175}{25}=7[/tex]
Hence, the minimum number of software packages that she must sell would be 7.
Final answer:
Alison needs to sell at least 7 software packages this week on top of her base salary to earn at least $400.
Explanation:
Alison wants to earn at least $400 this week by selling software packages. She earns a base $225 per week plus $25 for each software package sold. To determine the minimum number of software packages Alison must sell, we subtract her base salary from her desired earnings for the week:
Required earnings (>=$400) - Base salary ($225) = Sales required from software packages
$400 - $225 = $175
Now divide the sales required from software packages by the amount earned per package:
$175 / $25 = 7
Therefore, Alison needs to sell at least 7 software packages to meet her goal of $400
Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length of Y Z is 9, the length of X Z is 12, and the length of hypotenuse X Y is 15. Given △QRS ~ △XYZ, what is the value of tan(Q)? Three-fifths Three-fourths Four-fifths Four-thirds
Answer:
Three-fourths
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
∠QSR≅∠XZY ---> given problem
∠QRS≅∠XYZ ---> given problem
so
△QRS ~ △XYZ ----> by AA Similarity theorem
Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
That means
[tex]\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}[/tex]
∠Q≅∠X
∠R≅∠Y
∠S≅∠Z
In the right triangle XYZ
Find the tangent of angle X
[tex]tan(X)=\frac{YZ}{XZ}[/tex] ---> opposite side angle X divided by adjacent side angle X
substitute the given values
[tex]tan(X)=\frac{9}{12}[/tex]
Simplify
[tex]tan(X)=\frac{3}{4}[/tex]
Remember that
∠Q≅∠X
so
[tex]tan(Q)=tan(X)[/tex]
therefore
[tex]tan(Q)=\frac{3}{4}[/tex] ---->Three-fourths
Among all pairs of numbers with a sum of 232, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.
Answer:
Step-by-step explanation:
232/2=116
so 116,116 has maximum product
At the used bookstore, Keisha bought 24 novels. If 3/8 of the book the books are mystery novels and the rest are science fiction novels, how many science fiction novels did Keisha buy?
Keisha bought 15 science fiction novels.
Step-by-step explanation:
Given,
Number of novels bought by Keisha = 24
Mystery novels = 3/8 of total novels
Mystery novels = [tex]\frac{3}{8}*24=\frac{72}{8}[/tex]
Mystery novels = 9
Let,
x represent the number of science fiction novels.
Mystery novels + Science fiction novels = Total novels
[tex]9+x=24\\x=24-9\\x=15[/tex]
Keisha bought 15 science fiction novels.
Keywords: fraction, addition
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Rebecca moves to a large city that had two event stadiums. The larger stadium can hold 4.5 times 10^4 people, which is about 15 times as many people as the smaller stadium can hold. Which expression could represent the approximate amount of people the smaller stadium can hold?
Answer:
3,000 people
Step-by-step explanation:
Total number of people larger stadium can hold equals 4.5 times [tex]10^{4}[/tex] people,
which equals 45,000 people.
Now,
it is given that larger stadium can hold 15 times more people than small stadium .
So, smaller stadium will hold 15 times less people than the larger stadium ,
Which equals , [tex]\frac{45000}{15}[/tex] = 3,000 people.
Thus ,
Smaller stadium can hold a total of 3,000 people.
The common stock of Manchester & Moore is expected to earn 13 percent in a recession, 6 percent in a normal economy, and lose 4 percent in a booming economy. The probability of a boom is 5 percent while the probability of a recession is 45 percent. What is the expected rate of return on this stock?
Answer:
8.65%
Step-by-step explanation:
Given information:
Recession Return = 13%
Normal Return = 6%
Boom Return = -4%
Probability of a recession = 45 %
Probability of a boom = 5 %
Probability of a normal = 100 - 45 - 5 = 50%
We need to find the expected rate of return on this stock.
Expected rate of return is the sum of products of probability and returns of each state of economy.
Expected rate of return [tex]=13\%\times 45\%+6\%\times 50\%+(-4\%)\times 5\%[/tex]
[tex]=5.85\%+3\%-0.2\%[/tex]
[tex]=8.65\%[/tex]
Therefore, the expected rate of return on this stock is 8.65%.
A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is $90 with a standard deviation of $22. Monte’s Plumbing and Heating Service completed repairs on two heat pumps this morning. The labor cost for the first was $75 and it was $100 for the second. Assume the distribution of labor costs follows the normal probability distribution. Compute z values for each.
Answer:
Z value for the first pump = -0.68
Z value for the second pump = 0.45
Step-by-step explanation:
Data provided in the question:
Mean labor cost to repair a heat pump = $90
Standard deviation = $22
Labor cost for the first, X₁ = $75
Labor cost for the Second, X₂ = $100
Now,
Z value for the first pump = [X₁ - Mean] ÷ Standard deviation
thus,
Z value for the first pump = [ $75 - $90] ÷ $22
= - 0.68
Z value for the second pump = [X₁ - Mean] ÷ Standard deviation
thus,
Z value for the second pump = [ $100 - $90] ÷ $22
= 0.45
Answer:
z1= -0.6818
z2= 0.45
Step-by-step explanation:
Mean labor cost to repair the heat pump is μ= $90
standard deviation σ= $22
Labor cost for the first heat pump X_1= $75
labor cost for the second heat pump is X_2= $100
z value for the first heat pump
[tex]z_1= \frac{X_1-\mu}{\sigma}[/tex]
⇒ [tex]z_1= \frac{75-90}{22}[/tex]
= -0.6818
z value for the second heat pump
[tex]z_2= \frac{X_2-\mu}{\sigma}[/tex]
⇒[tex]z_2= \frac{100-90}{22}[/tex]
= 0.45
Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?
A. $506.00
B. $726.24
C. $900.00
D. $920.24
E. $926.24
Answer:
E. $926.24
Step-by-step explanation:
The total amount of interest paid is shown below:
1. For 6 months, the interest would be
= Invested amount × interest rate
= $10,000 × 2%
= $200
2. For 12 months, the interest would be
= (Invested amount + interest paid for 6 months) × interest rate
= ($10,000 + $200) × 3%
= $10,200 × 3%
= $306
3. For 18 months, the interest would be
= (Invested amount + interest paid for 6 months + interest paid for 12 months ) × interest rate
= ($10,000 + $200 + $306) × 4%
= $420
Now the total interest would be
= $200 + $306 + $420.24
= $926.24