Terri wants to know the height of the big Christmas tree on the town square. She stands 20 feet from the base of the tree. Elliot places a mirror on the ground between Terri and the tree so that she can see the top of the tree in the mirror. The mirror is located 16 feet from the base of the tree. If Terri's eye level is 5.5 feet from the ground, how tall is the tree?
Answers
Answer:
22ft
Step-by-step explanation:
Always good to try and draw out the scenario, it can make it more easily understandable.
Have a look at the pic.
Hope its clear.
Related Questions
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students. Ice Cream Candy Cake Pie Cookies 81 9 72 36 27 Which statement is the best prediction about the slices of pie the college will need? The college will have about 480 students who prefer pie. The college will have about 640 students who prefer pie. The college will have about 1,280 students who prefer pie. The college will have about 1,440 students who prefer pie.
Answers
The college will have about 640 students who prefer pie. We can calculate percentages based on the student sampling of 225 students (assuming it was a completely random sample, and not one taken just from a specific group, such as football players at half-time).
What is random sample?
A simple random sample is a subset of a statistical population where each member has an equal chance of being selected. Unbiased representation of a group is what a straightforward random sample is supposed to be.The researcher uses simple random sampling, a type of probability sampling, to randomly select a subset of individuals from a community. Every member of the population has the same chance of being selected.A random experiment has a result known as a sample. One particular value is chosen at random from a pool of potential values when we sample a random variable.A sample is that specific value. The probability distribution of the random variable specifies the possible values and their probabilities.To make a prediction, we need to assume that the preferences of the 225 students surveyed are representative of the entire student population of 4,000. We can use the proportion of students who prefer pie in the sample to make an estimate.
The proportion of students who prefer pie in the sample is:
36/225 = 0.16
We can use this proportion to estimate the number of students who prefer pie in the entire population:
4,000 x 0.16 = 640
Therefore, the best prediction about the slices of pie the college will need is that the college will have about 640 students who prefer pie. So the option "The college will have about 640 students who prefer pie" is the correct statement.
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three pieces of wood measuring 70m, 105m and 175m long have to be divided to planks of equal length what is the greatest possible length of each plank
Answers
Answer:
35 m
Step-by-step explanation:
I will assume the goal is not to waste any wood. We need to find a common length that will allow each piece of wood to be divided into whole pieces with nothing left over. The shortest plank is 70 m, but that length will cause a loss of 35 m on the 105m plank, and also 35m on the 175m plank after two 70m sections have been cut off (175 - 140 = 35).
Looking at the actual lengths, one might spot that they are all evenly divisible by 35. See the table below. The numbers under "35" are the result of the length divided by 35. They are all whole numbers. We can cut each plank into 35m sections and have none left over.
Length (m) 35 (factor)
70 2 planks
105 3 planks
175 5 planks
This will result in 10 35m planks.
No need to plank me.
Or
Mr. Mosley ordered pizzas for the volunteers at Highland School's fundraiser event. He ordered 12 large pizzas from the Roman Rounds pizzeria. Since this was a bulk order, Roman Rounds reduced the price of each large pizza by $2. The total came to $192. Which equation can you use to find the amount of money, p, Roman Rounds normally charges for a large pizza?
Answers
Equation that we can use to find the amount of money, p, Roman Rounds normally charges for a large pizza is 12(p - 2) = 192.
Let's use p to represent the normal price of a large pizza from Roman Rounds. Since Mr. Mosley ordered 12 large pizzas and received a $2 discount on each, he paid a total of $192. We can use this information to set up the following equation:
12(p - 2) = 192
In this equation, 12 represents the number of large pizzas that were ordered, and (p - 2) represents the discounted price of each pizza. The left side of the equation gives us the total amount that Mr. Mosley paid for the pizzas. By setting this expression equal to 192, we can solve for p, the normal price of a large pizza from Roman Rounds.
To solve for p, we first distribute the 12 on the left side of the equation:
12p - 24 = 192
Next, we add 24 to both sides of the equation:
12p = 216
Finally, we divide both sides of the equation by 12:
p = 18
Therefore, the normal price of a large pizza from Roman Rounds is $18.
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Joseph runs 212 miles on Monday. Each day after that, he runs the same 113 mile route every morning. His goal is to run at least 6 miles by the end of the week. Which inequality represents the least number of days after Monday that Joseph needs to run to reach his goal?
Answers
The inequality that represents the least number of days after Monday that Joseph needs to run to reach his goal is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
Number of miles that Joseph run on Monday = [tex]2\frac{1}{2}[/tex] miles
Number of miles that Joseph run each day after that = [tex]1\frac{1}{3}[/tex] miles
The inequality is the mathematical statement that shows the relationship between two expression using an inequality symbol. The inequality symbols are less than, greater than, less than or equal and greater than or equal.
Then the inequality will be
[tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
Where x is the number of days after Monday that Joseph needs to run to reach his goal
Therefore, the inequality is [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{3}x[/tex] ≤ 6
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The formula area of a trapezoid is A=1/2 h(b_1+b_2) solve for b_1
Please help ASAP
Answers
Answer: b1 = [tex]\frac{2A}{h} -b2[/tex]
Step-by-step explanation:
Algebra my friend...Algebra
So:
A = 0.5h(b1+b2)
A/(0.5h) =b1+b2
.: A/(0.5h) - b2 = b1
In other words:
b1 = [tex]\frac{A}{0.5h} -b2[/tex]
The 0.5 in the denominator can be rearranged to get the final answer:
b1 = [tex]\frac{2A}{h} -b2[/tex]
Find the area of an isosceles triangle whose one side is 10 cm greater than each of its equal sides and perimeter is 100 cm.
Answers
Answer:
the area of the isosceles triangle is approximately 104.49 cm^2.
Step-by-step explanation:
The perimeter of the triangle is 100 cm, so we can write an equation using the lengths of the sides:
x + x + (x + 10) = 100
3x + 10 = 100
3x = 90
x = 30
So the equal sides of the triangle have length 30 cm and the side that is 10 cm greater has length 40 cm.
To find the area of the triangle, we can use the formula for the area of an equilateral triangle:
Area = (sqrt(3) / 4) * (side length)^2
Area = (sqrt(3) / 4) * 30^2
Area = (sqrt(3) / 4) * 900
Area = (sqrt(3) / 4) * 30 * 30
Area = (sqrt(3) / 4) * 900
Area = (30 * sqrt(3)) / 2
Area = 45 sqrt(3)
The gradient of a curve at the point (x,y) is given by dy/dx=2(x+3)^1/2-x. The curve has a stationary point at (a,14), where a is a positive constant. Find the value of a.
Answers
Using the gradient of the curve given, the value of a is 6
What is the value of aThe stationary point of a curve is a point where the slope of the curve is equal to zero. So, to find the value of a, we need to set the derivative of the curve equal to zero and solve for x.
dy/dx = 2(x + 3)^(1/2) - x
Setting this equal to zero, we have:
2(x + 3)^(1/2) - x = 0
Expanding the square root and rearranging, we get:
x = 2(x + 3)^(1/2)
Squaring both sides of the equation, we have:
x^2 = 4(x + 3)
Expanding the right side and rearranging, we have:
x^2 - 4x - 12 = 0
Using the quadratic formula, we can find the values of x that satisfy this equation:
x = [-(-4) ± √((-4)^2 - 4(1)(-12))] / 2(1)
x = [4 ± √(16 + 48)] / 2
x = [4 ± √64] / 2
x = [4 ± 8] / 2
So, the two possible values of x are:
x = 6, x = -2
Since we are looking for a positive value of x, the only solution that works is x = 6.
Therefore, the value of a is equal to 6.
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question which of the following must be true for an estimator of a population parameter to be unbiased? responses the sampling distribution of the estimator is normal. the sampling distribution of the estimator is normal. the expected value of the estimator is equal to the population parameter. the expected value of the estimator is equal to the population parameter. the sampling distribution of the estimator is the same shape as the distribution of the population parameter. the sampling distribution of the estimator is the same shape as the distribution of the population parameter. the variability of the sampling distribution of the estimator is equal to the variability of the population parameter. the variability of the sampling distribution of the estimator is equal to the variability of the population parameter. the variability of the sampling distribution of the estimator is less than the variability of the population parameter.
Answers
The second statement in your question is the correct response.
What is the sampling distribution?
A sampling distribution is the probability distribution of a statistic (such as the sample mean or sample proportion) based on all possible random samples of a fixed size from a population.
The following statement must be true for an estimator of a population parameter to be unbiased:
The expected value of the estimator is equal to the population parameter.
Hence, the second statement in your question is the correct response.
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Daniel has a goal to complete a triathlon. The race consists of a 0. 93
-mile swim, a 24. 8
-mile bike ride, and a 6. 2
-mile run. In training, Daniel can swim at an average pace of 2. 2mph. He rides his bike at an average of 17. 8mph
and runs at 5. 9mph. Estimate how long it will take his to complete the triathlon
Answers
It will take Daniel approximately 2 hours and 52 minutes (172.066 minutes) to complete the triathlon.
To estimate how long it will take Daniel to complete the triathlon, we can calculate the time it will take him to complete each leg of the race and add them together.
Swim:
Distance = 0.93 miles
Speed = 2.2 mph
Time = Distance / Speed = 0.93 miles / 2.2 mph = 0.4236 hours = 25.416 minutes
Bike:
Distance = 24.8 miles
Speed = 17.8 mph
Time = Distance / Speed = 24.8 miles / 17.8 mph = 1.3933 hours = 83.6 minutes
Run:
Distance = 6.2 miles
Speed = 5.9 mph
Time = Distance / Speed = 6.2 miles / 5.9 mph = 1.0508 hours = 63.05 minutes
Total time = Swim time + Bike time + Run time
Total time = 25.416 minutes + 83.6 minutes + 63.05 minutes
Total time = 172.066 minutes
Therefore, it took 172.066 minutes which is approximately equal to 2 hours and 52 minutes by Daniel to complete the triathlon.
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!URGENT HELP! 100 points to any who are willing ^-^
Consider the function f(x) = [tex]2^{x}[/tex]. Find b so that the graphs of each of the functions listed are the same as the graph of function f.
• [tex]g(x) = 4^{bx}[/tex]
• [tex]h(x) = 8^{bx}[/tex]
• [tex]j(x) = (\frac{1}{2}) ^{bx}[/tex]
Side note:
To whom it may concern!
I do deeply appreciate all your help if you did or were willing to help me! Thank you for taking the time out of your day and life to bring aid to my little situation! Bless your kind soul.
Answers
For g(x), we have:
g(x) = 4^bx = (2^2)^bx = 2^(2bx)
Since 2^x = f(x), we can set 2bx = x to find b. Solving for b, we get:
b = 1/2
For h(x), we have:
h(x) = 8^bx = (2^3)^bx = 2^(3bx)
Since 2^x = f(x), we can set 3bx = x to find b. Solving for b, we get:
b = 1/3
For j(x), we have:
j(x) = (1/2)^bx = 2^(-bx)
Since 2^x = f(x), we can set -bx = x to find b. Solving for b, we get:
b = -1
So, for g(x) = 4^bx, b = 1/2; for h(x) = 8^bx, b = 1/3; and for j(x) = (1/2)^bx, b = -1.
mrs. starnes enjoys doing sudoku puzzles. the time she takes to complete an easy puzzle can be modeled by a normal distribution with mean 5.3 minutes and standard deviation 0.9 minute. what proportion of the time does mrs. starnes finish an easy sudoku puzzle in less than 3 minutes?
Answers
The proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes is approximately 0.0055, or 0.55%
We can use the normal distribution and the given mean and standard deviation to find the proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes.
First, we need to standardize the value of 3 minutes using the z-score formula:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get:
z = (3 - 5.3) / 0.9 ≈ -2.56
Next, we can use a standard normal distribution table or a calculator to find the proportion of the area under the standard normal distribution curve that corresponds to a z-score of -2.56. This proportion represents the proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes.
Using a standard normal distribution table, we can find that the area to the left of z = -2.56 is approximately 0.0055.
Therefore,
The proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes is approximately 0.0055, or 0.55%.
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A plumber cut a pipe into 5 equal pieces and had 27 cm of the pipe left. For a second
pipe 15m long, he cut 11 pieces of the same length as that of each piece cut from the
first pipe and had 15 cm of the second pipe left. What was the length, in cm, of each
shorter piece of the second pipe? What was the length of the first pipe originally?
Please input your answer:
Answers
Answer:
Step-by-step explanation:
Let's call the length of each shorter piece of the first pipe x. Then the total length of the first pipe would be 5x + 27 cm.
Similarly, the length of each shorter piece of the second pipe would be x and the total length of the second pipe would be 11x + 15 cm.
Since both pipes were cut into the same length pieces, we can set the two equations equal to each other:
5x + 27 = 11x + 15
Solving for x, we can find the length of each shorter piece:
6x = -12
x = -2
This means that each shorter piece of both pipes was -2 cm long, which is not physically possible. So, this solution is not valid. This means that the problem is underdetermined and that we cannot determine the length of each piece.
In the diagram, BA BE and CE CD.
What is mZDAE?
m2DAE =
Submit
B
68⁰
52%
E
Answers
mZDAE is a line segment that connects the midpoints of line segments BA and CE. In the diagram, its coordinates are (66⁰, 52%).
Use the vertex ( h, k ) and a point on the graph ( x, y ) to find the standard form of the equation of the quadratic function:
Vertex = (1,-5)
Point = (5,-7)
G( x )= Answer field 1
(x- Answer field 2
)^2 +Answer field 3
Answers
The standard form of the equation of the quadratic function is y = -1/8x^2 + 1/4x - 41/8
How to find the standard form of the equation of the quadratic functionFrom the question, we have the following parameters that can be used in our computation:
(h, k) = (1, -5)
(x, y) = (5, -7)
A quadratic function is represented as
y = a(x - h)^2 + k
So, we have
y = a(x - 1)^2 - 5
Given that
(x, y) = (5, -7)
We have
-7 = a(5 - 1)^2 - 5
This gives
16a = -2
So, we have
a = -1/8
Recall that
y = a(x - 1)^2 - 5
So, we have
y = -1/8(x - 1)^2 - 5
Expand
y = -1/8(x^2 - 2x + 1) - 5
This gives
y = -1/8x^2 + 1/4x - 41/8
So, the required equation is y = -1/8x^2 + 1/4x - 41/8
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double d, then subtract 6 from the result
Do not simplify any part of the expression.
Answers
Answer:
2d-6
Step-by-step explanation:
Since the d is doubled you are multipling then subtracting 6 from the result
.
What is the coefficient in this expression?
-17+(-b)+(-25)
Answers
Answer:
In the expression -17 + (-b) + (-25), the coefficient is a number that multiplies a variable. In this case, the coefficients are -17, -1 (which multiplies the variable "b"), and -25.
Step-by-step explanation:
which of the following approaches to building a multiple linear regression model involves taking all of the possible independent variables, and then systematically eliminating insignificant ones until only significant ones remain? forward selection. stepwise regression. backward elimination. back-checking for aic
Answers
The approaches to building a multiple linear regression model is option (C) Backward elimination
Here the multiple linear regression model involves taking all of the possible independent variables, and then systematically eliminating insignificant ones until only significant ones remain
We know the independent variable is the variable that does not depends on any other variables
Here the given elimination methods is eliminating insignificant ones until only significant ones remain
In the backward elimination method starts with explanatory variables in the regression model then starts to eliminates the least significant ones will eliminates one by one
Therefore, the suitable approach is backward elimination method
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Mario has a box. He wants to determine how much the box can hold. Which measurement should he calculate?
O area
O length
O perimeter
O volume
Answers
look at attachment
The graph of the relation G is shown below.
Give the domain and range of G .
Write your answers using set notation.
please explain it too I dunno what I'm doing btw I set the point worth to 50 points
Answers
Answer:
The answer is 15 and 22
Step-by-step explanation:
KHAN
Sara can read 19 pages an hour. How many pages can Sara read in 95 min? Round to the nearest whole number.
Answers
Answer:
Step-by-step explanation:
Convers 95 min into hours
95/60 = 1.58 Hours
Sara can read 19 pages per hour
Total pages in 95 min or 1.58 hours =
19 * 1.58 = 30.02
Rounding off to nearest whole number- 30
Hope it helps
Nick buys a car for $15,000. He gives the car dealer $5,000 and borrows the rest of the money at 7% simple interest for 5 years. What is the total amount of interest he will have to pay on the loan?
Answers
Answer: $3,500
Step-by-step explanation: 15000-5000=10000
0.7*10,000=700.
700*5=$3,500
how to find the average value of a function on an interval?
Answers
To find the average value of a function on an interval dividing the definite integral [tex]\int\limits^a_b f{(x)} \, dx[/tex] by the length of the interval.
The definition of average value of a function is -"The average value of a function is the height of the rectangle that has an area that is equivalent to the area under the curve of the function."
When there's a need to find the average value of a function, rather than adding up numbers we can just integrate, and instead of dividing by the number of values we can just divide by the length of the interval.
Adding values → Integration
Number of values → Length of the interval
When we use the length of the interval it makes more sense as we all know intervals have an infinite number of values, so it is more appropriate to use the length of the interval instead.
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Randal’s dad is installing a new pool in their backyard. The pool is a square and has an area of 144 ft .
Randal’s dad will then build a 7 ft wide deck to surround the pool. What is the outside perimeter of the deck?
Answers
Answer: Let's call the side length of the square pool "s". We know that the area of a square is equal to the length of one side squared, so we can set up an equation:
s^2 = 144
We can solve for s by taking the square root of both sides:
s = sqrt(144) = 12
So the side length of the pool is 12 feet.
The outside perimeter of the deck is equal to the perimeter of the square pool plus the width of the deck on each side (7 feet). So the outside perimeter is:
12 + 7 + 7 + 12 + 7 + 7 = 52 feet
So the outside perimeter of the deck is 52 feet.
Step-by-step explanation:
Answer: 52 feet
Step-by-step explanation:
First, we know this is a square. So, if the area is 144, square root of 144 is 12 (12 * 12 = 144)
Adding a width of 7 feet to each side means that we can add 12+12+7+7+7+7.
52 feet!
(っ◔◡◔)っ ♥
Hope this helps.
MM4343
Mel uses one fourth of a yard of ribbon to make a hair bow. How many hair bows can Mel make with 1 yard of ribbon?
Answers
Answer:
it's simple 4 that is 100% the correct answer
Zainab runs her own business where she leads guided day-long tours for small groups of tourists
in her city. Each tour has a maximum of 3 guests. Let X represent the number of customers
Zainab gets on a randomly chosen day. Based on previous data, here is the probability
distribution of X along with summary statistics:
X = # of customers
P(X)
Hy =
What are the mean and standard deviation of Y?
σy ≈
1
0.20 0.10
It costs Zainab $5 each day to pay for her own transportation to her business, and then each
customer she gets pays her $60. Let Y represent Zainab's net gain on a randomly chosen day.
dollars
dollars
2
0.40
Mean:
Standard deviation:
3
0.30
4x = 1.8
x 1.08
Answers
The mean of Y is 103 dollars. The standard deviation of X is 64.8 dollars
How to solve for the mean and the standard deviationThe mathematical expression that we would have to use i the representation of Y is Y = 60X - 5.
How to solve for the mean of Y
Y = exp(Y)
= 60 * EXP(X) - 5
the expected value of x is 1.8
= 60 * 1.8 - 5
= 103 dollars
then we have to solve for the standard deviation of Y
standard deviation of x = 1.08
= 60 * 1.08
= 64.8 dollars
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Abby loves riding Ferris wheels and
roller coasters. While visiting the Polk
County Fair, she first went on the
Ferris wheel 5 times and the roller
coaster 4 times, using a total of 26
tickets. Then, after taking a break and
having a snack, Abby went on the
Ferris wheel 5 times and the roller
coaster 3 times, using a total of 22
tickets. How many tickets does it take
to ride each attraction?
Answers
Answer:
ferris wheel: 2
roller coaster: 4
Step-by-step explanation:
Variables
y = ferris wheel tickets
x = roller coaster tickets
Two equations
5y + 4x = 26
5y + 3x = 22
Using Elimination (minus the top and bottom)
We get:
x = 4 (because 5y - 5y is zero, 4x - 3x is x, and 26 - 22 is 4)
Since the roller coaster price is know, you can sub it into any of the two equations and fine ferris wheel price.
5y + 3(4) = 22
5y + 12 = 22
5y = 10
y = 2
Therefore:
ferris wheel charges 2 tickets
roller coaster charges 4 tickets
Answer:
Step-by-step explanation:
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
Vince works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of 16 strands of lights to decorate 2 bushes and 1 tree. This afternoon, he strung lights on 3 bushes and 4 trees, using a total of 44 strands. Assuming that all bushes are decorated one way and all trees are decorated another, how many strands did Vince use on each?
Vince decorated every bush with
strands of lights and every tree with
strands.
The stemplot shows the years of experience for several teachers at Sycamore High School.
A stemplot titled Teaching Experience. The values are 2, 4, 5, 5, 5, 7, 9, 10, 12, 14, 15, 15, 18, 20, 24.
What is the IQR of the data?
6 years
10 years
12 years
22 years
Answers
The IQR of the data is 10 years and option B is the correct answer.
What is IQR?The dispersion of the middle 50% of the sample is measured by the interquartile range, or IQR, which is the difference between the top and lower quartiles.
The given data is: 2, 4, 5, 5, 5, 7, 9, 10, 12, 14, 15, 15, 18, 20, 24.
The median of the data is:
M = 15 + 1 /2 = 16/2 = 8th value.
M = 10
Ignoring the median divide the data into two parts.
The lower quartile median is 4th term:
Q1 = 5
The upper quartile median is 12th term:
Q2 = 15
IQR = Q2 - Q1
IQR = 15 - 5 = 10 years.
Hence, the IQR of the data is 10 years and option B is the correct answer.
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The height of a cone is 10 centimeters. The radius is 4 centimeters. What is the volume of this cone? Around your answer to the nearest hundredth. Do not include units in your answer
Answers
Answer: 167.55 cm.
Step-by-step explanation:
Cone volume formula is V=1/3hπr².
Substitute...
V= 1/3 (10) (π) (4)^2
V= 53 1/3 π
V= 167.55 cm
Hope this helps!
MM
A toy company is building dollhouse furniture. A rectangular door of a dollhouse has a height of 5 centimeters and a width of 3 centimeters. What is the perimeter of the door on a scale drawing that uses the scale 2:8?
A. 4
B. 10
C. 16
D. 64
Answers
The required perimeter of the door on the scale drawing is 4 cm, which is option A.
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here,
To find the perimeter of the door on the scale drawing, we need to first find the dimensions of the door on the scale drawing. We can use the scale 2:8 to convert the actual dimensions of the door to the corresponding dimensions on the scale drawing:
Height on scale drawing = (2/8) x 5 cm = 1.25 cm
Width on scale drawing = (2/8) x 3 cm = 0.75 cm
The perimeter on the scale drawing = 2 x (height on scale drawing + width on scale drawing)
Perimeter on scale drawing = 2 x (1.25 cm + 0.75 cm)
Perimeter on scale drawing = 2 x 2 cm
The perimeter on the scale drawing = 4 cm
Therefore, the perimeter of the door on the scale drawing is 4 cm, which is option A.
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if 3 is subtracted to a number and the sum is multiplied by 5 the number thus obtained is 575 find the original number
Answers
Answer:
118
Step-by-step explanation:
Let the original number be x.
After subtracting 3, the result is x - 3.
When this result is multiplied by 5, we get (x - 3) * 5 = 575.
Expanding and solving for x, we have:
5x - 15 = 575
5x = 590
x = 118
So the original number was 118.
