the actual height of the backboard is 8.18 feet.
What is proportion?A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Given
We have been given that Derek places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches. We are asked t find the height of the backboard, if the backboard has a shadow of 8.5 feet.
We will use proportions to solve our given problem as ratio between sides ruler will be equal to ratio of sides of background.
[tex]\frac{Actual height of ruler}{Shadow of ruler} = \frac{Actual height of black board}{Shadow of black board} \\\\\frac{12}{11} =\frac{Actual height of black board}{7.5} \\\\Actual height of black board = \frac{12}{11} * 7.5 = 8.18\\[/tex]
Therefore, the actual height of the back-board is 8.18 feet.
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A set of 5 numbers has an average of 50. The largest element in the set is 5 greater than 3 times the smallest element in the set. If the median of the set equals the mean, what is the largest possible value in the set
Answer:
5×3=15
15×3=45
therefore the largest value is 45
The largest possible value in the set is 92. The set has an equal mean and median. So, the set is {29, 29, 50, 50, 92}.
What are the mean and median of a set of data?Mean:
For a set of data, the average of all the data values is said to be its mean.
Median:
When the set is arranged in ascending order, the middle term is said to be its median (if there are an odd number of data values in the set) or the average value of the two middle terms is the median (if there are an even number of data values in the set).
Calculation:It is given that,
there are 5 numbers in the set
Mean = 50 and Median = Mean
So, Median = 50
Since there are 5 numbers in the set (odd number), the median is the third(middle) number.
Consider the first or smallest number as 's'.
Then the largest number = 3s + 5
By minimizing each term we get,
first term = s
second term = s
third term = 50
fourth term = 50
fifth term = 3s+5
If the mean is 50, then the sum of all the terms = 50 × 5 = 250
So,
s + s + 50 + 50 + 3s + 5 = 250
⇒ 5s + 105 = 250
⇒ 5s = 145
∴ s = 29
Thus, the smallest number is 29
Then, the largest number = 3s + 5 = 3 × 29 + 5 = 92
Therefore, the largest number in the given set is 92.
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Pls help me !!! due today:(
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "equations, expressions". The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
math related pls help
Hello and Good Morning/Afternoon:
Let's take this problem step by step:
Let's consider what the problem wants:
⇒ the value of (f-g)(y)
Let's consider what the problem gives us:
⇒ the value of f(y) and g(y)
Let's consider the relationship between f(y), g(y) and (f-g)(y)
⇒ [tex](f-g)(y)=f(y)-g(y)[/tex]
Let's solve for (f - g)(y)
[tex]\hookrightarrow(f-g)(y) = f(y)-g(y) = 5y^2-2y+1-(-3y^2-y-2)\\=5y^2-2y+1+3y^2+y+2=8y^2-y+3[/tex]
Answer: 8y²- y + 3
Hope that helps!
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Solve 3a
17
7
8
9
- (2² + 1)² + a
when a = 8
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming the equation should be:}[/tex]
[tex]\mathbf{3a - (2^2 + 1)^2 + a}[/tex]
[tex]\huge\textbf{Simplify it: }[/tex]
[tex]\mathbf{3a - (2^2 + 1)^2 + a}[/tex]
[tex]\mathbf{= 3(8) - (2^2 + 1)^2 + 8}[/tex]
[tex]\mathbf{= 24 - (2^2 + 1)^2 + 8}[/tex]
[tex]\mathbf{= 24 - (4 + 1)^2 + 8}[/tex]
[tex]\mathbf{= 24 - 5^2 + 8}[/tex]
[tex]\mathbf{= 24 - 25 + 8}[/tex]
[tex]\mathbf{= -1 + 8}[/tex]
[tex]\mathbf{= 7}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{Option\ B. 7}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphiitrite1040:)}[/tex]Sampling distribution. a quarterback threw 1 interception in his first game, 2 interceptions in his second game, 5 in terceptions in his third game, and then he retired. consider the values of 1, 2, and 5 to be a population. assume that samples of size 2 are randomly selected (with replacement) from the population
a. list the 9 different possible samples and find the mean of each sample
b. what is the mean of the sample means from part a?
c. is the mean of the sampling distribution from part t equal to the mean of the population of the three listed values? are those means always equal?
(a) The Sample mean of each sample is 1, 2, 5, 1.5, 3, 3.5, 3, 1.5,3,3.5.
(b) The mean of the sample means from part (a) is 8/3.
(c) Yes, The mean of the sample distribution is always equal to the mean of the Population.
According to the questions,
Game number 1 2 3 Total
Number of interceptions 1 2 5 8
a) Element 1 Element 2
1 1
2 2
5 5
1 2
1 5
2 5
2 1
5 1
5 2
Sample mean of each sample is 1, 2, 5, 1.5, 3, 3.5, 3, 1.5,3,3.5.
b) The mean of the sample means from part a.
(1+2+5+1.5+3+3.5+1.5+3+3.5)/9 = 8/3
The mean of the sample means from part (a) is 8/3
c) Mean of the populations = (1+2+5)/3 = 8/3
The mean of the sample distribution from part b. is 8/3
Yes, The mean of the sample distribution is always equal to the mean of the Population
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An architect wants an artistic flair to the house he is building, so he designs windows that are three fourths of a circle in shape. The builder is making trim for the windows and needs to know the length of the arc of the outer rim of the window. If the central angle is 270 degrees, and the radius of the partial circle is 30 inches, how much trim is needed for each window? Round your answer to the nearest inch, and enter the number only.
The amount of rim needed for each window is 141.4 in
How to find the length of the outer rim?Since the outer rim is the length of an arc, we use the formula for length of an arc of a circle.
What is an arc?An arc is part of section of the circumference of a circle
What is the length of an arc?So, length of arc, L = Ф/360 × 2πR where
Ф = central angle of arc and R = radius of circle.Gven that for the window rim
Ф = angle of the rim = 270° and R = radius of the rim = 30 inSubstituting the values of the variables into the equation for L, we have
L = Ф/360 × 2πR
L = 270°/360° × 2π × 30 in
L = 3/4 × 2π × 30 in
L = 3/2 × π × 30 in
L = 3 × π × 15 in
L = 45π in
L = 141.37 in
L ≅ 141.4 in
So, the amount of rim needed for each window is 141.4 in
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Write a function of the geometric sequence with a starting term of 6 and a common ratio of 3. Find the sixth term.
A function for the described sequence is; f(n) = 6• 3^(n-1) and the sixth term is; 1458.
What is the sixth term of the sequence?Since, it follows that the first term of the sequence is; 6 and the common ratio is 3, it follows that the recursive function that represents the sequence is; f(n) = 6• 3^(n-1).
Additionally, by substitution of 6 for n; f(6) = 1,458.
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which statemennt is false?
Answer:
B. Every integer is also an irrational number.
On a sunny day, Andrew, who is 1.9 m tall, casts a shadow that is 3.5 m long. A nearby tree casts a shadow that is 28.0 m long. To the nearest tenth of a metre, how tall is the tree?
Answer:
15.2
Step-by-step explanation:
The explanation is in the photo.. but basically this question is about similar triangles and you need to find the scale factor to find the height.
Hope it helps
the height of the tree is approximately 15.2 meters.
To find the height of the tree, we can set up a proportion between Andrew's height and the height of the tree based on their respective shadow lengths.
Let's denote the height of the tree as "h" meters.
The proportion between the height and shadow lengths can be written as:
h / 28.0 = 1.9 / 3.5
Now, we can solve for "h":
h = (1.9 / 3.5) * 28.0
h ≈ 15.2 meters
To the nearest tenth of a meter, the height of the tree is approximately 15.2 meters.
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The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy or New York, New York:
Maximum Minimum Q1 Q3 IQR Median Mean σ
Rome 16 0 3 13 10 8.5 8 5.4
New York 20 1 4.5 6 1.5 5.5 7.25 5.4
Which of the choices below best describes how to measure the center of this data? (5 points)
Group of answer choices
Both centers are best described with the mean.
Both centers are best described with the median.
The Rome data center is best described by the mean. The New York data center is best described by the median.
The Rome data center is best described by the median. The New York data center is best described by the mean.
It's NOT C "The Rome data center is best described by the mean. The New York data center is best described by the median." already tried, its incorrect.
The best description on measurement of the center of this data is; C. The Rome data center is best described by the mean. The New York data center is best described by the median.
How to find the center of the data?If we make the box and whisker plot of the Rome and New York data, we will see that there will clearly be an outlier in the New York data.
Thus;
Due to the fact that the data set for New York has an outlier and the mean is skewed, it means that we would use the median.
Finally, we see that the Rome data set is symmetrical because it has no outlier, and as such we can use the mean.
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a machine makes 36 widgets in 20 minutes. at that rate, how many widgets will the machine make in an 8-hour day?
kể tên các cặp góc kề bù
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I really need help for my hw please help !!!!!!!
Answer:
1. 5.46 inches
2. 111% rounded to the nearest percent
3. 85.9 tons
4. 367.2 ft.
5. 49 percent
6. 466.7 inches
Step-by-step explanation:
1. .28 x 19.5
2. 97 = 87x Divide both sides by 87
1.11 = x This gives our answer as a decimal. Move the decimal 2 places to the right to make a percent. 111%
3. 146 = 1.7x to change a percent to a decimal move the decimal to places to the left. Divide both sides by 1.7 and round
x = 85.9
4. (2.7) 136 = x
367.2 = x
5. x123 = 60 Divide both sides by 123
x = 0.4878 Move the decimal two places to the right and round to make a percent. 48.8
6. .12x = 56 Divide both sides by .12
x = 466.7
When you multiply a number by 25 you get another number that is 250 more than 1000. find the number
Answer:
50
Step-by-step explanation:
1000+250=1250
After that Just do it in reverse:
1250/25=50
Alissa is analyzing an exponential growth function that has been reflected across the y-axis. She states that the domain of the reflected function will change because the input values will be the opposite sign from the reflected function. Simon disagrees with Alissa. He states that if an exponential function is reflected across the y-axis, the domain will still be all real numbers.
Which student is correct and why?
Alissa is correct because the domain will change from negative to positive x-values.
Alissa is correct because a reflection across the y-axis will change the possible input values of the reflected function.
Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input.
Neither student is correct.
Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input for an exponential growth function.
Verification of Choice
Let us consider the following exponential growth function.
y = Aeˣ ...........................(1)
This equation changes when it is reflected across the y axis and becomes,
y = Ae⁻ˣ ...........................(2)
Here, the set of all x values for which y is defined is known as the domain of this exponential growth function.
Therefore, the domain of exponential growth function 1 is the set of all real numbers, given by, x ∈ [-∞,∞]
The domain of function 2, which is a reflection of function 1, will also consist entirely of real numbers and will be given by x ∈ [-∞,∞ ]
Therefore, between Alissa and himself, Simon is right when he asserts that even if an exponential growth function is reflected across the y-axis, the domain will still consist only of real values.
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No penalties have been given. Fencer X attacks. Fencer Y makes a parry, and scores a riposte to the valid target of Fencer X. During the parry, Fencer Y strikes Fencer Xs mask with the bell guard. What should the Referee do
Fencer X attacks. Fencer Y makes a parry, and scores a riposte to the valid target of Fencer X. During the parry, Fencer Y strikes Fencer Xs mask with the bell guard. annual the touch fencer Y recieves a RED CARD.
what are the fencing rules ?
Penalty cards or flags are also used in modern fencing. Each card has a unique meaning. A fencer who receives a yellow card is warned, but no further action is taken. A fencer who receives a red card is warned, and their opponent receives a touch. A fencer who receives a black card is disqualified from the competition and may be disqualified from the tournament, expelled from the venue, or suspended from future tournaments if the offence is serious. However, black cards are rarely given to fencers. It should be noted that spectators can (and occasionally are) carded or expelled.
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Shota invests $2000 in a certificate of deposit that earns 2, percent interest each year write a function that gives the total value v(t) in dollars, of the investment t years from now
V(t)=2000(1.02)^t function that gives the total value in dollars of the investment t years from now given that Shota invests $2000 in a certificate of deposit that earns 2 percent interest each year. This can be obtained by using the formula of compound interest formula.
What is the required function?Equation of compound interest compounded yearly,
A = P(1 + R/100)^t
where,
A = amount
P = principal amount
R = rate
t = number of years
Given that P = $2000, R = 2%, number of years = t,
V(t) = 2000(1+2/100)^t
V(t) = 2000(1+0.02)^t
V(t) = 2000(1.02)^t
Hence V(t)=2000(1.02)^t function that gives the total value in dollars of the investment t years from now given that Shota invests $2000 in a certificate of deposit that earns 2 percent interest each year.
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Consider this quadratic equation.
x2 + 2x + 7 = 21
The number of positive solutions to this equation is
.
The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is
Answer:
1 positive solution (and 1 negative)
the greatest solution is about 2.87
Step-by-step explanation:
so, it is
x² + 2x + 7 = 21
x² + 2x - 14 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -14
x = (-2 ± sqrt(2² - 4×1×-14))/(2×1) =
= (-2 ± sqrt(4 + 56))/2 = (-2 ± sqrt(60))/2 =
= (-2 ± sqrt(4×15))/2 = (-2 ± 2×sqrt(15))/2 =
= -1 ± sqrt(15)
x1 = -1 + sqrt(15) = 2.872983346... ≈ 2.87
x2 = -1 - sqrt(15) = -4.872983346...
The polynomial equation x^4 + x^3 + x^2 + x + 1 = 0 has zero positive real roots. Please select the best answer from the choices provided T F
There are zero positive real roots for the given polynomial equation [tex]x^4 + x^3 + x^2 + x + 1 = 0[/tex]. This is explained by Descarte's rule of signs. So, the best choice is T (true).
What is Descarte's rule of signs?Descarte's rule of signs tells about the number of positive real roots and negative real roots.The number of changes in signs of the coefficients of the terms of the given polynomial f(x) gives the positive real zeros of the polynomial.The number of changes in signs of the coefficients of the terms of the given polynomial when f(-x) gives the negative real zeros of the polynomial.Calculation:The given polynomial equation is [tex]x^4 + x^3 + x^2 + x + 1 = 0[/tex]
On applying Descarte's rule of signs,
[tex]f(x)=x^4 + x^3 + x^2 + x + 1[/tex]
Since there are no changes in the signs of the coefficients of any of the terms in the above polynomial, the polynomial has no positive real roots.
[tex]f(-x)=(-x)^4+(-x)^3+(-x)^2+(-x)+1\\ = x^4-x^3+x^2-x+1[/tex]
Since there are four changes in the signs of the coefficients of the terms of the given polynomial when f(-x), the polynomial has 4 negative real roots.
Therefore, the given polynomial equation has zero positive real roots. So, the correct choice is T(true).
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Find the equation of a line through (3, 1) and perpendicular to 10x + 3y = 5
Answer:
y = (3/10)x + 1/10
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. First, we need to rearrange the given equation to determine the slope of the original line.
10x + 3y = 5 <----- Original equation
3y = -10x + 5 <----- Subtract 10x from both sides
y = (-10/3)x + 5 <----- Divide both sides by 3
Now, we can tell that the slope of the original line is m = -10/3. The perpendicular line should have an opposite-signed, reciprocal slope to that of the original. Therefore, the new slope is m = 3/10.
We can find the value of "b" by plugging the new slope and values from the Point (3, 1) into slope-intercept form.
m = 3/10
x = 3
y = 1
y = mx + b <----- Slope-intercept form
1 = (3/10)(3) + b <----- Insert values
1 = 9/10 + b <----- Multiply 3/10 and 3
10/10 = 9/10 + b <----- Create common denominators
1/10 = b <----- Subtract 9/10 from both sides
Now that we know the values for "m" and "b", we can construct the equation of the perpendicular line.
y = (3/10)x + 1/10
I think of a number, subtract 5 and then multiply by 2. my answer is 80. what is my number?
Answer:
200
Step-by-step explanation:
Just do it in reverse and reverse "roles" multiplying Becomes Devidng and Devidng Becomes multiplying:
80/2=40, 40x5=200
The measures of the angles of a triangle
are shown in the figure below. Solve for x.
60°
(4x+3)°
(2x+9)⁰
Answer:
x = 18
Step-by-step explanation:
In order for a triangle to be a triangle, all angles must add up to 180.
This means that we can create an equation to solve for x, using the angles given.
180 = 60 + (4x+3) + (2x+9) --> remove brackets and combine like terms
180 = 60 + 6x + 12
180 = 72 + 6x
108 = 6x
18 = x
Charlotte is driving at 52.7 mi/h and receives a text message. She looks down at her phone and takes her eyes off the road for 4.99 s. How far has Charlotte traveled in feet during this time
Answer:
385.7 ft
Step-by-step explanation:
The relation between speed, distance, and time is ...
distance = speed × time
Compatible unitsThe speed is given in miles per hour, but the time is given in seconds and the distance is wanted in feet. This suggests a conversion of speed to feet per second is appropriate.
[tex]\dfrac{52.7\text{ mi}}{\text{h}}\times\dfrac{1\text{ h}}{3600\text{ s}}\times\dfrac{5280\text{ ft}}{1\text{ mi}}=\dfrac{52.7\cdot22\text{ ft}}{15\text{ s}}=77.29\overline{3}\text{ ft/s}[/tex]
DistanceThe distance traveled is the product of this speed and the time period.
[tex]\dfrac{77.29\overline{3}\text{ ft}}{1\text{ s}}\times4.99\text{ s}=385.6937\overline{3}\text{ ft}\approx\boxed{385.7\text{ ft}}[/tex]
f(x) 2 square root -x^2+10 x what’s the domain
The domain of the function are all real numbers greater than 10
Domain of a functionDomain are values of the independent variables for which the function exist.
Given the function below;
[tex]f(x)=2\sqrt{-x^2+10x}[/tex]
For the function to exist, then;
-x^2+10x = 0
-x^2 = -10x
x = 10
Hence the domain of the function are all real numbers greater than 10
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Which of the following shows the correct order of the numbers?
5/6, 12/13, 0.8
A.) 5/6 < 0.8 < 12/13
B.) 0.8 < 5/6 < 12/13
C.) 0.8 < 12/13 < 5/6
The correct order of the numbers is 0.8 < 5/6 < 12/13. The correct option is B.) 0.8 < 5/6 < 12/13
Magnitude of numbersFrom the question, we are to determine the correct order of the numbers
The given numbers are
5/6, 12/13, and 0.8
Convert the fractions to decimals
5/6 = 0.8333
12/13 = 0.923
Thus, the numbers are
0.8333, 0.923, and 0.8
Order the numbers from the smallest to the largest
0.8 < 0.8333 < 0.923
≡ 0.8 < 5/6 < 12/13
Hence, the correct order of the numbers is 0.8 < 5/6 < 12/13. The correct option is B.) 0.8 < 5/6 < 12/13
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Sanjay and felipe are putting together a 500-piece puzzle. sanjay could do the entire puzzle by himself in 6 hours, while it would take felipe 8 hours to do the puzzle alone. a table showing rate in part per hour, time in hours, and part of puzzle complete. the first row shows sanjay, and has blank, t, t. the second row shows felipe, and has blank, t, t. use the table to write and solve an equation to determine the approximate amount of time it would take sanjay and felipe to do the puzzle if they were working together.
Sanjay and Felipe would take a time of 3.4 hours to do the puzzle if they were working together.
What is the time?Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future.
The amount of time that something exists or continues to happen as measured or measurable.
The duration of events or the gaps between them can be measured, compared, or even ordered using time.
Time taken by Sanjay= 6 hours
Time taken by Felipe= 8 hours
Time taken by both if they work together,
=[tex]\frac{1}{1/6+1/8}[/tex]
=[tex]\frac{1}{\frac{4+3}{24} }[/tex]
=24/7
=3.4 hours
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Answer:
the answer is C
Step-by-step explanation:
Which side lengths form a right triangle?
Choose all answers that apply:
A:
11,13,√290
B:
7, 24, 25
C: 2, 5, 7
Answer:
B
Step-by-step explanation:
Use the Pythagorean theorem, 7^2+24^2=25^2
49+576=625
625=625
All the other answers do not satisfy the Pythagorean theorem (a^2+b^2=c^2)
Answer: A, B
Step-by-step explanation:
A right triangle's sides have a special property that the sum of the squares of the two legs is equal to the square of the hypotenuse. This is also known as the Pythagorean Theorem.
Let's check if this theorem holds true for each triangle.
A[tex]11^2+13^2=(\sqrt{290})^2\\ 121 + 169=290\\ 290 = 290[/tex]
The Pythagorean Theorem holds true, so this is a right triangle.
B[tex]7^2+24^2=25^2\\ 49 + 576 = 625\\ 625=625[/tex]
The Pythagorean Theorem holds true, so this is a right triangle.
C[tex]2^2+5^2=7^2\\ 4+25=49\\ 29 = 49[/tex]
This is a false statement, which doesn't make this triangle a right triangle. We could have use the triangle inequality theorem to prove that this isn't a triangle at all, and therefore not a right triangle, but I encourage you to learn about it and try it yourself.
Which equation would find the distance between the two points show on the coordinate plane?
The equation would find the distance between the two points is
[tex]\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2} }[/tex]
According to the question,
The equation would find the distance between the two points is
[tex]\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2} }[/tex]
If (x₁, y₁) and (x₂, y₂) be any point in the plane then the distance between the two points equation is [tex]\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2} }[/tex]
Hence, the equation would find the distance between the two points is
[tex]\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2} }[/tex]
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Si a,b y c son números dígitos tales que a + b + c es igual a 20. ¿Cual es el valor de abc + bca + cab?
Basado en la información, el valor de abc + bca + cab debe ser de 60.
¿Cuál es el valor de a+b+c?El valor de la combinación de estás tres letras es de 20.
¿Cuál es el valor de abc + bca + cab?Según la propiedad conmutativa el orden de los factores sumados no debe afectar su resultado, por lo que:
abc = 20bca = 20cab= 2020+20+20 = 60
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A certain journey by train takes 5 hours at the speed of 45 km/h. What will be the speed of the train to complete the same journey in 3 hours?
A certain journey by train takes 5 hours at the speed of 45 km/h. What will be the speed of the train to complete the same journey in 3 hours?
Answer:
Journey taken time 5 hour at speed of 45km/hr
So,
1 hour=45/5=9km/hr
Therefore,3 hour=(9x3)km/hr.
(please mark me brainliest if my answer was good)