Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. For [tex]0 ≤ x ≤ 2, F(1) = (1^3/12) = 0.0833.So, P(X ≤ 1) = 0.0833.[/tex] Hence, the correct option is (a) P(X ≤ 1).
Given that X denotes the amount of time a book on two-hour reserve is actually checked out, and the cdf is the following:
[tex]cdf: 0 , x<0f(x) = ((x^2)/4) , 0 <= x <= 21 , 2<= x[/tex]
To use the cdf to obtain the following.P(X ≤ 1)
So, the probability distribution function is the derivative of the cumulative distribution function.
∴ f(x) = d/dx(F(x))
Also, from the cdf, we know that:
[tex]f(x) = 0 when x < 0.f(x) = ((x^2)/4) when 0 ≤ x ≤ 2.[/tex]
f(x) = 1 when x ≥ 2.
Using the above conditions, we have to calculate the following:
(a) P(X ≤ 1)
Here, P(X ≤ 1) = F(1).
When[tex]0 ≤ x ≤ 2, F(x) = ∫[0,x] f(t)dt=∫[0,x] (t^2/4)dt=[t^3/12]0x=(x^3/12)[/tex]
Thus, for[tex]0 ≤ x ≤ 2, F(x) = (x^3/12).[/tex]
for such more question on Time
https://brainly.com/question/26862717
#SPJ11
Round to the nearest tenth.
Answer:
x=16.3
Step-by-step explanation:
sine: opposite side ÷ hypotenuse
sine(x)= 7 ÷ 25 = 0.28
sine^-1(0.28) = 16.3
x = 16.3
Answer:
16.3 rounded to the nearest tenth
Step-by-step explanation:
The formula for the sine rule is Sin A / a= Sin B / b = Sin C / c which is as, Sin V / v = Sin X / x = Sin S / s
Sin 90 / 25 = Sin X / 7, that is,
1 / 25 = Sin X / 7 (cross multiply)
Make Sin X the subject of the formula;
Sin X = 7 / 25
X = Sin^-1(7 / 25)
X = 16.26 = 16.3 rounded to the nearest tenth
Need the answers for A and B
The sοlutiοn οf the given prοblem οf interest cοmes οut tο be Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.
What dοes interest actually mean?Tο calculate the simple interest rate, divide the amοunt by the cοst οf financing, the amοunt οf time left, and οther variables. The simple return strategy in marketing is principal student lοans hrs. This methοd is the mοst basic methοd fοr figuring οut invοlvement. The mοst typical methοd fοr calculating incοme is as a share οf the principal amοunt. Tο put this intο perspective, if he wants tο bοrrοw $100 frοm a single οf these friends .
Here,
a. The fοllοwing methοd can be used tο determine the mοnthly payment fοr a lοan:
=> The mοnthly payοut = (P*r) / (1 - (1+r)(-n)).
We must first determine the entire lοan amοunt, including interest, that Reh must pay back. After 4.5 years οf interest accrual, the lοan sum is:
=> [tex]9900 \times (1 + 0.0429/12)^{(12 \times 4.5)[/tex] = 12,723.97
The οverall debt balance is $12,723.97.
The numbers can then be entered intο the fοrmula as fοllοws:
=> (12723.97*(0.0429/12)) / (1 - (1+(0.0429/12))(-12*10))
is the fοrmula fοr the mοnthly payοut.
Payment due each mοnth: $131.19 (rοunded tο the nearest dοllar)
Reh's mοnthly payment is therefοre $131, rοunded tο the clοsest dοllar.
b. The fοllοwing fοrmula can be used tο determine the tοtal interest charged οver the lοan's term:
=> tοtal interest = (mοnthly payment X n) - P .
There have been a tοtal οf:
=> 120 is equal tο ten years times οne year.
The entire interest paid is thus:
=> ($3,943.80) (tοtal mοnthly installments * n) - P
=> (131.19 * 120) - 9900 (rοunded tο the nearest dοllar)
Sο, rοunded tο the clοsest dοllar, Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.
To know more about interest visit:
brainly.com/question/28792777
#SPJ1
Which angle is vertical to ∠3?
The angle that is vertical to angle 3 is angle 1
What is vertical angle?Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.
This means that angles that are vertical are angle s that are opposite to each other. In the diagram above, angle 2 is opposite to angle 4 and angle 1 and angle 3.
Therefore all the angles will make a point. This means the sum of the angles is 360°.
angle 2 and angle 3 are adjascent to each other and angle 1 and 4 are adjascent to each other
Therefore the angle that is vertical to the angle 3 is angle 1
learn more about vertical angles from
https://brainly.com/question/1673457
#SPJ1
A statistics tutor wants to assess whether her remedial tutoring has been effective for her five students. She decides to conduct a related samples t-test and records the following grades for students prior to and after receiving her tutoring.
Tutoring
Before After
2. 4 3. 1
2. 5 2. 8
3. 0 3. 6
2. 9 3. 2
2. 7 3. 5
Test whether or not her tutoring is effective at a 0. 05 level of significance. State the value of the test statistic. (Round your answer to three decimal places. )
t =
Compute effect size using estimated Cohen's d. (Round your answer to two decimal places. )
d =
The critical value for a 0.05 level of significance is 1.96, so the calculated t-test statistic (-1.166) is lower than the critical value and therefore does not reject the null hypothesis.
The related samples t-test is used to determine if there is a statistically significant difference between the two sets of data. In this case, the t-test is used to determine if the students' grades have improved after receiving tutoring.
To calculate the t-test statistic, we need to first calculate the mean and standard deviation of the before and after data sets.
For the before data set, the mean is 2.56 and the standard deviation is 0.8. For the after data set, the mean is 3.22 and the standard deviation is 0.5.
We can then calculate the t-test statistic using the following formula:
t = (mean before - mean after) / (standard deviation before + standard deviation after / √n)
where n is the number of samples.
In this case, n = 5, so the t-test statistic is:
t = (2.56 - 3.22) / (0.8 + 0.5 / √5) = -1.166
Learn more about t-test statistic here:
https://brainly.com/question/15236063
#SPJ4
Una cooperativa de vivienda desea comprar un terreno valorizado en S/ 240 000. Para ello disponen de tres modalidades de pago:
Primera modalidad: cuota inicial de 20% y cuotas mensuales fijas de S/ 5 000.
Segunda modalidad: cuota inicial de 10% y cuotas mensuales fijas de S/. 9 000.
Tercera modalidad: Sin cuota inicial y cuotas mensuales fijas de S/. 12000
11 Si se opta por la primera modalidad, ¿cuánto dinero ya se habrá pagado al término del sexto mes de aportaciones?
a. S/. 48 000 b) S/. 78000 c) S/. 50000
12 ¿Qué expresión representa el dinero pagado al término del enésimo mes en la segunda modalidad?
a. 24 000 + 9 000n b. 24000n + 9000 c. 48000 +5000n
13 Si la cooperativa al término del décimo mes ya ha pagado el 50% del precio del terreno, ¿qué modalidad de pago eligieron?
a. Primera
b. Segunda
c. Tercera
Answer:
Step-by-step explanation:
The total amount paid at the end of sixth month is S/78,000. So, the correct answer is (b). Total amount paid at the end of the nth month is 24,000n + 9,000. So, the correct answer is (b). If the cooperative has already paid 50% of the price of the land by the end of the tenth month, the payment option did they choose is 20% down payment and fixed monthly payments of S/5,000. So, the correct option is (a).
For the first payment option, the down payment is 20% of S/240,000, which is S/48,000. The remaining balance is S/192,000, which is paid in fixed monthly payments of S/5,000. Therefore, at the end of the sixth month, the total amount paid is:
S/48,000 + 6 x S/5,000 = S/78,000
So, the answer is (b) S/78,000.
The amount of money paid at the end of the nth month for the second payment option is the sum of the down payment and the total monthly payments up to that month. The down payment is 10% of S/240,000, which is S/24,000. The total monthly payments up to the nth month is S/9,000 x n. Therefore, the expression for the total amount paid at the end of the nth month is:
S/24,000 + S/9,000 x n = (3S + 8n)/72
So, the answer is (b) 24,000n + 9,000.
We can find out which payment option they chose by comparing the total amount paid up to the tenth month for each option to half of the price of the land.
For the first payment option, the down payment is S/48,000 and the total monthly payments up to the tenth month is
10 x S/5,000 = S/50,000.
Therefore, the total amount paid up to the tenth month is:
S/48,000 + S/50,000 x 10 = S/480,000/25
For the second payment option, the down payment is S/24,000 and the total monthly payments up to the tenth month is
10 x S/9,000 = S/9,000.
Therefore, the total amount paid up to the tenth month is:
S/24,000 + S/9,000 x 10 = S/24,000 + S/900
For the third payment option, there is no down payment, and the total monthly payments up to the tenth month is
10 x S/12,000 = S/1,200.
Therefore, the total amount paid up to the tenth month is:
S/1,200 x 10 = S/12,000
Comparing each total amount paid up to the tenth month to half of the price of the land (S/240,000 x 0.5 = S/120,000), we see that only the first payment option meets the condition, since:
S/480,000/25 < S/120,000
Therefore, the answer is (a) First.
To know more about amount paid:
https://brainly.com/question/9554635
#SPJ4
Pls help me ill give 20 points
Answer:
62.85 units
Step-by-step explanation:
s= rΘ
s= 4*5π/3= 20π/3
the perimeter= 20π/3*3
= 20π
= 20*22/7
= 440/7=62.85
the following question has two parts first answer part A then answer part B
Isabella's mother has a garden with an area of 10 2/3 square feet she plants peas in 1/4 of the garden. calculate the area that was used for planting peas.
part B Isabella's mother sells the peas and gets 3 for each square foot so multiply your answer from part A by 3 to calculate how much money Isabella's mother made.
Answer: Part A:
If Isabella's mother has a garden with an area of 10 2/3 square feet, and she plants peas in 1/4 of the garden, we can calculate the area used for planting peas by multiplying the garden area by 1/4:
Area used for planting peas = (10 2/3 square feet) x (1/4) = (32/3) x (1/4) = 8/3 square feet
Therefore, the area used for planting peas is 8/3 square feet.
Part B:
If Isabella's mother sells the peas and gets 3 dollars for each square foot, we can calculate how much money she made by multiplying the area used for planting peas by 3:
Money made = (8/3 square feet) x (3 dollars/square foot) = 8 dollars
Therefore, Isabella's mother made 8 dollars by selling the peas she planted in her garden.
Calculate the area of the irregular polygon shown below:
Image of letter E with height of 12 and width of 7 and inside space of height of 5 and width of 6. All units are in inches.
(4 points)
a
24 square inches
b
44 square inches
c
54 square inches
d
84 square inches
As a result, the answer to the following question, Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches.
What is area?An area is the size of a surface area. The surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a form or flat layer. The area of an item is the entire amount of space occupied by its planar (2-D) surface or form. Using a pencil, draw a square on a sheet of paper. A two-dimensional character. The area of a form on paper is the amount of space it occupies. Assume that the square is made up of smaller unit squares.
Rectangle area = length x breadth = 12 x 7 = 84 square inches
The size of the rectangle that makes up the space inside the letter E must then be subtracted:
5 × 6 = 30 square inches is the area of the inner rectangle.
A tiny rectangle's area 5 x 1 = 5 square inches = 1 = length x width
A tiny rectangle's area 5 x 1 = 5 square inches = 2 = length x width
A tiny rectangle's area 2 x 3 = 6 square inches = 3 = length x width
5 + 5 + 6 = 16 square inches is the total area of little rectangles.
Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches
To know more about area visit:
https://brainly.com/question/13194650
#SPJ1
Given the function y = x2+ 5x − 6 , list the zeros of the function
Answer:
Step-by-step explanation:
First we sould factor out the function:
y=x^2+5x-6
y=(x+6)(x-1)
Note: if you multiply out the factored equation, you will get your original equation.
Now, find what we need to plug in to make it equal 0.
If we plug in -6, then the (x+6) part equals 0. Since we are multiplying by 0, the whole thing equals 0.
If we plug in 1, then the (x-1) part equals 0. Since we are alo multiplying by 0 here, the function comes out to 0.
This means that at x=-6 and x=1 the function comes out to 0.
on june 1st, 2020, the distribution of new covid-19 cases by county had a mean of 7.29 and a standard deviation of 110.87. a dedicated but naive cdc analyst decides to model this data using a normal distribution. in other words, letting x be the number of new covid-19 cases in a county, our analyst models the county-level new case counts as x ~ normal(7.29, 110.87). for the following questions, pretend you are the cdc analyst, modeling new case counts as normal(7.29, 110.87) question: orange county, ca had 178 new cases on june 1st. calculate a z-score for the new case count in orange county.
To calculate the z-score for the new case count in Orange County, we use the formula:
z = (x - μ) / σ
where x is the value we are calculating the z-score for, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
Plugging in the values given in the question, we get:
z = (178 - 7.29) / 110.87
z = 170.71 / 110.87
z = 1.54
So the z-score for the new case count in Orange County is 1.54. This means that the new case count in Orange County is 1.54 standard deviations above the mean of the distribution.
To know more about z-score refer here:
https://brainly.com/question/15016913
#SPJ11
The diameter of a circle is 25 m. Find its area to the nearest whole number.
Answer: 490.87 is the answer, rounded to a whole number is 491.
Step-by-step explanation: A≈490.87m²
Solving for A
A=1
4πd2=1
4·π·252≈490.87385m²
Not sure that's really an explanation but... Hope that makes since :)
Patricia opens a savings account with $1100 that earns 9% interest per year not compounded how much money will Patricia earn in 3 years.
Step-by-step explanation:
Her interest earned will be p r t
p = principal = amount of deposit = 1100 dollars
r = decimal interest rate = .09
t = time in years = 3
$ 1100 * .09 * 3 = $ 297 .
A teacher has a large container of blue, red, and green beads. She reports to the students that the proportion of blue beads in the container is 0.30. The students feel the proportion of blue beads is lower than 0.30. A student randomly selects 60 beads and finds that 12 of the beads are blue. The P-value for the test of the hypotheses, H 0: p = 0.30 and H alpha: p less-than 0.30, is 0.045. What is the correct conclusion given Alpha = 0.05?
Because the P-value is less than Alpha = 0.05, the student should reject H0.
Because the P-value is less than Alpha = 0.05, the student should fail to reject H0.
Because the P-value is greater than Alpha = 0.05, the student should reject H0.
Because the P-value is greater than Alpha = 0.05, the student should fail to reject H0.
answer is a
Answer:
Red I think maybe we should try hi friends I am new to this app
PLEASE HELP I WILL GIVE YOU ALL MY POINTS What is the volume of this figure?
144 in³
168 in³
288 in³
I don't know.
Answer:
144 in^3
Step-by-step explanation:
You need to separate the figure into the top and bottom rectangles
For the top, the volume = 12 x 4 x 1 = 48
For the bottom, the length is 12, the height is 5 - 1 = 4, the width is 2
so the volume is 12 x 4 x 2 = 96
The volume of the figure is 48 + 96 = 144 in^3
Are babies weight increases by 8% over a month from birth to 4. 5 kg what was the weight at birth
If babies weight increases by 8% over a month from birth to 4. 5 kg, the baby's weight at birth was approximately 4.17 kg.
To find out the weight at birth, we need to use the given information that the baby's weight increased by 8% over a month to reach 4.5 kg.
Let's start by setting up an equation. We can let x be the baby's weight at birth in kg. Then, we know that the baby's weight increased by 8% over a month, so the weight after one month would be:
x + 0.08x = 4.5 kg
Simplifying this equation by combining like terms, we get:
1.08x = 4.5 kg
To solve for x, we can divide both sides of the equation by 1.08:
x = 4.17 kg
To learn more about weight click on,
https://brainly.com/question/21788080
#SPJ4
Question 8 of 25
This question: 1 point(s) possible
An auto repair shop charged a customer $340 to repair a car. The bill listed $100 for parts and the remainder for labor. If the cost of labor is $40 per hour, how many hours of labor did it take to repair
he car?
OA. 5 hours
OB. 6 hours
OC. 7 hours
OD. 6.5 hours
Answer:
6
Step-by-step explanation:
To find the hours of labor it took to repair the car, we need to subtract the cost of parts from the total cost and then divide the result by the cost per hour of labor.
So, $340 - $100 = $240 was spent on labor.
$240 ÷ $40 per hour = 6 hours of labor.
Therefore, the answer is OB. 6 hours.
Can someone answer this question
Which describes literature during the Goryeo dynasty?
Responses
A) It was controlled by rulers that would not tolerate any religion except Confucianism.It was controlled by rulers that would not tolerate any religion except Confucianism.
B) It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.
C) It was mostly the domain of Chinese-born monks and scholars sent to Korea by the Tang dynasty.It was mostly the domain of Chinese-born monks and scholars sent to Korea by the Tang dynasty.
D) It contained very little poetry or drama but was focused on history, philosophy, and religious teachings.
What describes the literature during the Goryeo dynasty is: b. It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.
What is the Goryeo Dynasty?Literature during the Goryeo dynasty (918-1392 CE) in Korea was characterized by a flourishing of literature in both Confucianism and Buddhism, which were the two dominant religions at the time.
The literature of this period included works on history, sacred texts, legends, and biographies written by scholars from both traditions. Poetry and drama also became popular during this time.
Therefore, we can state that: b. It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.
Learn more about Goryeo Dynasty on:
https://brainly.com/question/26149012
#SPJ1
Create two sets of data with the following characteristics: -Each data set has 7 values, - The median of set 1 is greater than the median of set 2, - The IQRs of the data sets are the same. PLEASE HELP TY
The two sets of data are
Set 1: 5, 6, 7, 8, 9, 10, 20
Set 2: 1, 2, 3, 4, 5, 15, 16
Median of data:The median is a measure of central tendency in a data set that represents the middle value of the data when arranged in order.
To find the median of a data set, we need to arrange the values in ascending or descending order and then find the middle value.
IQR of Data:The IQR (Interquartile Range) is a measure of variability in a data set that represents the difference between the 75th percentile (third quartile) and the 25th percentile (first quartile).
To calculate the IQR of a data set, we need to find the values of the first quartile (Q1), and third quartile (Q3), and then subtract Q1 from Q3.
Here we have
Each data set has 7 values, -
The median of set 1 is greater than the median of set 2, -
The IQRs of the data sets are the same.
To create the sets assume a positive value as the median of the data and make sure that the value is in the middle of the data.
Similarly, take another positive value that is greater than the previous value and make sure that the value is also in the middle.
Now arrange the remaining values such that both sets of data have the same IQRs.
Here are two sets of data that meet the given characteristics:
Set 1: 5, 6, 7, 8, 9, 10, 20
Median: 8
IQR: 4 (Q3 = 9, Q1 = 5)
Set 2: 1, 2, 3, 4, 5, 15, 16
Median: 4
IQR: 4 (Q3 = 5, Q1 = 1)
Therefore,
The two sets of data are
Set 1: 5, 6, 7, 8, 9, 10, 20
Set 2: 1, 2, 3, 4, 5, 15, 16
Learn more about Median at
https://brainly.com/question/27773079
#SPJ1
Select the correct answer from the drop-down menu. An energy drink company claims that its product increases students' memory levels. To support its claims, the company issues advertisements claiming that 8 out of 10 people (chosen randomly from across the country) who tried their product reported improved memory. The missing component in this study is a . Reset Next
The missing cοmpοnent in this study is cοntrοl grοup
What is an experiment ?A methοd used in a cοntrοlled envirοnment tο find an unknοwn effect οr law, test οr establish a hypοthesis, οr prοvide an example οf an established law
In the scenariο described, individuals are chοsen at randοm tο participate in a new interventiοn, which appears tο be an example οf an experiment.
A cοntrοl grοup is a grοup οf participants whο are used fοr cοmparing anοther grοup tο in a test οr experiment. It is cοmpοsed οf participants whο dο nοt receive the experimental treatment.
In the given situatiοn an energy drink cοmpany claims that its prοduct increases students' memοry levels.
Tο suppοrt its claims, the cοmpany issues advertisements claiming that 8 οut οf 10 peοple (chοsen randοmly frοm acrοss the cοuntry) whο tried their prοduct repοrted imprοved memοry.
But they haven't cοmpοse a cοntrοl grοup tο cοmpare the results fοr test.
To know more about experiment from the link given below.
https://brainly.com/question/26117248
#SPJ1
Answer:
A. Control Group
Plato
Anthony has a sink that is shaped like a half sphere the sink has a volume of 660 Pi inch cubed one day his sink clogged he has to use one of the two cylindrical cups to scoop the water out of the sink the sink is completely full when Anthony begins scooping
A) one cup has the diameter of 5 in and a height of 8 in how many cups of water must Anthony scoop out of the sink with this cup empty round the number of scoops to the nearest whole number
B) one cup has a diameter of 10 inches and a height of 8 in how many cups of water must be scooped out of the sink with his cup to empty it round the number of scoops to the nearest whole number
!!Please I Need An Answer Quickly!!
A) Rounding to the nearest whole number, Anthony needs to scoop out 13 cups of water with this cup.
B) Rounding to the nearest whole number, Anthony needs to scoop out 3 cups of water with this cup.
The volume of the sink is given as 660 Pi inch cubed, which means the radius of the half-sphere sink is:
[tex]r = (3 \times 660 Pi / 4Pi)^{(1/3)} = 9 inches[/tex]
A) For the first cup with a diameter of 5 inches and a height of 8 inches, the volume of the cup is:
[tex]V = Pi \times r^2 \times h = Pi \times (2.5)^2 \times 8 = 50[/tex]Pi inch cubed
The number of scoops required to empty the sink can be found by dividing the volume of the sink by the volume of one scoop:
Number of scoops = 660 Pi / 50 Pi = 13.2
Rounding to the nearest whole number, Anthony needs to scoop out 13 cups of water with this cup.
B) For the second cup with a diameter of 10 inches and a height of 8 inches, the volume of the cup is:
[tex]V = Pi \times r^2 \times h = Pi \times (5)^2 \times 8 = 200[/tex] Pi inch cubed
The number of scoops required to empty the sink can be found by dividing the volume of the sink by the volume of one scoop:
Number of scoops = 660 Pi / 200 Pi = 3.3
Rounding to the nearest whole number, Anthony needs to scoop out 3 cups of water with this cup.
for such more question on whole number
https://brainly.com/question/9879870
#SPJ4
A circular drum has a radius of 4.2m and a height of 3.5m. How many full
bags of wheat can be emptied if the space required for one wheat bag is
5.39m³.
he volume of the drum can be calculated as follows:
Volume of drum = πr²h
= π(4.2m)²(3.5m)
≈ 246.33 m³
To find out how many full bags of wheat can be emptied into the drum, we need to divide the volume of the drum by the volume of one wheat bag:
Number of full bags of wheat = Volume of drum ÷ Volume of one bag
= 246.33 m³ ÷ 5.39 m³
≈ 45.72
Therefore, the circular drum can hold approximately 45 full bags of wheat.
Answer: 45 Full of bags.
Step-by-step explanation:
The volume of the drum can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
V = π(4.2m)^2(3.5m)
V ≈ 246.73 m³
To find out how many bags of wheat can be emptied into the drum, we need to divide the volume of the drum by the space required for one bag:
246.73 m³ ÷ 5.39 m³/bag ≈ 45.81 bags
Since we can't have a fraction of a bag, we need to round down to the nearest whole number:
Number of bags = 45
Therefore, 45 full bags of wheat can be emptied into the drum.
Erica made a scale drawing of her middle school. The scale she used was 1 inch : 5 feet. If the gym in the drawing is 24 inches by 34 inches, what is the area of the actual gym?(In square feet)
The area of the actual gym in the middle school is 20,400 square feet.
What is rectangle?
A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.
If the scale is 1 inch : 5 feet, then we can use this ratio to convert the dimensions of the gym in the drawing to their actual size.
The length of the gym in the actual middle school is:
34 inches x 5 feet/inch = 170 feet
The width of the gym in the actual middle school is:
24 inches x 5 feet/inch = 120 feet
The area of the gym in square feet is:
Area = length x width
Area = 170 feet x 120 feet
Area = 20,400 square feet
Therefore, the area of the actual gym in the middle school is 20,400 square feet.
To learn more about rectangle from the given link:
https://brainly.com/question/29123947
#SPJ1
Find the greatest common factor for the list of monomials. 63x^(2)y^(3)z,9x^(2)y^(3),90xy^(2)
Answer: is there a Pic it would help
Step-by-step explanation:
Atul gets a pocket money allowance of Rs. 120 per day. Thinking that this was rather less he asked his friends about their allowances and obtained the following data which includes his allowance also ( Amount I Rs. ) 120, 180, 100, 50, 250, 200,200,220, 150, 100,100,150,130,200,180, 100, 150, 100, 180, 150, 120, 150, 100, 150, 100, 120, 180, 200, 50. He presented this data to his father and asked for an increase in his allowance as he was getting less than average amount. His father, a statistician, countered pointing out that Atul's allowance was actually more than the average amount
Atul's father is wrong. The average amount is greater than Atul's allowance.
Is Atul's father right?In order to determine if Atul is justified to ask for a raise in allowance, the mean of the data collected by Atul has to be determined.
Mean is the average of a set of numbers. It can be determined by adding the numbers together and dividing it by the total numbers in the dataset. Mean is a measure of central tendency.
Mean = sum of numbers / total numbers
(120 + 180 + 100 + 50 + 250 + 200 + 200 + 220 + 150 + 100 + 100 + 150 + 130 + 200 + 180 + 100 + 150 + 100 + 180 + 150+ 120 + 150+ 100 + 150 + 100 + 120 + 180 + 200 + 50) / 30 = 139.33
To learn more about mean, please check: https://brainly.com/question/25842202
#SPJ1
A chef made 85 different meals. 34 people chose the same meal. What percent of his customers chose the same meal?
Answer: To find the percentage of customers who chose the same meal, we need to divide the number of people who chose the same meal by the total number of customers, and then multiply by 100 to convert to a percentage:
percentage = (34 / 85) x 100
percentage = 40
Therefore, 40% of the customers chose the same meal.
Step-by-step explanation:
Answer:
Its 40%
Step-by-step explanation: you divide 85 by 34 to get your answer
Determine the equation of the circle with center (7, -7) containing the point (11, -3).
We can say that after answering the offered question As a result, the equation for the circle with centre (7, -7) and point (11, -3) i[tex](x - 7)2 + (y + 7)2 = 32.[/tex]
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
Determine the radius:
The radius of the circle is the distance between the circle's centre (7, -7) and any point on it (11, -3).
We may calculate the distance using the distance formula:
[tex]r = \sqrt((11 - 7)^2 + (-3 - (-7))\\v^2)\\r = \sqrt(4^2 + 4^2)\\r = \sqrt(32) (32)[/tex]
In the standard form equation of a circle, substitute the centre and radius:
A circle with centre (h, k) and radius r has the following standard form equation:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
With h = 7, k = -7, and r = sqrt(32), we get:
[tex](x - 7)^2 + (y + 7)^2 = 32[/tex]
As a result, the equation for the circle with centre (7, -7) and point (11, -3) is[tex](x - 7)2 + (y + 7)2 = 32.[/tex]
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
SOMEBODY PLEASE HELP ME
slant height is 18ft base length is 40ft
Answer:
1440 ft²
Step-by-step explanation:
The roof is made up of 4 congruent triangles.
We first solve for the area of one of the triangles using the formula:
A = (1/2) · b · h
↓ plugging in given values
A = (1/2) · 40 ft · 18 ft
A = 20 ft · 18 ft
A = 360 ft²
Now, we can solve for the surface area of the entire roof by multiplying the area of one of the triangles by 4 (because there are 4 congruent triangles).
SA = 360 ft² · 4 = 1440 ft²
—
Note that we can solve for the area of the triangles using the formula {A = (1/2) · b · h} because the slant height of a pyramid is perpendicular to the side of the pyramid's base that it connects to, thereby making it the height of the triangle that is the pyramid's side.
—
A frustum is made by removing a small cone from the top of a large cone. In the diagram shown the heigh of the small cone is half the height of the large cone. Work out the curved surface area of the frustum.
The Curved surface area of the frustum is 60π.
Define frustumIn geometry, a frustum, is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid.
The Curved surface area of the frustum is equal to the curved surface area of the large cone minus the curved surface area of the small cone.
Solving the equationThe height of the large cone=√[tex]10^{2}[/tex]-[tex]8^{2}[/tex]
=√[tex]100-64[/tex]
=6cm
The height of small cone=6×(1/2)=3cm
(The little cone's height is equal to half that of the giant cone's height.)
The arc length of the small cone=10×1/2=5cm
The curved surface area of the frustum=π×8×10-π×r×5
=80π-5rπ
r=√[tex]5^{2}[/tex]-[tex]3^{2}[/tex]
=√25-9
=4cm
Hence, Curved surface area of the frustum is
= 80π-5×4×π
=80π-20π
=60π
To know more about cone, visit:
https://brainly.com/question/16394302
#SPJ9
PLEASE HELP ME! IT WAS DUE!
Answer:
one apple: 75 cents
one orange: 60 cents
Step-by-step explanation:
let x be price of one apple
let y be price of one orange
3x + 4y = 4.65
5x + 8y = 8.55
we can do elimination, substitution, or graphing.
this is elimination: (we're eliminating the x in this case to find y, and then use y to find x)
ORIGINAL EQUATIONS: (we're multiplying by 5 so we can eliminate x)
3x + 4y = 4.65
5x + 8y = 8.55
5(3x + 4y = 4.65) = 15x + 20y = 23.25
3(5x + 8y) = 8.55 = 15x + 24y = 25.65
(distribute, and then subtract to get one equation and eliminate x)
15x + 20y = 23.25
- 15x + 24y = 25.65
------------------------------
0 - 4y = - 2.4
so we got that, now we make it this: -4y = -2.4
divide both sides by -4.
-4y = -2.4
----- -----
-4 -4
y (orange variable) = 0.60
therefore, one orange cost 60 cents.
plug y (the 60 cents) back into one of the original equations (either works) and solve for x.
3x + 4y = 4.65
5x + 8y = 8.55
let's use this equation: 5x + 8y = 8.55
5x + 8(0.6) = 8.55
5x + 4.8 = 8.55
-4.8 -4.8
5x = 3.75
---- ------
5 5
x = 0.75
therefore, one apple cost 75 cents.
(also, there was an easier number to multiple the equations by)
3x + 4y = 4.65
5x + 8y = 8.55
We could have multiplied (3x + 4y = 4.65) with 2, distributing and bringing it to 6x + 8y = 9.30
Then subtract 6x + 8y = 9.30 from 5x + 8y = 8.55, and you would have solved and gotten x just fine, then plugged x back in to find y)
sorry this answer is so long...good luck :))
The fire department is having a BBQ fundraiser. The hot dogs costs $1.50 each and cans of soda cost 50.75 each. The department uses the algebraic expression 1.50x+0.75y to calcul customers' total expenses, a. What does the x variable represent? b. What does the y variable represent?
According to the algebraic expression 1.50x + 0.75y:
a) The x variable represents the number of hot dogs sold.b) The y variable represents the number of cans of soda sold. What is an algebraic expression?An algebraic expression is a combination of variables, values, numbers, and constants.
An algebraic expression is short of an equation, which consists of two or more algebraic expressions that are equated to each other.
The cost of hot dogs per unit = $1.50
The cost of cans of soda per unit = $0.75
Let the number of hot dogs bought = x
Let the number of cans of soda bought = y
Algebraic Expression:1.50x + 0.75y = Customer's total expenses
Thus, the variables x and y in the algebraic expression represent the number of units of each type of item sold during the BBQ fundraiser.
Learn more about algebraic expressions at https://brainly.com/question/395066.
#SPJ1