The equation representing the pool draining in slope-intercept form is y = -12x + 38000 and the time for the pool to fully drain is 3167 minutes.
What is a linear equation?It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.
The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.
As we know,
The standard form of the straight line is:
y = mx + b
The slope in this case is m, and the y-intercept is b.
From the data given:
y = -12x + 38000
Plug y = 0 to find how long it will take for the pool to fully drain:
0 = -12x + 38000
x = 3167 minutes
To fill it back up, the y-intercept is 0.
The slope is given M = 16
y = 16x
Now plug y = 38000 to find how long it will take for the pool to fill back up
38000 = 16x
x = 2375 minutes
Thus, the equation representing the pool draining in slope-intercept form is y = -12x + 38000 and the time for the pool to fully drain is 3167 minutes.
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The nth term of a sequence is 50-n2. Find the thurd term of the sequence.
The third term of the sequence is 41.
Given,
Tn = 50 - n²
Tn = 50 - (3)²
Tn = 50 - 6
Tn = 41
As the third term is required substitute the value in the main equation 50 - n² which gives T3 = 41.
As the third term is necessary, replace 50 - n² in the main equation, yielding T3 = 41.
Arithmetic Progression is a series of numbers in which the difference between consecutive terms is constant. One approach is to calculate the arithmetic mean. To do this, sum all the values and divide the sum by the number of values. For arithmetic sequences, use the expression a = a1 + (n1) d. where a is the term, a1 is the difference of the first term, and d is the difference of the subsequent term.
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17<9+X
O A. x> 8
OB. x > 26
O C. x < 26
O O
D. x < 8
Answer:
A
Step-by-step explanation:
17 < 9 + x ( subtract 9 from both sides )
8 < x , then
x > 8
1. Between which two whole numbers is
√12?
Convince Me!
2. Which of the two numbers is a better
estimate for √12? Explain.
The two whole numbers between which is √12 are 3 and 4.
What is an example of a whole number?
Any positive number that does not contain a fractional or decimal component is referred to as a whole number. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers, for instance, as a result. -3, 2.7, or 3 12 are examples of non-whole numbers.
The closest perfect squares near 12 are 16 and 9 which are the perfect squares of 4 and 3 respectively Therefore the root of 12 lies between 3 and 4.
i.e 3 < √12 < 4
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What is the value of this expression when m = 3 and n=−1?
−4(m−n)2
Answer:
-32
Step-by-step explanation:
m=3 , n=-1 ( given )
then, -4(m-n)2 = -4(3-(-1))2 = -32
Express in decimal notation 4.93 x 10^(3)
The decimal notation of 4.93 x 10³ will be 4930.00.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression is;
4.93 x 10³
Now, Solve for decimal notation as;
4.93 x 10³ = 4.93 x 10 x 10 x 10
= 49.3 x 10 x 10
= 493 x 10
= 4930.00
Thus, The decimal notation of 4.93 x 10³ will be 4930.00.
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a bus comes by every 14 minutes. the times from when a person arives at the busstop until the bus arrives follows a uniform distribution from 0 to 14 minutes. a person arrives at the bus stop at a randomly selected time. round to 4 decimal places where possible.
a) The mean of this distribution is 7 min
b) The standard deviation is 4.0414 min
a) The mean is the midpoint between the ends or 7 min
variance is (b-a)^2/12 or 196/12 or 16.3333 min
b) standard deviation is sqrt(V)= 4.0414 min
the complete question is
a bus comes by every 14 minutes. the times from when a person arives at the bus stop until the bus arrives follows a uniform distribution from 0 to 14 minutes. a person arrives at the bus stop at a randomly selected time. round to 4 decimal places where possible.
a) The mean of this distribution is
b) The standard deviation is
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Help with these 3 questions!!
Brainliest/30pts
Answer: 1.c 2.a 3.c
Step-by-step explanation:
Answer:
first picture
1 and 2 are congruent because they are a pair of corresponding angles
second picture
A = B
This is because they are alternate exterior angles and they equal the same thing
third picture
angle 5
it is also an alternate interior angle
If the two triangles shown below are similar
based on the given information, complete
the similarity statement, otherwise choose
the "Not Similar" button.
C
2 in
4 in
ABCA ~ A
A
8 in
B
G
H
16 in
Answer: Similar by SAS
Step-by-step explanation:
Note that [tex]\frac{AC}{AB}=\frac{JG}{HG}=\frac{1}{4}[/tex].
So, the triangles are similar by SAS (since the congruent angle is included between the proportional sides).
expand and simplify 7(x-2)-2(x-3)
Answer:
5x-8
Step-by-step explanation:
7x-14-2x+6
-14+6=-8
7x-2x=5x
HELP ASAP (100 POINTS)
The equation for the line of best fit for change in temperature, y, to amount of snow, s, is given by ŷ = − 2.6s + 1.1. On Friday, the observed amount of snow was 1.3 inches and the temperature change was 1.2 degrees. Find and interpret the residual.
1.08; The line of best fit underpredicts the temperature change.
−1.08; The line of best fit overpredicts the temperature change.
−3.48; The line of best fit overpredicts the temperature change.
3.48; The line of best fit underpredicts the temperature change.
Answer:
3.48; The line of best fit underpredicts the temperature change.Step-by-step explanation:
ŷ = − 2.6s + 1.1.
residual value = Measured value - Predicted value
Measured value = actual y-coordinate of the point, y
Predicted value = value of y from the equation, y1
residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)
residual value = y - y1
For s = 1.3
y = 1.2
value of y from the equation, y1:
y1 = -2.6*(1.3) + 1.1
y1 = -3.38 + 1.1
y1 = -2.28
residual value = y - y1
residual value = 1.2 - -2.28
residual value = 1.2 + 2.28
residual value = 3.48Interpretation:
Since the predicted value is far less than the observed value, the line of best fit underpredicts the temperature change.
Answer:
3.48; The line of best fit underpredicts the temperature change.
Step-by-step explanation:
i took the test :)
between 9 am and 6:36 am, the water in a swimming pool decreased by 8/25 in. assuming that the water level decreased at a constant rate, how much did the water level drop each hour
Answer: 2/15 in/hour
Step-by-step explanation:
[tex]\displaystyle\\1)\ 6:36=\\\\6\frac{36}{60}=\\\\6\frac{3(12)}{5(12)}=\\\\6\frac{3}{5}=\\\\\frac{6*5+3}{5}=\\\\\frac{30+3}{5}=\\\\\frac{33}{5} \ hours[/tex]
[tex]\displaystyle\\2)\ 9-\frac{33}{5} =\\\\\frac{9(5)-33}{5}=\\\\\frac{45-33}{5} =\\\\\frac{12}{5}\ hours[/tex]
[tex]\displaystyle\\3)\ \frac{8}{25}:\frac{12}{5} =\\\\\frac{8}{25}*\frac{5}{12} =\\\\\frac{8(5)}{25(12)} =\\\\\frac{2*4*5}{5*5*4*3} =\\\\\frac{2}{5*3} =\\\\\frac{2}{15}\ in/hour[/tex]
Type the missing number to complete the proportion. 80 minutes for 22 songs minutes for 11 songs Submit
80 : 22 :: x : 11
x = (11 x 80) / 22
x = 880/22
x = 40
The missing number is 40
In September, Liberty Elementary School collected 32,537 cans for a fundraiser. In October, they collected 207,492 cans.
a. About how many cans were collected during September and October? Round to the nearest thousand.
b. Which of these estimates will produce a more accurate answer rounding to the nearest thousand or rounding to the nearest ten thousand?
Rounding off to nearest ten thousand gives the most accurate answer as 240,000 cans.
Given that, the number of cans collected during September = 32,537 and the number of cans collected during October = 207,492.
What is rounding off numbers?Rounding numbers means adjusting the digits (up or down) to make rough calculations easier. The result will be an estimated answer rather than a precise one.
a) Now, the number of cans were collected during September and October = 32537+207492 = 240,029
To the nearest thousand is 240,000
b) Rounding 32,537 to the nearest thousand is 32000 and rounding 207,492 to the nearest thousand is 207,000
Sum = 32000+207000 = 239,000
Rounding 32,537 to the nearest ten thousand is 30000 and rounding 207,492 to the nearest ten thousand is 210,000
Sum = 30000+210,000 = 240,000
Therefore, rounding off to nearest ten thousand gives the most accurate answer as 240,000 cans.
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One endpoint of a line segment is (10,-1). The point (7,-2) i s one-third of the way from that endpoint to the other endpoint. Find the other endpoint
The coordinates of the other endpoint of the Line segment is (-2,-5).
If M(x.y) divides the line formed by two points A(a,b) and B(c,d) into a ratio m:n. Then the coordinates of the point M can be found out by using the formula,
x = (mc + na)/(m+n)
y = (md + nb)/(m+n)
This above mentioned formula is known as The section Formula.
The one of the End point of the line is (10,-1) and the point (7,-2) is dividing the line in the ratio of 1:3.
Let us assume the other end point to be (a,b).
Now, applying Section Formula,
7 = [(1)(a)+(3)(10)]/4 and
-2 = [(1)(b)+(3)(-1)]/4
Further solving,
a = -2 and
b = -5
So, the coordinates of the endpoint is (-2,-5).
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[6-34] the manufacturer of a new fiberglass tire claims that its average life will be at least 40,000 miles. to verify this claim, sample of 15 tires are tested. sample mean was 41.1 (in 1000 miles), and sample standard deviation was 2.50. assuming the measurements were random sample from a normal distribution, calculate 95% one-sided confidence interval for true mean tire life. choose lower-bound or upper-bound, whichever is appropriate. (round to 2 decimals.)
The assumption that the sample means follow a roughly normal distribution is used to calculate a confidence interval for a population mean with a known standard deviation.
A confidence interval gives a range of values that will probably include the actual mean. For example, let's say that our sample has a mean of x=10 and we have generated the 90% confidence interval (5, 15), with EBM = 5. For instance, we might not be able to speak to everyone in Colorado if we wanted to find out the typical age of Colorado residents who enjoy bananas. However, we could conduct in-depth interviews with a representative sample and make an educated guess or calculation to provide us with a range of ages.
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Which value does NOT represent the shaded portion of the model shown? A 3/5 B. 0.3 C. 60% D. 0.6
Answer:
B
Step-by-step explanation:
All the rest = 3/5, 3 shaded out of 5
:]
use the 68-95-99.7 rule to find the proportion of runners whose body weight is between 48.7 and 67.9 kg.
Based on the complete question, the Normal Distribution Graph will resemble the one in the figure attached.
Also, note that using the 68-95-99.7 rule, the proportion of runners between 48.7 and 67.9 kg is 0.8385.
What is the 68-95-99.7 rule?
The 68-95-99.7 rule, also known as the empirical rule, is a statistician's shorthand for remembering the percentage of values in a normal distribution that fits within an interval estimate: 68%, 95%, and 99.7% of the variables lie within one, two, and three standard deviations of the mean, correspondingly.
To compute the proportion of runners whose body weight is between 48.7 and 67.9 kg with the help of the 68-95-99.7 rule:
We know given that:
The mean = 63.1 and
the standard deviation (SD) = 4.8.
Where the weight is 67.9kg, we know that the distance between this and the mean is 4.8, that is;
67.9 - mean
= 67.9 - 63.1
= 4.8 [1*SD]
In the same way,
48.7 corresponds to 48.7-63.1 = -14.4 [ -3*SD]
Hence, based on the rule,
the probability of the weight occurring between -1*SD and 1*SD = 68%; and the probability of the weight occurring between -3*SD and 3*SD = 99.7%.Therefore, the probability of the weight occurring between -3*SD and 1*SD = (99.7+68)/2= 83.85%
= 0.8385.
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Full Question:
A study of elite distance runners found a mean body weight of 63.1 Kilograms (kg), with a standard deviation of 4.8kg.
Assuming the distribution of weights is approximately normal, make a sketch of the weight distribution (like the one below) with a horizontal axis marked in kilograms.Use the 68-95-99.7 rule to find the proportion of runners whose body weight is between 48.7 and 67.9 kgJaime, ralph, marvin and victor decided to put up a small business. their initial investment is in the ratio of 8:3:12:2 respectively and marvin's had ivested php 240,000. interms of profit they have decided to split them base on the ratio of their investment. in the first three months of their company made a total of php 150,000 profit. based on marvin's initial deposit. how much did victor invested?
Answer:
php 40,000
Step-by-step explanation:
In the ratio, Marvin corresponds to 12 and Victor to 2.
Marvin invested php 240,000.
His part of the ratio is 12.
240,000/12 = 20,000
Victor's part in the ratio is 2.
Victor's investment amount is 2 × php 20,000 = php 40,000
46 over48 Are the ratios and proportional? 69 over 84 (1 point) A Yes, because they both reduce to the equivalent fraction 1 3 B Yes, because the cross products 46 84 and 48.69 are equal. C No, because one has a quotient of 06 and the other has a quotient of 0.571428- 2 D No, because one ratio reduces to 3 3 7 2 and the other reduces to
The ratios aren't proportional as D. No, because one ratio reduces to different values.
What is a ratio?A ratio is simply used to show the comparison between the numbers that are illustrated in a data.
In this case, the fractions that are given include 46/48 and 69/84.
To have an equivalent ratio, it's important to have the numerator and the denominator divided by the same number.
In this case, this isn't possible with 46/48 and 69/84.
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Match each problem to its solution.32672.72671.7216Jeff wants to buy a new guitar that costs$1,701.04. Currently, he has 51,029.32How many more dollars does he need tobuy the guitar?Rose walks 3.2 miles every day. How manymiles will she have walked in 5 days?Christie was on a road trip. She traveled320.95 miles on day one, 231.45 miles onday two, and 120.32 miles on day three.How many miles did she travel duringher three-day trip?Hugh drove 774.4 miles. His car averaged24.2 miles per gallon of gas. How manygallons of gas did the car use?No
Rose walks 3.2 miles every day. How many miles will she have walked in 5 days?
3.2*5 = 16 miles
Christie was on a road trip. She travelled 320.95 miles on day one, 231.45 miles on day two, and 120.32 miles on day three. How many miles did she travel during her three-day trip?
320.95 + 231.45 + 120.32 = 672.72 miles
Hugh drove 774.4 miles. His car averaged 24.2 miles per gallon of gas. How many gallons of gas did the car use?
774.4/24.2 = 32 gallons
3(4v - 6) - 4( v + 6) simplify use distributive property
Answer:
8v - 42
Step-by-step explanation:
Simplify:Distributive property: a* (b + c) = (a*b) + (a*c)
3(4v - 6) - 4(v + 6) = (3*4v) + (3*(-6) ) + (-4*v + (-4)*6) )
= 12v - 18 - 4v - 24
= 12v - 4v - 18 - 24
Combine like terms [ 12v & (-4v) ] and combine constants [ (-18) & (-24)]
= 8v - 42
how to simplify -7 ( 3x - 7y) ?
9+x=11 what is the value of x?
Answer: the answer to that problem is
X=2
What percentage of this shape is shaded?
Answer:
Answer:
Step-by-step explanation:
There are 9 squares filled halfway, and 5 squares filled completely.
9 x 0.5 = 4.5
4.5 + 5 = 9.5
There are 25 squares in the shape.
9.5 / 25 = 0.38
38% of the square is shaded.
If x and y are in direct proportion and y is 56 when x is 7, find y when x is 9
The variable y has a value of 72 when x equals 9
How to determine the value of y from xThe variation statement is given as
x and y are in direct proportion
This means that
y = kx
Where k represents the constant of variation
Using the values given from the question, we have
(x, y) = (7, 56)
This gives
56 = 7k
Divide both sides by 7
k = 8
So, we have
y = 8k
The value of y when x = 9 is calculated as
y = 8 * 9
Evaluate the products
y = 72
Hence, the value of y is 72
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What is the probability that the sample proportion is greater than .43?
Simply put, probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.
Calculate probability ?
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.Probability and odds are two distinct ideas.Odds are calculated by dividing the likelihood of an event by the likelihood that it won't. Theoretical Probability is one of three main categories of probability.Scientific Probability.Probability axiomatically. Sampling is frequently used to calculate the percentage of a population that possesses a particular attribute, such as the percentage of all defective goods that come off an assembly line or the percentage of all customers who enter a store and make a purchase before leaving.The proportions of the population and sample are represented by the letters p and p, respectively.
Therefore,
p = 0.43
if, in fact, 43% of shoppers make a purchase before leaving a store;
p = 78/200
= 0.39
if, in a sample of 200 shoppers, 78 make a purchase.
The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.
It will be represented as a random variable by the letter P.
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5/7 times 44.4
Two answers
Answer:
2x44/7
Step-by-step explanation:
Answer:
Step-by-step explanation:
well it very confusing to some but,...31.7142857143 and i don't know the other one :) ;).
The width of a desk is 25 inches, or 63.5 centimeters. If a measurement in inches varies directly with a measurement in centimeters, what is the length, in centimeters, of a notebook that is 11 inches long? Round your answer to the nearest hundredth, if necessary.
2.54 centimeters
4.33 centimeters
27.94 centimeters
47.63 centimeters
The notebook's length in centimeters is 27.94 cm.
Since we are provided that
The desk's width is 25 inches.
Convert into cm.
There is a stated measurement of 25 inches = 63.5 cm.
As previously stated, a measurement in inches differs directly from a measurement in centimeters.
As a result, we have said that
If the notebook's length is 11 inches
Let 'x' be the length of the notebook in cm.
As a result of the question,
[tex]\frac{25}{63.5} = \frac{11}{x}[/tex]
[tex]x=\frac{698.5}{25}[/tex]
x = 27.94 cm
Hence the length of note book is 27.84 cm.
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Allison’s family spent $38.78 on school supplies. If Allison paid 1/4 of the bill, how much did she pay?
Answer:$9.695
Step-by-step explanation:
1/4 is 0.25 so this means Allison is paying 25% of the bill. Then all you have to do is times 38.78 with 0.25 and you get $9.695 or $9.70.
Answer:
$9.70
Step-by-step explanation:
You can do this question several way on a calculator:
1/4 × 38.78
OR
.25 × 38.78
OR (I like this one)
38.78 ÷ 4
All these calculations will give you the result 9.695
Since this is a real-world money problem, we would round this number to 9.70.
Allison paid $9.70.
You have saved some money to purchase five different songs to download to your portable music device. Solve an inequality that represents the prices you can pay for each song if you have saved no more than 20 dollars.
If you have saved some money to purchase five different songs to download to your portable music device. The inequality that represents the prices you can pay for each song if you have saved no more than 20 dollars is : 5 x ≤ 20.
InequalityGiven:
Numbers of different songs to download = 5
Cost = $20
Hence,
The inequality is ; 5 x ≤ 20
Now let solve the inequality
5 x ≤ 20
x = 20 /5
x = 4
So,
= x ≤ 4
Therefore the inequality is 5 x ≤ 20.
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