The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.
What is the capacity?Capacity refers to the product of the length, width, and height of a three-dimensional object or space.
The capacity of an object means the same as its volume.
Olympic-size swimming pools have the following standard dimensions:
Length = 50 m
Width = 25 m
Height = 2 m
Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)
= 660,000 gallons (2,500 x 1,000 ÷ 3.785)
An interval estimate shows the lower and upper limits.
6 x 105 gallons = 630 gallons
Thus, the capacity of the swimming pool is Option B.
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Question Completion with Answer Options:A. 100 gallons to 500 gallons
B. 500 gallons to 1,000 gallons
C. 1,000 gallons to 1,500 gallons
D. 1,500 gallons to 2,000 gallons
Use the diagram to complete the statement.
The value of the side CB in the right angled triangle is found as 4√2 units.
Describe the Pythagorean theorem?The Pythagoras theorem, commonly known as the Pythagorean theorem, says that if a triangle has a right angle (90 degrees), the square of the hypotenuse equals equal to the sum of a squares of the opposite two sides.It describes the connection between the three sides of such a right-angled triangle.For the given question,
The diagram is given;
AB = 7 units.
AG = 3 units.
GB = 7 - 3 = 4 units.
GC = 4 units.
In right angled triangle GCB, apply Pythagorean theorem.
CB² = GB² + GC²
CB² = 4² + 4²
CB² = 2(4)²
Taking square root both side.
CB = 4√2
Thus, the value of the side CB in the right angled triangle is found as 4√2 units.
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What is the equivalent equation to the given equation?
x = x² - 20
The equivalent equation to the given equation i.e, x = x² - 20 is x² - x - 20 = 0
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
The given expression is,
x = x² - 20
We have to make the equation in quadratic form i.e, ax² + bx + c = 0
so, first take x to the right side
0 = x² - 20 - x
Now swap the equation,
x² - 20 - x = 0
put 'x' term in middle and constant term at last like this,
x² - x - 20 = 0
Hence, The equivalent equation to the given equation i.e, x = x² - 20 is x² - x - 20 = 0
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How does knowing the x-intercepts and the vertex of a
function help you graph a quadratic function?
A graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
With the help of the vertex and the x-intercept, the equation of the parabola can be formed which helps to graph a quadratic function because the equation of the parabola resembles the quadratic function,
Thus, a graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.
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Find the value of n(AnB) if
n(A)=5 n(B)=7 and n(AUB)= 10
what is n(AnB)=?
PLEASE HELP
By using the concept of set operation, the result obtained is
[tex]n(A \cap B) = 2[/tex]
What is a set?
Set is a well defined collection of distinct objects. The members of a set are called elements of a set. Set can be empty as well as non empty.
Set can be finite as well as infinite.
The number of elements inside a set is known as cardinal number of the set
Operations on set are union, intersection, set difference and symmetric difference
Concept of set operation has been used here
n(A)=5 n(B)=7 and n(AUB)= 10
[tex]n(A \cap B) = n(A) + n(B) - n(A \cup B)[/tex]
[tex]n (A \cap B) = 5 + 7 -10\\n(A \cap B ) =2[/tex]
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The sum of two numbers is 130 and their difference is 34 Let x be the first number and y be the second
number Set up a system of equations and use the elimination method to find the numbers. You must
show your work
10. A theater sold 800 tickets for Friday night's performance, One child ticket costs $4.50 and one adult
ticket costs $6.00. The total amount collected was $4.500. How many of each type of ticket were sold?
11. The postal service offers flat-rate shipping for priority mail in special boxes. Malia shipped 4 small
boxes and 2 medium boxes, which cost her $54 to ship. Meanwhile, Stephen shipped 1 small box and
2 medium boxes, and paid $33. How much does it cost to ship these two sizes of boxes?
Step-by-step explanation:
9)=
By the question:-
x + y = 130-i
x - y = 34-ii
Now,
Add i and ii,
x + y + x -y = 164
or, 2x = 164
so, x = 82
Now,
x -y = 34
or, 82 - y = 34
so, y = 48
The numbers are 82 and 48.
10) =
Let adults ticket be x and childs ticket be y.
x + y = 800
x = 800 - y - eqn i
4.5x + 6y = 4500
Substituting x's value from eqn i,
4.5(800-y) + 6y = 4500
or, 3600 - 4.5y + 6y = 4500
or, 1.5y = 900
so, y = 600
Now,
x + y = 800
or, x + 600 = 800
so, x = 200
Hence, 600 adult tickets were sold and 200 child tickets were sold.
11)=
Let cost of one small box be x and one medium box be y.
So,
4x + 2y = 54-eqn i
x + 2y = 33-eqn ii
subtracting eqn i from ii,
x + 2y - 4x - 2y = - 21
or, -3x = - 21
so, x = 7
Now,
x + 2y = 33
or, 2y = 33 - 7
or, y = 26/2
so, y = 13
So, cost of one small box is $7 and medium box is $13.
Use the product-to-sum identities to rewrite the following expression as a sum or difference.
2sin(2x)sin(2x)
The sum form of the trigonometric function 2 · sin 2x · sin 2x by product-to-sum formula is 1 - cos 4x.
How to transform a product of trigonometric functions into a sum of trigonometric functions
Herein we find the definition of a trigonometric function defined as a product of trigonometric function, this can be transformed into a sum of trigonometric functions by means of the following product-to-sum formula:
sin α · sin β = [cos (α - β) - cos (α + β)] / 2
First, write the trigonometric function defined in the statement:
2 · sin 2x · sin 2x
Second, use the product-to-sum formula by considering α = β = 2 · x:
2 · [[cos (2x - 2x) - cos (2x + 2x)] / 2]
cos 0 - cos 4x
1 - cos 4x
Third, write the resulting expression:
2 · sin 2x · sin 2x = 1 - cos 4x
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Luis has $80 in his checking account. He makes a deposit of $100, and the write a check for $40
Answer: 140 is the answer
Step-by-step explanation: Luis adds 100 to his account so which makes the account balance 180 and then writes a check so he takes 40 out of his account which means he has 140 left in his account
Joey has 80 pens and 30 of them are red. What percent are red?
Answer:
Step-by-step explanation:
Which graph represents the function f(x) = –|x + 3|?
Answer:
The answer would be A. (Not sure if its A B C or D question but I will have picture below)
Step-by-step explanation:
Hope this helps you! :))
Last Friday, Kira and Marcy got dinner at Seaside Sushi restaurant. Kira ordered 2 pieces of tuna and 5 pieces of crab. Marcy ordered 3 pieces of tuna and 6 pieces of crab. Did Kira and Marcy order the same ratio of tuna pieces to crab pieces?
Answer:
no
Step-by-step explanation:
because Kira ordered 5 pieces of crab while Marcy has ordered 6 pieces of crab
State whether the following variables have a positive correlation, negative correlation, or no correlation.
3.)
(a.)Height of a person and how often he or she attends religious services. __________________________________
(b.)Average property tax in a school district and salary of teachers __________________________
(c.)Weight of a person and shoe size. ____________________________
The types of correlation seen between positive correlation, negative correlation, or no correlation, in the variables is:
a. Height of a person and how often he or she attends religious services. - No correlation (b.)Average property tax in a school district and salary of teachers - Positive correlation (c.)Weight of a person and shoe size. - Positive correlation What is the correlation between property taxes and teacher salaries?One of the main sources of funding for school districts is the property tax charged. This means that increased property taxes will lead to more money being available for teacher salaries which might then increase. There is therefore a positive correlation between the two.
The same is true for the weight of a person and shoe size. This is because the heavier a person is, the larger their shoe size according to research.
There is however no correlation between the height of a person and their attendance of religious services.
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There are 4 squares and 16 triangles. What is the simplest ratio of squares to
triangles?
Answer:
1 : 4
Step-by-step explanation:
There are 4 squares and 16 triangles.
That is,
Squares : Triangles
4 : 16
To write it in its simplest ratio, divide both by 4.
Squares : Triangles
1 : 4
If the quotient is 0 , what is the dividend?
Answer: 0
Step-by-step explanation:
If the dividend and the divisor are the same, the quotient is always 1. If the dividend is the, then the quotient would always be 0. A division equation with 0 dividend and 0 divisor is not valid.
Answer: All real numbers
Step-by-step explanation: Anything that's being divided by 0, is always going to be 0. For example, 0/7 is always 0.
Mrs. Boyer is buying folding chairs that are on sale for $8. She has $56. Which inequality
can be solved to show the number of chairs c Mrs. Smith can buy?
a. 8c ≤ 56
b.8 >56
c. 56c<58
d. 56c>28
An inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56
In this question we have been given Mrs. Boyer is buying folding chairs that are on sale for $8.
She has $56
We need to find an inequality that can be solved to show the number of chairs c Mrs. Smith can buy.
A price of one chair is $8
So, the price of 'c' number of chairs would be 8c
But she has $56
So, to find the number of chairs she can buy, we need to divide 56 by 8
We can write is as 8c = 56
⇒ c = 7
But she might buy less that 7 chairs.
So, we write above relation in inequality form as,
8c ≤ 56
Therefore, an inequality that can be solved to show the number of chairs c Mrs. Smith can buy 8c ≤ 56
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332x39 how do you work it out
Alma ran a marathon. The graph shows the distance she ran during the marathon. Use the drop-down menus to complete the statements based on the graph.
From the proportional relationship graphed, it is found that:
The labeled point means that in 2 hours she ran 16 miles.In 1 hour, Alma ran 8 miles.Her distance changed at a unit rate of 8 miles per hour, so Alma's speed was of 8 miles per hour.If Alma ran faster, the slope of the graph would be greater.What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0, meaning that the relationship passes through the origin.
When the two variables x and y are direct proportional, the output variable y is obtained multiplying the input variable x by the constant of proportionality k, according to the rule presented follows:
y = kx.
From point (2,16) in this problem, the constant is given as follows:
k = 16/2 = 8.
Hence the equation is:
y = 8x.
Meaning that her rate is of:
8 miles per hour.
If she ran faster, the slope = constant would increase, as it represents the velocity.
Missing InformationThe problem is given by the image at the end of the answer.
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find quotient of 5 divided by 3/10
The quotient of 5 divided by 3/10 is equal to 50/3
How to divide by a fraction?When we want to divide by a fraction, we just need to replace that division by the product with the inverse of the fraction.
So, if we want to divide A by the fraction (b/c), then we can write:
A÷(b/c)
That will be equal to A*(c/b), so:
A÷(b/c) = A*(c/b)
Here we want to divide 5 by 3/10, then we need to solve:
5÷(3/10)
Using the above rule we will get:
5÷(3/10) = 5*(10/3) = 50/3
That is the quotient.
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Estimate 17.140 - 03.179 by first rounding each number to the nearest tenth.
Answer: 13.9
Step-by-step explanation:
17.140 rounded to the nearest tenth is 17.1
03.179 rounded to the nearest tenth is 3.2
17.1 - 3.2 = 13.9
what is -3 > -2x + 7 ?
1 A father is three times as old as his daughter. If the father is 31 years older than his daughter, what are their ages?
father age 46.5
daughter age 15.5
46.5 - 15.5 = 31
Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger, the result is four more than the smaller. Which equation below could be used to find the smaller number?
(1) 2x-3(x+1)=x+4
(2) 3(x+1)-2x = x+4
(3) 2x-3(x+2) = x+4
(4) 3(x+2)-2x = x+4
Answer:
(4)
Step-by-step explanation:
Let's make the smaller number equal to x. Since they are consecutive odd numbers, the larger number is x+2.
Twice the smaller number is 2x. Three times the larger number is 3(x+2). If twice the smaller is subtracted from three times the larger, then the expression should be: 3(x+2) - 2x
Then, since the result of this is four more than the smaller, this expression is x+4.
Finally, we put it all together, so we get: 3(x+2) - 2x = x + 4. Option 4 is our correct answer.
Hence, the option (4) is correct.
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger, the result is four more than the smaller.
Let us assume the smaller number is [tex]x[/tex].
The larger number is [tex](x+2)[/tex].
Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger than it is
[tex]3(x+2)-2x[/tex]
So, the result is four more than the smaller.
i.e., [tex]3(x+2)-2x=x+4[/tex]
Hence, the option (4) is correct.
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Mark earns a salary of £28000 per annum. At the end of the on increase first year he is given he is of 3%.. At end of the second given an increase of 2.5%. Work out Mark's salary at the end of the two years.
Answer:
£27839
Step-by-step explanation:
O×M=N (original x multiplier = original value)
£28000×0.97%=£27160< 1st year decrease
£27160x1.025=£27839<2nd year increase
a- 10 units
b-12.0 units
c-11.4 units
d-13.4 units
Using the distance formula, the distance between the point is √130.
In the given question we have to find the distance between given point in the graph.
From the graph the given points are (4,4) and (-3, -5).
The formula for the distance between point is
Distance = √{x(2)-x(1)}^2+{y(2)-y(1)}^2
From the given points; x(1)=4, y(1)=4, x(2)= -3 and y(2)= -5.
Now putting the value:
Distance = √{-3-4}^2+{-5-4}^2
Distance = √{-7}^2+{-9}^2
Distance = √49+81
Distance = √130
The distance between the point is √130.
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Suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as its length and jointly as its width and the square of its height. Suppose also that a beam 5 inches wide, 2 inches high, and 10 feet long can support a maximum of 8 tons. What is the maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long?
The maximum weight that could be supported by a beam that is 6 inches wide, 2 inches high, and 24 feet long is 3.33.
How to find the maximum weight ?G = C×(w×h²/l)
Where,
C = constant
C = G×l/(w²h²)
Weight (w) = 6 in
Height (h) = 2 in
Length (l)= 10 ft
Maximum ton (G) = 8 t
C = 8×10/(6×2²)
C = 80/24
C = 10/3
G = (10/3)×(w×h²/l)
So, Maximum weight
G = (10/3)×(6×2²/24)
G = 10/3 t
G = 3.33 tones
The maximum weight is 3.33 tones.
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It takes an older computer 3 times as long to send out a company's email as it does a newer computer. Working together, it takes the two computers 15 minutes to send out the email. How long will it take the older computer to send out the email on its own?
60 minutes will be taken by the older computer to send out the email on its own.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
one computer takes x minutes and the other takes 3x minutes
in 1 minute, they send (1/x) and (1/3x) of the total message
together, (15/x)+(15/3x)=1, the full message
multiply by 3x to clear fractions
45+15=3x
60=3x
Divide both sides by 3
20=x
So for older computer 60 minutes it take to send out the email on its own.
Hence, 60 minutes will be taken by the older computer to send out the email on its own.
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Write a quadratic function f whose zeros are 7 and -5.
Answer:
f(x) = x² -2x -35
Step-by-step explanation:
You want a quadratic function that has zeros 7 and -5.
FactorsEach zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).
f(x) = (x -7)(x +5)
f(x) = x² -2x -35
__
Additional comment
You may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.
sum: 7-5 = 2
product: (7)(-5) = -35
quadratic: f(x) = x² -2x -35
Evaluate the expression when x =-4
Answer:
22. 2 (-4) = -8
23. (2(-4) + 11) = (-8 + 11) = 3
24. -3 (5 (-4) = -3 (-20) = 60
Answer:
22. 8
23. 3
24. -60
Step-by-step explanation:
You want the values of the given absolute value expressions when x = -4.
23. 2|x|The absolute value function changes the sign to positive, if it isn't already.
2|-4| = 2(4) = 8
24. |2x +11||2(-4) +11| = |-8 +11| = |3| = 3
25. -3|5x|-3|5(-4)| = -3|-20| = -3(20) = -60
Write a coordinate rule for the dilation.
Answer: 584390
Step-by-step explanation: the r4u819
add w and the sum of 9 and 4
The addition of w, 9 and 4 is (w+13).
According to the question,
We have the following information:
We need to add w, 9 and 4.
We already know that a variable can only be added or subtracted from the terms having the same variables. For example, 8x can only be added to 5x but not 5y.
So, in this case, w is the variable and it can not be added to any other term because the other two are whole numbers.
Now, the whole numbers can be easily added.
So, we have the following expression:
w+9+4
w+13
Hence, the addition of w, 9 and 4 is (w+13).
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Graph g(x) = -2x - 3.
The graph of the function g(x) = -2x - 3 is attached below.
Graph:
Graph refers a diagram that represents the variation of a variable in comparison with that of one or more other variables.
Given,
Here we have the function g(x) = -2x - 3
Now, we need to plot the graph of the function.
In order to plot the graph for the given function,
First we have to take some sample values for the given function and then apply it on the given function to generate the table to plot the graph.
Now, we have to take -2, -1, 0, 1, 2 are the samples value for x.
Then we get the value of the function as,
x = -2 => g(-2) = -2(-2) - 3 = 4 - 3 = 1
x = -1 => g(-1) = -2(-1) - 3 = 2 - 3 = -1
x = 0 => g(0) = -2(0) - 3 = 0 - 3 = -3
x = 1 => g(-2) = -2(1) - 3 = -2 - 3 = -5
x = 2 => g(2) = -2(2) - 3 = -4 - 3 = -7
Now, we can get the table like the below
Now, we have to plot the graph through this table, then we get the graph like the following.
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