Answer:
45,489.6 pounds!
Step-by-step explanation:
To solve this problem, first we need to find the volume of the pool.
We know that the dimensions of the pool are:
Width = 9ft
Length = 18ft
Height = 54in = 4.5 ft
So the volume of the pool is:
Volume = Width x Length x Height = 9ftx18ftx4.5ft = 729ft^3
We know that one cubic foot of water weights about 62.4 pounds. To fill the pool, we will need 729ft^3 of water.
So the weight of the water is:
Weight = 729ft^3 x 62.4 pounds/ft = 45,489.6 pounds!
Need help ASAP math
Answer:
C
Step-by-step explanation:
We know it's direct variation using the direct variation equation.
[tex]y=kx[/tex]
Where k is the constant.
Since 7 times x is the y values, [tex]k=7[/tex]
Now we can substitute 7 into k of the direct variation equation.
[tex]y=7x[/tex]
What is equivalent to (81m^6)^1/2
Answer:
[tex]\large\boxed{(81m^6)^\frac{1}{2}=9m^3}[/tex]
Step-by-step explanation:
[tex]81=9^2\\\\m^6=m^{3\cdot2}=(m^3)^2\qquad\text{used}\ (a^n)^m=a^{nm}\\\\\left(81m^6\right)^\frac{1}{2}=\bigg(9^2\left(m^3\right)^2\bigg)^\frac{1}{2}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\left(9^2\right)^\frac{1}{2}\bigg(\left(m^3\right)^2\bigg)^\frac{1}{2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=9^{2\cdot\frac{1}{2}}\left(m^3\right)^{2\cdot\frac{1}{2}}=9^1(m^3)^1=9m^3[/tex]
Other method:
[tex]Use\ a^\frac{1}{n}=\sqrt[n]{a}\to a^\frac{1}{2}=\sqrt[2]{a}=\sqrt{a}\\\\\left(81m^6\right)^\frac{1}{2}=\sqrt{81m^6}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{and}\ (a^n)^m=a^{nm}\\\\=\sqrt{81}\cdot\sqrt{m^{3\cdot2}}=9\sqrt{(m^3)^2}\qquad\text{use}\ \sqrt[n]{a^n}=a\to\sqrt{a^2}=a\\\\=9m^3[/tex]
The Gross National Product (GNP) is the value of all the goods and services produced in an economy, plus the value of the goods and services imported, less the goods and services exported. During the period 1994-2004, the GNP of Canada grew about 4.8% per year, measured in 2003 dollars. In 1994, the GNP was $5.9 billion.
Assuming this rate of growth continues, in what year will the GNP reach $10 trillion?
A. 2103
B.2152
C. 2164
D.2168
Answer:
B.2152
Step-by-step explanation:
To solve this we are using the standard exponential growth equation:
[tex]y=a(1+b)^x[/tex]
where
[tex]y[/tex] is the final value after [tex]x[/tex] years
[tex]a[/tex] is the initial value
[tex]b[/tex] is the growing rate in decimal form
[tex]x[/tex] is the time in years
We know from our problem that the GNP is growing 4.8% per year, so [tex]b=\frac{4.8}{100} =0.048[/tex]. We also know that the GDP in 1994 was $5.9 billion and the desired GNP is $10 trillion, so [tex]a=5,900,000,000[/tex] and [tex]y=10,000,000,000,000[/tex].
Replacing values
[tex]y=a(1+b)^x[/tex]
[tex]10,000,000,000,000=5,900,000,000(1+0.048)^x[/tex]
[tex]10,000,000,000,000=5,900,000,000(1.048)^x[/tex]
Divide both sides by 5,900,000,000:
[tex]\frac{10,000,000,000,000}{5,900,000,000} =(1.048)^x[/tex]
Take natural logarithm to both sides
[tex]ln(1.048)^x=ln(\frac{10,000,000,000,000}{5,900,000,000})[/tex]
[tex]xln(1.048)=ln(\frac{10,000,000,000,000}{5,900,000,000})[/tex]
Divide both sides by ln(1.048)
[tex]x=\frac{ln(\frac{10,000,000,000,000}{5,900,000,000})}{ln(1.048)}[/tex]
[tex]x[/tex] ≈ 158
We now know that Canada's GNP will reach $10 trillion after 158 years from 1994, so to find the year we just need to add 158 years to 1994:
1994 + 158 = 2512
We can conclude that the correct answer is B.2152
What is the square root of 125
Answer:
11.1803
Step-by-step explanation:
Answer:
The square root of 125 is 11.1803398875
Step-by-step explanation:
You know that 10 times 10 is 100. You would then go up from there to 11. If you need to round it, do it to the hundredths place though.
Find the probability of x = 5 successes in n = 8
trials for the probability of success p = 0.3 on
each trial. Round to the nearest thousandth.
A.) 5.6
B ) 0.46
C.) 0.254
D.) 0.047
La letra C puede ser la respuesta correcta pero tengo mis dudas.
The probability of x = 5 successes in n = 8
trials for the probability of success p = 0.3 IS A.) 5.6
What is binomial probability?Binomial possibility refers to the opportunity of exactly x successes on n repeated trials in a test that has two feasible outcomes (generally known as a binomial test). If the possibility of fulfillment on an individual trial is p, then the binomial chance is nCx⋅px⋅(1−p)n−x.The letter p denotes the probability of achievement on one trial and q denotes the probability of a failure on one trial. The n trials are impartial and are repeated using the same situations.Learn more about probability here:-https://brainly.com/question/24756209
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a punch recipe calls for 2parts soda to 3 parts fruit juice. if you use 8 cups of soda, of soda how much fruit juice do need
Answer:
12 parts of fruit juice
To maintain the 2:3 ratio of soda to fruit juice, if you use 8 cups of soda, you would need 12 cups of fruit juice.
The punch recipe calls for 2 parts soda to 3 parts fruit juice. If you are using 8 cups of soda, you need to determine how much fruit juice is required using the given ratio. To do this, we can set up a proportion:
Soda: 2 parts
Fruit juice: 3 parts
If 2 parts are represented by 8 cups of soda, then 1 part would be 4 cups of soda (since 8 divided by 2 equals 4). Therefore, for 3 parts of fruit juice, we need 3 times 4 cups, which is 12 cups of fruit juice.
Here is the calculation:
2 parts : 3 parts
8 cups : x cups
x = rac{3}{2} times 8 cups
x = 3 times 4 cups
x = 12 cups
So, you will need 12 cups of fruit juice to maintain the proper ratio if using 8 cups of soda.
Please explain your answer. THX!!!
Answer:
tan(5x/8)
Step-by-step explanation:
given expression
[tex]\frac{tan(1/2x)+tan(1/8x)}{1-tan(1/2x)tan(1/8x)}[/tex]
Using the trigonometric identity
tan(a+b)= [tex]\frac{tan(a) + tan(b)}{1-tan(a)tan(b)}[/tex]
here a= 1/2x and b=1/8x
putting the values we get
=tan(1/2x+1/8x)
=tan(5/8x)!
Which subset(s) of numbers does 8 2/3
belong to?
Answer:
Rational number/integer
A cylindrical container with a diameter of 0.5 feet and a height of 5 feet is filled with gas that costs $60 per cubic foot. What is the total value of the gas in the container if it's filled completely?
Total value in dollars, to the nearest penny:
Answer: $235,62
Step-by-step explanation:
You need to use the formula for calculate the volume of a cylinder:
[tex]V=\pi r^2h[/tex]
Where "r" is the radius and "h" is the height.
You know that the cylindrical container has a diameter of 0.5 feet and a height of 5 feet (Remember that the radius if half the diameter):
[tex]r=\frac{0.5ft}{2}=0.25ft\\\\h=5ft[/tex]
Then, you need to substitute these values into [tex]V=\pi r^2h[/tex] to get the volume of the cylindrical container:
[tex]V=\pi (0.5ft)^2(5ft)[/tex]
[tex]V=3.92ft^3[/tex]
Since the gas costs $60 per cubic foot, you need to multiply the volume of the container by $60 to get the total value of the gas in the container if it's filled completely. Then:
[tex]total\ value=(3.92)(\$60)=$235,62[/tex]
What does N equal help me please
for (A^x)^y = A^xy
Thus for (3^-5)^-2 = 3^n
n = -5×-2 =10
Answer:
n=10
Step-by-step explanation:
We know that a^b^c = a^(b*c)
3 ^-5^-2 = 3^(-5*-2)
= 3^(10)
3^n = 3^10
n = 10
When buying a candy bar, there is a 20% chance that it will also include a coupon for a second candy bar. A student
wants to determine the probability that, if she buys 7 candy bars, more than 2 will include a coupon.
To do this, she uses a random number table to pick 7 numbers from 1 to 5. She lets 1 represent a candy bar with a
coupon and numbers 2 through 5 represent a candy bar without a coupon.. She repeats this for a total of 16 trials. Theresults are shown in the table.
5144543 2114445 2113415 4341112
3423143 3435251 1324353 3223233
2155545 4222542 4443352 5222235
1455141 4554414 5154443 3153242
Select from the drop-down menus to correctly complete each statement
To estimate the probability that more than 2 out of 7 candy bars will include a coupon, the student must count the numberof trials with Choose ________ and divide by the number of trials.
This gives an estimated probability of about Choose _________.
Answer:
Step-by-step explanation:
1 represent a candy bar with a coupon and numbers 2 through 5 represent a candy bar without a coupon.
Now we are asked to find the probability that, if she buys 7 candy bars, more than 2 will include a coupon.
Total number of outcomes=16
Number of favorable outcomes(i.e. the outcome which have more than 2 one) = 3
( Since the outcomes are: 2113415 4341112 1455141 )
Hence, the probability is the ratio of Number of favorable outcomes to the total number of outcomes.
i.e. [tex]Probability=\dfrac{3}{16}\\\\\\Probability=0.1875[/tex]
Wendy made two rectangular prism jewelry boxes, one small and one large. The dimensions of the large jewelry box are three
times the dimensions of the small jewelry box. If the surface area of the small jewelry box is 79 cm2, what is the surface area of the
large jewelry box?
A. 474 cm squares
B. 237 cm squared
C. 711 squared
D. 2,133 cm squared
Answer:
C
Step-by-step explanation:
The scale factor is a quantity that "scales" another quantity.
Since, the dimensions of large is "3 times" that of the smaller box, the scale factor is 3.
This means, that we can multiply any dimension (length, width, or height) of the small box by 3 to get respective dimension of large box.
Remember, to get area, we need to multiply by scale factor squared. To get volume, we need to multiply by scale factor cubed.
Since, surface area is given of smaller box, we need to multiply by scale factor squared (3^2 = 9) to get surface area of larger box.
Hence, 79 * 9 = 711 cm^2
C is the correct answer.
2. Find the number of permutations of the letters in the
word SMART.
Answer:
The number of permutations of the letters in the word SMART are 120
Step-by-step explanation:
Permutations are events of multiplicative type, where the number of possibilities decreases and if the order of a permutation is an arrangement of a set of objects in a defined order.
The number of possible permutations when taking objects from the set of elements will be, following the same reasoning: [tex]P_{n} =n![/tex]
The number of permutations of the letters in the word SMART is:
[tex]P_{5} =5!=5.4.3.2.1=120[/tex]
.
Write an algebraic expression for the
phrase below.
12 less than twice a number n
Answer:
2n-12 ( n is the unknown number)
Answer:
12-2n
Step-by-step explanation:
12 less which means you have to subtract 12 from twice a number n so 2 times n
so 12-2n
will give brainliest plzz answer!!!!!Find the solution to the system of equations by using either graphing or substitution.
y = 6 – x and y = x – 2
(2, 4)
(–4, 2)
(4, 2)
no solution
The correct answer should be x=4, y=2 or (4, 2)
help, the picture is above
Answer:
B
Step-by-step explanation:
Put in order smallest to largest:
43, 46, 48, 50, 50, 51, 52, 55, 57, 57, 58
Identify the median (middle number). That's 51. So we can split this into a lower half and an upper half:
Lower half: 43, 46, 48, 50, 50
Upper half: 52, 55, 57, 57, 58
The lower quartile starts at the median of the lower half: 48.
The upper quartile ends at the median of the upper half: 57.
So the answer is B.
Write .0487 as a percent.
A) 0.0487%
B) .487%
C) 4.87%
D) 48.7%
[tex]\text{Hey there!}[/tex]
[tex]\text{Decimals can run out 100}[/tex]
[tex]\text{So,}\frac{0.0487\%}{1}\times\frac{100}{100}[/tex]
[tex]\text{Cross multiply: .0487}\times100=4.87\\ 100\times1=100[/tex]
[tex]\text{We get:}\frac{4.87}{100}[/tex]
[tex]\text{We could get rid of the 100 value because it is labeled as: per}[/tex]
[tex]\text{But, you can keep the 4.87 because it is the percentage of .0487}[/tex]
[tex]\boxed{\boxed{\text{Answer:C.) 4.87\%}}}[/tex] [tex]\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Final answer:
Decimal .0487 converts to 4.87% when we move the decimal point two places to the right. The correct answer is C, 4.87%.
Explanation:
To convert the decimal .0487 into a percent, we need to move the decimal point two places to the right, in accordance with the process described for converting decimals to percents. This gives us 4.87%, which means the correct answer is option C.
16 is 80% of what number
Answer:
20
Step-by-step explanation:
This reads mathematically exactly how it is stated in words. The word "is" means =, the word "of" means multiply, and "what number" is x. Therefore, the equation from that looks like this: 16 = .80x. Don't forget that you cannot use a percent in an equation without first changing it to its decimal equivalency. Solve that for x by dividing both sides by .80 to get that x = 20
The number that when 80 % is found of it, would give the result of 16 is the number 20.
What is 80 % of 20 ?To determine the number that 16 is 80% of, you can set up an equation using algebra.
Let's represent the unknown number with the variable "x." The equation can be written as:
16 = 80% of x
To solve for "x," we need to isolate it on one side of the equation.
Since 80% is equivalent to 0.8 as a decimal, we can rewrite the equation as:
16 = 0.8x
To solve for "x," divide both sides of the equation by 0.8:
16 / 0.8 = 0.8x / 0.8
Simplifying the equation:
20 = x
Therefore, the number that 16 is 80% of is 20.
Find out more on percentages at https://brainly.com/question/843074.
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The volume of a rectangular prism is represented by the function x3 + 9x2 + 6x − 16. The length of the box is x + 2, while the height is x + 8. Find the expression representing the width of the box.
Answer:
width = (x-1)
Step-by-step explanation:
The volume of the prisms is defined in the problem as
Volume = x^3 + 9x^2 + 6x − 16
Volume = width*height* length
And we know that,
length = (x+2)
height = (x+8)
We can find the roots of the equation, which happen to be
x = -8
x = -2
x = 1
(See image below)
This means that the volume can be represented as
Volume = x^3 + 9x^2 + 6x − 16 = (x+8)(x+2)*(x-1)
Therefore,
The width = (x-1)
The amount of money that high school students spend on fast food each month is usually between $50 and $200. However, there are a few students who do not eat fast food at all. What measure of spread would be most appropriate to measure the amount of money that high school students spend on fast food per month?
A. Mean
B. Interquartile Range
C. Range
D. Standard Deviation
B. Interquartile Range
In a hexagon, all but one of the angles have a measure of 110. What is the measure of the remaining angle?
Answer:
Part 1) The measure of the remaining angle is [tex]60\°[/tex]
Part 2) Is a 10 sided polygon (decagon)
Part 3) Yes, is possible for a triangle to have angles measures of 1°, 2° and 177°
Step-by-step explanation:
Part 1)
we know that
The sum of the measures of the interior angles of a polygon is equal to the formula
[tex]S=(n-2)180\°[/tex]
where
n is the number of sides of polygon
In this problem we have a hexagon
so
n=6 sides
Substitute
[tex]S=(6-2)180\°=720\°[/tex]
Let
x-----> the measure of remaining angle of the hexagon
[tex]6*(110\°)+x\°=720\°[/tex]
[tex]x=720\°-660\°=60\°[/tex]
Part 2) The sum of the measures of the interior angles of a polygon is [tex]1440\°[/tex]. What kind of polygon is it?
we know that
The sum of the measures of the interior angles of a polygon is equal to the formula
[tex]S=(n-2)180\°[/tex]
where
n is the number of sides of polygon
In this problem we have
[tex]S=1440\°[/tex]
substitute in the formula and solve for n
[tex]1440\°=(n-2)180\°[/tex]
[tex]n=(1440\°/180\°)+2=10\ sides[/tex]
therefore
Is a 10 sided polygon (decagon)
Part 3) Is it possible for a triangle to have angles measures of 1°, 2° and 177° ?
we know that
In any triangle the sum of the measures of the interior angles must be equal to 180 degrees
In this problem we have
1°+ 2°+ 177°=180°
therefore
Yes, is possible for a triangle to have angles measures of 1°, 2° and 177°
If f(x) = x+7 and g(x)=1/x what is (f o g)(x)?
For this case we have the following functions:
[tex]f (x) = x + 7\\g (x) = \frac {1} {x}[/tex]
We must find [tex](f_ {0} g) (x):[/tex]
By definition:
[tex](f_ {0} g) (x) = f (g (x))[/tex]
So, evaluating g(x) in f(x) we have:
[tex](f_ {0} g) (x) = f (g (x)) = \frac {1} {x} +7[/tex]
ANswer:
[tex]\frac {1} {x} +7[/tex]
Option D
Factor the expression completely 8y-36
Please help fast
Answer:
4(2y−9)
Step-by-step explanation:
lets factor out "4" out of the equation 8y-36
so u will get: 4(2y−9)
hope this helps
please help!!!!!!!!!!!!
Answer:
see answers in bold below
Step-by-step explanation:
a. The area of each red triangle is given by the formula for the area of a triangle:
A = 1/2·bh
The base is 14 ft - 10 ft = 4 ft. The height is shown as 4 ft, so the area of each triangle is ...
A = (1/2)(4 ft)(4 ft) = 8 ft²
Then the red area is that of the two triangles:
red area = 2·(8 ft²) = 16 ft²
The white rectangle area is the product of its length and width:
white area = (8 ft)(4 ft) = 32 ft²
The area of the whole central parallelogram is the product of its length and width:
parallelogram area = (14 ft)(8 ft) = 112 ft²
But the yellow area is the difference between this value and the white area:
yellow area = 112 ft² -32 ft² = 80 ft²
__
b. The area to be primed is the sum of the areas to be painted different colors:
primed area = red area + white area + yellow area
= 16 ft² + 32 ft² + 80 ft²
primed area = 128 ft²
_____
In the attached figure, each grid square is 2 ft.
Up and Running Auto Shop keeps track of their regular customers' data to see if there is a relationship between the life of a car's engine (y) and the number of times the oil is changed (x). When the data is shown on a scatter plot, the equation for the line of best fit is y = 0.4125x + 0.1576. What is the relationship between 0.4125 and the life of the car's engine?
Answer:
Strong and Positive Relation
Step-by-step explanation:
Here, when we plot the graph of y = 0.4125x + 0.1576
Then we see that the graph has a positive correlation as we increase the value of x, the value of y is also increasing. So, Life of Car's Engine and Number of Times the Oil is Changed has a Positive relation.
And if our scatter plot is horizontal, vertical or we unable to draw the line of best fit then it has no or little correlation but here we see that line is not lie in either case. So, the relationship is strong but not very strong.
Answer :
A) 0.4125 shows how much the longevity of the engine increases with each oil change.
B) 0.4125 shows the expected longevity with no all changes.
C) 0.4125 shows the expected longevity for all engines, with or without oil changes.
D) 0.4125 is the expected decrease in longevity for each year without an oil change.
Step-by-step explanation: THE answer IS A!!
( i just took the test)
An airplane is traveling at 400 miles per hour. Which equation can be used to find the total distance the plane will travel in h hours?
1. d = h ÷ 400
2. d = h + 400
3. d = 400 x h
4. d = 400 - h
The equation that can be used to find the total distance the plane will travel in h hours is d = 400 × h
Total distance traveled by the plane = d miles
Total hours traveled = h hours
total speed of the plane = 400 miles per hour
Distance traveled = speed × time
d = 400 × h
d = 400h
Therefore, the equation that can be used to find the total distance the plane will travel in h hours is d = 400 × h
Read more:
https://brainly.com/question/11766874
The correct option is 3. [tex]\ d = 400 \times h[/tex]
To determine the total distance \(d\) an airplane will travel given its speed and time, we use the formula:
[tex]\[\text{Distance} = \text{Speed} \times \text{Time}\][/tex]
Given:
[tex]\text{Speed of the airplane} = \text{400 miles per hour}[/tex]
[tex]Time = \(h\) hours[/tex]
Plugging in the values:
[tex]\[d = 400 \times h\][/tex]
PLEASE HELP ME ASAP PLEASE FAST!!!!!!!!!!!!! PLEASE HELP
Answer:
Number the boxes on the left 1–8 from top to bottom. Then their correct order on the right is 3, 7, 8, 4, 6, 5, 2, 1
Step-by-step explanation:
Trade the cube root for a 1/3 power:
(875x^5y^9)^(1/3)
Distribute the 1/3 power:
(125·7)^(1/3)·x^(5/3)·y^(9/3)
Further distribute the powers, rewrite the improper fractions:
125^(1/3)·7^(1/3)·x^(3/3+2/3)·y^3
Write 125 as a cube and simplify 3/3:
(5^3)^(1/3)·7^(1/3)·x^(1+2/3)·y^3
Simplify the cube root of a cube and the x term:
5·7^(1/3)·x·x^(2/3)·y^3
Group the terms with fractional exponents:
5·x·y^3·(7^(1/3)·x^(2/3))
Factor out the 1/3 exponent:
5xy^3·(7x^2)^(1/3)
Trade the 1/3 exponent for a cube root symbol:
5xy^3·∛(7x^2)
1.2, 3, 7.5, 18.75, ...
Which formula can be used to describe the sequence?
Answer:
The formula is:
[tex]a_n=1.2(\frac{5}{2})^{n-1}[/tex]
Step-by-step explanation:
The geometric sequences are those in which the division between the terms [tex]a_{n + 1}[/tex] and [tex]a_n[/tex] of the sequence are equal to a constant common reason called "r"
The geometrics secencias have the following form:
[tex]a_n=a_1(r)^{n-1}[/tex]
Where [tex]a_1[/tex] is the first term of the sequence
In this sequence we have the following terms
1.2, 3, 7.5, 18.75
Then notice that:
[tex]\frac{3}{1.2}=\frac{5}{2}\\\\\frac{7.5}{3}=\frac{5}{2}\\\\\frac{18.75}{7.5}=\frac{5}{2}[/tex]
Then:
[tex]r=\frac{5}{2}[/tex] and [tex]a_1=1.2[/tex]
Finally the formula is:
[tex]a_n=1.2(\frac{5}{2})^{n-1}[/tex]
Answer:
Answer: "f(x) = 1.2(2.5)x-1"
Step-by-step explanation:
The graph above shows the cost of hay. Jethro bought 9 bales of hay. Based on the graph, what is the total cost that he paid for the hay?
A.
$22.50
B.
$31.50
C.
$36.00
D.
$27.00
Answer:
b
Step-by-step explanation:
what is measure of angle P?
Answer: [tex]P=61.93\°[/tex]
Step-by-step explanation:
You know that:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
And the arctangent is:
[tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]
You can observe a right triangle in the figure.
Since you need to find the measure of the angle P, then:
[tex]\alpha=P\\opposite=15cm\\adjacent=8cm[/tex]
Knowing this, you can substitute these values into [tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]:
[tex]P=arctan(\frac{15cm}{8cm})[/tex]
Therefore, the measure of the angle P to the nearest hundreth is:
[tex]P=61.93\°[/tex]