Answer:
The answer is 28ft.
Step-by-step explanation:
A radius will always be exactly half of the diameter: meaning, the diameter is double the length of the radius.
A set of cards includes 24 yellow cards,18 green cards,and 18 blue cards. What is the probability that a card chooses at random is not green?.
➷ Find the total number of cards:
24 + 18 + 18 = 60
Find the total number of cards that aren't green:
24 + 18 = 42
The probability would be 42/60
This could be simplified to 7/10
✽➶ Hope This Helps You!
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Answer:
710
Step-by-step explanation:
7/10
Which is the equation of the given line in slope-intercept form
Answer: The Slope-Intercept Form equation is y=mx+b
i think the answer is y=3x+2 but i hope this helps
The equation of the line in Slope-intercept form is y = -3x + 2.
The correct choice is option C. y=-3x+2.
Let's, find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b). The slope represents the steepness of the line, and the y-intercept is the point where the line crosses the y-axis.
From the graph, we can see that the line passes through the points (-1, 5) and (1, -1). Using the slope formula, we can calculate the slope as follows:
m = (y2 - y1) / (x2 - x1)
m = (-1 - 5) / (1 - (-1))
m = -6 / 2
m = -3
Now that we know the slope, we can plug it into the slope-intercept form of the equation and solve for b:
y = mx + b
y = -3x + b
We can find the value of b by substituting the coordinates of one of the points on the line into the equation. For example, we can use the point (-1, 5):
5 = -3(-1) + b
5 = 3 + b
b = 5 - 3
b = 2
Therefore, the equation of the line in slope-intercept form is y = -3x + 2.
option C. is correct choice y=-3x+2.
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FIND X. ASSUME SG IS TANGENT TO CIRCLE O AT POINT S.
We have a right triangle 9,12,15 which is 3,4,5 scaled.
So OG=15 and OH=9 (the radius) so x = 15-9 = 6
Answer: 6
For what value of x is the rational expression below equal to zero? x-9/(x-4) (x+4)
Answer:
The value of x is 9
Step-by-step explanation:
* It first we must to talk about the rational expression
- The rational expression is defined for all values of x except
the values make the denominator = zero
Ex: If the rational expression is a/b, then b ≠ 0 to be defined
* In any rational expression we must to avoid any values
make denominator = zero
* If we want to make rational expression equal to zero then we
must put the numerator equal to zero
* Now lets look to our problem
∵ The rational expression (x - 9)/(x - 4)(x + 4)
- To make this rational expression equal to zero, we must
equate the numerator by zero
∴ x - 9 = 0 ⇒ add 9 to both sides
∴ x = 9
* The value of x is 9
* Remember ⇒ x must not equal to 4 or -4 to avoid make
this rational expression undefined
Which are the first five terms of a geometric sequence in which the second term is 6 and the fourth term is 54?
now, let's recall that a geometric sequence is one that uses some "r" common ratio to get the next term, by simply multiplying the current term by it.
[tex]\bf \begin{array}{|cl|ll} \cline{1-2} term&value\\ \cline{1-2} a_1&\underline{\qquad }\\&\\ a_2&6\\&\\ a_3&\underline{6(r)}\\&\\ a_4&6(r)(r)\\&\\ &54\\ \cline{1-2} \end{array}\qquad \implies \begin{array}{llll} 54=6r^2\implies \cfrac{54}{6}=r^2\implies 9=r^2\\\\ \sqrt{9}=r\implies 3=r \end{array} \\\\[-0.35em] ~\dotfill\\\\ a_1=6\div 3\implies a_1=2~\hfill a_3=6(3)\implies a_3=18[/tex]
and of course, the next term or a₅ = 54(3) --> a₅ = 162.
The first five terms are 2, 6, 18, 54, 162
Given,
The second term is 6.
The fourth term is 54.
We need to find the first five terms of a geometric sequence.
What is a geometric sequence?A sequence where each term after the first is found by multiplying the previous one with a common ratio.
The sequence is given by:
a, ar, ar^2, ar^3, ar^4, ar^5,...
The nth term is given by:
a_n = ar^(n-1)
We have,
Second term = 6
a_2 = ar^(2-1)
6 = ar^1
6 = ar
a = 6/r _____(1)
Fourth term = 54
a_4 = ar^(4-1)
54 = ar^3
a = 54/r^3 ______(2)
From (1) and (2)
6/r = 54/r^3
r^3/r = 54/6
r^2 = 9
r = 3
Putting in (1)
a = 6/r
a = 6/3
a = 2
We have,
a = 2 and r = 3
Find the first five terms of a geometric sequence.
It is given by:
a, ar, ar^2, ar^3, ar^4
2, 2x3, 2x9, 2x27, 2x81
2, 6, 18, 54, 162
The first five terms are 2, 6, 18, 54, 162
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f your score on your next statistics test is converted to a z score, which of these z scores would you prefer: minus2.00, minus1.00, 0, 1.00, 2.00? Why? A. The z score of minus2.00 is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores. B. The z score of 1.00 is most preferable because it is 1.00 standard deviation above the mean and would correspond to an above average test score. C. The z score of minus1.00 is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average test score. D. The z score of 0 is most preferable because it corresponds to a test score equal to the mean. E. The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.
Answer:
E. The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.
Step-by-step explanation:
A z score tells us how many standard deviations away from the mean a given value is.
The higher the z-score, the farther above the mean the value is. Since we are referring to the score on a test, we want the value to be as far above the mean as possible; this means that our best choice out of those given is 2.00, since it is 2 standard deviations above the mean.
Which is the distance between parallel lines with the equations 3x-5y=1 and 3x-5y=-3
The distance between the parallel lines 3x - 5y = 1 and 3x - 5y = -3 is 4/√34 units.
Explanation:To find the distance between two parallel lines with equations 3x - 5y = 1 and 3x - 5y = -3, we need to use the formula for distance between two parallel lines in a coordinate plane. This formula is:
Distance = |C2 - C1| / sqrt(A^2 + B^2)
In this case, your A coefficient is 3, the B coefficient is -5, and the constants (C1 and C2) are -1 and 3 respectively (from the given equations). Substituting these values into the formula gives:
Distance = |3 - (-1)| / sqrt(3^2 + (-5)^2)
Distance = 4 / sqrt(9 + 25)
Distance = 4 / sqrt(34)
So, the distance between parallel lines with equations 3x - 5y = 1 and 3x - 5y = -3 is 4/sqrt(34) units.
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Final answer:
The distance between the parallel lines described by the equations 3x-5y=1 and 3x-5y=-3 is calculated using a standard formula for the distance between parallel lines, resulting in a distance of 4 / √34.
Explanation:
The distance between two parallel lines can be calculated using a formula once the equations of the lines are in standard form. The equations 3x-5y=1 and 3x-5y=-3 are indeed in standard form and clearly show that the lines are parallel because they have the same coefficients for x and y. To find the distance between these parallel lines, one can use the formula involving the absolute difference of the constants in the equations and the square root of the sum of squares of the coefficients of x and y.
The formula for the distance d between two parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is given by:
d = |C2 - C1| / √(A² + B²)
Applying this to our equations, we have:
A = 3, B = -5, C1 = 1, and C2 = -3.
Thus,
d = |-3 - 1| / √(3² + (-5)²) = 4 / √(9 + 25) = 4 / √34
Distance between parallel lines, standard form, and formula are essential in solving this problem.
Which equation represents a line that is parallel to the line whose equation is 2x + 3y =12
The line parallel to the equation 2x + 3y = 12 can be expressed in the form y = -2/3x + c, where c is any arbitrary constant. This is because parallel lines share the same slope.
Explanation:In mathematics, parallel lines have the same slope. To find an equation that is parallel to an existing line, we need to find the slope of the existing line and use that same slope for the parallel line. We know that your line equation is 2x + 3y =12. Let's rewrite this in the y = a + bx form, where a is the y-intercept and b is the slope.
So, subtract 2x from both sides to get the equation in the form of 3y = -2x +12. Now, divide the entire equation by 3 to isolate y. You get y = -2/3x + 4. Here, the slope (b) is -2/3. Any line parallel to this one must also have a slope of -2/3.
Thus, the parallel line is y = -2/3x + c, where c is any arbitrary constant.
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To find a line parallel to 2x + 3y = 12, you must use the same slope, which is -2/3. Any line of the form y = (-2/3)x + b, where b is any number, will be parallel to the original line.
Explanation:To find an equation for a line parallel to the given line 2x + 3y = 12, we need to find a line with the same slope. First, we rearrange the given equation into slope-intercept form (y = mx + b), where m represents the slope, and b represents the y-intercept.
The original equation can be rewritten as:
3y = -2x + 12
y = (-2/3)x + 4
The slope of this line is -2/3. Any line parallel to this line will have the same slope, -2/3. The general form of the equation for any parallel line will be:
y = (-2/3)x + b
where b can be any real number.
Here are a couple of examples of lines that are parallel to the original:
y = (-2/3)x + 1y = (-2/3)x - 5Both have the same slope (-2/3) as the original line but different y-intercepts.
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A lion can run 50 miles per hour. This is 20 miles per hour faster than a house cat. Find the speed of the hous cat
The lion runs 50 miles per hour which is 20 more than a house cat. 20 mph + house cat mph = 50 → house cat mph = 30mph
You just have to calculate the difference.
50-20=c
c=30
(75 points to correct answer!) Use the diagram to solve for segments SW and WQ. Show your work and/or explain how you determined the answer.
Show your work, please!
Answer:
Check out lesson 3.09, It'll help ;)
What shape would be the cross section from a vertical slice of a hexagonal pyramid?
Answer:
It depends
Step-by-step explanation:
The shape will have a number of sides equal to the number of faces it intersects (counting the base). Depending on the shape of the hexagonal base, the symmetry of the peak, and where the slicing is done, the vertical slice could have 3, 4, 5, 6, or 7 sides, so could be anything from a triangle to a heptagon.
(Please help i only have 20 min left, Thank you!!)
Write this polynomial in descending order: –4x5 + 4x3 + x7 – 10 + 2x4.
Answer:
[tex]{x}^{7} - 4 {x}^{5} + 2 {x}^{4} + 4 {x}^{3} - 10[/tex]
Step-by-step explanation:
To write a polynomial in descending order means writing the polynomial in decreasing powers of x.
The given polynomial expresion is
[tex] - 4 {x}^{5} + 4 {x}^{3} + {x}^{7} - 10 + 2 {x}^{4} [/tex]
We start from the term with the highest degree and end with term with the least degree.
[tex] {x}^{7} - 4 {x}^{5} + 2 {x}^{4} + 4 {x}^{3} - 10[/tex]
Therefore the given polynomial written in descending order is
[tex]{x}^{7} - 4 {x}^{5} + 2 {x}^{4} + 4 {x}^{3} - 10[/tex]
Prove that any minimum spanning tree t of g is also a bottleneck spanning tree of g.
Answer:
Step-by-step explanation:
can you explain a little bit more ?
What is the length of EF?
The length of EF is 3.8. Option A
To determine the value of the side, we have to make use of the sine rule, this rule is represented as;
sin A/a = sin B/b
Such that;
a and b are the lengths of the sidesA and B are the measure of the anglesNow, substitute the values, we have;
sin 75/EF = sin 50/3
cross multiply the values, we get;
EF = 3sin 75/sin 50
find the values
EF = 3(0.96)/0.766
EF = 2.88/0.766
Divide the values
EF = 3. 8
Which of the following represents (Picture provided)
Answer:
B.
Step-by-step explanation:
You are given the double inequality
[tex]1<x\le 6.[/tex]
This means that x is greater than 1 and less than or equal to 6.
Thus, point 1 must be excluded (with bracket "(") and 6 must be included (with bracket "]").
Hence, the correct answer is [tex](1,6].[/tex]
Answer:
b. [tex](1,6][/tex]
Step-by-step explanation:
The given inequality is [tex]1\:<\:x\le6[/tex].
We use the parenthesis [tex]()[/tex] to represent an open interval < or >.
We use the square brackets [tex][][/tex] to represent a closed interval [tex]\le[/tex] or [tex]\ge[/tex].
[tex]1\:<\:x\le6[/tex] represents [tex](1,6][/tex].
The correct choice is B.
A park began with a population of 8 rabbits. Every year, the rabbit population triples. How long will it take for the population to reach 1,944 rabbits?
Answer:
It will take 5 years for the population to reach 1,944. Option D is correct.
Step-by-step explanation:
Initial population = I = 8
Final population = F = 1944
number of years = x
As given, the population is tripled every year that can be calculated using:
F = I*3^x
By putting values in this equation, we get
1944 = 8*3^x
1944/8 = 3^x
243 = 3^x
3^x = 243
3^x = 3^5
x = 5 bases are same so powers can be simplified.
Therefore, it will take 5 years for the population to reach 1,944. Option D is correct.
Answer:
8 • 3^y = R
Step-by-step explanation:
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the manager at a hotel wants to know how often do his costomers rent boats at the nearby lake.Which sampling method will give valid results
Answer: ❤️Hello!❤️He asks every tenth customer who checks into the hotel. Hope this helps! ↪️ Autumn ↩️
Please help me out!!!!!!!!!!!!
Answer:
y = 19Step-by-step explanation:
The diagonals in the parallelogram intersect by dividing in half.
Therefore we have the equation:
2y + 22 = 79 - y subtract 22 from both sides
2y = 57 - y add y to both sides
3y = 57 divide both sides by 3
y = 19
Write an inequality for the situation. No more than 5 books are in your backpack.
A park is shaped like a rectangle with a length 5 times its width (w). What is a simplified expression for the distance between opposite corners of the park?
Answer:
w√26
Step-by-step explanation:
A rectangle is a four sided shape with 4 perpendicular angles. It has two pairs of parallel sides which are equal in distance: width and length. The width here is w and the length is 5w or 5 times the width. A diagonal can be drawn between opposite corners that splits the triangle into two equal right triangles. The distance of this diagonal is found using the Pythagorean Theorem a² + b² = c². In the rectangle a = w and b = 5w. Substitute these values and simplify using a square root operation.
w² + (5w)² = c²
w² + 25w² = c²
26w² = c²
√26w² = c
w√26 = c
I need 7714 solar panels to power my new workshop . If each box contains 24 panels ,about how many boxes should I purchase.
Answer: 321.4167 or about 322 boxes
Step-by-step explanation:
Evaluate the log without a calculator ( Show your work )
[tex]log_{81} 27[/tex]
Answer:
[tex]\log_{81}(27)=\frac{3}{4}[/tex]
Step-by-step explanation:
The given logarithm is
[tex]\log_{81}(27)[/tex]
Let us change to base 3.
[tex]\log_{81}(27)=\frac{\log_3(27)}{\log_3(81)}[/tex]
[tex]\log_{81}(27)=\frac{\log_3(3^3)}{\log_3(3^4)}[/tex]
[tex]\log_{81}(27)=\frac{3\log_3(3)}{4\log_3(3)}[/tex]
[tex]\log_{81}(27)=\frac{3(1)}{4(1)}[/tex]
[tex]\log_{81}(27)=\frac{3}{4}[/tex]
Answer:
3/4 ( or 0.75).
Step-by-step explanation:
let y = log81 27, then:
27 = 81^y ( by the definition of a logarithm).
27 = 3^3 and 81 = 3^4
So 27 = 81 ^3/4
so y = log81 27 = = 3/4.
Eli, Freda and Geoff were given ?800 to share in the ratio of their ages. Eli is 9 years old,Feda is 13 years old and Geoff is 18 years old. How much should they each get? Eli- Freda- Geoff-
Answer:
This would probely be 266.
Step-by-step explanation:
There are three kids so I would divide them by three. Or multiply 266 by three. Of course there would still be 2$ left.
Answer:
Share of Eli, Freda and Geoff will be $180, $260, $360 respectively.
Step-by-step explanation:
Eli, Freda and Geoff were given $800 to share in the ratio of their age.
Their ages were 9 years, 13 years and 18 years respectively.
Ratio of their ages will be 9 : 13 : 18
Now share of Eli will be = [tex]\frac{9}{9+13+18}\times 800[/tex]
= [tex]\frac{9\times 800}{40}[/tex]
= $180
Share of Freda will be = [tex]\frac{13}{9+13+18}\times 800[/tex]
= $260
Share of Geoff will be = [tex]\frac{18}{9+13+18}\times 800[/tex]
= $360
Therefore, share of Eli, Freda and Geoff will be $180, $260, $360 respectively.
Please answer this multiple choice question!
Answer:
d. 11.3 cm
Step-by-step explanation:
The radius of the circle is the length CP, which can be found using the Pythagorean theorem. Since CQ ⊥ PR, you know that Q is the midpoint of PR and PQ = 8 cm.
Then the Pythagorean theorem tells you ...
CP² = CQ² +PQ² = (8 cm)² + (8 cm)² = 128 cm²
CP = √128 cm = 8√2 cm
CP = 11.3 cm
Answer:
[tex]\large\boxed{d.\ 11.3\ cm}[/tex]
Step-by-step explanation:
Look at the picture.
CQ is a perpendicular bisector of PR. Therefore QR = QP.
[tex]PR=16\ cm\to QP = 16 cm : 2 = 8\ cm[/tex]
The segment CP is a radius of the given circle.
We have the right triangle CQP. Use the Pythagorean theorem:
[tex]CQ^2+QP^2=CP^2[/tex]
Substitute CQ = 8 cm and QP = 8 cm.
[tex]CP^2=8^2+8^2\\\\CP^2=64+64\\\\CP^2=128\to CP=\sqrt{128}\\\\CP\approx11.3\ cm[/tex]
Please Help!! A septic tank has the shape shown in the figure. How many gallons does it hold? (1 cu ft = 7.48 gallons.) (Round to the nearest gallon)
The overall volume is the sum of the volume of a cylinder of height 5'9" and diameter 3'6", and a sphere of diameter 3'6" (two hemispheres = full sphere).
Volume of the cylinder = (area of the base) x (height) = pi * (diameter/2)^2 * 5.75ft = 3.1415 * (3.5ft/2)^2 * 5.75 ft = 55.32 ft^3
Volume of the sphere = 4/3 * pi * (3.5ft)^3 / 8 = 22.45 ft^3
Total volume = (Volume of cylinder) + (Volume of sphere) = (55.32 + 22.45) ft^3 = 77.77 ft^3
The tank holds 641 gallons since the volume of the tank is 85.66 cubic feet. The tank has a cylindrical part and two hemispheres.
What is the volume of the cylinder?The volume of the cylinder is V=Bh or V=2πrh.
Where B is the base area, h is the height of the cylinder and r is the radius.
What is the volume of the hemisphere?The formula for the volume of a hemisphere: V = (2/3)πr³
Where r is the radius of the hemisphere.
Calculating the Volume of the septic tank:The tank has a cylindrical part and two hemispheres.
So, the volume of the tank = (volume of the cylinder) +2 (volume of the hemisphere)
Finding the volume of the cylinder:
The height of the cylinder is h=5'9'' and the diameter is 3'6''.
(1 feet = 12 inches)
So, the diameter = 3 feet 6 inches = 3+(6/12) feet = 3.5 feet
Then, the radius r = 3.5/2 = 1.75 feet and
The height h=5 feet 9 inches = 5 + (9/12) feet = 5.75 feet
The volume of the cylinder = 2πrh
= 2π×1.75×5.75
= 63.22 cubic feet
Finding the volume of the hemisphere:
The diameter of the sphere is 3'6'' i.e., 3.5 feet
So, radius r = 1.75 feet
Then the volume of a hemisphere:
V = (2/3)πr³
= (2/3)π×(1.75)³
= 11.22 cubic feet
So,
The volume of the tank = (volume of the cylinder) +2 (volume of the hemisphere)
⇒ Volume of the tank = 63.22 + 2×11.22 =85.66 cubic feet.
Since it is given that for 1 cubic ft it holds 7.48 gallons then for 85.66 cubic ft it holds 85.66 × 7.48 = 640.73 gallons
Rounding to the nearest gallon. So, it holds 641 gallons.
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PLEASE HELP WILL GIVE BRAINLIEST
What are the sine, cosine, and tangent of Θ = 7 pi over 4 radians?
Answer:
Step-by-step explanation:
see attached
a)
[tex]\sin (\dfrac{7\pi}{4})=-\dfrac{1}{\sqrt{2}}[/tex]
b)
[tex]\cos \dfrac{7\pi}{4}=\dfrac{1}{\sqrt{2}}[/tex]
c)
[tex]\tan \dfrac{7\pi}{4}=-1[/tex]
Step-by-step explanation:We are asked to find the value of:
a)
[tex]\sin \dfrac{7\pi}{4}[/tex]
We know that:
[tex]\dfrac{7\pi}{4}=2\pi-\dfrac{\pi}{4}[/tex]
Hence, we have:
[tex]\sin (\dfrac{7\pi}{4})=\sin (2\pi-\dfrac{\pi}{4})\\\\\\\sin (\dfrac{7\pi}{4})=-\sin (\dfrac{\pi}{4})[/tex]
Since,
[tex]\sin (2\pi-\theta)=-\sin \theta[/tex]
Hence, we have:
[tex]\sin (\dfrac{7\pi}{4})=-\dfrac{1}{\sqrt{2}}[/tex]
b)
[tex]\cos \dfrac{7\pi}{4}[/tex]
[tex]\cos (\dfrac{7\pi}{4})=\cos (2\pi-\dfrac{\pi}{4})\\\\\\\cos (\dfrac{7\pi}{4})=\cos (\dfrac{\pi}{4})[/tex]
Since,
[tex]\cos (2\pi-\theta)=\cos \theta[/tex]
Hence, we have:
[tex]\cos \dfrac{7\pi}{4}=\dfrac{1}{\sqrt{2}}[/tex]
c)
[tex]\tan \dfrac{7\pi}{4}[/tex]
[tex]\tan (\dfrac{7\pi}{4})=\tan (2\pi-\dfrac{\pi}{4})\\\\\\\tan (\dfrac{7\pi}{4})=\tan (\dfrac{\pi}{4})[/tex]
Since,
[tex]\tan (2\pi-\theta)=-\tan \theta[/tex]
Hence, we have:
[tex]\tan \dfrac{7\pi}{4}=-1[/tex]
A group of neighbors is holding an end of summer block party. They buy p packs of hot dogs, with 8 hot dogs in each pack. All together, they have 56 hot dogs for the party. Write an equation to describe this situation
Answer:
56 divided by 8 would equal p.
Step-by-step explanation:
If you want to find how many packs there are, it would be 56 divided by 8 would equal p.
Brainiest Please :D
Answer:
The equation is [tex]p*8=56[/tex]
Step-by-step explanation:
The neighbors buy a number of packs (p) of hot dogs and each one has 8 hot dogs. To calculate the number of hot dogs resulting we have to multiply the packs (p) by the number of hot dogs in each pack (8), this is:
[tex]p*8=56[/tex]
Then to calculate p we have to clear it:
[tex]p=\frac{56}{8} =7[/tex]
The number of packs bought were 7.
Your friend's swimming pool is in the shape of a rectangular prism, with a length of 25 feet, a width of 8 feet, and a height of 5 feet. a. What is the volume of your friend's swimming pool? b. Your swimming pool is in the shape of a cylinder with a diameter of 16 feet and has the same volume as your friend's pool. What is the height of your pool? Round your answer to the nearest whole number. c. While you were on vacation, 6 inches of water evaporated from your pool. About how many gallons of water evaporated from your pool? ( ) 3 1 ft 7.5 gal ? Round your answer to the nearest whole number.
Answer:
Part a) [tex]V=1,000\ ft^{3}[/tex]
Part b) [tex]h=5\ ft[/tex]
Part c) [tex]=718\ gal[/tex]
Step-by-step explanation:
Part a) What is the volume of your friend's swimming pool?
we know that
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
substitute the values
[tex]V=(25)(8)(5)=1,000\ ft^{3}[/tex]
Part b) Your swimming pool is in the shape of a cylinder with a diameter of 16 feet and has the same volume as your friend's pool. What is the height of your pool?
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]V=1,000\ ft^{3}[/tex]
[tex]r=16/2=8\ ft[/tex] ----> the radius is half the diameter
substitute and solve for h
[tex]1,000=\pi (8)^{2} h[/tex]
[tex]h=1,000/(64 \pi)[/tex]
[tex]h=1,000/(64*3.14)=5\ ft[/tex]
Part c) While you were on vacation, 6 inches of water evaporated from your pool. About how many gallons of water evaporated from your pool?
remember that
[tex]1\ ft=12\ in[/tex]
so
[tex]6\ in=6/12=0.5\ ft[/tex]
Find the volume of water for [tex]h=5-0.5=4.5\ ft[/tex]
[tex]V=(3.14)(8)^{2}(4.5)=904.32\ ft^{3}[/tex]
so
the volume of water evaporated is equal to
[tex]1,000\ ft^{3}-904.32\ ft^{3}=95.68\ ft^{3}[/tex]
convert to gallons
remember that
[tex]1\ ft^{3}=7.5\ gal[/tex]
so
[tex]95.68\ ft^{3}=95.68*7.5=718\ gal[/tex]
a. The volume of the rectangular prism is 1000 cubic feet. b. The height of the cylindrical pool is 4 feet. c. About 750 gallons of water evaporated from the pool.
Explanation:a. The volume of the rectangular prism can be found by multiplying the length, width, and height. So, the volume is 25 * 8 * 5 = 1000 cubic feet.
b. Since the two pools have the same volume, we can use the formula for the volume of a cylinder (V = πr²h) to find the height of the cylinder. We know the diameter is 16 feet, so the radius is half of that, which is 8 feet. Plugging it into the formula, 1000 = 3.142 * 8² * h. Solving for h, we find h = 4 feet.
c. To find the gallons of water evaporated, we need to convert the units. 6 inches is 0.5 feet. The volume evaporated is 25 * 8 * 0.5 = 100 cubic feet. Since 1 cubic foot is equal to 7.5 gallons, the amount evaporated is 100 * 7.5 = 750 gallons.
3 out of five picks are orange . If 12 picks are orange , how many picks are there in all?
20 picks in total .
It took the high school hockey team 5h to travel to a tournament in Thunder Bay. They travelled by bus and plane a total distance of 1320km. If the bus averaged 40km/h and the plane averaged 600km/h, determine the time they spent travelling by plane.
Answer:
It took 2 hours by plane
Step-by-step explanation:
let bus is represented by x and plane is represented by y
the total distance of bus and plane will be represented by equation:
40 x + 600 y = 1320 (1)
the total time taken by bus and plane will be represented by:
x + y = 5 (2)
solving equations (1) and (2) simultaneously:
Multiply by 40 on both sides in eq (2) and then subtract (1) and (2)
40 x + 600 y = 1320
40 x + 40 y = 200
_______________
560 y = 1120
y = 1120/ 56
y= 2
since plane is represented by y so, the time they spent travelling by plane is 2 hours.
Final answer:
By setting up and solving a system of equations based on the total travel time and distance, we find that the time spent travelling by plane is 2 hours.
Explanation:
To determine the time spent travelling by plane, we start by setting up two equations based on the given information.
Let x represent the time spent on the bus and y represent the time spent on the plane. The total travel time is given as 5 hours, and the total distance travelled is 1320 km.
Therefore, we have two equations:
x + y = 5 (total time equation)40x + 600y = 1320 (total distance equation)We can solve this system of equations by first expressing x in terms of y from the first equation:
x = 5 - y
Substituting x in the second equation:
40(5 - y) + 600y = 1320
Solving for y, we find that the time spent travelling by plane is 2 hours.