Answer:
The tank can hold 4110.26 gallons of water.
Step-by-step explanation:
In order to solve this question we need to compute the volume of this tank, the volume is given by:
V = (area of the base)*height
Since the base is circullar, it is given by:
area of the base = pi*r^2
So we have:
V = height*pi*r^2
The radius of circle is the diameter divided by 2, so in this case r = 10/2 = 5 ft. We can now use the values on the equations:
V = 7*3.14*(5)^2 = 549.5 ft^3
Since each cubic foot holds 7.48 gallons of water the volume in gallons is:
V = 549.5*7.48 = 4110.26 gallons
The tank can hold 4110.26 gallons of water.
To find the number of gallons a cylindrical tank can hold, calculate the volume in cubic feet using the formula V = πr^2h, where the diameter is 10 feet (radius is 5 feet) and the height is 7 feet, then multiply the volume by 7.48 gallons per cubic foot.
Explanation:To calculate the number of gallons a cylindrical tank can hold, we first need to find the volume of the cylinder in cubic feet and then convert that volume to gallons. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
Since the diameter of the tank is given as 10 feet, the radius (r) would be half of that, which is 5 feet. The height (h) is given as 7 feet. Plugging these values into the formula, we get:
V = π(5)^2(7) = π(25)(7) = π(175) cubic feet.
Using the conversion factor 7.48 gallons per cubic foot, we can find the total gallons the tank holds:
Gallons = Cubic feet × 7.48 gallons/cubic foot
Gallons = π(175) × 7.48 gallons/cubic foot
We thus calculate the total volume in gallons.
1. Find the Median Average of these distances run by 8 marathon runners:
10 km, 15 km, 12 km, 14 km, 8km, 16 km, 11 km, 15 km
Answer:
13
Step-by-step explanation:
Organizing the numbers
8 10 11 12 14 15 15 16
The median are both 12 and 14 but to get one median you add the two numbers 12 + 14 which equals 26. 26 divided by 2 numbers equals 13
Does anyone know what 8x1/6 is?
Answer: 1.33333333333
Step-by-step explanation: 8x1=8
8/6=1.33333333333
You have learned some new ways in this module to prove that triangles are similar Please describe some of these new postulates and include a diagram on the whiteboard to help explain how they are applied.
Answer:
TA = 6 units
GT = 10 units
Step-by-step explanation:
Angle G is common to both triangles, so that's a congruent angle.
Since RT is parallel to EA,
Angle R = Angle E
And
Angle T = Angle A
When two triangles have the same distribution of angles, they are similar (by AAA).
Therefore GRT and GEA are similar
GE/GR = GA/GT
8/5 = 16/(16-x)
16-x = 16 × 5/8
16 - x = 10
x = 16 - 10
x = 6
GT = 16 - x = 16 - 6 = 10
Bradley spins the spinner below 30 times. A success occurs when the spinner lands on a number that is greater than 6.
Answer:A. 1/4 - 3/4
Step-by-step explanation:For future students
Determine the number of x-intercepts that appear on a graph of each function.f (x) = (x + 5)3(x - 9)(x + 1)
Answer:
there are three x-intercepts
Step-by-step explanation:
-5, -1, 9 are all the x-intercepts that appear on the graph.
Answer: 3
Step-by-step explanation:
egde
Margaret is planning a wedding reception. She wants to spend less than her budget of 5,676, and margaret has already spent 2,652. The meal price per guest is 28. How many guests, x, can margaret invite to the reception and stay under budget?
Final answer:
To determine how many guests Margaret can invite to stay under budget, follow the steps to calculate the maximum number of guests based on the remaining budget and meal price per guest.
Explanation:
To determine how many guests Margaret can invite to stay under budget, follow these steps:
Calculate how much budget Margaret has left: $5,676 - $2,652 = $3,024.Divide the remaining budget by the meal price per guest to find out the maximum number of guests she can invite: $3,024 ÷ $28 = 108. Therefore, Margaret can invite a maximum of 108 guests and stay under budget.Randy went to the store and brought a shirt that cost $42.00 before taxes and discount. The shirt was on sale for a discount of 20% before tax. The sales taxes was 3%. What did randy pay for the shirt after discount and tax
Answer:
Step-by-step explanation:
The 20% discount amounted to ...
0.20 × $42.00 = $8.40
so the price before tax was ...
$42.00 -8.40 = $33.60
The tax amount is 3% of this value, so is ...
0.03 × $33.60 = $1.008 ≈ $1.01
So the total price paid for the shirt was ...
$33.60 +1.01 = $34.61
Randy paid $34.61 for the shirt after discount and tax.
___
Alternate solution
You can realize that the 20% discount means that Randy will pay 80% of the original price of the shirt. Similarly, the 3% added tax means Randy will finally pay 103% of the discounted price. Then the total price Randy pays is ...
$42.00×0.80×1.03 = $34.608 ≈ $34.61
Finx X: 7x=35
A) 3
B) 5
C) 7
D) 10
Answer: [tex]x=5[/tex]
Divide both sides by 7
[tex]7x/7=35/7\\x=5[/tex]
Answer:
[tex]7x = 35 \\ \frac{7x}{7} = \frac{35}{7} \\ x = 5[/tex]
hope this helps you...
A company advertises two car tire models. The number of thousands of miles that the standard model tires last has a mean \mu_S = 60μ S =60 and standard deviation \sigma_S = 5σ S =5. The number of miles that the extended life tires last has a mean \mu_E = 70μ E =70 and standard deviation \sigma_E = 7σ E =7. If mileages for both tires follow a normal distribution, what is the probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire?
Answer:
0.123
Step-by-step explanation:
Use the random variable E - S, which will follow a normal distribution with a mean of 70 - 60 = 10 and SD = \sqrt{5^2+7^}
P(E - S < 0) = 0.123
The probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123.
What is the normally distributed data?Normally distributed data is the distribution of probability which is symmetric about the mean.
The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.
A company advertises two car tire models. The number of thousands of miles that the standard model tires last has a mean and standard deviation,
[tex]\mu_S= 60[/tex]
[tex]\sigma_S = 5[/tex]
The number of miles that the extended life tires last has a mean and standard deviation,
[tex]\mu_E = 70[/tex]
[tex]\sigma_E = 7[/tex]
Use the E-S random variable rule,
[tex]E=\mu_E-\mu_s\\E=70-60\\E=10[/tex]
Similarly, the value of S,
[tex]E=\sqrt{\sigma^2_E+\sigma^2_s}\\S=\sqrt{7^2+5^2}\\S=\sqrt{49+25}\\S=\sqrt{74}\\S=8.60[/tex]
For this E-S value, the value of probability from the table of normal distribution, we get as 0.123.
[tex]P(E - S < 0)=0.123[/tex]
Thus, the probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123.
Learn more about the normally distributed data here;
https://brainly.com/question/6587992
An isosceles right triangle is always 45 45 90 triangle.
True
False
Answer:
Yes, an isosceles triangle is always 45 45 90 so its TRUE!!
Answer:
[tex]\huge \boxed{\mathrm{True}}[/tex]
Step-by-step explanation:
An isosceles right triangle is always 45 45 90 triangle.
An isosceles right triangle has a right angle or 90 degrees angle.
An isosceles right triangle has two angles equal in size.
If one angle is a right angle, then the other two will be 45 45.
Can the sides of a triangle have lengths 9.2, 7.8, and 2.1?
Step-by-step explanation:
9.2 + 7.8 = 17 > 2.1
7.8+2.1= 9.9> 9.2
9.2+2.1= 11.3 > 7.8
Since, sum of any two sides is greater than the third side, a triangle can have these lengths
12 + x = 0.80(x + 20)
Solve the linear equation
Answer:
20
Step-by-step explanation:
12+x=0.8(x+20)
Divide both sides by 0.8:
15+1.25x=x+20
Subtract x from both sides:
0.25x+15=20
Subtract 15 from both sides:
0.25x=5
Multiply both sides by 4:
x=20. Hope this helps!
Answer:
x = 20
Step-by-step explanation:
12 + x = 0.80(x + 20)
Distribute the 0.80 on the right side.
12 + x = 0.8x + 16
Subtract 0.8x from both sides.
12 + 0.2x = 16
Subtract 12 from both sides.
0.2x = 4
Divide both sides by 0.2.
x = 20
Mary is buying tickets for a movie.
• Each adult ticket costs $9.
Each child ticket costs $5.
Mary spends $110 on tickets.
- Mary buys 14 total tickets.
Answer:
adult 10
child 4
Step-by-step explanation:
for example,we buy x tickets for adults,y tickets for children.
so we can know x+y=14,9x+5y=110
5(x+y)=70
110-70=40
40/(9-5)=10,this is for adults
the rest are for child
Answer:9×10=90+15=105+5=110
Step-by-step explanation:
The circumference of a circle is 38.936 meters. What is the circle's diameter?
What’s the answer to this
Step-by-step explanation:
undefined
Answer:
C) Undefined
Step-by-step explanation:
When the slope on a graph is straight there is no slope so therefore it is undefined.
a fish tank holds 513 gallons but leaks at a rate of 4 gallons per day and 684 gallons but leak at a rate of 7 gallons per day . after how many days will the amount of water in the two tanks be the same
PLEASE HELP!!!! The edges of the diameter of a circle are at (-3,-8) and (5,7).
Write the equation of the circle in general form.
Please show your work.
Answer:
x^2 + y^2 -2x +y -71 = 0
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, so is ...
((-3, -8) +(5, 7))/2 = (-3+5, -8+7)/2 = (1, -1/2)
The square of the radius of the circle can be found from the Pythagorean theorem. The x- and y- differences between an end point and the center are the legs of a right triangle with r as the hypotenuse.
r^2 = (5 -1)^2 +(7 -(-1/2))^2 = 4^2 +7.5^2 = 16 +56.25
r^2 = 72.25
__
The standard form equation of the circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2
(x -1)^2 +(y -(-1/2))^2 = 72.25
Eliminating parentheses, we have ...
x^2 -2x +1 +y^2 +y +0.25 = 72.25
Subtracting the right-side constant and rearranging to descending powers, we find the general form of the equation to be ...
x^2 + y^2 -2x +y -71 = 0
_____
Comment on the work
Of course, you know that ...
(a -b)^2 = a^2 -2ab +b^2
This helps you simplify the squares of binomials.
Each student receives one of 4 calculator models and one of 3 types of ruler. How many possible outcomes are there if a student gets one ruler and one calculator?
Answer:
24 possible outcomes
Step-by-step explanation:
Combination has to do with selection. For example, if r object is selected from a pool of n objects, the number if possible ways can be expressed according to the combination formula:
nCr = n!/(n-r)!r!
Applying this in question, if each student receives one of 4 calculator models and one of 3 types of ruler, the number of ways this can be done is:
4C1 × 3C1
4C1 = 4!/(4-1)!1! {If a student gets one calculator)
4C1 = 4×3×2/3×2
4C1 = 4ways
3C1 = 3!/(3-2)!1! {If a student gets a ruler}
3C1 = 3×2/1
3C1 = 6ways
Total number of possible outcomes if a student gets one ruler and one calculator will be 4×6 = 24ways
What is the only solution of 2x2 + 8x = x2 - 16?
Answer:
it is 2
Step-by-step explanation:
Please help Asap will mark (Brainliest)
Kyleigh put a large rectangular sticker on her notebook. The height of the sticker measures 16 centimeters. The base is half as long as the height.The area of the notebook that the sticker covers is ____________ square centimeters.
Answer: The area of the notebook that the sticker covers is 128 cm^2
Step-by-step explanation:
The equation for the area of a rectangle should be:
[tex]A=bh[/tex]
-The height of the stickers measures 16 cm:
[tex]height = 16cm[/tex]
-So, if the base is half as long as the height, you divide it by 2:
[tex]base=\frac{16}{2}=8cm[/tex]
-Then, you substitute it:
[tex]A=16[/tex] · [tex]8[/tex]
-Result:
[tex]128cm^2[/tex]
Which expression is equivalent to 1/2- (-8)?
Answer:
1/2 + 8 is equivalent to 1/2 - (-8)
0.5 - (-8) is ALSO equivalent to 1/2 - (-8)
0.5 + 8 is another equation that is equivalent to 1/2 - (-8)
Step-by-step explanation:
Step-by-step explanation:
0.5-(-8) is equal to it
Simplify the following equation. (6x+4)+(5-2x)
Answer:
the correct answer is...
Step-by-step explanation:
4x+9
What is the only unknown (variable) needed to find the volume of a sphere?
Sphere
The radius of the sphere is the only unknown variable need to find the volume of a sphere.
Step-by-step explanation:
Sphere is a geometrical three dimensional round figure with every point on its surface equidistant from its center. It is a three dimensional representation of a circle. A line which connects from the center to the surface is called radius of the sphere.The diameter of the sphere is the longest straight line which passes through the center of the sphere.
The volume of sphere is given by:
Volume of sphere(V) = [tex]\frac{4}{3}\pi r^{3} \\[/tex]
where V is the volume of the sphere
r is the radius of the sphere
[tex]\pi = \frac{22}{7}[/tex] = 3.14
Hence the only unknown variable to find the volume of a sphere is the radius.
Let f= {(-5,1).( - 4,0).(0,6)}
Find f(0)
f(0)=
Given:
It is given that the coordinates of the function are [tex]f=\{(-5,1),(-4,0),(0,6)\}[/tex]
We need to determine the value of f(0)
Value of f(0):
The value of f(0) is the value of the function when the input is 0.
We need to determine the value of f(0) when the input is x = 0
Thus, from the coordinates of the function [tex]f=\{(-5,1),(-4,0),(0,6)\}[/tex], it is obvious that the input value of the function is x = 0 , then the value of the function f(0) = 6.
Thus, when the input value x = 0, the output is f(0) = 6.
Therefore, the value of f(0) = 6.
The reciprocal parent function is translated 5 units right and 3 units up. Write an equation to represent the new function.
Transformations:
y=ax-h+k
Answer:
The new function is [tex]y=\frac{1}{x-5}+3[/tex] , where x ≠ 5
Step-by-step explanation:
The reciprocal parent function is [tex]f(x)=\frac{1}{x}[/tex] , where x ≠ 0
The translation of f(x) to the right h units is f(x - h)
The translation of f(x) up k units is f(x) + k
The translation of f(x) to the right h units and up k units is f(x - h) + k
∵ The equation of the reciprocal parent function is [tex]y=\frac{1}{x}[/tex]
∵ The function is translated 5 units right
∴ h = 5
- That means 5 is subtracted from x ⇒ (x - 5)
∵ The function is translated 3 units up
∴ k = 3
- That means y added by 3
∴ [tex]y=\frac{1}{x-5}+3[/tex]
The new function is [tex]y=\frac{1}{x-5}+3[/tex] , where x ≠ 5
A bag contains 52 balls lettered from a to z and A to Z (i.e. uppercase or lowercase letters). One ball is withdrawn. What is the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D)?
the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D) is 0.557
Step-by-step explanation:
Here we have ,A bag contains 52 balls lettered from a to z and A to Z (i.e. uppercase or lowercase letters). One ball is withdrawn. We need to find What is the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D)? Let's find out:
There are 26 lowercase letters and 26 uppercase letters ! According to question we need to choose a ball which is either a lowercase ( i.e. from 26 letters ) or earlier in the alphabet than d ( or D ) which is A or B or , C .
Probability = (Favorable outcome)/(Total outcome)
Favorable outcome = 26+3=29
Total Outcome = 52
So ,
⇒ [tex]Probability = \frac{29}{52}[/tex]
⇒ [tex]Probability = 0.557[/tex]
Therefore , the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D) is 0.557
Final answer:
To calculate the probability of drawing a ball that is lower case or earlier in the alphabet than 'd', we count the number of qualifying balls (29) and divide by the total number (52), resulting in a probability of 29/52.
Explanation:
The student's question is about calculating the probability of drawing a ball from a bag that either contains a lower case letter or a letter that comes earlier in the alphabet than the letter 'd'. Given that the bag contains 52 balls, with each letter of the alphabet represented in both upper and lower case, we can calculate the probability by counting the number of balls that satisfy the condition and dividing by the total number of balls.
There are 3 letters in the alphabet before 'd' (‘a’, ‘b’, and ‘c’) and each comes in two forms (upper and lower case), so there are 3 * 2 = 6 balls that meet the 'earlier in the alphabet than d' criterion. Since there are 26 letters in the alphabet and each has a lower case form, there are 26 balls that are lower case.
To avoid double-counting the lower case balls ‘a’, ‘b’, and ‘c’, we subtract those 3 balls from the 26 lower case balls, resulting in 23. Adding these 23 to the 6 balls already counted, we have a total of 29 balls that satisfy either condition. The probability is therefore 29/52.
Solve the equation 2x2 + 15x – 9 = -26 to the nearest tenth.
Choose all the sets containing the number
Use the spinner to identify the probability to the nearest hundredth of the pointer
landing on a non-shaded area.
What is the slope of (2,3) and (4,6)
Answer:
The slope is 3/2
Step-by-step explanation:
6-3=3 4-2=2 3/2