The home repair crew worked for 9 days.
What is the duration of the home repair crew's work to charge $925?To determine the number of days the home repair crew worked for, we can use algebra. Let's assume that the number of days they worked for is represented by "d". We know that they charge $75 per day plus a $250 service fee, so we can set up the following equation:
75d + 250 = 925
Simplifying the equation, we get:
75d = 675
Dividing both sides by 75, we get:
d = 9
However, we need to keep in mind that the $250 service fee is a one-time charge, not a daily charge. So we need to subtract that from the total amount to get the actual amount charged for the days worked:
925 - 250 = 675
Dividing 675 by the daily rate of $75, we get:
675 / 75 = 9
Therefore, the home repair crew worked for 9 days.
Learn more about Algebra
brainly.com/question/29131718
#SPJ11
2. Rectangle WXYZ with vertices W(-3,-4), X(0,-5), Y(-2,-11),
and Z(-5, -10); 180° rotation about N(2,-3)
The rectangle WXYZ after a 180° rotation about the point N(2,-3) is W(3,-2), X(0,-1), Y(2,5), and Z(5,4).
To perform a 180° rotation about the point N(2,-3), we can follow these steps:
1. Translate the rectangle and the point N to the origin by subtracting their respective coordinates from each vertex and point.
2. Perform the rotation by multiplying the coordinates of each vertex and point by the 2x2 rotation matrix:
[cos(180°) -sin(180°)]
[sin(180°) cos(180°)]
which simplifies to:
[-1 0]
[ 0 -1]
3. Translate the rectangle and the point N back to their original positions by adding their respective coordinates to each vertex and point.
Let's apply these steps to rectangle WXYZ and point N:
1. Translate the rectangle and point N to the origin:
W' = (-3 - 2, -4 + 3) = (-5, -1)
X' = (0 - 2, -5 + 3) = (-2, -2)
Y' = (-2 - 2, -11 + 3) = (-4, -8)
Z' = (-5 - 2, -10 + 3) = (-7, -7)
N' = (2 - 2, -3 + 3) = (0, 0)
2. Perform the rotation using the matrix:
[-1 0]
[ 0 -1]
W'' = [-1 0] * [-5, -1] = [5, 1]
[0 -1]
X'' = [-1 0] * [-2, -2] = [2, 2]
[0 -1]
Y'' = [-1 0] * [-4, -8] = [4, 8]
[0 -1]
Z'' = [-1 0] * [-7, -7] = [7, 7]
[0 -1]
N'' = [-1 0] * [0, 0] = [0, 0]
[0 -1]
3. Translate the rectangle and point N back to their original positions:
W = [5 - 2, 1 - 3] = (3, -2)
X = [2 - 2, 2 - 3] = (0, -1)
Y = [4 - 2, 8 - 3] = (2, 5)
Z = [7 - 2, 7 - 3] = (5, 4)
N = [0 + 2, 0 + 3] = (2, 3)
Therefore, the rectangle WXYZ after a 180° rotation about the point N(2,-3) is W(3,-2), X(0,-1), Y(2,5), and Z(5,4).
Learn more about "rectangle": https://brainly.com/question/25292087
#SPJ11
Find the lateral surface area. Bases are isosceles triangles.
29 110 56
To find the lateral surface area of a prism with isosceles triangle bases, you'll need the following information: the slant height and the perimeter of the base.
Based on the numbers you provided (29, 110, and 56), it appears that you have the dimensions of an isosceles triangle with side lengths 29, 29, and 110 units. To find the slant height, we can use the Pythagorean theorem on one of the right triangles formed by the base and the altitude (height) of the isosceles triangle. Let's call the height h and the slant height s.
(1/2 * 110)^2 + h^2 = 29^2
3025 + h^2 = 841
h^2 = 841 - 3025 = -2184 (invalid, as there cannot be a negative height)
It seems like there is an error in the provided dimensions, as the side lengths do not form a valid isosceles triangle. Please double-check the dimensions and provide the correct information so I can help you find the lateral surface area.
To know more about Isosceles Triangle:
https://brainly.com/question/1475130
#SPJ11
Use three strategies to find 3r in terms of x and y, where dx Strategy 1: Use implicit differentiation directly on the given equation Strategy 2: Multiply both sides of the given equation by the denominator of the left side, then use implicit differentiation. Strategy 3: Solve for y, then differentiate. Do your three answers look the same? If not, how can you show that they are all correct answers?
We can follow the following strategies separated by comma's : Use implicit differentiation directly on the given equation, Multiply both sides of the given equation by the denominator of the left side, then use implicit differentiation
, Solve for y, then differentiate.
Strategy 1: Use implicit differentiation directly on the given equation Start by taking the derivative of both sides of the equation with respect to x: dy/dx = (3x^2 + 2xy)/(2y - 3) . Now solve for 3r:
3r = (dy/dx)(2y - 3)/(2x)
3r = (3x^2 + 2xy)/(4x)
3r = (3/4)x + (1/2)y
Strategy 2: Multiply both sides of the given equation by the denominator of the left side, then use implicit differentiation
Start by multiplying both sides of the equation by (2y - 3): (2y - 3)y = 3x^2 + 2xy . Simplify:
2y^2 - 3y = 3x^2 + 2xy
Now take the derivative of both sides with respect to x:
d/dx(2y^2 - 3y) = d/dx(3x^2 + 2xy)
4y(dy/dx) - 3(dy/dx) = 6x + 2y(dy/dx)
Solve for dy/dx:
dy/dx = (6x - 3y)/(2y - 4y) = (3x - y)/(y - 2)
Now solve for 3r:
3r = (dy/dx)(2y - 3)/(2x)
3r = ((3x - y)/(y - 2))(2y - 3)/(2x)
3r = (3/4)x + (1/2)y
Strategy 3: Solve for y, then differentiate Start by solving the given equation for y: 2y^2 - 3y = 3x^2 + 2xy
2y^2 - 2xy - 3y - 3x^2 = 0
Use the quadratic formula:
y = (2x ± sqrt(4x^2 + 24x^2))/4
Simplify:
y = (x ± sqrt(7)x)/2
Now take the derivative of y with respect to x:
dy/dx = (1 ± (1/2)sqrt(7))/(2)
Solve for 3r:
3r = (dy/dx)(2y - 3)/(2x)
3r = ((1 ± (1/2)sqrt(7))/(2))(2(x ± sqrt(7)x)/2 - 3)/(2x)
3r = (3/4)x + (1/2)y
All three strategies result in the same answer for 3r in terms of x and y, which is (3/4)x + (1/2)y. This can be shown by simplifying the expressions obtained in each strategy and verifying that they are equivalent. Unfortunately, we cannot proceed with the explanation as the given equation is missing from the student question. Please provide the equation involving x, y, and r to receive a detailed step-by-step explanation of the three strategies.
Learn More About Implicit Differentiation: https://brainly.com/question/20319481
#SPJ11
Select all of the following that represent the part of the grid that is shaded.
A ten-by-ten grid has 7 columns shaded.
A.
70
100
B.
7
10
C.
70
10
D.
0. 07
E.
0. 7
A ten-by-ten grid has 7 columns shaded. All of the following that represent the part of the grid that is shaded are : The correct answer is (A) 70 and (B) 7.
The information given in the problem tells us that a ten-by-ten grid has 7 columns shaded. Since there are a total of 10 columns in the grid, this means that 7/10 of the columns are shaded.
To express this as a percentage, we can divide 7 by 10 and multiply by 100:
(7/10) x 100 = 70%
Therefore, 70 represents the percentage of columns that are shaded in the grid. Option (A) is correct.
Alternatively, we can express the same proportion as a decimal by dividing 7 by 10:
7/10 = 0.7
Therefore, 0.7 represents the proportion of columns that are shaded in the grid. Option (E) is incorrect because it shows 0.7 as a fraction instead of a decimal.
Option (B) is also correct because it correctly identifies the number of shaded columns as 7. Option (C) is incorrect because it includes both the percentage and the number of shaded columns, which is redundant. Option (D) is incorrect because it shows the proportion of shaded columns as a decimal with an extra zero.
To know more about grid, refer to the link below:
https://brainly.com/question/29774894#
#SPJ11
) On January 2, 2019, Helmkamp Company purchased a $30,000 machine. It had an estimated useful life of 5 years and a residual value of $3,000. What is the amount of depreciation expense for 2020, the second year of the asset's life, using the double declining-balance method? (Round intermediary calculations to two decimal places and your final answer to the nearest dollar. )
The required answer is the double declining-balance method is $9,840.
To calculate the depreciation expense for 2020 using the double declining-balance method, we first need to determine the asset's straight-line depreciation rate. This is calculated by subtracting the residual value from the cost of the asset and dividing by the asset's useful life:
Depreciation base = $30,000 - $3,000 = $27,000
Annual depreciation expense (straight-line) = Depreciation base / Useful life = $27,000 / 5 = $5,400
Next, we need to determine the double declining-balance rate, which is twice the straight-line rate. Therefore:
Double declining-balance rate = 2 x (1 / Useful life) = 2 x (1 / 5) = 0.40 or 40%
Now we can calculate the depreciation expense for 2020:
Depreciation expense (2020) = Book value (beginning of year) x Double declining-balance rate
The book value at the beginning of 2020 would be the cost of the asset minus accumulated depreciation for the first year:
Book value (beginning of 2020) = $30,000 - ($5,400 x 1) = $24,600
As a result, depreciation increases during the initial year of possession and decreases thereafter.
Therefore:
Depreciation expense (2020) = $24,600 x 0.40 = $9,840
So the amount of depreciation expense for 2020, the second year of the asset's life,
using the double declining-balance method is $9,840.
To know more about the double declining-balance. Click on the link.
https://brainly.com/question/30451432
#SPJ11
If sin a = -4/5
and sec B =5/3
for a third-quadrant angle a and a first-quadrant angle Ã, find the following
(a)
sin(a + B)
(b)
tan(a + b)
(c) the quadrant containing a + B
O Quadrant I
O Quadrant II
O Quadrant III
O Quadrant IV
Since sin(a) is negative and a is in the third quadrant, we can use the Pythagorean identity to find cos(a):
[tex]cos^2(a) + sin^2(a) = 1[/tex]
[tex]cos^2(a) + (-4/5)^2 = 1[/tex]
[tex]cos^2(a) = 9/25[/tex]
cos(a) = -3/5 (since a is in the third quadrant)
Similarly, since sec(B) = 5/3, we can use the definition of secant to find cos(B):
sec(B) = 1/cos(B) = 5/3
cos(B) = 3/5
(a) To find sin(a + B), we can use the sum formula for sine:
sin(a + B) = sin(a) cos(B) + cos(a) sin(B)
= (-4/5)(3/5) + (-3/5)(4/5)
= -12/25 - 12/25
= -24/25
(b) To find tan(a + B), we can use the sum formula for tangent:
tan(a + B) = (tan(a) + tan(B)) / (1 - tan(a) tan(B))
To find tan(a), we can use the identity: [tex]tan^2(a) + 1 = sec^2(a)[/tex]
[tex]tan^2(a) = sec^2(a) - 1 = (5/3)^2 - 1 = 16/9[/tex]
tan(a) = -4/3 (since a is in the third quadrant)
To find tan(B), we can use the identity: tan(B) = sin(B) / cos(B) = 4/3
Plugging these values into the formula for tan(a + B), we get:
tan(a + B) = (-4/3 + 4/3) / (1 + (-4/3)(4/3))
= 0 / (1 - 16/9)
= 0
(c) To determine the quadrant containing a + B, we need to consider the signs of sin(a + B) and cos(a + B).
From part (a), we know that sin(a + B) is negative. To determine the sign of cos(a + B), we can use the Pythagorean identity:
[tex]sin^2(a + B) + cos^2(a + B) = 1[/tex]
Substituting sin(a + B) = -24/25, we get:
[tex](-24/25)^2 + cos^2(a + B) = 1[/tex]
[tex]cos^2(a + B) = 1 - (-24/25)^2[/tex]
cos(a + B) = ±7/25
Since cos(a + B) is positive in the first and fourth quadrants, and negative in the second and third quadrants, we can conclude that a + B is in the third quadrant, since cos(a + B) is negative and sin(a + B) is negative.
To know more about Pythagorean identity refer here
https://brainly.com/question/10285501#
#SPJ11
PLS HELP!
Joanna went school supply shopping. She spent $23.25 on notebooks and pencils. Notebooks cost $2.49 each and pencils cost $1.08 each. She bought a total of 15 notebooks and pencils. How many of each did she buy?
Answer: 10 pencils and 5 notebooks.
Step-by-step explanation:
We will create a system of equations using the information given. Let n be equal to the number of notebooks and p be equal to the number of pencils.
She spent $23.25 on notebooks and pencils. Notebooks cost $2.49 each and pencils cost $1.08 each.
$2.49n + $1.08p = $23.25
She bought a total of 15 notebooks and pencils.
n + p = 15
Next, we will solve for p by substituting.
n + p = 15 ➜ n = 15 - p
$2.49n + $1.08p = $23.25
$2.49(15 - p) + $1.08p = $23.25
$37.35 - $2.49p + $1.08p = $23.25
$37.35 - $1.41p = $23.25
-$1.41p = -$14.10
p = 10 pencils
Lastly, we will solve for n by substituting:
n = 15 - p
n = 15 - 10
n = 5
If 7 + 2x = 3x - 1, then what is x?
Answer:
7 + 2x = 3x - 1
3x-2x = 7+1
x = 8
Step-by-step explanation:
is the function f(x)=-x^(2)-8x+19 minimum or maximum value
Answer:
minimum
Step-by-step explanation:
Lisa invested money into a bank account. The value of the account after t years can be found using the function f(t)=6320(1.054)t . What is the initial value of the account?
The initial value of the account is: 6320
How to solve compound interest problems?Compound interest is defined as the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 10% interest each year, you'll have $110 at the end of the first year.
The general formula to find compound interest is:
A = P(1 + r/n)^t
where:
A is final amount
P is initial principal balance
r is interest rate
n is number of times interest applied per time period
t is number of time periods elapsed
We are given the equation as:
f(t) = 6320(1.054)^(t)
Thus, the initial value is 6320
Read more about compound interest at: https://brainly.com/question/24274034
#SPJ1
The volume of a paper cone of radius 2. 4cm is 95. 4 cm3. The paper is cut along the slant height from O to AB. The cone is opened to form a sector OAB of a circle with centre O. Calculate the sector angle x°. [The volume, V, of a cone with radius r and height h is V= 1/3 x pi x r^2 x h. ]
The sector angle formed by the cone when it is opened is 54°.
V = 95.4 cm³
r = 2.4 cm
Calculating the height of the cone using the volume formula,
V= 1/3 x π x r² x h
Substituting the values -
95.4 = 1/3 x 3.14 x 2.4² x h
95.4 = 6.03 x h
h = 15.8 cm
Calculating the slant height using the Pythagoras theorem -
l = √(h² + r²)
Substituting the values -
l = √(15.8² + 2.4²)
l = 16
Calculating the curved surface area of the cone -
= πrl
= π(2.4)(16)
= 120.6 cm².
Calculating the sector angle of the sector formed -
The curved surface area of the cone = area of the sector formed by the cone
= 120.6 cm².
Area of a sector in a circle = ∅/360 × πr²,
120.6 = ∅/360 × (3.14)(16²)
120.6 = ∅/360 × 803.84
(120.6)(360) = (∅)(803.84)
43,416/803.84 = ∅
∅ = 54°
Read more about cone on:
https://brainly.com/question/6613758
#SPJ4
Peter gets a part-time job cleaning and maintaining his community's swimming pool and spa. 40 Here are some facts about the pool and spa. There is an outlet for a vacuum halfway along the side of the pool. What is the approximate length the hose should be to reach any part of the pool surface from there? Show your work. Answer Between _and _ft.
The length of the hose to reach any part of the pool surface from there will be 22.36 feet.
How to calculate the length:Length of hose = √(L² + W²)
The pool is 20 feet long and 10 feet wide, the length of the hose needed would be approximately:
Length of hose = √(20² + 10²) = √500 = 22.36 feet
Therefore, Peter would need a vacuum hose that is approximately 22.36 feet long to reach any part of the pool surface from the outlet.
Learn more about length on
https://brainly.com/question/28322552
#SPJ1
Helppppppppppppppppp
Answer:
it would be at point (6,3)
Step-by-step explanation:
If you were to reflect it over the x-axis you would get (-6,3)
he circumference of an inflated basketball is 29.516 inches. What is the volume of the basketball? Use 3.14 for π. Round final answer to the nearest whole number.
Use 3.14 for π. PLSSSS HELPPP
the volume of the basketball is approximately 490 cubic inches. we can get this answer by using volume formula of volume
what is approximately ?
"Approximately" means almost, but not exactly. It is used to indicate that a value or quantity is very close to the true or exact value, but there may be a small difference or error. In mathematical terms, an approximate value is an estimate or a rounded value that is used
In the given question,
To find the volume of the basketball, we first need to find its radius.
Circumference of a sphere = 2πr
29.516 = 2 * 3.14 * r
r = 29.516 / (2 * 3.14) ≈ 4.7 inches (rounded to one decimal place)
Now, we can use the formula for the volume of a sphere:
Volume of sphere = (4/3) * π * r^3
Volume of basketball = (4/3) * 3.14 * (4.7)^3
Volume of basketball ≈ 490 cubic inches (rounded to the nearest whole number)
Therefore, the volume of the basketball is approximately 490 cubic inches..
To know more about approximately , visit:
https://brainly.com/question/30945002
#SPJ1
Would anyone be willing to help me out with a few math questions? I'm up late and could really use the help!
Marcus estimated the mass of a grain of sugar as 6 x 10-4 gram. Based on that
estimate, about how many grains of sugar are there in a small bag of sugar
that weighs 0. 24 kilogram?
There are 400,000 grains of sugar in a small bag of sugar that weighs 0.24 kilograms.
To find out how many grains of sugar are there in a small bag of sugar that weighs 0.24 kilograms, based on Marcus' estimate, follow these steps:
1. Convert the mass of the bag of sugar from kilograms to grams: 0.24 kg * 1000 g/kg = 240 g.
2. Use Marcus' estimate of the mass of a grain of sugar: 6 x 10^-4 g.
3. Divide the total mass of the bag of sugar by the mass of a single grain of sugar: 240 g / (6 x 10^-4 g/grain).
Now, let's perform the calculation:
240 g / (6 x 10^-4 g/grain) = 240 g / 0.0006 g/grain = 400,000 grains.
To learn more about weight
https://brainly.com/question/15468401
#SPJ11
Data was taken on carpooling in Tallahassee,
Florida. For each person's daily commute, the number
of people in the car was recorded. The results are
summarized in the bar graph at left. What is the
median number of people in the car?
100
80
60-
Percent of population
20
0+
2
3 4 or more
Number of people in car
Answer:34
Step-by-step explanation:
A cup has a capacity of 320 ml. It takes 58 cups to fill a bucket and 298 buckets to fill a tank. By rounding to 1 significant figure, estimate the capacity of the tank in litres.
______________________________
Notes: 1L = 1,000ml BUCKET:= 320ml × 58= 18,560mlTANK:= 18,560ml × 298= 5,382,000ml= 5,382,000ml ÷ 1,000= 5,382= ~ 5.4LThe Capacity of The Tank Is Approx. 5.4L_______________________________
Gertrude bought a used car for $14,890. She was surprised that the dealer then added $1,280. 54 as a sales tax. What was the sales tax rate for this purchase? Round to one decimal place
The sales tax rate for Gertrude's car purchase was 8.6%.
Gertrude bought a used car for $14,890. She was surprised that the dealer then added $1,280. 54 as a sales tax. The total cost of Gertrude's car purchase, including the sales tax, was $14,890 + $1,280.54 = $16,170.54. Let x be the sales tax rate, expressed as a decimal. Then we can set up the equation:
$14,890 * x = $1,280.54
Solving for x, we get:
x = $1,280.54 / $14,890 ≈ 0.086
Multiplying by 100 to convert to a percentage, we get 8.6%. Therefore, the sales tax rate for Gertrude's car purchase was 8.6%.
For more questions like Taxes click the link below:
https://brainly.com/question/1362871
#SPJ11
The average first year teacher salary in a certain state is known to be $52,000 with a standard deviation of $1500. A researcher tests this claim by averaging the salaries of 25 first year teachers and finding their average salary to be $52,525. Is there significant evidence to suggest that the claim is wrong at the 5% significance level?
Option C is correct. No, the least value is smaller than the critical value.
Null hypothesis (H₀): The average first-year teacher salary is $52,000.
Alternative hypothesis (Ha): The average first-year teacher salary is not $52,000.
The significance level is 5% (or 0.05), which means we will reject the null hypothesis if the probability of obtaining the observed result is less than 5%.
Calculate the standard error of the mean:
Standard Error = Standard Deviation / √n
where n is the number of samples (n = 25 in this case).
Standard Error = $1500 / √25
= $1500 / 5
= $300
Now, perform the hypothesis test using a t-test since the sample size is relatively small (n < 30) and the population standard deviation is unknown.
t-score = (Sample Mean - Population Mean) / Standard Error
t-score = ($52,525 - $52,000) / $300
t-score = $525 / $300
t-score = 1.75
To find the critical value at a 5% significance level with 24 degrees of freedom (n - 1), we can consult a t-table. At a 5% significance level (two-tailed test), the critical t-value is approximately ±2.064.
Since the calculated t-score (1.75) is not greater than the critical t-value (2.064), we fail to reject the null hypothesis.
Therefore, option C is correct. No, the least value is smaller than the critical value.
To learn more on Statistics click:
https://brainly.com/question/30218856
#SPJ12
Complete question:
The average first year teacher salary in a certain state is known to be $52,000 with a standard deviation of $1500. A researcher tests this claim by averaging the salaries of 25 first year teachers and finding their average salary to be $52,525. Is there significant evidence to suggest that the claim is wrong at the 5% significance level?
A. Yes, the least value is greater than the critical value
B. No, the least value is larger than the critical value
C. No, the least value is smaller than the critical value
D. yes, the least value is smaller than the critical value
A rectangular fish tank needs to hold 500 gallons, and it needs to be two feet deep. The top will be open. A. Find the width and length of the tank that will use the smallest amount of glass. B. The tank will be filled with enough water so that there will be two inches of head space. Find the weight of the water in the tank
The weight of the water in the tank is approximately 3,809 pounds.
A. To find the width and length of the tank that will use the smallest amount of glass, we need to consider the surface area of the tank. Let's use "x" to represent the length and "y" to represent the width. The formula for the surface area of a rectangular tank is:
Surface Area = 2xy + 2xz + 2yz
Since the top of the tank will be open, we can ignore the surface area of the top. We know that the tank needs to hold 500 gallons and be 2 feet deep, so we can use the formula for the volume of a rectangular tank to solve for one of the variables:
Volume = Length x Width x Depth
500 = xy x 2
xy = 250
Now we can substitute this into the surface area formula and simplify:
Surface Area = 2(250) + 2xz + 2yz
Surface Area = 500 + 2xz + 2yz
To minimize the surface area, we need to differentiate this formula with respect to one of the variables and set it equal to zero. Let's differentiate with respect to x:
d(Surface Area)/dx = 2z
Setting this equal to zero, we get:
2z = 0
z = 0
This doesn't make sense, so let's try differentiating with respect to y:
d(Surface Area)/dy = 2z
Setting this equal to zero, we get:
2z = 0
z = 0
Again, this doesn't make sense. We can conclude that the surface area is minimized when x = y, so the tank should be square. Since xy = 250, we can solve for the side length of the square:
x^2 = 250
x ≈ 15.81 feet
So the tank should be approximately 15.81 feet by 15.81 feet to use the smallest amount of glass.
B. The volume of the water in the tank will be:
Volume = Length x Width x Depth
Volume = 15.81 x 15.81 x 1.67
Volume = 397.25 gallons
Since the tank needs to hold 500 gallons with 2 inches of head space, we can find the weight of the water using the formula:
Weight = Volume x Density
The density of water is approximately 8.34 pounds per gallon, so:
Weight = 397.25 x 8.34
Weight ≈ 3,313.69 pounds
So the weight of the water in the tank will be approximately 3,313.69 pounds.
A. To minimize the amount of glass used for the rectangular fish tank, you'll need to create a tank with equal width and length (a square base). Since the tank needs to hold 500 gallons and is 2 feet deep, you can use the formula: Volume = Length × Width × Depth. Convert 500 gallons to cubic feet (1 gallon ≈ 0.1337 cubic feet), so 500 gallons ≈ 66.85 cubic feet.
66.85 = Length × Width × 2
33.425 = Length × Width
Since the length and width are equal, you can solve for one of the dimensions:
Length = Width = √33.425 ≈ 5.78 feet
So, the tank dimensions will be approximately 5.78 feet by 5.78 feet by 2 feet.
B. To find the weight of the water in the tank, first determine the volume of the water. There will be 2 inches of headspace (2 inches ≈ 0.167 feet), so the water depth is 2 - 0.167 = 1.833 feet. The volume of the water is:
Volume = Length × Width × Depth = 5.78 × 5.78 × 1.833 ≈ 61.05 cubic feet
To find the weight of the water, multiply the volume by the weight of water per cubic foot (62.43 lbs/cubic foot):
Weight = 61.05 × 62.43 ≈ 3,809 lbs
learn more about volume of a rectangle here: brainly.com/question/30759574
#SPJ11
There are ten slips of paper in a box, each numbered 1-10. If Gerard reaches into the box without looking, what is the probability that he will get a number less than 3?
69 ptssssssss
Answer: 1/5
Step-by-step explanation:
There are 10 slips of paper.
The only numbers less than three are 1 and 2
The probability that he will pick up a slip of paper less than three is 2 since only 1 and 2 are less than three.
Therefore the probability is 2/10, and when simplified, it is 1/5.
Therefore the answer is 1/5.
If you have any more questions feel free to ask in the comments! I'd be happy to help!
A grocery store’s earnings in dollars can be modeled by the equation y 5 0. 75x 2 0. 15x, where x represents the number of tomatoes that they sell. If they sell 200 tomatoes in one day, how much money do they earn?
The grocery store's earning income is $30,030 if they sell 200 tomatoes in one day.
We need to find how much the grocery store earns when it sells 200 tomatoes in one day. When The grocery store’s earnings in dollars can be modeled by the equation,
y = 0.75x² + 0.15x
where,
x = number of tomatoes they sell = 200
To find the earnings we need to substitute x in the equation it can be given as,
y = 0.75x² + 0.15x
y = 0.75(200)² + 0.15(200)
y = $30,030
Therefore, the grocery store's earning income is $30,030 if they sell 200 tomatoes in one day.
To learn more about income :
https://brainly.com/question/30157678
#SPJ4
can someone help me?
Answer:12
Step-by-step explanation:
A bank is offering 3. 5% simple interest on a savings account. If you earned $525 in interest in 2 years, how much did you deposit in the savings?
The amount deposited is 7500 in the bank with 3. 5% simple interest on a savings account.
To solve this problem, we need to use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal (amount deposited)
r = Interest rate per year (as a decimal)
t = Time (in years)
In this case, we know that the interest rate is 3.5% or 0.035 as a decimal.
We also know that the interest earned is $525, and the time period is 2 years.
So, we can plug in these values and solve for the principal:
525 = P * 0.035 * 2
Simplifying the equation, we get:
525 = 0.07P
Dividing both sides by 0.07, we get:
P = 7500
Therefore, the amount deposited in the savings account was $7500.
Learn more about simple interest : https://brainly.com/question/25845758
#SPJ11
The square below has an area of x^ 2 − 12 x + 36 What expression represents the length of one side of the square?
The length of one side of the square is x - 6 units
How to determine the lengthThe formula for calculating the area of a square is expressed as;
A = a²
Such that the a is the length of its side
From the information given, we have that;
Area = x^ 2 − 12 x + 36
solve the quadratic expression, we have that;
x² - 6x - 6x + 36
group in pairs
(x²- 6x) - (6x + 36)
factorize the terms
x(x - 6) - 8(x - 6)
Then, we have;
(x - 6) and (x - 6) units
Learn about squares at: https://brainly.com/question/25092270
#SPJ1
After a teacher handed out
m packs of notebooks with c notebooks in each pack, he has 13 notebooks left. how many notebooks did he originally have?
The teacher originally had [tex]m*c + 13[/tex] notebooks.
How many notebooks the teacher originally had?If the teacher handed out m packs of notebooks with c notebooks in each pack, then the total number of notebooks that he gave out would be [tex]m*c[/tex].
If he gave out m packs of notebooks with c notebooks in each pack and has [tex]13[/tex] notebooks left, then the total number of notebooks he originally had would be:
[tex]m*c + 13[/tex]
Therefore, the expression for the total number of notebooks originally had by the teacher is [tex]m*c + 13[/tex].
To learn more about such notebook problems:
brainly.com/question/2150889
#SPJ11
A consumers group is concerned with the mean cost of dining in a particular restaurant. a random sample of 40 charges (in dollars) per person has a mean charge of $39. 7188 with standard deviation of $3. 5476. is there sufficient evidence to conclude that the mean cost per person exceeds $38. 0
The test statistic is calculated to be 4.05, which is greater than the critical value of 2.704 at a significance level of 0.05, indicating strong evidence to reject the null hypothesis and conclude that the mean cost per person exceeds $38.0.
To test if there is sufficient evidence to conclude that the mean cost per person exceeds $38.0, we can perform a one-sample t-test.
Using the given information, the test statistic is calculated as
t = (39.7188 - 38.0) / (3.5476 / √(40)) = 4.05.
Using a t-table with 39 degrees of freedom (n-1), the p-value is found to be less than 0.01.
Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean cost per person exceeds $38.0.
To know more about Null hypothesis:
https://brainly.com/question/28920252
#SPJ4
I need this problem solved.
The relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
You can compare various data sets using bar graphs.
In a line graph, the data is represented by tiny dots, and the line that connects them indicates what happens to the data.
So, we have the coordinates:
(-1, 3); (-2, 4); (1, 2); (2, 4)
Now, plot it on the graph as follows:
(Refer to the graph attached below.)
(-1, 3) and (-2, 4) are in the 2nd quadrant, and (1, 2) and (2, 4) are in the 1st quadrant.
Therefore, the relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).
Know more about a graph here:
https://brainly.com/question/19040584
#SPJ1
Correct question:
Express the relation (-1, 3); (-2, 4); (1, 2); (2, 4) on the graph.
Eighth grade AA.1 Find the slope of a greph DIM
Look at this graph:
AY
100
90
80
70
60
50
40
0
30
20
10
10 20 30 40 50 60 70
80 90 100
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Video
D
Questi-
answe
3
Ti
elar
00
HR
Sma
out
Sign
The slope of this graph is equal to 2.
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given points into the formula for the slope of a line, we have the following;
Slope, m of graph = (80 - 0)/(100 - 60)
Slope, m of graph = 80/40
Slope, m of graph = 2.
Read more on slope here: brainly.com/question/3493733
#SPJ1