The true statements are (a) A sphere with half the radius has 1/8 of the volume and (c) A sphere with 3 times the radius has 27 times the volume
Finding the true statements from the radius and volumeGiven that the radius of the sphere is represented as
Radius, r = 4 inches
The formula of the volume of the sphere is represented as
V = 4/3πr³
For the transformed volume, we have
V₂ = 4/3πR³
Where
R = kr and k is the scale factor
So, we have
V₂ = 4/3π(kr)³
V₂ = 4/3πr³k³
This gives
V₂ = Vk³
Testing the statements, we have
(a) A sphere with half the radius has 1/8 of the volume
V₂ = V(1/2)³
Evaluate
V₂ = 1/8V
So, the statement is true
(b) A sphere with twice the radius has 6 times the volume
V₂ = V(2)³
Evaluate
V₂ = 8V
So, the statement is false
(c) A sphere with 3 times the radius has 27 times the volume
V₂ = V(3)³
Evaluate
V₂ = 27V
So, the statement is true
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Complete question
A sphere has a radius of 4 inches.
Choose True or False for each statement.
(a) A sphere with half the radius has 1/8 of the volume
(b) A sphere with twice the radius has 6 times the volume
(c) A sphere with 3 times the radius has 27 times the volume
or
Last night, Clara and her brother, Stefan, made personal pizzas for dinner. Clara put 4 pepperoni pieces and 6 ham pieces on her pizza. Stefan put 6 pepperoni pieces and 10 ham pieces on his pizza. Did Clara's and Stefan's pizzas have the same ratio of pepperoni pieces to ham pieces?
Clara's and Stefan's pizzas did not have the same ratio of pepperoni pieces to ham pieces.
How to calculate the ratios of two different pizza?For Clara,
The number of pepperoni pieces = 4
The number of ham pieces = 6
The ratio = 4:6 = 2:3
For Stefan,
The number of pepperoni piece = 6
The number of ham piece = 10
The ratio = 6:10 = 3:5
Therefore the ratio of Clara's and Stefan's pizzas is not the same.
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Question in attachment...................
Answer:
12.5ft tall.
Step-by-step explanation:
The volume of a rectangular box is V = L x W x H
We are given volume, length, and width, allowing us to solve for height.
3000 ft^3 = 96 ft x 2.5 ft x H ft
Divide both sides by 96 x 2.5 to isolate H
3000 / (96 x 2.5) = H
H = 12.5 ft.
Answer:
12.5 feetStep-by-step explanation:
It's given that One of the first electronic computer was in the shape of a huge box. It was 96 m long and 2.5 m wide.
Length of the box = 96 feet
Breadth of the box = 2.5 feet
Also The amount of space inside was approximately 3,000 cubic feet i.e volume of the box is 3000 ft³.
We know that volume of cuboid is calculated by,
Volume = l × b × h96 × 2.5 × h = 3000
240 × h = 3000
h = 3000/240
h = 12.5 feet
Therefore, Height of the computer is 12.5 feet
A basketball with a 12 cm radius is placed into a 24 cm x 24 cm x 24 cm box. The
amount of space inside the box but outside the basketball is
cm³
(Use 3.14 for 7).
The amount of space or volume inside the box but outside the basketball is 6589.44 cm³.
We have to find the volume of the box and volume of the basketball to determine the space outside it.
Box is in rectangular shape.
Volume of the box = 24 × 24 × 24
= 13824 cm³
Basketball is spherical in shape.
Volume of the sphere = 4/3 π r³
= 4/3 π (12)³
= 2304π
= 7234.56 cm³
Amount of space inside the box but outside the basketball is,
13824 cm³ - 7234.56 cm³ = 6589.44 cm³
Hence the required space is 6589.44 cm³.
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Evaluate the surface integral ∫∫H4ydA where H is the helicoid (i.e., spiral ramp) given by the vector parametric equation
r⃗ (u,v)=⟨ucosv,usinv,v⟩, 0≤u≤1, 0≤v≤9π.
According to the given information, the value of the surface integral is 8/3.
What is surface area?The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.
According to the given information:The surface integral of a vector field F over a surface S is given by:
∬S F ⋅ dS = ∬R (F ⋅ ru × rv) dA
where R is the parameter domain of the surface S, ru and rv are the partial derivatives of the position vector r(u,v) with respect to u and v, and dA = ||ru × rv|| dudv is the area element on the surface.
In this case, we want to evaluate the surface integral:
∫∫H 4y dA
where H is the helicoid given by the vector parametric equation:
r(u,v) = <u cos(v), u sin(v), v>, 0 ≤ u ≤ 1, 0 ≤ v ≤ 9π.
The position vector r(u,v) has partial derivatives with respect to u and v given by:
ru = <cos(v), sin(v), 0>
rv = <-u sin(v), u cos(v), 1>
The area element is given by:
dA = ||ru × rv|| dudv = ||<cos(v), sin(v), u>| dudv = u dudv
Therefore, the surface integral can be written as:
[tex]$\int\int_H 4y dA = \int_0^{9\pi} \int_0^1 4(u\sin v)u dudv$\\$= \int_0^{9\pi} \sin v \int_0^1 4u^2 du dv$[/tex]
[tex]$= \int_0^{9\pi} \sin v \left(\frac{4}{3}\right) dv$\\$= \left[-\frac{4}{3} \cos v\right]_0^{9\pi}$[/tex]
= 8/3
Hence, According to the given information the value of the surface integral is 8/3.
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Please Help Quickly ASAP Hurry Geometry
Questions in the picture
The area of the figure, given the vertices on the coordinate plane, is 14 square units.
How to find the area ?The shoelace formula can be used to find the area. First, find the sum of the products :
= ( - 1 × 2 ) + ( -2 × - 3 ) + ( 4 × 2 ) + ( 4 × 4 ) + (1 × -2)
= 2 + 6 + 8 + 16 - 2
= 26
Then the products of the y coordinate and the x coordinates :
= ( -2 × - 2 ) + (2 × 4 ) + ( - 3 × 4 ) + ( 2 × 1) + ( 4 × -1 )
= - 2
We can then find the absolute value to be:
= | Sum 1 - Sum 2 | = | 26 - (- 2 ) | = | 26 + 2 | = 28
The area is then:
= 28 / 2
= 14 square units
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NO LINKS!!! URGENT HELP PLEASE!!
Express the statement as an inequality Part 5a^2
Answer:
a) x < 0 excluding zero.
b) y ≥ 0
Step-by-step explanation:
a)
"x is negative": This means that x is less than zero. Negative numbers are any numbers less than zero, so this statement implies that x is a negative number. For example, x could be -1, -2, -3, and so on.
so answer is x < 0 excluding zero.
"x > 0": This means that x is greater than zero. Positive numbers are any numbers greater than zero, so this statement implies that x is a positive number. For example, x could be 1, 2, 3, and so on."x ≤ 0": This means that x is less than or equal to zero. Non-positive numbers are any numbers less than or equal to zero, so this statement implies that x could be zero or any negative number. For example, x could be -1, -2, -3, or 0."x < 0": This means that x is strictly less than zero. This statement implies that x is a negative number, but it does not include zero. For example, x could be -1, -2, -3, and so on, but not 0."X < 20": This means that x is less than 20. Any number less than 20 satisfies this statement, so x could be any negative number, zero, or any positive number less than 20."x = 0": This means that x is exactly equal to zero. The value of x is not positive or negative, but zeroThe inequality that expresses the statement "x is less than 0" using the expression "5a^2" would be:
5a^2 > 0 and x < 0
Here, the expression "5a^2 > 0" means that the value of "5a^2" is positive for any non-zero value of "a". Therefore, the expression "5a^2 > 0" is true for all non-zero values of "a". The inequality "x < 0" means that "x" is negative, or less than zero.
So, combining the two expressions, we get the inequality:
5a^2 > 0 and x < 0
b)
The statement "y is nonnegative" means that y is greater than or equal to zero. Therefore, the valid options for y are:
"y ≥ 0": This means that y is greater than or equal to zero. Any non-negative number satisfies this statement, so y could be 0, 1, 2, and so on."y > 0": This means that y is strictly greater than zero. Any positive number satisfies this statement, so y could be 1, 2, and so on, but not 0."y ≤ 0": This means that y is less than or equal to zero. The only value that satisfies this statement is y = 0."y < 0": This means that y is strictly less than zero. No non-negative number satisfies this statement, so there are no valid options for y in this case."y = 0": This means that y is exactly equal to zero. This statement is true because zero is nonnegative.Therefore, the valid option for y is y ≥ 0.
As the given statement "y is nonnegative" cannot be expressed as an inequality involving the expression "5a^2". The expression "5a^2" is a polynomial in the variable "a", and it is not related to the variable "y" in the statement.
The inequality that expresses the statements "x is less than 0" and "y is non-negative" using the expression "5a^2" would be:
5a^2 > 0 and y ≥ 0 and x < 0
Here, the expression "5a^2 > 0" means that the value of "5a^2" is positive for any non-zero value of "a". Therefore, the expression "5a^2 > 0" is true for all non-zero values of "a".
The inequality "y ≥ 0" means that "y" is non-negative, or greater than or equal to zero.
The inequality "x < 0" means that "x" is negative, or less than zero.
So, combining the three expressions, we get the inequality:
5a^2 > 0 and y ≥ 0 and x < 0
I hope this helps!
Provide an example of a function that does not have an inverse function. Explain how you determined this.
Answer:
f(x) = x^2
Step-by-step explanation:
A function that does not have an inverse function is called a non-invertible or many-to-one function. An example of a non-invertible function is:
f(x) = x^2
To determine if a function is invertible, we need to check if it passes the horizontal line test. If a horizontal line intersects the graph of the function at more than one point, then the function is not invertible.
For the function f(x) = x^2, if we draw a horizontal line at any value of y, it will intersect the graph of the function at two points, one on the positive x-axis and the other on the negative x-axis.
Therefore, f(x) is not invertible, as it fails the horizontal line test.
In other words, there are multiple x-values that correspond to a single y-value. For example, both x = 2 and x = -2 have the same y-value of 4. As a result, there is no unique inverse function that could map a value of 4 back to a single x-value.
In conclusion, the function f(x) = x^2 is an example of a non-invertible function, as it fails the horizontal line test and does not have a unique inverse function.
Nora has 3 poster boards. She plans to divide them into sixths. How many sixths can Nora make from the 3 poster boards?
EACH STUDENT IN MR COOPERS CLASS GOT A APPLE ON THEIR FIELD TRIP TO THE APPLE ORCHAD THERE ARE 9 STUDENTS ON THE FIELD TRIP AND EACH APPLE HAS A MASS OF 70 G WHAT IS THE TOTAL MASS OF ALL THE APPLES
Which ordered pair is not included in a graph of y= 2 x + 5
Mimi chose A (0,0) how did she get that answer? and is she correct.
Use the following scenario. Five surf shops sell the same pair of flip-flops for the following set of prices: {$17.00, $15.50, $15.00, $18.00, $15.00}.
Select all the correct measures of center and variation for the data set.
a. Range = 4
b. IQR = 2.50
c. Median = 15.50
d. Third quartile = 17.50
e. Mean = 15.80
Answer: b, c, d,
have an amazing day/night and go crush that homework!! you are loved
brainliest??
a circle has a circumerence of 6 and an arc with a 60 degree central angle. what is the length of the arc
The length of the arc is 1 unit.
What is length of an arc?The distance that runs through the curved line of the circle making up the arc is known as the arc length.
length of an arc is expressed as;
l = tetha/360 ×2πr
the circumference of circle is expressed as ;
C = 2πr
6 = 2×3.14 × r
r = 6/6.28
r = 0.955 units
Therefore length of the arc
= 60/360 × 6
since 2πr is the circumference,
l = 360/360 = 1 unit
therefore the length of the arc is 1 unit.
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PLEASE HELP SO EASY !! ALGEBRA 2
The amount after 5 years with a principal of $5000 compounded quarterly at an interest rate of 2.25% annually is $5593.60 approximately.
What is compound interest?Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment but also on any accumulated interest from previous periods. In other words, it's the interest earned on the principal amount plus any interest earned previously.
To calculate the amount after 5 years, we need to use the formula for compound interest:
A = P × {1 + r ÷ (n × 100)} ∧ (n × t)
where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $5000, r = 2.25% , n = 4 (since interest is compounded quarterly), and t = 5.
After applying these values, we get:
A = $5000 x (1 + 2.25/400) ⁴ ˣ ⁵
A = $5000 x (1.005625) ²⁰
A = $5000 x 1.1871955
A = $5593.60 (rounded off to 2 decimals)
Therefore, the amount after 5 years with a principal of $5000 compounded quarterly at an interest rate of 2.25% annually is $5593.60 approximately.
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The table shows several input and output values of a quadratic function f(x)
x f(x)
3.0 3.00
4.0 5.00
4.5 5.25
5.0 5.00
6.0 3.00
Which statements is tru about the function?
a) The maximum value of f(x) is 6
b) The maximum value of f(x) is 5.25
c) The zeroes of the function are 2 and 4
d) The zeroes of the function are 4 and 5
Answer:-by-step explanation:
the function has the x-intercept of (-2, 0)
the function has the y-intercept of (0, -8)
the function has the x-intercept of (4, 0)
EASY!! I ONLY NEED HELP WITH #39 & #40
39) The balance in the account after 6 years is $4,073.62.
40) The balance in the account after 6 years is $4,134.83
What is the formula for compound interest?
[tex]A = P(1 + \frac{r}{n} )^{(nt) }[/tex]
Here P is the principal,A is the balance, r is the annual interest rate, n is the number of times the interest is compounded per year, t is the time in years.
39) Here given that P = $3500, r = 2.16% = 0.0216, n = compounded quarterly = 4 and t = 6.
So, [tex]A = 3500(1 + \frac{0.0216}{4})^{(4 \times 6)} = 4,073.62[/tex]
Therefore, the balance in the account after 6 years is $4,073.62.
40)Here given,P = $3500, r = 2.29% = 0.0229, n = 12 (compounded monthly), and t = 6.
[tex]A = 3500(1 + \frac{0.0229}{12})^{(12 \times 6)} = 4,134.83[/tex]
Therefore, the balance in the account after 6 years is $4,134.83.
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Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.)
F(x, y, z) = [tex]xyz^3[/tex] i + [tex]x^2z^3[/tex] j + [tex]3x^2yz^2[/tex] k
Answer:its is conservative
Step-by-step explanation:
Write the 10th term of each sequence. first term 7 and common difference 15
As a result, the sequence's tenth term is 142 as the 10th term of the arithmetic sequence with a first term of 7 and a common difference of 15.
what is arithmetic progression ?An arithmetic progress (AP) in mathematics is a set of numbers where each term following the first is formed by adding a predetermined constant to the term before it. The mathematical progression's common difference is the name of this unchanging constant. For instance, the number progression 3, 7, 11, 15, 19,... has a common difference of 4 and is an arithmetic progression. The formula: yields the nth word of an arithmetic progression. a n = a 1 + (n - 1)d where n is the desired term's number, a n is the sequence's nth term, a 1 is its first term, d is its clear differentiation, and n is its number.
given
We can use the following formula to determine the 10th term of the arithmetic sequence with a first term of 7 and a common difference of 15:
a n = a 1 + (n - 1) * d
where a n represents the nth term in the series, a 1 represents the first term, d represents the common difference, and n is the desired term's number.
Inputting the values provided yields:
[tex]a 10 = 7 + (10 - 1) (10 - 1) * 15 \\a 10 = 7 + 9 * 15 \\a 10 = 7 + 135 \\a 10 = 142[/tex]
As a result, the sequence's tenth term is 142 as the 10th term of the arithmetic sequence with a first term of 7 and a common difference of 15.
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Find the area
Round to nearest tenth
The area of the triangle is 87.6 cm².
How to find the area of a triangle?The area of the triangle can be found as follows:
Therefore,
area of a triangle = 1 / 2 bh
where
b = base of the triangleh = height of the triangleTherefore,
b = 17 cm
h = 10.3 cm
Hence,
area of a triangle = 1 / 2 × 17 × 10.3
area of a triangle = 1 / 2 × 175.1
area of a triangle = 87.55
area of a triangle = 87.6 cm²
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eading Tools
Two students began a proof of the law of sines.
C
A
Student I
sin(A)=
Sin(B) =
bsin(A) =h
asin(B) = h
bsin(A)= asin(B)
sin(A)=sin(B)
b
Student 2
sin(A)=
sin(B) ==
asin(A) = h
bsin(B) = h
B
asin(A)=bsin(B)
sin(A)=sin(B)
a
Which student correctly started the proof, and what should that student do next to complete the proof?
Answer: no answer
Step-by-step explanation:
The measurements of the circumstances and radii of circles with different areas are recorded and analyzed. Which statement justifies why this information can be used to approximate the value of pi?
A. The area of a circle varies inversely as the radius.
B. The circumference of a circle varies inversely as the radius.
C. The circumference of a circle varies directly as the radius.
D. The area of a circle varies directly as the radius.
The correct answer is C. The circumference of a circle varies directly as the radius.
What is circumference?It is calculated by multiplying the diameter of a circle by pi, or by measuring the length of a curved line that encloses the shape.
The relationship between the circumference of a circle and its radius is a linear equation, where the circumference is equal to two times pi times the radius, or C = 2πr.
The circumference of a circle varies directly as the radius, meaning that if the radius of a circle is doubled, the circumference will also double.
This linear relationship can be used to approximate the value of pi, which is a constant ratio between the circumference and the diameter of any circle.
Therefore, the statement that justifies why the measurements of the circumference and radii of circles with different areas can be used to approximate the value of pi is that the circumference of a circle varies directly as the radius.
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Hassim's Fireworks & Cycles had free cash flow of R129 550 this year, and expects this to grow by 3% each year for the foreseeable future. The company has a weighted average cost of capital of 8%. What is the value of the company today? 01R 119 186 O2 R 139 914 4. R1 271 945 R2 668 730
Answer:
To calculate the value of Hassim's Fireworks & Cycles today, we can use the formula for the present value of a growing perpetuity:
PV = FCF / (r - g)
where PV is the present value, FCF is the free cash flow, r is the weighted average cost of capital, and g is the growth rate.
Substituting the given values, we get:
PV = 129550 / (0.08 - 0.03)
PV = 2591000
Therefore, the value of Hassim's Fireworks & Cycles today is R2,591,000.
5 cubic cm
pls help help help
The value of 5 cubic cm in liters, can be converted to be
How to convert cubic centimeters to liters ?To convert cubic centimeters (cm³) to liters (L), we can use the following conversion factor:
1 L = 1000 cm³
This means that 1 liter is equal to 1000 cubic centimeters. To convert cubic centimeters to liters, we can divide the number of cubic centimeters by 1000.
For example, to convert 5 cubic cm to liters:
5 cm³ ÷ 1000 = 0.005 L
Therefore, 5 cubic cm is equal to 0.005 liters (or 5 mL).
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Full question:
5 cubic cm to Liters
Help please !!!!!!!!!!!!!!!!!!!!!
The constant of proportionality is 2/3
The length of the missing sides of triangle NRF are:
RF = 4.5
NR = 6
Similar Triangles : Calculating the constant of proportionalityFrom the question, we are to calculate the constant of proportionality in the similar triangles
Constant of proportionality =
Corresponding side length on triangle GTY / Corresponding side length on triangle NRF
Constant of proportionality = GY / NF
Constant of proportionality = 6 / 9
Constant of proportionality = 2/3
We are to find the length of the missing sides of triangle NRF
By the similarity theorem, we can write that
3 / RF = 6 / 9
3 / RF = 2/3
Cross multiply
2 × RF = 3 × 3
2 × RF = 9
RF = 9/2
RF = 4.5
4 / NR= 6 / 9
4 / NR= 2/3
Cross multiply
2 × NR = 4 × 3
2 × NR = 12
NR = 12/2
NR = 6
Hence,
The length of the missing sides are
RF = 4.5
NR = 6
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1. Mason has a credit card debt of $15,600 that he would like to reduce by applying $8,500 of his inheritance money to the
balance.
In addition, he would like to modify his debt payment plan to pay off the remaining balance in 24 months rather than 60
months.
His credit card has an APR of 18%. How much will these changes save Mason in finance charges (interest)?
Hint: 1st, subtract 8500 from 15,600 to find the remaining balance he will pay in 24 months.
Use the formula
P=PV* (1/(1-(1+0)^n) where PV is the remaining balance, i-0.18/12, and n-24 months.
2nd, multiply your answer in step 2 by 24 months to find out the total amount you paid in 24 months.
3rd, find the interest you paid by subtracting 7100 from the amount you found in step 2.
4th, find out how much you would have paid had you not reduced the amount you owed by 8500 (in other words, 15,600).
Use the same monthly formula in step 1 where PV-15,600, i-0.18/12, and n-60 months.
5th, multiply the answer in step 4 by 60 months to find out how much you paid in total.
6th, to find the interest, subtract the amount in step 5 from 15,600 to find the interest.
Finally, find the difference between step 3 and step 6, and that is how much you saved.
a. $1,407.04
b. $3,302.59
c. $6,760.96
d. $8,168.40
What amount of a 80% acid solution must be mixed with a 55% solution to produce 600 mL of a 60% solution?
Answer:The amount of a 80% acid solution that must be mixed with a 55% solution to produce 600 mL of a 60% solution can be calculated using a simple algebraic equation. Let x represent the amount of the 80% acid solution in mL that needs to be mixed with the 55% solution.
The equation can be set up as follows:
0.80x + 0.55(600 - x) = 0.60(600)
Step-by-step explanation: The left-hand side of the equation represents the total amount of acid in the mixture. The first term, 0.80x, represents the amount of acid from the 80% solution, and the second term, 0.55(600 - x), represents the amount of acid from the 55% solution. The right-hand side of the equation represents the total amount of acid in the final 60% solution, which is 60% of 600 mL.
By solving this equation for x, we can determine the amount of the 80% acid solution that needs to be mixed with the 55% solution. Once we have the value of x, we can then calculate the amount of the 55% solution by subtracting x from 600 mL.
Internal Link: For a verified answer on a similar topic, check out this link: https://brainly.com/question/1234567 intext:Answer Expert Verified.
Let x=amount of 80% solution needed
Then 600-x=amount of 30% solution needed
Now we know that the pure acid in the 80% solution (0.80x) plus the amount of pure acid in the 30% solution ((0.30)(600-x)) has to equal the amount of pure acid in the final mixture(0.40*600), so our equation to solve is:
0.80x+0.30(600-x)=0.40*600 get rid of parens
0.80x+180-0.30x=240 subtract 180 from each side
0.80x+180-180-0.30x=240-180 collect like terms
0.50x=60 divide each side by 0.50
x=120 ml---------------------amount of 80% solution needed
600-x=600-120=480 ml---------------amount of 30% solution needed
CK
120*0.80+480*0.30=0.40*600
96+144=240
240=240
George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months. He followed the steps below to determine the number of cars he needs to sell in the next month to have a mean number of sales per month of 24.Step 1: Find the total cars needed to have a mean of 24: .Step 2: Find the total cars sold: .Step 3: Subtract the total cars sold from the total cars needed: .Step 4: State the answer: George needs to sell 26 cars next month. Where did George make his first mistake?Step 1Step 2Step 3Step 4
George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months.
George's first mistake was in Step 1 where he tried to find the total number of cars he needs to sell in the next month to have a mean number of sales per month of 24. To find this value, George should have multiplied the desired mean number of sales per month (24) by the total number of months (7) to get the total number of cars needed to have a mean of 24 over 7 months. However, it seems that George skipped this step and directly assumed that the total number of cars needed for a mean of 24 in the next month is simply 24.
Let's go through each step to explain
Step 1 Find the total cars needed to have a mean of 24
To find the total number of cars George needs to sell over the next 7 months to have a mean of 24 cars sold per month, he should multiply the desired mean (24) by the number of months (7)
Total cars needed = 24 * 7 = 168
Step 2 Find the total cars sold
To find the total number of cars George sold over the past 7 months, he should add up the individual sales for each month:
Total cars sold = 18 + 22 + 26 + 12 + 25 + 20 + 19 = 142
Step 3 Subtract the total cars sold from the total cars needed
To find the number of cars George needs to sell in the next month to meet his target mean of 24 cars sold per month over the past 8 months, he should subtract the total number of cars sold from the total cars needed
Cars needed in the next month = Total cars needed - Total cars sold
Cars needed in the next month = 168 - 142 = 26
Step 4 State the answer
George needs to sell 26 cars next month to have a mean of 24 cars sold per month over the past 8 months.
Therefore, George's mistake was in Step 1 where he did not correctly calculate the total number of cars he needs to sell over the next 7 months to have a mean of 24 cars sold per month.
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Which equation best shows that 48 is a multiple of 3?
Choose 1 answer:
A
B
C
144= 3 x 48
3 = 48 ÷ 16
52 = 48 + 3
D3=48-45
The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test range from 0 to 500. Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem‑and‑leaf plot.
In 2019, 147,400 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was Xbar=282. We want to estimate the mean score in the population of all eighth‑graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation =40.
If we take many samples, the sample mean Xbar varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score in the population. What is the standard deviation of this sampling distribution?
Give your answer to four decimal places.
The standard deviation of the sampling distribution is approximately 0.3292.
What is central limit theorem?The behaviour of the sampling distribution of the mean is described by the central limit theorem, a key conclusion in statistics. It asserts that regardless of how the population distribution is shaped, if a random sample of size n is taken from a population with mean and standard deviation, the distribution of sample means will tend towards a normal distribution as n increases.
Because it enables us to utilise the normal distribution to draw conclusions about the population mean based on sample means, the central limit theorem has significant practical ramifications. Additionally, it offers a foundation for confidence interval estimation and statistical hypothesis testing.
The standard deviation is given by the formula:
SD = σ/√(n)
Now, substituting the value of σ = 40, n = 147,400 we have:
SD = σ/√(n) = 40/√(147400) ≈ 0.3292
Hence, the standard deviation of the sampling distribution is approximately 0.3292.
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How many gallons of a 80% alcohol solution and a 20% alcohol solution must be mixed to get 9 gallons of 60% alcohol solution?
In linear equation, x = 6 gallons (of 80% alcohol)
y = 3 gallons (of 20% alcohol)
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Let
x = liters of 80% alcohol
y = liters of 20% alcohol
There are two unknowns, we need two equations
x + y = 9. (1)
0.80x + 0.20y = 0.60(x+y) (2)
From (1)
x + y = 9
y = 9-x
Substitute the value of y into (2) and solve for x:
0.80x + 0.20y = 0.60(x+y)
0.80x + 0.20(9-x) = 0.60(x+9-x)
0.80x + 1.8 - 0.20x = 0.60(9)
0.80x + 1.8 - 0.20x = 5.4
0.6x = 3.6
x = 6 gallons (of 30% alcohol)
Substitute x=6 into (1) and solve for y:
x + y = 9
6 + y = 9
y = 3 gallons (of 60% alcohol)
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A motorboat travels 106 kilometers in 2 hours going upstream. It travels 142 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Step-by-step explanation:
Rate UP stream = ( s - w) = 106 km / 2 hr
( where s = boat speed w = current speed )
(s-w) = 53 km/hr
Rate DOWNstream = ( s+w) = 142 / 2 = 71 kmhr
( s-w) + ( s+w) = 53 + 71 km/hr
2s = 124
s = 62 km /hr then s+w = 71 shows w = 9 km/hr