The amount n = $ 400.72 as fraction is A = 10,018/25
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the amount be represented as n
Let the fraction be represented as A
Now , To write "four hundred dollars and seventy two cents" as a fraction, we can first write it as the sum of its parts:
$ 400.72 = $ 400 + $ 0.72
Next, we can convert the cents portion to a fraction by dividing by 100:
$ 0.72 = 72/100
Now we can combine the two parts by adding them as fractions:
$ 400.72 = $400 + $0.72 = $400 + 72/100
To convert this to a fraction, we need to find a common denominator, which is 100:
$ 400.72 = ($ 400 x 100 + 72) / 100
= 40,072 / 100
Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor of 4 gives:
$ 400.72 = 10,018/25
Hence , "four hundred dollars and seventy two cents" is equivalent to the fraction 10,018/25 in reduced form
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The given amount in fraction is [tex]\frac{40072}{100}[/tex] and its reduced fraction is [tex]\frac{10018}{25}[/tex].
1. Understanding the Total Amount in Cents:
Four hundred dollars and seventy-two cents' is equivalent to 400 dollars + 72 cents. First converting everything to cents. Since 1 dollar is equal to 100 cents:
[tex]four\ hunder\ dollars\ and\ seventy\ two\ cents = 400 \times 100\ \text{cents} + 72\ \text{cents}= 40072\ cents[/tex]
2. Since 1 dollar = 100 cents, dividing total amount in cents by 100:
[tex]Total\ amount= \frac{40072}{100}[/tex]
Reducing the fraction by dividing numerator and denominator by 4:
[tex]Reduced\ Fraction = \frac{10018}{25}[/tex]
If the radius of the circle is decreased by a factor of One-third, what happens to the circumference?
The circumference decreases by a factor of One-third.
The circumference decreases by a factor of 3.
The circumference increases by a factor of One-third.
The circumference increases by a factor of 3.
Answer:
the circumference decreases by a factor 1/3.
Step-by-step explanation:
Answer:
A: The circumference decreases by a factor of One-third
Find the sum of 13/20 and 0.72
Give your answer as a decimal.
The sum of 13/20 and 0.72 when expressed in decimal form gives us the answer as; 1.37.
How to convert fraction to decimal?
We want to find the sum of ¹³/₂₀ and 0.72
This is expressed as;
¹³/₂₀ + 0.72
Now, we want to express the fraction as a decimal. Thus, let us convert to decimal as; ¹³/₂₀ = 0.65
Thus, we now have the decimal expression;
0.65 + 0.72 = 1.37
Thus, we can conclude that the sum of 13/20 and 0.72 when expressed in decimal form gives us 1.37.
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The sum of 13 / 20 and 0.72 when expressed in decimal form gives us the answer as; 1.37.
To find the sum of 13 / 20 and 0.72, we can first convert 13/20 to a decimal by dividing 13 by 20.
This is expressed as;
13 / 20 + 0.72
Now, we want to express the fraction as a decimal. Thus, let us convert to decimal as; 13 / 20 = 0.65
Thus, we now have the decimal expression;
0.65 + 0.72 = 1.37
Thus, we can conclude that the sum of 13 / 20 and 0.72 when expressed in decimal form gives us 1.37.
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Consider this cube with a volume of 64 cubic centimeters. What can be concluded of this cube? Check all that apply. The expression s2, where s represents the side length, was used to solve for the volume. This is a perfect cube. The side length is 8. The side length is 4. Taking the cube root of the volume will determine the side length.
Answer:
(B)This is a perfect cube.
(D)The side length is 4.
(E)Taking the cube root of the volume will determine the side length.
Step-by-step explanation:
Given a cube with a volume of 64 cubic centimeters.
The following conclusions can be reached:
(B)This is a perfect cube.
64=4 X 4 X4
(D)The side length is 4.
Volume of a Cube =[tex]s^3[/tex]
4 X 4 X4 =64 cubic centimeters.
(E)Taking the cube root of the volume will determine the side length.
[tex]\sqrt[3]{64}=4 cm[/tex]
These are not valid conclusions.
(A)The expression [tex]s^2[/tex], where s represents the side length, was used to solve for the volume.
(C)The side length is 8.
Answers on edugenuity
B
D
E
A car rental companies standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge (in dollars) is given by the function , where is the number of miles driven. The company also offers an option to insure the car against damage. The insurance charge (in dollars) is given by the function . Let be the total charge (in dollars) for a rental that includes insurance. Write an equation relating to . Simplify your answer as much as possible.
The rental's total charge that includes insurance, represented by T(m), is the sum of the standard charge function C(m) and the insurance charge I, as in the equation T(m) = C(m) + I.
The question provided is incomplete as the functions for the standard charge and the insurance charge are not specified. However, assuming the functions are given by C(m) for the standard charge, where m is the number of miles driven, and I for the insurance charge, the total charge would be represented by the function T(m). The equation that relates the total charge to both the standard charge and the insurance charge would therefore be T(m) = C(m) + I. Simplifying the equation does not apply in this case as the individual functions are not provided for further manipulation.
a cone has a diameter of 8ft and height of 3ft. What’s the volume?
Step-by-step explanation:
1/3 πr²h
Given
diameter (d) = 8ft
radius (r) = d/2 = 8/2 = 4 ft
height (h) = 3 ft
Volume of cone
[tex] \frac{1}{3} \times \pi {r}^{2} h[/tex]
[tex] \frac{1}{3} \times 3.14 \times {4}^{2} \times 3[/tex]
[tex] \frac{150.72}{3} [/tex]
=50.24 ft³
The cone formula is V=1/3(pi*r^2)h, plug in what you know 150pi=1/3(pi*r^2)8.
Multiply both sides by 3: 450pi=(pi*r^2)8
Divide by 8: 56.25pi=pi*r^2
Divide by pi: 56.25=r^2
Square root both sides: 7.5=r
Multiply by 2 to find diameter: d=15
The soot produced by a garbage incinerator spreads out in a circular pattern. The depth, H(r), in millimeters, of the soot deposited each month at a distance r kilometers from the incinerator is given by H(r)=0.116eâ2.3r.Write a definite integral (with independent variable r) giving the total volume of soot deposited within 5 kilometers of the incinerator each month.
Answer:
V = integral of [ 0.116e^(-2.3r) * 2πr (10^3) ] dr with upper limit of 5 and lower limit of 0. Unit in m^3.
Step-by-step explanation:
H(r) = 0.116e^(-2.3r)
H(r) = millimeters
r = kilometers
We'll use Riemann's sum to approximate the total area underneath the region of the integral.
Using Riemann's sum, we break the region into rings of radius r and width ∆r.
Area of rings = πr^2
Area of the rings with radius r and width ∆r, then becomes=
π(r+ ∆r)^2 - πr^2
On expanding:
Area = π[ r^2 + 2r∆r + (∆r)^2] - πr^2
= πr^2 + 2πr∆r + π(∆r)^2 - πr^2
= 2πr∆r + π(∆r)^2
Area = ∆r(2πr + π∆r)
Area/∆r = 2πr + π∆r
At lim ∆r tends to zero
Area/∆r = 2πr + 0 = 2πr
Area = 2πr∆r
Volume = Area * depth
= Area * H(r)
∆V approximately equal to:
2πr∆r * H(r)
Sum of the contribution for all the rings for the volume (total volume):
V approximately sum of [H(r) *2πr∆r]
V ≈ ∑H(r)· 2πr∆r.
Taking the limit as ∆r tends to zero,
V = integral of [ 0.116e^(-2.3r) * 2πr ] dr with upper limit of 5 and lower limit of 0.
The term H(r) and Area are not in the same unit. We would convert both to meters.
H(r) = mm = 10^(-3)m
Area = km^2 = km*km
= (10^3)m * (10^3)m = (10^6)m^2
V = integral of [(10^-3m) * 0.116e^(-2.3r) *2πr (10^6m^2) dr] with upper limit of 5 and lower limit of 0.
V = integral of [ 0.116e^(-2.3r) * 2πr (10^3) dr ] with upper limit of 5 and lower limit of 0. Unit in m^3.
g(n) = n - 5; Find g(2)
Answer:
g(2) = -3
Step-by-step explanation:
g(n) = n - 5;
Let n=2
g(2) = 2-5
= -3
Answer:
g(2)= -3
Step-by-step explanation:
We want to find what g is, when n is 2, so we can substitute 2 in for n.
g(n)=n-5
g(2)=2-5
g(2)= -3
3x+3y=-x+5y which ordered pair is a solution of the equation
Though there are multiple solutions to the given equation, the two ordered pairs that are solutions would be both (1, 2) and (2, 4).
Hope this helps!
The character's backstory in the example best connects to
which theme?
ad
mall
Kindness is more important than beauty
Greed can destroy relationships with others,
Alle can have serious consequences,
A weakness can be turned into a strength
Answer:
D. A weakness can be turned to strength
Answer:
d
Step-by-step explanation:
The surface area of a spherical beach volleyball is
approximately 1387 square centimeters. Which of the
following is closest to the radius, in centimeters, of the
volleyball?
6.9
. 10.5
• 18.6
• 21.0
Answer: 18.1 inches
Step-by-step explanation: A volleyball is spherical in shape, and the surface area of a sphere is giving by the formula
from the data giving, the surface area was calculated to be 227 square inches. from the above formula, we define the radius, r to be the subject of formula, we arrive at
if we substitute for the surface area, we arrive at
Hence the radius of the volleyball will be 18.1 inches
Hope this helps
An inlet pipe on a swimming pool can be used to fill the pool in 2020 hours. The drain pipe can be used to empty the pool in 2121 hours. If the pool is 2323 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool
Answer:
If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, it will take 140 hours to fill the pool
Step-by-step explanation:
An inlet pipe can fill the pool in hours = 20
Inlet pipe 1 hour work = [tex]\frac{1}{20}[/tex]
A drain pipe can empty the pool in 21 hours
Drain pipe 1 hour work =[tex]\frac{1}{21}[/tex]
Inlet pipe and drain pipe 1 hour together work = [tex]\frac{1}{20}-\frac{1}{21}=\frac{1}{420}[/tex]
Now we are given that the pool is 2/3 filled
So, remaining portion to be filled =[tex]1 - \frac{2}{3} = \frac{1}{3}[/tex]
So, Inlet pipe and drain pipe fill [tex]\frac{1}{420}[/tex] in hours = 1
So, they can fill 1/3 in hours = [tex]\frac{1}{\frac{1}{420}} \times \frac{1}{3} =140 hours[/tex]
Hence If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, it will take 140 hours to fill the pool
If someone could answer this problem and explain how to do it that would be a HUGE help thanks-
Answer:
10 meters
Step-by-step explanation:
The triangles are similar, by a scale factor of 2, so if QR is 10, then ST is 1/2 or 5
We can use trig functions to find SP
sin P = opp/ hyp
sin 30 =5/SP
SP sin 30 =5
Divide each side by sin 30
SP = 5 / sin 30
SP =10
Answer:
C. 10 meters
Step-by-step explanation:
sin(30) = QR/QP
½ = 10/QP
QP = 20
PS = ½ × 20
PS = 10
A goat is tied at one corner of a 12 feet by 16 feet barn. If the rope is 24 feet long, find the area of the region outside the barn, in which the goats can graze.
Answer:
1520.5 ft²
Step-by-step explanation:
A diagram can be helpful.
The total area is the sum of ...
3/4 of a circle with radius 24 ft
1/4 of a circle with radius 12 ft
1/4 of a circle with radius 8 feet
__
The area of a whole circle is given by ...
A = πr²
so our grazing area is ...
A = (3/4)π(24 ft)² + (1/4)π(12 ft)² + (1/4)π(8 ft)²
= π(432 ft² +36 ft² +16 ft²) = 484π ft²
A ≈ 1520.5 ft²
A polling company took before an 5 polls in the week that a mayoral 66%,56%, 55%, 60% 63% of the total votes. That candidate recieved 64 % of the total vote during the actual election. Find the percent errot in the average of the company's polling results to the nearest tenth of a percent. Show your work.
Answer:
6.7%
Step-by-step explanation:
In this question, we are to calculate the percentage error in in the average polling results calculated.
Firstly, what this means is that we calculate the average of the total votes.
That would be ; (66 + 56 + 55 + 60 + 63)/5 =
300/5 = 60%
we now proceed to calculate the percentage error in the company’s result.
Mathematically;
percentage error = (Actual value - expected value)/expected value * 100%
Here the actual value is 64% and the expected is 60%
% error = (64-60)/60 * 100 = 4/60 * 100 = 6.67%
This is 6.7% to the nearest tenth of a percent
Jiminy's Cricket Farm issued a bond with 15 years to maturity and a semiannual coupon rate of 5 percent 3 years ago. The bond currently sells for 92 percent of its face value. The company's tax rate is 22 percent. A. What is the pretax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.G., 32.16.) b. What is the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.G., 32.16.)
The pretax cost of debt is 5.43% and the aftertax cost of debt is 4.24%.
Explanation:To calculate the pretax cost of debt, we need to find the current yield of the bond. The current yield is the annual coupon payment divided by the market price. In this case, the coupon rate is 5% and the market price is 92% of the face value. Therefore, the current yield is (0.05 * face value) / (0.92 * face value), which simplifies to 0.0543 or 5.43%.
To calculate the aftertax cost of debt, we need to multiply the pretax cost of debt by (1 - tax rate). In this case, the tax rate is 22%. Therefore, the aftertax cost of debt is 5.43% * (1 - 0.22), which simplifies to 4.24%.
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Need help please answer worth 25 points
The equation is [tex]-\frac{1}{2} x+3[/tex]
This is what you should input in the chart:
(0,3)
(3,2)
(6,1)
(9,0)
(12,-1)
(15,-2)
The exterior angles of a quadrilateral have measures of 72°, 58°, 2xº, and 3xº. Find the value of x.
x=
Answer:
46
Step-by-step explanation:
72 + 58 + 2x + 3x = 360
5x = 230
x = 46
Following is a sample of five matched pairs. Sample 1 20 20 23 18 22 Sample 2 23 16 15 14 18 Let μ1 and μ2 represent the population means and let μD = μ1 - μ2. A test will be made of the hypotheses H0: μD = 0 versus H1: μD > 0. Can you reject H0 at the α = 0.01 level of significance? A) No B) Yes C) Cannot be determined
Answer:
No, we can't reject [tex]H_0[/tex] at the α = 0.01 level of significance.
Step-by-step explanation:
We are given the sample of five matched pairs below ;
Sample 1 (B) : 20, 20, 23, 18, 22
Sample 2 (A) : 23, 16, 15, 14, 18
Let [tex]\mu_1[/tex] = population mean for first sample
[tex]\mu_2[/tex] = population mean for second sample
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_D[/tex] = 0 {means that there is no difference between the population means of both samples}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_D[/tex] > 0 {means that three is positive difference between the population means of both samples, i.e. population mean of first sample is higher than the population mean of second sample}
The test statistics that will be used here is Paired data test statistics;
T.S. = [tex]\frac{\bar D-\mu_D}{\frac{s_D}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar D[/tex] = [tex]\bar B -\bar A[/tex] = 20.6 - 17.2 = 3.4
[tex]s_D=\sqrt{\frac{\sum D_i^{2}-n \bar D^{2} }{n-1}}[/tex] = [tex]\sqrt{\frac{121-5 \times 3.4^{2} }{5-1}}[/tex] = 3.975
n = sample size = 5
So, test statistics = [tex]\frac{3.4-0}{\frac{3.975}{\sqrt{5} } }[/tex] ~ [tex]t_4[/tex]
= 1.913
Now at 0.01 significance level, the t table gives critical value of 3.747 at 4 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 3.747 > 1.913, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the there is no difference between the population means of both samples.
Answer:
No, we can't reject at the α = 0.01 level of significance.
Step-by-step explanation:
the other response is right
h(t) = t + 3; Find h(1)
h(t) = t+3
Find h(1)
h(1) = 1+3
h(1) = 4
The answer is 4.
A survey of students at a large university found that 82% had purchased textbooks from an off-campus vendor at least once during their college career. If 45 students are randomly sampled, what is the probability that at least 40 students have purchased textbooks from an off-campus vendor at least once during their college career? g
Answer:
Probability that at least 40 students have purchased textbooks from an off-campus vendor at least once during their college career is 0.0688.
Step-by-step explanation:
We are given that a survey of students at a large university found that 82% had purchased textbooks from an off-campus vendor at least once during their college career.
Also, 45 students are randomly sampled.
Let [tex]\hat p[/tex] = sample proportion of students who have purchased textbooks from an off-campus vendor at least once during their college career.
The z-score probability distribution for sample proportion is given by;
Z = [tex]\frac{\hat p- p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion = [tex]\frac{40}{45}[/tex] = 0.89
p = population proportion of students who had purchased textbooks from an off-campus vendor at least once during their college career = 82%
n = sample of students = 45
Now, probability that at least 40 students have purchased textbooks from an off-campus vendor at least once during their college career is given by = P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.89)
P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.89) = P( [tex]\frac{\hat p- p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{0.89-0.82}{\sqrt{\frac{0.89(1-0.89)}{45} } }[/tex] ) = P(Z [tex]\geq[/tex] 1.50) = 1 - P(Z < 1.50)
= 1 - 0.9332 = 0.0688
The above probability is calculate by looking at the value of x = 1.50 in the z table which ha an area of 0.9332.
Therefore, the required probability is 0.0688.
x/10=−1
help ive got no idea it would be helpful if you could explain how as well please
Answer:
x = -10.
Step-by-step explanation:
x / 10 = -1
To solve the equation we isolate the x on one side.
Whatever operation we do one one side of the equation we have to do the same on the other side so that the balance is maintained.
Here to isolate x we multiply both sides by 10:
x
-- * 10 = -1 * 10
10
x = -10.
Hope this helps.
How can a shape have parallel sides but not perpendicular sides?
Answer:
Parallelogram are quadrilaterals with opposite sides parallel, but adjacent sides not perpendicular. If the sides have equal lengths, then it is called a rhombus.
Step-by-step explanation:
Because the sides of the shape meet at angles which are not 90 degrees, so they cannot be perpendicular.
What are parallel lines?Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.
A shape can have parallel sides but not perpendicular sides if it is not a rectangle or a square. Examples of such shapes include parallelograms, trapezoids, and rhombuses. In these shapes, the sides are parallel to each other, but they are not perpendicular to each other.
Because the sides of the shape meet at angles which are not 90 degrees, so they cannot be perpendicular.
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Solve the linear programming problem by the method of corners. Maximize P = 6x − 4y subject to x + 2y ≤ 50 5x + 4y ≤ 145 2x + y ≥ 25 y ≥ 7, x ≥ 0 The maximum is P = 1 Incorrect: Your answer is incorrect. at (x, y) = .
Answer:
The maximum is P=112.4 at (23.4,7)
Step-by-step explanation:
From the graph, the coordinates of the vertices of the feasible region are:
(0,25)
(9,7)
(23.4, 7)
(15,17.5)
Substituting these values in the objective function, P.
At (0,25), P = 6x − 4y=6(0)-4(25)=-100
At (9,7), P = 6x − 4y=6(9)-4(7)=26
At (23.4,7), P = 6x − 4y=6(23.4)-4(7)=112.4
At (15,17.5), P = 6x − 4y=6(15)-4(17.5)=20
Since the objective is to maximize,
The maximum is P=112.4 at (23.4,7)
To solve the linear programming problem, graph the inequalities to find the feasible region, then compute the function P = 6x − 4y at each corner point of the feasible region to find the maximum value. The values of x and y must also uphold all the inequalities.
Explanation:The subject of the problem is a linear programming problem, and to solve it, we first identify the feasible region by graphing inequalities. This involves graphing x + 2y ≤ 50, 5x + 4y ≤ 145, 2x + y ≥ 25, y ≥ 7, and x ≥ 0. The feasible region would be formed by the area enclosed within those lines.
Next, we find the corner points of the feasible region because, in a linear programming problem, the maximum and minimum always occur at the vertices or corner points. Let's calculate these corner points.
Finally, we evaluate the function P = 6x − 4y at each corner point and find the value of P that would be maximized. It's crucial to remember that the values of x and y must satisfy all the given inequalities.
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20 POINTS PLEASE HELP
Identify a zero of the function x^2+2x-3
a) -3
b) -1
c) 0
d) 2
Answer:
A
Step-by-step explanation:
Essentially, if we plug in any of the given choices into the function and we get 0, then that's our answer.
A) (-3)^2 + 2 * (-3) - 3 = 9 - 6 - 3 = 0 - correct
B) (-1)^2 + 2 * (-1) - 3 = 1 - 2 - 3 = -4 - incorrect
C) 0^2 + 2 * 0 - 3 = -3 - incorrect
D) 2^2 + 2 * 2 - 3 = 4 + 4 - 3 = 5 - incorrect
So, the answer is A.
The alternative, more "formal" way of doing this problem is to factor the quadratic: x^2 + 2x - 3 = (x + 3)(x - 1) = 0
Then set each of these equal to 0: x + 3 = 0 and x - 1 = 0
We get the values of x = -3 and x = 1. Only -3 is one of the answer choices, so A is correct.
Hope this helps!
Answer:
a) -3
Step-by-step explanation:
Zero of a function is the x-value where y = 0
x² + 2x - 3 = 0
x² + 3x - x - 3 = 0
x(x + 3) - (x + 3) = 0
(x - 1)(x + 3) = 0
x = 1, -3
Find a23 in the sequence -18 -34 -50 -66
Answer:
-288
Step-by-step explanation:
-18*16
cause its going by 16's
pls mark me brainliest
a23 = -288
Sequence:A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite). In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important.A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions. An indexed family, which is a function from an index set that may not be a set of numbers to another set of elements, can be thought of as a generalization of the idea of a sequence.Solution -As the sequence is going by [tex]16[/tex].
∴ [tex]-18[/tex] × [tex]16=-288[/tex]
Therefore, [tex]a23=-288[/tex].
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The sample mean foot length of a simple random sample of 25 third-graders is 22.5 cm. The standard error of the mean is 0.8 cm. Which one of the following is a correct interpretation for the standard error of the mean? A.The typical distance between each individual foot length in the sample and the sample mean foot length is approximately 0.8 cm. B.The typical distance between one sample mean foot length and another sample mean foot length is 0.8 cm. C.The typical distance between each individual foot length in the population and the true mean foot length is approximately 0.8 cm. D.The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm E.The typical distance between each individual foot length in the sample and the true mean foot length is approximately 0.8 cm.
The standard error of the mean pertains to the variability of the mean between different samples, rather than the variability of individual measurements. Therefore, the correct interpretation is D. The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm.
Explanation:The most accurate interpretation for the standard error of the mean in the context of the given problem is: D. "The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm".
The standard error of the mean (SEM) demonstrates the standard deviation of the sampling distribution of the means. It measures how far the sample mean of the data is likely to be from the true population mean. SEM gives us an estimate of the precision of our sample mean in relation to the true population mean. It's important to recognize that SEM is not about the dispersion of individual measurements, but rather about the dispersion of sample means.
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2) To bake a cake, we need 2 eggs for every cup of sugar. If we need to make 21 cakes for a bake sale how many eggs and cups of sugar will we need?
Step-by-step explanation:
It means every cake needs 2 eggs and 1 cup of sugar
So first we will multiply 21 by 2 to get the number of eggs = 21 ×2 = 42
So answer is 21 cups and 42 eggs
If the base of the triangle decreased from 2 yards to 1 yard, what would be the difference in the area?
Answer:
5/16 yd[tex]^{2}[/tex]
Answer:
B
Step-by-step explanation:
The mean number of words per minute (WPM) read by sixth graders is 8888 with a standard deviation of 1414 WPM. If 137137 sixth graders are randomly selected, what is the probability that the sample mean would be greater than 89.8789.87 WPM? Round your answer to four decimal places.
Noticing that there is a pattern of repetition in the question (the numbers are repeated twice), we are assuming that the mean number of words per minute is 88, the standard deviation is of 14 WPM, as well as the number of sixth graders is 137, and that there is a need to estimate the probability that the sample mean would be greater than 89.87.
Answer:
"The probability that the sample mean would be greater than 89.87 WPM" is about [tex] \\ P(z>1.56) = 0.0594[/tex].
Step-by-step explanation:
This is a problem of the distribution of sample means. Roughly speaking, we have the probability distribution of samples obtained from the same population. Each sample mean is an estimation of the population mean, and we know that this distribution behaves normally for samples sizes equal or greater than 30 [tex] \\ n \geq 30[/tex]. Mathematically
[tex] \\ \overline{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex] [1]
In words, the latter distribution has a mean that equals the population mean, and a standard deviation that also equals the population standard deviation divided by the square root of the sample size.
Moreover, we know that the variable Z follows a normal standard distribution, i.e., a normal distribution that has a population mean [tex] \\ \mu = 0[/tex] and a population standard deviation [tex] \\ \sigma = 1[/tex].
[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]
From the question, we know that
The population mean is [tex] \\ \mu = 88[/tex] WPMThe population standard deviation is [tex] \\ \sigma = 14[/tex] WPMWe also know the size of the sample for this case: [tex] \\ n = 137[/tex] sixth graders.
We need to estimate the probability that a sample mean being greater than [tex] \\ \overline{X} = 89.87[/tex] WPM in the distribution of sample means. We can use the formula [2] to find this question.
The probability that the sample mean would be greater than 89.87 WPM
[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex] \\ Z = \frac{89.87 - 88}{\frac{14}{\sqrt{137}}}[/tex]
[tex] \\ Z = \frac{1.87}{\frac{14}{\sqrt{137}}}[/tex]
[tex] \\ Z = 1.5634 \approx 1.56[/tex]
This is a standardized value and it tells us that the sample with mean 89.87 is 1.56 standard deviations above the mean of the sampling distribution.
We can consult the probability of P(z<1.56) in any cumulative standard normal table available in Statistics books or on the Internet. Of course, this probability is the same that [tex] \\ P(\overline{X} < 89.87)[/tex]. Then
[tex] \\ P(z<1.56) = 0.94062 \approx 0.9406[/tex]
However, we are looking for P(z>1.56), which is the complement probability of the previous probability. Therefore
[tex] \\ P(z>1.56) = 1 - P(z<1.56) = 1 - 0.9406[/tex]
[tex] \\ P(z>1.56) = P(\overline{X}>89.87) = 0.0594[/tex]
Thus, "The probability that the sample mean would be greater than 89.87 WPM" is about [tex] \\ P(z>1.56) = 0.0594[/tex].
Jenaya is reading a book. She is 75% finished. She read 120 pages. How many pages is the total book?
Answer:
160 pages.
Step-by-step explanation:
75% = 120 pages so , by proportion, 100% = 120 * 100/75
= 120 * 4/3
= 40 * 4
= 160 pages.
Answer:
160 pages
Step-by-step explanation:
75% of x = 120
Turn 75% into a fraction or decimal
75/100 * x = 120
0.75 * x =120
0.75 is multiplying with x so to get rid of 0.75, we have to multiply both sodes by 0.75
x = 120/0.75
x = 160
So there are a total of 160 pages in the book.