Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which may also be given in the form of a statement. Therefore the required statement in the question is option C. Add 3 to the product of one-fourth and 8, then divide by 5.
Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which can be given in the form of a statement. When a given expression consists of both numbers and alphabets, then it forms an algebraic expression. It can also be given in the form of a statement.
Given in the question:
([tex]\frac{1}{4}[/tex] x 8 + 3) ÷ 5
This can be given in a statement form as; Add 3 to the product of one-fourth and 8, then divide by 5.
The appropriate statement that describes the given expression is: Add 3 to the product of one-fourth and 8, then divide by 5 i.e Option C.
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ASAP HELP ME WITH THIS QUESTION
witch expression is equivalent
The equivalent expression of -14 - 6 is -14 - (+6)
What are equivalent expression?Equivalent expressions are expressions that have the same value when evaluated
How to determine the equivalent expression?The expression is given as:
-14 - 6
Put the terms of the expression in brackets
-14 - (6)
Rewrite 6 as +6
-14 - (+6)
Hence, the equivalent expression of -14 - 6 is -14 - (+6)
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Geometry and Modeling:
Mike completely filled the container shown below with 616 small cubes that were each [tex]\frac{1}{2}[/tex] inch long.
Part A: Calculate the volume of the prism.
Part B: Crate a graphical model of a prism with base 5.5 by 3.5 that has the same volume as Part A.
Show how Mike can calculate the volume of the prism, in cubic inches, by using a volume formula instead of filling the container with small cubes.
A) AB and BC
B) AC and BD
tell if each pair of segments is congruent
a. Line AB and line BC are not congruent because their distance of separation are not equal
b. Line AC and line BD are not congruent because their distance of separation are not equal
How to proof the statementFrom the number line drawn, we have the following deductions;
Line AB = -5 to -2 = 3
Line BC = -2 to 0 = 2
Line AC = -5 to 0 = 5
Line AD = -5 to 5 = 10
Line BD = -2 to 5 = 7
We can see that;
a. Line AB and line BC are not congruent because their distance of separation are not equal
b. Line AC and line BD are not congruent because their distance of separation are not equal
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Which expression represents the
number of reams of paper the company
produced during the second year?
The expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰
Writing an ExpressionFrom the question, we are to determine the expression that represents the number of reams of paper the company produced during the second year
From the given information,
During the first year of operation,
The company produced 8.4 × 10⁹ reams of paper
And
During the second year,
the company produced 5.6 times the number of reams of paper that it produced during the first year.
Thus,
The number of reams of paper the company produced during the second year = 5.6 × 8.4 × 10⁹ reams of paper
The number of reams of paper the company produced during the second year = 47.04 × 10⁹ reams of paper
= 4.704 × 10¹ × 10⁹ reams of paper
= 4.704 × 10¹⁰ reams of paper
Hence, the expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰
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Please help I need to turn this in by Monday!
Answer: Rational, Irrational, Rational, Natural, Natural, Integer
Step-by-step explanation:
-4.2 is a rational number as it can be converted into a fraction
3√5 is an irrational number as it can't be converted into a fraction
5/3 is a rational number as it is a fraction
9 is a natural number as it is a positive whole number
√16 is a natural number as despite the square root, √16 is 4 which is a natural number
-8/2 is an integer as -8/2 is -4 which is a negative whole number
Find the volume of a cylinder that has a height of 6.5 feet and a radius of 1.3 feet.
Answer:
34.51ft³
Step-by-step explanation:
The formula to find the volume of a cylinder is :
V = π r² h
Here,
r ⇒ radius ⇒ 1.3ft
h ⇒ height ⇒ 6.5ft
Let us find now.
V = π r² h
V = π × ( 1.3 )² × 6.5
V = π × 1.69 × 6.5
V = 34.51ft³
If k and b are constant such that lim x approach infinity (kx+b-(x^3+1)/(x^2+1)=0. Find the values of k and b
Combining the terms into one fraction, we have
[tex]kx + b - \dfrac{x^3+1}{x^2+1} = \dfrac{(k-1)x^3 + bx^2 + kx + b - 1}{x^2+1}[/tex]
If this converges to 0 as [tex]x\to\infty[/tex], then the degree of the numerator must be smaller than the degree of the denominator.
To ensure this, take [tex]k=1[/tex] and [tex]b=0[/tex]. This eliminates the cubic and quadratic terms in the numerator, and we do have
[tex]\displaystyle \lim_{x\to\infty} \frac{x - 1}{x^2 + 1} = \lim_{x\to\infty} \frac{\frac1x - \frac1{x^2}}{1 + \frac1{x^2}} = 0[/tex]
Alternatively, we can compute the quotient and remainder of the rational expression.
[tex]\dfrac{x^3+1}{x^2+1} = x - \dfrac{x-1}{x^2+1}[/tex]
Then in the limit, we have
[tex]\displaystyle \lim_{x\to\infty} \left(kx + b - x + \frac{x-1}{x^2+1}\right) = (k-1) \lim_{x\to\infty} x + b = 0[/tex]
Both terms on the left vanish if [tex]k=1[/tex] and [tex]b=0[/tex].
What are the first five terms in the recursive sequence defined by the following? (only one is correct)
a1= 1
a2=1
an= an-2+an-1
a) {1,1,2,3,5}
b) {1,1,0,-1,-1}
c) {2,3,5,8,13}
d) {1,-1,2,-3,5}
Answer:
d 1-12-3-5 is the answer
the five-number summary calculated in part C to create a box plot representing the data. Draw a box plot representing the following data. Be sure to mark the outlier. 10 13 15 12 12 4 12 17 12 13 15 18 10 11 20 19 Lines Shapes Fill: Line: Width: 2 pt
The five-number summary is:
Minimum: 4
Quartile Q1: 11.25
Median: 12.5
Quartile Q3: 16.5
Maximum: 20
The box plot is attached below.
What is the Five-number Summary?The five-number summary of a data that is displayed on a box plot include: minimum and maximum values, lower and upper quartiles, and the median.
Given the data, 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19, the five-number summary is:
Minimum: 4
Quartile Q1: 11.25
Median: 12.5
Quartile Q3: 16.5
Maximum: 20
There are no outliers. Thus, the box plot that represents the five-number summary is shown in the image attached below.
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Answer: it is correct i got it from edmentum
Step-by-step explanation:
In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.
1. What is the expected mean for a sample of 150 women?
2. What is the standard deviation of the mean for a sample of 150 women?
3. What is the probability of 150 women having a sample mean below 160 pounds?
4. What is the probability of 150 women having a sample mean above 175 pounds?
5. What is the probability of 200 women having a sample mean below 160 pounds? Note the change in sample size.
6. What is the probability of 200 women having a sample mean above 175 pounds?
Step-by-step explanation:
1.
the expected sample mean is always the general mean : 168.5 pounds.
2.
the SD of a sample is the general SD / sqrt(sample size).
in our case
the sample SD = 68/sqrt(150) = 5.55217675...
3.
if we are looking for only the probability that any single woman is below 160 pounds, we would use the normal z calculation :
z = (x - mean)/SD = (160 - 168.5)/68 = -8.5/68
but we have here the question about the probability of the mean value of a whole sample of 150 women.
so, we need to adapt the z-calculation by the principle of 2) for the SD of a sample :
z = (x - mean)/(SD × sqrt(sample size)) =
= (160 - 168.5)/(68 × sqrt(150)) = -8.5/(68×sqrt(150)) =
= -0.010206207 ≈ -0.01
that gives us in the z-table the p-value 0.49601
this 0.49601 is the probability that a sample of 150 women has a mean value of below 160 pounds.
4.
similar to 3.
the z value we are looking for
z = (175 - 168.5)/(68 × sqrt(150)) = 6.5/(68 × sqrt(150)) =
= 0.007804747... ≈ 0.01
that gives us the p-value 0.50399.
that would be the probability of a sample mean of 175 or below.
to get above 175 we need to get the other side of the bell-curve :
1 - 0.50399 = 0.49601
so, this case has about the same probability as 3.
5.
as 3), just with the sqrt(200) instead of the sqrt(150).
z = -8.5/(68 × sqrt(200)) = -0.008838835... ≈ 0.01
so, the probability is still about the same as in 3) :
0.49601
6.
as 4) just with sqrt(200).
z = 6.5/(68 × sqrt(200)) = 0.006759109... ≈ 0.01
so, the probability is still about the same as for 4) :
0.49601
The answers are :
1) The expected mean for a sample of 150 women is 168.5 pounds.
2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.
3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.
4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.
5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.
6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.
What is probability ?
Probability is a measure of the likelihood of event to occur. The probability of all the events in a sample space adds up to 1.
1)
We know that the expected mean of a sample is always equal to general mean.
As per the question, mean weight is 168.5 pounds.
This implies :
The expected mean for a sample of 150 women is :
= 168.5 pounds
2)
The standard deviation (SD) of the mean for a sample of 150 women is :
= 68 / (√150)
= 5.55
3)
The probability of 150 women having a sample mean below 160 pounds will be represented by z and will be :
z = ( x - mean) / ( SD × (√sample size))
= (160 - 168.5) / (68 × √150)
= 0.01
If we use the z table then the probability will be :
= 0.49601
4)
Similarly as part 3 :
z = (175 - 168.5) / (68 × √150)
z = 0.01 (approximately)
The probability of 150 women having a sample mean below 175 pounds will be :
= 0.50399
And the probability of 150 women having a sample mean above 175 pounds will be :
= 1 - 0.50399
= 0.49601
5)
Here , we have to find probability of 200 women , so 150 in formula of z in 3rd part will be replaced by 200.
i.e.,
z = (160 - 168.5) / (68 × √200)
z = 0.01 ( approximately)
and probability will be :
= 0.49601
6)
Here , we have to find probability of 200 women , so 150 in formula of z in 4th part will be replaced by 200.
z = (175 - 168.5) / (68 × √200)
z = 0.01
And probability equal to :
= 0.49601
Therefore , the answers are :
1) The expected mean for a sample of 150 women is 168.5 pounds.
2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.
3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.
4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.
5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.
6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.
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A COUPLE PLAN TO HAVE THREE CHILDREN.
A) LIST ALL THE POSSIBILITIES FOR THE SAMPLE SPACE.
B) WHAT IS THE PROBABILITY THAT THEY HAVE AT MOST TWO BOYS?
C) WHAT IS THE PROBABILITY THAT THEY HAVE AT LEAST TWO GIRLS?
D) WHAT IS THE PROBABILITY THAT THEY ARE ALL OF THE SAME SEX?
Using the sample space and probability concepts, we have that:
A) All the possibilities for the sample space are: {{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.
B) The probability is: 7/8.
C) The probability is: 1/2.
D) The probability is: 1/4.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The sample space is the set that contains all possible outcomes, hence in this problem, considering G for girl and B for boy, it is given by:
{{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.
For item B, 7 outcomes have at most two boys, hence the probability is 7/8.
For item C, 4 outcomes have at least two girls, hence the probability is 4/8 = 1/2.
For item D, 2 outcomes have all the babies with the same sex, hence the probability is 2/8 = 1/4.
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what the milk and and butter
Answer:
1/4 cups of milk and 1 1/3 Tbsp of butter.
Step-by-step explanation:
Milk : 3/4 multiplied by 1/3 = 3/12 = 1/4
Butter : 4 multiplied by 1/3 = 4/3 = 1 1/3
PLEASE HELP 100 POINTS!!!!!!
A piecewise function g(x) is defined by g of x is equal to the piecewise function of x cubed minus 9 times x for x is less than 3 and negative log base 4 of the quantity x minus 2 end quantity plus 2 for x is greater than or equal to 3
Part A: Graph the piecewise function g(x) and determine the domain. (5 points)
Part B: Determine the x-intercepts of g(x). Show all necessary calculations. (5 points)
Part C: Describe the interval(s) in which the graph of g(x) is positive. (5 points)
Answer:
A) See attached for graph.
B) (-3, 0) (0, 0) (18, 0)
C) (-3, 0) ∪ [3, 18)
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad \textsf{if }x\geq 3\end{cases}[/tex]
Therefore, the function has two definitions:
[tex]g(x)=x^3-9x \quad \textsf{when x is less than 3}[/tex][tex]g(x)=-\log_4(x-2)+2 \quad \textsf{when x is more than or equal to 3}[/tex]Part AWhen graphing piecewise functions:
Use an open circle where the value of x is not included in the interval.Use a closed circle where the value of x is included in the interval.Use an arrow to show that the function continues indefinitely.First piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies g(3)=(3)^3-9(3)=0 \implies (3,0)[/tex]
Place an open circle at point (3, 0).
Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.
Second piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)[/tex]
Place an closed circle at point (3, 2).
Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.
See attached for graph.
Part BThe x-intercepts are where the curve crosses the x-axis, so when y = 0.
Set the first piece of the function to zero and solve for x:
[tex]\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}[/tex]
Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.
Set the second piece to zero and solve for x:
[tex]\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}[/tex]
Therefore, the x-intercept for the second piece is (18, 0).
So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).
Part CFrom the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.
Interval notation: (-3, 0) ∪ [3, 18)
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What is the solution to the system of equations?
y = 2/3 x + 3
X= -2
The solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)
Solving system of equationsFrom the question, we are to determine the solution to the given system of equations
The given system of equation is
y = 2/3 x + 3 ----------- (1)
x= -2 ----------- (2)
The value of x has been given in the second equation of the system of equations.
Now, we will determine the value of y
From the second equation, we have that
x = -2
Substitute the value of x into the first equation,
y = 2/3 x + 3
y = 2/3 (-2) + 3
y = -4/3 + 3
y = 5/3
Hence, the solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)
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At a hockey game, a vender sold a combined total of 210 sodas and hot dogs. The number of sodas sold was 36 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
123 soda and 87 hot dogs
Step-by-step explanation:
Let s = # soda and h = # hot dogs
s + h = 210 s = h + 36 Substitute the h + 36 for s into the first equation
s + h = 210
(h + 36) + h = 210
h + 36 + h = 210 Combine the h's
2h + 36 = 210 Subtract 36 from both sides
2h = 174 Divide both sides by 2
h = 87 This is the number of hot dogs. Substitute this into either equation above to find the sodas.
s + h = 210
s + 87 = 210
s = 123
OR
s = h + 36
s = 87 + 36
s = 123
Amy and Richard each solved an equation using the quadratic formula.
Amy's Equation and Method
Latex: 4x^2+7x-20=0
4
x
2
+
7
x
−
20
=
0
Step 1: Latex: x=\frac{-7\pm \sqrt{7^2-4(1)(20)}}{2(4)}
x
=
−
7
±
√
7
2
−
4
(
1
)
(
20
)
2
(
4
)
Step 2: Latex: x=\frac{-7\pm \sqrt{49-80}}{8}
x
=
−
7
±
√
49
−
80
8
Step 3: Latex: x=\frac{-7\pm \sqrt{-31}}{8}
x
=
−
7
±
√
−
31
8
Step 4: Latex: x=\frac{-7\pm i\sqrt{31}}{8}
x
=
−
7
±
i
√
31
8
Richard's Equation and Method
Latex: x^2-6x+8=0
x
2
−
6
x
+
8
=
0
Step 1: Latex: x=\frac{6\pm \sqrt{(-6)^2-4(1)(8)}}{2(1)}
x
=
6
±
√
(
−
6
)
2
−
4
(
1
)
(
8
)
2
(
1
)
Step 2: Latex: x=\frac{6\pm \sqrt{36-32}}{2}
x
=
6
±
√
36
−
32
2
Step 3: Latex: x=\frac{6\pm \sqrt{4}}{2}
x
=
6
±
√
4
2
Step 4: Latex: x=\frac{6+\sqrt{4}}{2}
x
=
6
+
√
4
2
and Latex: x=\frac{6-\sqrt{4}}{2}
x
=
6
−
√
4
2
Step 5: Latex: x=\frac{6+2}{2}
x
=
6
+
2
2
and Latex: x=\frac{6-2i}{2}
x
=
6
−
2
i
2
Step 6: Latex: x=4
x
=
4
and Latex: x=3-i
x
=
3
−
i
Both students made a mistake.
Describe the mistake each student made.
Explain what each student needs to do to fix their mistake.
Create your own quadratic equation, and explain how to use the quadratic formula to solve it. Be specific, using Latex: a\textsf{, }b\textsf{,} and Latex: c
c
of your equation and giving the solutions to the equation you chose.
Number your responses from 1 to 3 so your instructor can tell which question you're responding to. You may not receive full credit if your teacher cannot determine that you've answered each question.
Search entries or author
The mistake each student made and what each student needs to do to fix their mistake is;
Amy didn't include the negative sign for the 20, so she should include itRichard added a negative sign underneath the radicalQuadratic equationx² - 6x + 8 = 0
x = - b ± √b² - 4ac / 2a
where,
a = 1b = -6c = 8x = - b ± √b² - 4ac / 2a
= -(-6) ± √(-6)² - 4(1)(8) / 2(1)
= 6 ± √36 - 32 / 2
= 6 ± √4 / 2
= 6 ± 2 / 2
x = 6/2 + 2/2 or 6/2 - 2/2
= 3 + 1 or 3 - 1
x = 4 or 2
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If 5 bags weigh the same as 3 blocks, how many blocks will 9 bags weigh?
OA) 3 blocks
OB) 4.4 blocks
OC) 5.4 blocks
OD) 15 blocks
Answer: C. 5.4 Blocks
Step-by-step explanation:
Given information
5 bags = 3 blocks
Set variable
Let x be the number of blocks
Constructure proportional equation
[tex]\frac{3}{5} } ~=~\frac{x}{9}[/tex]
Cross multiply the fraction
[tex](3)~*~(9)~=~(5)~*~(x)[/tex]
[tex]27~=~5x[/tex]
Divide 5 on both sides
[tex]27~/~5~=~5x~/~5[/tex]
[tex]\Large\boxed{x=5.4~blocks}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
oc
Step-by-step explanation:
5 times .6 equals 3
9 times .6 equals 5.4
Please help
Use the parabola tool to graph the quadratic function f(x)=−2(x+4)^2−3
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Due to length restrictions, we kindly invite to read the explanation of this question and the image of parabola on Cartesian plane attached below to see the results.
How to graph a quadratic function
To graph a parabola, we shall follow the following procedure:
Mark the vertex of the parabola on the Cartesian plane.Mark at least two pairs of values on the Cartesian plane, one on the right of the vertex and other on the left of the vertex.Match the points to create the resulting curves.By following all the steps, we generate the curve with the help of a graphing tool.
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what is 4,928 will rounded to the nearest hundred
Answer:
4900
Step-by-step explanation:
When rounding a number such as 4928 to the nearest hundred, we use the following rules:
A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.
C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
In this case, Rule B applies and 4928 rounded to the nearest hundred is:
4900
Answer:
Step-by-step explanation:
4,928, look at the last two numbers 28 if they are above 50 you round up, if below 50 round down,
The answer is 4,900
If there are 12 donuts per box, which of the following equations will give you the number of boxes, x, that Joe needs to buy?
The equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60
Writing an equationFrom the question, we are to determine the equation that will give the number of boxes, x, that Joe needs to buy
From the given information,
Joe needs 60 donuts to feed his construction crew
Also,
There are 12 donuts per box
This means he needs to buy 60/12 boxes of donut
Since the number of boxes Joe needs to buy is x
∴ 60/12 = x
60 = 12x
12x = 60
Hence, the equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60
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a fisherman travels 9mi downstream with the current in the same time he travels 3 mi upstream against the current. if the speed of the current is 5mph what is the speed at which the fisherman travels in still water
Answer:
10 mph
Step-by-step explanation:
speed of boat in still water = x
speed of current = 5
speed of boat with current (downstream) = x + 5
speed of boat against current (upstream) = x - 5
distance downstream = 9
distance upstream = 3
time = t
speed = distance/time
distance = speed × time
downstream:
9 = (x + 5)t
upstream:
3 = (x - 5)t
9 = xt + 5t
3 = xt - 5t
9 = xt + 5t
-3 = -xt + 5t
-----------------
6 = 10t
t = 0.6
9 = (x + 5)0.6
15 = x + 5
x = 10
A poll was conducted by a home mortgage company regarding home ownership in the United States. The company polled 1,488 Americans and found that 69% of those polled own a home. What is the approximate margin of error, assuming a 99% confidence level?
If the sample size is 1488 and confidence interval of 99% then the margin of error is 0.03088.
Given sample size of 1488, percentage of those polled own a home be 69% and confidence level be 99%.
We are required to find the approximate margin of error.
Margin of error is the difference between calculated values and real values.
n=1488
p=0.69
Margin of error=z*[tex]\sqrt{p(1-p)/n}[/tex]
Z score when confidence level is 99%=2.576.
Margin of error=2.576*[tex]\sqrt{0.69(1-0.69)/1488}[/tex]
=2.576*[tex]\sqrt{(0.69*0.31)/1488}[/tex]
=2.576*[tex]\sqrt{0.2139/1488}[/tex]
=2.576*[tex]\sqrt{0.0001437}[/tex]
=2.576*0.01198
=0.03088
Hence if the sample size is 1488 and confidence interval of 99% then the margin of error is 0.03088.
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Answer:
0.031
Step-by-step explanation:
Plato/Edmentum
Marin corporation had a projected benefit obligation of $3235000 and plan assets of $3474000 at January 1, 2020 . Marin also had a net acturial loss of $505740 in accumulated OCI at January 1, 2020.The average remaining service period of Marin's employees is 7.80 years . Compute Marin's minimum amortization of the actuarial loss. Minimum amortization of the actuarial loss
the minimum amortization is given as 20300 dollars
How to solve for the amortizationWe have the value of A to be $3235000
while we have the value of B to be $3474000
Of these two values the greatest or the highest is that of the option B.
Next we have to find the corridor value using 10 percent
0.10 * 3474000
= 347400
$505740 - 347400
= 158340
The number of years = 7.8
minimum amortization = 158340/7.8
= 20300 dollars
Hence the minimum amortization is given as 20300 dollars
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hey can you help me answer this question by giving me the answer?
The value of f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].
Given a function f(x)=4-2x+6[tex]x^{2}[/tex].
We are told to find out the value of f(a), f(a+h) and [f(a+h)-f(a)]/hwhere h≠0.
Function is like a relationship between two or more variables expressed in equal to form.The value which we entered in the function is known as domain and the value which we get after entering the values is known as codomain or range.
f(a)=4-2a+6[tex]a^{2}[/tex] (By just putting x=a).
f(a+h)==[tex]4-2(a+h)+6(a+h)^{2}[/tex]
=4-2a-2h+6([tex]a^{2} +h^{2} +2ah[/tex])
=4-2a-2h+6[tex]a^{2} +6h^{2} +12ah[/tex]
=[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]
[f(a+h)-f(a)]/h=[[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]-(4-2a+6[tex]a^{2}[/tex] )]/h
=[tex](6a^{2} +6h^{2} -2a-2h+12ah)/h[/tex]
=[tex](6h^{2} -2h+12ah)/h[/tex]
=6h+12a-2.
Hence the value of function f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].
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Captain's Autos sells 22 used cars on
Monday, and 18 cars on Tuesday. This was
25% of the number of sales for the week.
How many cars did they sell altogether that
week
Answer:
160
Step-by-step explanation:
22 + 18 = 25 percent
40 = 25 percent
100 / 25 = 4
40 x 4 = 160.
What is the value of 8x-25 when x is equal to 12?
Answer:
71
Step-by-step explanation:
Evaluate for x=12
(8)(12)−25
(8)(12)−25
=71
Answer:
71
Step-by-step explanation:
To evaluate [tex]8x - 25[/tex] when [tex]x = 12[/tex], we have to replace x with 12 in the expression:
[tex]8x - 25[/tex]
⇒ [tex]8(12) -25[/tex]
⇒ [tex]96 - 25[/tex]
⇒ [tex]\bf 71[/tex]
Which is the best approximation of the solutions to the system of equations graphed below?
According to the direct inspection, we conclude that the best approximation of the two solutions to the system of quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)
What is the solution of a nonlinear system formed by two quadratic equations?
Herein we have two parabolae, that is, polynomials of the form a · x² + b · x + c, that pass through each other twice according to the image attached to this question. We need to estimate the location of the points by visual inspection on the Cartesian plane.
According to the direct inspection, we conclude that the best approximation of the two solutions, that is, the point where the two parabolae intercepts each other, to the system of two quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)
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7
O x-3
O x-1
O x + 1
O x + 3
3
2-
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
3
N
3
I NEED HELP !!!!!
Answer:
x-1 gave ggs is it correct
In 1965, about 44% of the U.S. adult population had never smoked cigarettes. A national health survey of 1360 U.S. adults (selected randomly) during 2020 revealed that 626 had never smoked cigarettes. Using α = 0.05, test whether there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes. State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.
Using the z-distribution, it is found that since the p-value is greater than 0.05, there is not enough evidence to conclude that there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is still of 44%, that is:
[tex]H_0: p = 0.44[/tex]
At the alternative hypothesis, it is tested if the proportion is now different of 44%, that is:
[tex]H_1: p \neq 0.44[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]p = 0.44, n = 1360, \overline{p} = \frac{626}{1360} = 0.4603[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.4603 - 0.44}{\sqrt{\frac{0.44(0.56)}{1360}}}[/tex]
z = 1.51
What is the p-value and the conclusion?Using a z-distribution calculator, for a two-tailed test, as we are testing if the proportion is different of a value, with z = 1.51, the p-value is of 0.1310.
Since the p-value is greater than 0.05, there is not enough evidence to conclude that there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes.
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