Answer:
Systems of linear equations are used in the real world by economists and entrepreneurs to find out when supply equals demand.It's all about the mullah, and if you don't know the numbers when you have a business, it might fail.
Step-by-step explanation:
3 tenths plus 17 hundredths=
Answer: [tex].47[/tex]
3 tenths is written as
Decimal: [tex].3[/tex]
Fraction: [tex]\frac{3}{10}[/tex]
17 hundredths is written as
Decimal: [tex].17[/tex]
Fraction: [tex]\frac{17}{100}[/tex]
Add
[tex]3/10+17/100[/tex]
[tex]=.47[/tex]
Fraction Form
[tex].47=\frac{47}{100}[/tex]
if 7x=3y and 5y=7z then X/Z?
The value of the expression x/z is 3/5.
What is simplification of an expression?Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.
For the given situation,
The expressions are
7x=3y ------ (1)
5y=7z ------ (2)
From equation 1,
[tex]7x=3y[/tex]
⇒ [tex]x=\frac{3y}{7}[/tex]
From equation 2,
[tex]5y=7z[/tex]
⇒ [tex]z=\frac{5y}{7}[/tex]
Now, [tex]\frac{x}{z}= \frac{\frac{3y}{7} }{\frac{5y}{7} }[/tex]
⇒ [tex]\frac{x}{z}=(\frac{3y}{7})(\frac{7}{5y} )[/tex]
⇒ [tex]\frac{x}{z}=(\frac{3}{5})[/tex]
Hence we can conclude that the value of the expression x/z is 3/5.
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One method for estimating abundance of animals is known as line-intercept sampling. The theory of this method, when applied to Alaska wolverines, predicts that the proportion p equals.453 of attempts to locate wolverine tracks should be successful. Suppose that biologists will make 100 attempts to locate wolverine tracks in random locations in Alaska. What is the mean of the sampling distribution of p with hat on top if the proportion predicted by line-intercept sampling is correct
Answer:
0.6848
Step-by-step explanation:
Mean of \hat{p} = 0.453
Answer = 0.453
Standard deviation of \hat{p} :
= \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} = \sqrt{\frac{0.453(1-0.453)}{100}} = 0.0498
Answer = 0.0498
P(0.0453 - 0.05 < p < 0.0453 + 0.05)
On standardising,
= P(\frac{0.0453-0.05-0.0453}{0.0498} <Z<\frac{0.0453+0.05-0.0453}{0.0498})
= P(-1.0044 < Z < 1.0044) = 0.6848
Answer = 0.6848
Using the Central Limit Theorem, it is found that the mean of the sampling distribution of the sample proportions is 0.453.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this problem:
Sample of 100, thus [tex]n = 100[/tex].Proportion of 45.3%, thus [tex]p = 0.453[/tex].By the Central Limit Theorem, the mean is [tex]\mu = p = 0.453[/tex].
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A manufacturer estimates that its product can be produced at a total cost of C(x) = 45,000 + 100x + x3 dollars. If the manufacturer's total revenue from the sale of x units is R(x) = 4000x dollars, determine the level of production x that will maximize the profit. (Round your answer to the nearest whole number.)
The level of production (x) that will maximize the profit is approximately 36 units.
The profit is the revenue (R(x)) minus the cost (C(x)). So, we have:
P(x) = R(x) - C(x)
Given Functions:
Cost Function: C(x) = 45,000 + 100x + x³ dollars
Revenue Function: R(x) = 4000x dollars
Substitute the given functions into the profit function:
P(x) = R(x) - C(x)
P(x) = 4000x - (45,000 + 100x + x³)
P(x) = 4000x - 45,000 - 100x - x³
Simplify the profit function:
P(x) = -x³ + 3900x - 45,000
Find the critical points by differentiating the profit function and setting it to zero:
P'(x) = -3x² + 3900
Set P'(x) = 0 and solve for x:
-3x² + 3900 = 0
-3x² = -3900
x²= 1300
x = ±√1300
x = ±36.06
Evaluate the second derivative (P''(x)) to determine if these critical points are maxima or minima:
P''(x) = -6x
Substitute the critical points (x = ±36.06) into P''(x):
P''(x)= -6(36.06)
= -216.36 (negative value)
Since the second derivative is negative at x ≈ ±36.06, it confirms that x = 36.06 is a maximum point.
So, the level of production (x) that will maximize the profit is approximately 36 units.
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To determine the level of production that maximizes profit, we calculate the profit function, differentiate it to find critical points, and then identify the maximum. The critical points are found by setting the first derivative of the profit function to zero and solving for x.
Explanation:To determine the level of production x that will maximize the profit for the manufacturer, we first need to calculate the profit function. Profit, P(x), is the difference between total revenue, R(x), and total cost, C(x).
The profit function is defined as P(x) = R(x) - C(x). Using the given cost function C(x) = 45,000 + 100x + x^3 dollars and the revenue function R(x) = 4000x dollars, we get:
P(x) = 4000x - (45,000 + 100x + x^3)
This simplifies to:
P(x) = -x^3 + 3900x - 45,000
To find the production level that maximizes profit, we need to determine the critical points by differentiating P(x) and setting the derivative equal to zero. The derivative of P(x) is:
P'(x) = -3x^2 + 3900.
Setting P'(x) = 0 gives:
-3x^2 + 3900 = 0
Solving for x yields two critical points, but only one will maximize profit. We can find this maxima by testing which value of x gives the higher P(x) or by using the second derivative test. After finding the correct value of x, we round it to the nearest whole number as the final answer.
Match each
Match each investment characteristic to the level of risk involved.
growth
savings
speculation
high risk because returns are not guaranteed, but time frames are set
moderate risk because expectations of returns are reasonable and average
low risk because of steady interest without fluctuation in value
High Risk because returns are not guaranteed, but time frames are set
—Speculation
Moderate Disk because expectations of returns are reasonable and average
—Growth
Low Risk because of steady Interest without fluctuation in value
—Savings
In investment terms, growth corresponds to high risk as returns aren't guaranteed, savings relate to low risk due to steady interest income, and speculation signifies moderate risk as it has reasonable return expectations.
Explanation:The types of investment can be associated with different levels of risk as follows:
Growth is correlated with high risk because the returns are not guaranteed, but time frames are set. For example, investing in a start-up tech firm may have great potential for growth, but also carries a significant risk if the company does not succeed. Savings are associated with low risk due to steady interest without fluctuation in value. This might be a savings account or a fixed-rate bond, where the earnings are steady and dependable, and there is little risk of losing your initial investment. Speculation presents a moderate risk because expectations of returns are reasonable and average. This could be investments in commodities, real estate or foreign exchange, where there is some risk involved but also the potential for significant gains. Learn more about Investment Risk here:
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Find the product of 102 cm and 0.33 cm.
Answer:
33.66 cm
Step-by-step explanation:
Multiply to find the product.
The length of a rectangle is five less than its width. The area of the rectangle is 84 square feet. Write a quadratic equation in standard form, ax^2+bx+c=0
Given:
The length of a rectangle is 5 less than its width.
The area of the rectangle is 84 square feet.
We need to determine the quadratic equation in standard form that represents the area of the rectangle.
Dimensions of the rectangle:
Let l denote the length of the rectangle.
Let w denote the width of the rectangle.
Since, it is given that the length is 5 less than its width, it can be written as,
[tex]l=5-w[/tex] and [tex]w=w[/tex]
Area of the rectangle:
The area of the rectangle can be determined using the formula,
[tex]A=length \times width[/tex]
Substituting A = 84, [tex]l=5-w[/tex] and [tex]w=w[/tex], we get
[tex]84=(5-w)\times w[/tex]
[tex]84=5w-w^2[/tex]
Adding both sides of the equation by w², we have;
[tex]w^2+84=5w[/tex]
Subtracting by 5w on both sides, we get;
[tex]w^2-5w+84=0[/tex]
Thus, the quadratic equation in standard form for the area of the rectangle is [tex]w^2-5w+84=0[/tex]
lists the amount of U.S. cash per capita in circulation as of June 30 in the given year. Use linear approximation to estimate the amount, C(2010), of cash per capita in circulation in the year 2010.
Answer:
C(2010) = $1312 using linear approximation.
Step-by-step explanation:
The full complete question is attached to this solution.
The full table is given as
Year | 1970 | 1980 | 1990 | 2000
Cash |$180 |$262 |$564 | $938
we are told to use linear approximation to obtain C(2010)
Linear approximation, Mathematically, results in
C(2010) = C(2000) + C'(t) [t]
where t = years since 2010 = (Year - 2000)
Linear approximation gives C'(t) as the rate of change of C with time
C'(t) = (ΔC/Δt)
We will be using the latest year for this approximation.
ΔC = C(2000) - C(1990) = 938 - 564 = $374
Δt = 2000 - 1990 = 10
C'(t) = (374/10) = $37.4 per year.
C(2010) = C(2000) + C'(t) [t]
t = 2010 - 2000 = 10
C(2000) = $938
C'(t) = $37.4 per year
C(2010) = 938 + (37.4)(10) = $1312
Hope this Helps!!!
The amount, C(2010), of cash per capita in circulation in the year 2010 = $1312.
The full table is given as
Year | 1970 | 1980 | 1990 | 2000
Cash |$180 |$262 |$564 | $938
we are told to use linear approximation to obtain C(2010)
Linear approximation, Mathematically, results in
C(2010) = C(2000) + C'(t) [t]
where t = years since 2010 = (Year - 2000)
Linear approximation gives C'(t) as the rate of change of C with time
C'(t) = (ΔC/Δt)
We will be using the latest year for this approximation.
ΔC = C(2000) - C(1990) = 938 - 564 = $374
Δt = 2000 - 1990 = 10
C'(t) = (374/10) = $37.4 per year.
C(2010) = C(2000) + C'(t) [t]
t = 2010 - 2000 = 10
C(2000) = $938
C'(t) = $37.4 per year
C(2010) = 938 + (37.4)(10) = $1312.
Complete question:
(PLS HELP, I WILL MARK BRAINLIEST) what is a very easy way to multiply mixed fractions.
Answer:
1. Change each number to an improper fraction.
2. Simplify if possible.
3. Multiply the numerators and then the denominators.
4. Put answer in lowest terms.
Step-by-step explanation:
A study conducted by the Pew Research Center reported that 58% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of 15 cell phone owners is studied. What is the probability that 10 or more of them used their phones for guidance on purchasing decisions? Round your answer to 2 decimal places
Final answer:
The student is asked to calculate the probability that 10 or more out of 15 cell phone owners use their phones for help with purchasing decisions, with a 58% chance each. The calculation is done using the binomial probability formula and the answer is rounded to two decimal places.
Explanation:
The student seeks to determine the probability that 10 or more cell phone owners out of a sample of 15 use their phones for guidance on purchasing decisions, given that 58% of cell phone owners do so. This question can be addressed using the binomial probability formula:
[tex]P(X ≥ k) = Σ (nCk * p^k * (1-p)^(n-k))[/tex]
n is the sample size (15 in this case),k is the number of successes (10, 11, 12, 13, 14, or 15 in this case),p is the probability of success on a single trial (0.58), andnCk is the combination of n items taken k at a time.To find the total probability of 10 or more successes, we sum the probabilities of having 10, 11, 12, 13, 14, or 15 successes. Each of these probabilities is found by plugging the appropriate numbers into the binomial formula. In practice, to simplify the calculation, one might use statistical software or a binomial probability calculator.
After calculating these probabilities and summing them up, we round the answer to two decimal places as per the instruction given in the question.
What is the solution of the equation
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
Equations
The following equation will be solved
[tex]\displaystyle \frac{2}{x+3}-\frac{3}{4-x}=\frac{2x-2}{x^2-x-12}[/tex]
Changing signs of the second term on the left side
[tex]\displaystyle \frac{2}{x+3}+\frac{3}{x-4}=\frac{2x-2}{x^2-x-12}[/tex]
Operating
[tex]\displaystyle \frac{2(x-4)+3(x+3)}{x^2-x-12}=\frac{2x-2}{x^2-x-12}[/tex]
Simplifying denominators, provided
[tex]x^2-x-12\neq 0[/tex]
[tex]2(x-4)+3(x+3)=2x-2[/tex]
Operating
[tex]2x-8+3x+9=2x-2[/tex]
Solving
[tex]\boxed{x=-1}[/tex]
Since
[tex](-1)^2-(-1)-12=-10\neq 0[/tex]
Solution (1)
The following definitions are used: a relation on a set A is defined to be irreflexive if, and only if, for every x A, x R x; asymmetric if, and only if, for every x, y A if x R y then y R x; intransitive if, and only if, for every x, y, z A, if x R y and y R z then x R z. The following relation is defined on the set A = {0, 1, 2, 3}. Determine whether the relation is irreflexive, asymmetric, intransitive, or none of these. (Select all that apply.) R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)}
The relation R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} is not irreflexive, asymmetric, or intransitive.
Explanation:To determine whether the relation R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} is irreflexive, asymmetric, or intransitive, we will analyze each property.
Irreflexive: Since every element in the relation has the form (x, x) where x is an element of A, and all such pairs exist in R2, the relation is not irreflexive.Asymmetric: Since the relation contains (x, y) and (y, x) pairs for some x, y in A, it violates the definition of an asymmetric relation. Therefore, R2 is not asymmetric.Intransitive: The relation R2 does not violate the transitive property. For example, (0,1) and (1,2) are in R2, and it also contains (0,2), satisfying the transitive property. Therefore, R2 is not intransitive.Therefore, the relation R2 is none of the given properties (irreflexive, asymmetric, or intransitive).
the sum The first six terms of a geometric series is 15,624 and the common ratio is 5 what is the first term of the series
Answer:
4
Step-by-step explanation:
The sum of the first n terms of a geometric series is:
S = a₁ (1 − r^n) / (1 − r)
Given n = 6, S = 15624, and r = 5:
15624 = a₁ (1 − 5^6) / (1 − 5)
a₁ = 4
if f(x) =6x -4,whats is f(x) when x =8?
Answer:
44
Step-by-step explanation:
Input 8 into x
f(8)=6(8)-4
f(8)=48-4
f(8)=44
The mean of the sample is 24.444 squares with a standard deviation of 2.45 squares. Single-ply toilet paper requires 26 squares to absorb one-quarter cup of water. Josh would like to carry out a test to determine if there is convincing evidence that the mean number of squares of Fluffy that are needed to absorb one-quarter cup of water is fewer than 26 squares. What is the appropriate test statistic and P-value of this test?
Answer:
t = -2.69 , p = 0.0078
Step-by-step explanation:
We have the following data:
Sample Mean = x = 24.444
Sample Standard Deviation = s = 2.45
Sample size = n = 18
Josh wants to test that mean number is lesser than 26. So our test value is 26 i.e.
u = 26
Since Josh wants to test that mean would be fewer than 26, so this would be a left tailed test with a less than sign in Alternate Hypothesis. Therefore, the hypothesis would be:
[tex]H_{o}: u\geq 26\\H_{a}: u<26[/tex]
Since, we do not know the value of Population standard deviation, and we have the value of sample standard deviation, we will use One-Sample t-test for the population mean.
The formula to calculate the test-statistic would be:
[tex]t=\frac{x-u}{\frac{s}{\sqrt{n}}}[/tex]
Substituting the values in this formula gives us:
[tex]t=\frac{24.444-26}{\frac{2.45}{\sqrt{18}}}\\t=-2.69[/tex]
This means, the test statistic would be -2.69
Since, the sample size is 18, the degrees of freedom would be:
Degrees of freedom = df = n - 1 = 17
To find the p-value we need to check the p-value against test statistic of 2.69, with 17 degrees of freedom and One-tailed test. This value comes out to be:
p-value = 0.0078
Therefore, the correct answer would be:
t = -2.69 , p = 0.0078
the composition of the senate of the 107th congress is 53 republicans, 42 democrats, and 5 independents. a new committee is being formed to study ways to benefit the arts in education. if 3 senators are selected at random to head the committee, find the probability
Answer:
The correct answer is 161700.
Step-by-step explanation:
Total number of members of the senate of 107th congress is 100 in which there are 53 republicans, 42 democrats and 5 independents.
A new committee is to be formed from these 100 congressmen to study the benefits of arts in education.
Number of senators required to head the new committee is 3.
Therefore total number of ways 3 members are selected in the population of 100 congressmen is given by [tex]\left[\begin{array}{ccc}100\\3\end{array}\right][/tex] = 161700.
Thus there are 161700 ways one can select 3 senators to head a committee.
Jalene lost 12 pounds in the first 3 weeks of his diet if he lost a total of 84 pounds how many weeks did it take him
Answer:
21 weeks.
Step-by-step explanation:
To start, you have to get the pounds lost per week.
12/3=4
4 pounds lost per week.
Next, find out how many weeks it takes by solving this equation,
4x=84
Divide 84/4=21
Therefore, it took 21 weeks to lose 84 pounds.
Find the quadratic equation of the form y=ax^ 2 +bx+c, whose graph passes through the points (2, 3) ( -2,7)and (1, - 2) .
Answer:
y = 2x^2 -x -3
Step-by-step explanation:
It can be convenient to use the quadratic regression capability of a graphing calculator or spreadsheet. That's what we did in the attachment.
__
Fill in the given points in the equation to find three linear equations in a, b, c.
3 = a(2^2) +b(2) +c
7 = a(-2)^2 +b(-2) +c
-2 = a(1^2) +b(1) +c
Subtracting the last equation from the first two gives ...
(3) -(-2) = (4a +2b +c) -(a +b +c) ⇒ 5 = 3a +b
(7) -(-2) = (4a -2b +c) -(a +b +c) ⇒ 9 = 3a -3b . . . . . [eq5]
Subtracting the second of these equations from the first gives ...
(5) -(9) = (3a +b) -(3a -3b) ⇒ -4 = 4b
b = -1
Dividing [eq5] by 3 gives ...
3 = a - b
3 = a -(-1)
2 = a
Using the original 3rd equation, we have ...
-2 = a +b +c
-2 = 2 +(-1) + c
-3 = c . . . . . . . . subtract 1
The desired quadratic is ...
y = 2x^2 -x -3
The school held there talent quest and this year they had 1,204 people in attendance. Last year the attendance was only 860. What was the percentage increase from last year?
Answer:
28.57℅
Step-by-step explanation:
If last year attendance was 860 and the attendance increases to 1204:
Attendance increment = 1204-860
= 344
%increase = increment/current attendance × 100%
% increase = 344/1204 × 100
℅ increase = 34400/1204
% increase = 28.57%
Therefore the percentage increase from last year is 28.57℅
If the height and base of the parallelogram shown are each decreased by 2 cm, what is the area of the new parallelogram?
complete question:
If the height and base of the parallelogram shown are each decreased by 2 cm, what is the area of the new parallelogram?
A parallelogram with a base of 10 centimetres and a height of 8 centimetres.
Answer:
area = 48 cm²
Step-by-step explanation:
A parallelogram is quadrilateral with 4 sides formed by 2 pair of parallel lines. The area of a parallelogram is represented as follows :
area of parallelogram = B × H
where
B = breadth
H = height
According to the question the height and the base each reduced by 2 cm.
The new base = 10 - 2 = 8 cm
The new height = 8 - 2 = 6 cm
area = B × H
area = 8 × 6
area = 48 cm²
The segments shown below could form a triangle.
A. True
B. False
Final answer:
The answer to whether the segments with lengths of 1, 8, and 8 can form a triangle is True.
Explanation:
Can Segments Form a Triangle?
To determine if the segments with lengths of 1 and 8 can form a triangle, we need to apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we have two sides that are each 8 units long, and one side that is 1 unit long.
Let's add the lengths of the two shorter segments: 1 + 8 = 9.
This sum is greater than the length of the other segment, which is 8. Now, we will check the sum of the other two possible pairs:
8 + 8 = 16, which is greater than 1.8 + 1 = 9, which is also greater than 8.Since all combinations of the sums of two sides are greater than the third side, these segments can indeed form a triangle.
Thus, the answer to whether the segments with lengths of 1, 8, and 8 can form a triangle is True.
what is the answer for x because i got x/2- 5=4
Answer:
x/2=5+4=9
x=9*2=18
x=18!
An experiment consists of selecting a letter at random from the letters in the word IRRESISTIBLE and observing the outcomes. What is the appropriate sample space for this experiment
Sample space for the experiment is {B, E, I, L , R , S, T } .
Hence option D is correct.
Given, that the word IRRESISTIBLE .
An experiment consist of selecting a letter at random from the letters in the given word.
The number of distinct letters in the word is 7 i.e I is 3 times in the word but consider it as single letter.
Therefore the appropriate sample space for the experiment is {B, E, I, L , R , S, T } .
Thus the option D is correct.
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The sample space for an experiment consists of all possible outcomes or events that can occur. In this case, the experiment involves selecting a letter at random from the letters in the word "IRRESISTIBLE."
The appropriate sample space for this experiment would be the set of all individual letters that can be selected from the word. Therefore, the sample space is:
Sample space = {I, R, E, S, T, I, B, L}
Each element of the sample space represents a possible outcome of the experiment, which is selecting a specific letter from the word "IRRESISTIBLE."
It is important to note that the sample space only includes the individual letters as outcomes, and it does not consider the order or repetition of the letters in the word.
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A triangular prism has a height of 9 meters. The area of the triangular base measures 16 square meters. What is the volume of the triangular prism?
A. 15 cubic meters
B. 60 cubic meters
C. 72 cubic meters
D. 144 cubic meters
Answer:
D. 144 cubic meters
Step-by-step explanation:
Volume of triangular prism(V)= Area of a triangle(A)×height of the prism(H)
That is,
V=AH
Where,
A=Area of a triangle
H=Height of the prism
Given,
A=1/2× base×height=16 square meters
Height=9 meters
Therefore,
Volume of triangular prism=16 square meters×9 meters
=144 cubic meters
Answer: D. 144 cubic meters
Step-by-step explanation:
A triangular prism consists of 2 triangular faces(base) and 3 rectangular faces.
The formula for determining the volume of a triangular prism is expressed as
Volume = area of the triangular base × height of the prism
Area of triangular base = 1/2 base × height
From the information given,
Height of prism = 9 meters
Area of triangular base = 16 square meters
Volume of the triangular prism = 16 × 9 = 144 cubic meters
Men’s heights are normally distributed with mean 69.5 inches and a standard deviation of 2.4 inches.
Women’s heights are normally distributed with mean 63.8 inches and a standard deviation of 2.6 inches
The Gulfstream 100 is an executive jet that seats six and it has a doorway height of 51.6 inches.
a. What percentage of adult men can fit through the door without bending?
b. what percentage of adult women can fit through the door without bending?
c. Does the door design with a height of 51.6 inches appear to be adequate? Why didn’t engineers design a larger door?
d. What doorway height would allow 60% of men to fit without bending?
Answer:
a. The percentage of adult men that will fit through the door without bending is 0.
b. The percentage of adult women that will fit through the door without bending is 0.
c. No, it is not adequate. There must be another technical reasons to not use a larger door.
d. The doorway height that would allow 60% of men to fit without bending is 70.1 inches.
Step-by-step explanation:
a. To fit throught the door, the height has to be under 51.6. To calculate this proportion, we have to calculate the z-score for X=51.6 for the distribution of men's height N(μ=69.5, σ=2.4).
We can calculate the z-score as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{51.6-69.5}{2.4}=\dfrac{-17.9}{2.4}=-7.4583[/tex]
[tex]P(X<51.6)=P(z<-7.4583)=0[/tex]
The percentage of adult men that will fit through the door without bending is 0.
b. To fit throught the door, the height has to be under 51.6. To calculate this proportion, we have to calculate the z-score for X=51.6 for the distribution of women's height N(μ=63.8, σ=2.6).
We can calculate the z-score as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{51.6-63.8}{2.6}=\dfrac{-12.2}{2.6}=-4.6923[/tex]
[tex]P(X<51.6)=P(z<-4.6923)=0[/tex]
The percentage of adult women that will fit through the door without bending is 0.
c. No, it is not adequate. There must be another technical reasons to not use a larger door.
d. We can calculate this finding a z-value z1 for which P(z<z1)=0.60.
Looking in a standard normal distribution table, the value for z1 is z1=0.25335.
Then, transforming to our adult men's height distribution, we have:
[tex]X=\mu+z\sigma=69.5+0.25335*2.4=69.5+0.6=70.1[/tex]
The doorway height that would allow 60% of men to fit without bending is 70.1 inches.
The ratio of forks to knives in Isabella’s kitchen drawer is 4 to 5. There are
16 forks in the drawer. How many knives are there?
Answer:
20 knives
Step-by-step explanation:
the ratio of fork to knives is [tex]\frac{4}{5}[/tex] and their are 16 forks, so we put the ratio of fork and knives equal to number of fork and knives so its:
[tex]\frac{4}{5}[/tex] = [tex]\frac{16}{x}[/tex] We cross multiply
80 = 4x Divide both side by 4
x = 20
we can check too
16/20 if we simplify, its give us 4/5
There are 20 knives in Isabella's kitchen.
The ratio of forks to knives in Isabella’s kitchen drawer is 4 to 5.
Given that there are 16 forks in the drawer, we can set up a proportion to find the number of knives:
4/5 = 16/X
Cross multiply to get: 4X = 80
Divide by 4 to find X = 20
Therefore, there are 20 knives in Isabella's kitchen drawer.
five rock songs and six hip-hop songs on a disk jockeys playlist for a radio show. If the disc jockey shuffle the songs randomly, what is the possibility that all hip-hop song are played consecutively
Answer 39916800
Step-by-step explanation:
The probability that all hip-hop songs are played consecutively is 0.18%.
To calculate the probability that all hip-hop songs are played consecutively, to consider the total number of possible song arrangements and the number of arrangements where all hip-hop songs are consecutive.
The total number of song arrangements calculated using the concept of permutations. Since there are a total of 11 songs on the playlist, the number of possible arrangements is 11!.
Now, let's calculate the number of arrangements where all hip-hop songs are played consecutively treat the 6 hip-hop songs as a single unit or block. This means 6! ways to arrange the hip-hop songs within that block.
Since we have 5 rock songs remaining, we can arrange them in 5! ways.
Therefore, the total number of arrangements where all hip-hop songs are played consecutively is 6! ×5!.
To calculate the probability, we divide the number of favorable outcomes (where all hip-hop songs are played consecutively) by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = (6! × 5!) / 11!
Calculating the numerical value:
Probability = (720 × 120) / 39,916,800
Probability ≈ 0.00180
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The probability distribution for the number of automobiles lined up at a Lakeside Olds dealer at opening time (7:30 a.m.) for service is: Number Probability 1 0.05 2 0.30 3 0.40 4 0.25 On a typical day, how many automobiles should Lakeside Olds expect to be lined up at opening time?
Answer:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i) [/tex]
And replacing we got:
[tex] E(X) = 1*0.05 +2* 0.3 +3* 0.4 +4*0.25 = 2.85[/tex]
So we are going to expect about 2,85 automobiles for this case.
Step-by-step explanation:
For this case we define the random variable X as "number of automobiles lined up at a Lakeside Olds dealer at opening time (7:30 a.m.)" and we know the distribution for X is given by:
X 1 2 3 4
P(X) 0.05 0.30 0.40 0.25
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete
For this case we can calculate the epected value with this formula:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i) [/tex]
And replacing we got:
[tex] E(X) = 1*0.05 +2* 0.3 +3* 0.4 +4*0.25 = 2.85[/tex]
So we are going to expect about 2,85 automobiles for this case.
The expected number of automobiles at Lakeside Olds at opening time can be calculated as a weighted average, resulting in an expectation of approximately 3 cars.
Explanation:The expected number of automobiles lined up at Lakeside Olds at opening time would be calculated by multiplying each number of automobiles by its respective probability and then adding up those products. This is essentially calculating a weighted average.
So for the given data:
Multiply 1 (number of automobiles) by its probability of 0.05: 1*0.05 = 0.05Multiply 2 by its probability of 0.30: 2*0.30 = 0.60Multiply 3 by its probability of 0.40: 3*0.40 = 1.20Multiply 4 by its probability of 0.25: 4*0.25 = 1.00Add up those results: 0.05 + 0.60 + 1.20 + 1.00 = 2.85. Thus, on a typical day, Lakeside Olds should expect approximately 3 automobiles to be lined up at opening time.
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A moving sidewalk in an airport moves people between gates. It takes Jason's 8-year-old
daughter Josie 44 sec to travel 176 ft walking with the sidewalk. It takes her 7 sec to walk 21 ft
against the moving sidewalk in the opposite direction). Find the speed of the sidewalk and find
Josie's speed walking on a non-moving ground.
The side walk moves at Ft/sec
Answer:
The sidewalk moves at 0.5 ft/sec
Josie's speed walking on a non-moving ground is 3.5ft/sec
Step-by-step explanation:
Let x represent the speed of the side walk and y represent her walking speed
It takes Jason's 8-year-old daughter Josie 44 sec to travel 176 ft walking with the sidewalk
Distance = speed × time
176 = (x+y)×44
44x+44y = 176
x+y = 4 .......1
It takes her 7 sec to walk 21 ft against the moving sidewalk in the opposite direction).
21 = (y-x)7
7y - 7x = 21
y - x = 3 ......2
Add equation 1 to 2
2y = 7
y = 3.5 ft/sec
From equation 1
x + y = 4
x = 4 - 3.5 = 0.5
x = 0.5 ft/sec
The sidewalk moves at 0.5 ft/sec
Josie's speed walking on a non-moving ground is 3.5ft/sec
Answer: Josie's speed walking on a non-moving ground is 3.5 ft/sec
The side walk moves at 0.5 Ft/sec
Step-by-step explanation:
Let x represent Josie's speed walking on a non-moving ground.
Let y represent the speed of the sidewalk.
It takes Jason's 8-year-old daughter Josie 44 sec to travel 176 ft walking with the sidewalk. It means that the total speed at which she moved is
(x + y) ft/sec
Distance = speed × time
Therefore,
176 = 44(x + y)
Dividing both sides by 44, it becomes
4 = x + y- - - - - - - - - - - - - -1
It takes her 7 sec to walk 21 ft against the moving sidewalk in the opposite direction). It means that the total speed at which she moved is (x - y) ft/sec
Therefore,
21 = 7(x - y)
Dividing both sides by 7, it becomes
3 = x - y- - - - - - - - - - - - - -2
Adding equation 1 and 2, it becomes
7 = 2x
x = 7/2 = 3.5 ft/sec
Substituting x = 3.5 into equation 2, it becomes
3 = 3.5 - y
y = 3.5 - 3 = 0.5 ft/sec
PLEASE HELP ASAP!!!
When would you use a line graph?
A. if the data is given as data pairs
B. if the data is numerical
C. to compare categories
D. to compare change over time
You can also choose more than one
Answer:
d AND C
Step-by-step explanation: