Answer:
51,840
Step-by-step explanation:
The format of P(n, r) is used for permutations,
where [tex]P(n, r) = \frac{n!}{(n - r)!}[/tex]
To evaluate this expression, P(9,2), we use the formula of permutation,
We have the value of n = 9 and r = 2, thus,
[tex]P(n, r) = P(9, 2) = \frac{9!}{(9 - 2)!} =\frac{9!}{7!} =\frac{9*8*7!}{7!} = 9 *8 =72\\[/tex]
To evaluate this expression, P(6, 5), we use the formula of permutation,
We have the value of n = 6 and r = 5, thus,
[tex]P(n, r) = P(6, 5) = \frac{6!}{(6 - 5)!} =\frac{6!}{1!} =\frac{6*5*4*3*2*1!}{1!} = 6*5*4*3*2 = 720[/tex]
Therefore the product of P(9, 2) · P(6, 5) is
72 · 720 = 51,840
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The sum of a number and seven is six less than four times the number. Write an algebraic equation and solve to find the number.
Answer:
13/3 or 4.333
Step-by-step explanation:
Let the number be x
the sum of x and 7 is 6 less than 4x, giving the equation: x+7+6 = 4x
Solve:
x+7+6 = 4x
x+13 = 4x
13 = 3x
x = 13/3
PLEASE I NEED THIS FAST there are 3 denominations of bills in a wallet: $1, $5, and $10. there are 5 fewer $5-bills than $1-bills there are half as many $10-bills if there is $115 altogether, find the number of each type of bill in the wallet
The count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.
In the question, we are given that there are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills.
We are asked to find the count of each denomination, given there was altogether $115 in the bag.
We assume the number of $1-bills in the bag to be x.
Total amount in x bills of $1 = x * $1 = $x.
Given that there are 5 fewer $5-bills than $1-bills in the bag, number of $5-bills in the bag = x - 5.
Total amount in (x - 5) bills of $5 = (x - 5) * $5 = $5(x - 5).
Given that there are half as many $10-bills as $5-bills in the bag, number of $10-bills in the bag = (x - 5)/2.
Total amount in (x - 5)/2 bills of $10 = (x - 5)/2 * $10 = $5(x - 5).
Thus, the total amount in the bag = $x + $5(x - 5) + $5(x - 5).
But, the total amount in the bag = $115.
Thus, we get an equation:
$x + $5(x - 5) + $5(x - 5) = $115,
or, x + 5x - 25 + 5x - 25 = 115,
or, 11x = 115 + 50,
or, 11x = 165,
or, x = 165/11,
or, x = 15.
Thus, number of $1-bills = x = 15.
The number of $5-bills = x - 5 = 15 - 5 = 10.
The number of $10-bills = (x - 5)/2 = (15 - 5)/2 = 10/2 = 5.
Thus, the count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.
The provided question is incomplete. The complete question is:
There are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills. If there is $115 altogether, find the number of each type of bill in the wallet."
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Find the surface area of the figure. For calculations involving pi , give both the exact value and an approximation to the nearest hundredth of a unit. Let r=10 and h = 3.
Answer:
exact: SA = 260π in.²
approximate: SA = 816.81 in.²
Step-by-step explanation:
SA = 2πr² + 2πrh
r = 10 in.
h = 3 in.
SA = 2πr(r + h)
SA = 2π(10 in.)(10 in. + 3 in.)
SA = 260π in.²
SA = 816.81 in.²
What is the rise and the run please help
Answer:
-1
Step-by-step explanation:
Rise=2
Run=-2
2/-2=
-1
Jon rented a car a company that charged a daily rental fee and a mileage charge. He rented the car for 6 days and drove 400 miles and was charged $210. His friend Amanda later rented the same car for 7 days and drove 360 miles and was charged $229. What was the daily rental charge? How much did the company charge per mile?
Question 2 of 25
A 90% confidence interval for a proportion is found to be (0.22, 0.28). What is
the sample proportion?
A. 0.26
B. 0.24
C. 0.28
D. 0.25
SUBMIT
The sample proportion [tex]$\hat{p}=0.22+0.033=0.253$[/tex].
How to estimate the sample proportion?We know that the confidence interval for sample proportion exists estimated as;
90% confidence interval = Sample proportion Margin of Error
Here, let [tex]$\hat{p}[/tex] = sample proportion
Level of significance = 1 - 0.90 = 0.[tex]$(0.22,0.28)=\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$[/tex]10 or 10% Critical value of z at 5% (two-sided) level of significance exists 1.645.
So, 90% confidence interval [tex]$=\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$[/tex]
[tex]$0.22=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \ldots(1)$[/tex]
[tex]$0.28=\hat{p}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \ldots (2)[/tex]
From (1) and (2) , we get;
[tex]$&0.22+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\[/tex]
Simplifying the equation, we get
[tex]$&1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-0.22 \\[/tex]
[tex]$&2 \times 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.06 \\[/tex]
[tex]$&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\frac{0.06}{2 \times 1.645} \\[/tex]
[tex]$&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.02[/tex]
Now, squaring both sides, we get;
[tex]$\frac{\hat{p}(1-\hat{p})}{n}=0.0004 \\[/tex]
[tex]$n=\frac{\hat{p}(1-\hat{p})}{0.0004}[/tex]
Now, putting value of n in (1), we get;
[tex]$0.22=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$[/tex]
[tex]$0.22=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{\hat{p}(1-\hat{p})} \times 0.0004}$[/tex]
Simplifying the equation, we get
[tex]$0.22=\hat{p}-1.645 \times \sqrt{0.0004}$[/tex]
[tex]$0.22=\hat{p}-(1.645 \times 0.02)$[/tex]
[tex]$0.22=\hat{p}-0.033$[/tex]
[tex]$\hat{p}=0.22+0.033=0.253$[/tex].
The sample proportion [tex]$\hat{p}=0.22+0.033=0.253$[/tex].
Therefore, the correct answer is option D. 0.25.
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_A straight line L has equation 3y=5x-6. Find the gradient of L
Answer:
gradient = [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope/gradient and c the y- intercept )
given
3y = 5x - 6 ( divide through by 3 )
y = [tex]\frac{5}{3}[/tex] x - 2 ← in slope- intercept form
with gradient = [tex]\frac{5}{3}[/tex]
Find the area of the trapezoid 3cm 3cm 4cm 1cm
Answer:
8√2 cm²
Refer to the attached page,I've shown the complete calculation over there
what is - 1/5 ( -2 1/4) ?
The coefficient of 2(3)(6)Q is
Answer:
36Q
Step-by-step explanation:
multiply all together we have 36Q
8 -2 5\8 how do I solve this. Can u show me the steps
Answer:
= 5.375
Step-by-step explanation:
Use the algorithm method.
7 9 9 10
8 . 0 0 0
- 2 . 6 2 5
5 . 3 7 5
= 5.375
Answer:
5 3/8
Step-by-step explanation:
change it so that every number is a improper fraction and same denominator
64/8 - 21/8 = 43/8 = 5 3/8
120 high school seniors were asked,
"Are you going to the graduation
party?" Of those 120 students, 75 said yes. Estimate the population mean
that a senior will say they are going to the graduation party.
Using proportions, the estimate of the population percentage of seniors that will say they are going to the graduation party is of 62.5%.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The estimate of a population proportion is the sample proportion. In this problem, the sample proportion is of 75 out of 120 students, hence:
p = 75/120 = 0.625 = 62.5%.
The estimate of the population percentage of seniors that will say they are going to the graduation party is of 62.5%.
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s−3(s+6)= ASAP I NEED ANSWER PLEASE
Answer: −2(
Answer:
Simplified: −2s − 18
Step-by-step explanation:
Simplify the expression.
cd+(-6c)=150 when d=4
Answer:
c = -75
Step-by-step explanation:
cd + (-6c) = 150
d = 4
c(4) + (-6c) = 150
4c - 6c = 150
-2c = 150
c = -75
please help!!! the photo below
Answer:its (-2,1), (-6,-15)
Step-by-step explanation:
what’s the volume of the sphere
Answer:
[tex]\pi[/tex]([tex]r^{2}[/tex]h)
Step-by-step explanation:
r = radius
h = height
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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Find a formula for the nth term
of the arithmetic sequence.
First term -2
Common difference 8
an = [? ]n + []
divide 5 by 6 and 5/6 into a repeating decimal
_
Answer: 0.83
Step-by-step explanation:
5/6 = 0.8333...
_
0.8333... = 0.83
Times interest earned
Averill Products Inc. reported the following on the company’s income statement in 20Y8 and 20Y9:
20Y9 20Y8
Interest expense $440,000 $400,000
Income before income tax expense 5,544,000 4,400,000
a. Determine the times interest earned ratio for 20Y8 and 20Y9. Round to one decimal place.
20Y9 20Y8
Times Interest Earned
fill in the blank 1
fill in the blank 2
b. Is the change in the times interest earned ratio favorable or unfavorable?
The times interest earned ratio for 20Y8 and 20Y9 are 11 and 12.6 respectively.
The change in the times interest earned ratio is favorable.
According to the question,
In 20Y8 and 20Y9, Averill Products Inc. disclosed the following on its income statement:
For 20Y9,
Interest expense= $440,000
Income before income tax expense= $5,544,000
Times interest earned ratio= 5544000/440000 = 12.6
For 20Y8,
Interest expense=$400,000
Income before income tax expense=$4,400,000
Times interest earned ratio= 4400000/400000 =11
As the times interest earned ratio for 20Y9 is greater than that for 20Y8,the change in the times interest earned ratio is favorable.
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At Indianapolis Motor Speedway, one lap is 2.5 miles in length. The average speed of an Indy racing car is 190 miles per hour.
15. Find the length of one lap in yards.
16. How many seconds would it take to complete one lap?
Answer:
15. 4400 yards
16. 47.4 seconds
Step-by-step explanation:
15. 1 mile = 1760 yards
2.5 miles:
2.5(1760) = 4400 yards
16. t = 2.5/190 = 0.013150 h
1 hour = (60)(60) = 3600 seconds
Then 1 lap take
=(0.013150)(3600) = 47.4 seconds
Hope this helps
Composition of two functions:Basic
The functions, q(x) and r(x) are defined as 2•x + 1, and -5•x - 3, respectively, therefore;
[tex] \: (q \: \circ \: r) (1)= - 15[/tex]
[tex] \: (r \: \circ \: q) (1)= -18[/tex]
Which method can be used to evaluate the given composite functions?The given functions are;
q(x) = 2•x + 1
r(x) = -5•x - 3
The evaluation of the composite functions can be presented as follows;
[tex](q \: \circ \: r) (x)= q(r(x))[/tex]
Therefore;
[tex](q \: \circ \: r) (1)= q(r(1))[/tex]
r(1) = -5×1 - 3 = -8Which gives;
[tex](q \: \circ \: r) (1)= q( - 8)[/tex]
q(-8) = 2×(-8) + 1 = -15
Therefore;
[tex](q \: \circ \: r) (1)= - 15[/tex]
Similarly, we have;
[tex](r \: \circ \: q) (1)= r(q(1))[/tex]
q(1) = 2×1 + 1 = 3
r(3) = -5×3 - 3 = -18
Which gives;
[tex](r \: \circ \: q) (1)= -18[/tex]
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Pls answer before 8:00 pm
Answer:225 jeans.
Step-by-step explanation: What we need to do here is convert the number of jeans to a percentage. There were 25 jeans when 50 customers were surveyed and 25 is half of 50 or 50%. This means that if 450 pairs of pants are ordered half of them should be jeans. 450/2 = 225.
need heeeelp please
Answer:
1) log7 (5*8)= log7(40)
2) log2(11) -log2(9)=log2(11/9)
3)2log9 2=log9(2^2)
Cos3A ×cos2A =cos A ×cos 2A -sin4A×sin A=prove it
Answer:
Step-by-step explanation:
cosA×cos 2A-sin4A×sinA
=cosAcos2A-2sin2Acos2A sin A
=cos 2A(cosA-2sin2AsinA)
=cos 2A(cosA-2×2sinAcosAsin A)
=cos2A×cosA(1-4sin²A)
=cos 2AcosA(1-4(1-cos²A))
=cos2A×cosA(1-4+4cos²A)
=cos 2A(-3cosA+4cos³A)
=cos 2A(4cos³A-3cosA)
=cos 2A×cos3A
For what value of x is the rational expression below undefined?
3x+15/6-x
Let the function be (3x+15)/(6-x) then the value of x exists at -5.
What is the value of x?Given: Rational Expression (3x+15)/(6-x)
To find the value of x when given a rational expression equivalent to 0.
To estimate the value of x, convey the variable to the left side and convey all the remaining values to the right side. Simplify the values to estimate the result.
Consider, (3x+15)/(6-x) = 0
3x + 15 = 0(6-x)
3x + 15 = 0
Subtract 15 from both sides of the equation, e get
3x + 15 - 15 = 0 - 15
simplifying the above equation, we get
3x = 0 - 15
3x = -15
Divide both sides by 3, then we get
x/3 = -15/3
x = -5
Therefore, the value of x exists at -5.
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follow the steps to find the area of the shaded region. 14 46 14
The area of the shaded region is 8.1838. The area of the shaded region is calculated by subtracting the area of the triangle from the area of the sector of the circle.
How to calculate the area of the sector?The area of the sector of a circle with a radius 'r' and an angle of sector 'θ' is
A = (θ/360) πr² sq. units
How to calculate the area of a triangle with an angle?The area of the triangle with measures of two sides and an angle between them is
A = 1/2 × a × b × sinC sq. units
Where a and b are the lengths of sides and ∠C is the angle between those sides.
Calculation:It is given that,
The area of the sector shown in the diagram is 78.6794 cm² and the area of the triangle is 70.4956 cm².
Then to calculate the area of the shaded region, subtract the area of the sector and the area of the triangle. I.e.,
Area of the shaded region = Area of the sector - Area of the triangle
⇒ 78.6794 - 70.4956
⇒ 8.1838 cm²
Therefore, the required area of the shaded region is 8.1838 sq. cm.
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7. Find (f•g)(x) for the pair of functions.
f(x)=x+1
g(x) = 4x - 11
(f•g)(x) =
Answer:
(f•g)(x) = 4x² -7x -11
Step-by-step explanation:
The product of the two functions is the product of their respective definitions.
(f•g)(x)(f•g)(x) = f(x)•g(x) = (x+1)•(4x -11)
= x(4x -11) +1(4x -11) . . . . . use the distributive property
= 4x² -11x +4x -11 . . . . . . . and again
(f•g)(x) = 4x² -7x -11 . . . . . collect terms
What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3?
A.–6
B.–5
C.5
D.7
The y- coordinate that divides the directed line segment from J to K into a ratio of 2:3 is 5. Option C
How to determine the coordinatesLet's the point that divides the line segment as point S.
We have that,
Point S divides the line segment into ratio 2:3
The ratio 2:3 means that we are to divide the line segment into;
= 2+3
= 5 equal parts.
We then have that the horizontal distance between the two coordinates is 5
The vertical distance between the two coordinates is 10
Now, let's divide both vertical and horizontal distance into five equal parts,
Horizontal distance = 5/5 = 1
Vertical distance = 10/ 5 = 2
The horizontal distance is 1
The vertical distance is 2
For every one unit move to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.
The coordinate of point S that divides the line segment into 2 parts and 3 parts is (-5,5)
Thus, the y- coordinate that divides the directed line segment from J to K into a ratio of 2:3 is 5. Option C
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Find one value of x for which h(x)=4 and find h (-2)
the solutions are:
h(x) = 4 for x = 0h(-2) = 2How to find the value of x for which h(x) = 4?The only information of h(x) that we have is the given graph.
To find the value of x, we need to go to the vertical axis and find y = 4, then we move horizontally to the left until we meet the curve.
That intersection will give the value of x for which h(x) = 4.
Doing that, we conclude that h(x) = 4 when x = 0 (on the vertical axis).
Now we want to find h(-2), and we can do that using the graph.
By finding x = -2 on the horizontal axis and then moving up until we intercept the graph, we can see that:
h(-2) = 2
Concluding, the solutions are:
h(x) = 4 for x = 0h(-2) = 2If you want to learn more about parabolas:
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