Answer:
17h+1.75m=522 m=40h
Step-by-step explanation:
Let h= {the number of hours the driver drove}
Let m= the number of miles driven
The driver makes $17 for each hour working, so if the driver worked for hh hours, Luke would have to pay him 17h17h dollars. The cost of gas and maintenance is $1.75 per mile, so for mm miles Luke's costs would be 1.75m1.75m dollars. The total cost of the route 17h+1.75m17h+1.75m equals \$522:$522:
17h+1.75m=522
17h+1.75m=522
Since the driver drove an avearge of 40 miles per hour, if the driver drove hour, he would have driven 40 miles, and if the driver drove hh hours, he would have driven 40h40h miles, therefore mm equals 40h:40h:
m=40h
m=40h
Write System of Equations:
17h+1.75m= 522
m=40h
The truck is going for a run for 6 hours and the system of the equation to solve a further problem related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
The following are the different costs of the truck that Luke must be pay while running a truck:
Luke must pay the driver $17 per hour of driving.A truck has an expense of $1.75 per mile driven for gas and maintenance.Let ' x ' be the total time of driving a truck in hours.
and ' y ' be the total mile distance that is covered by the truck.
Therefore, the system of the equation for the overall running cost for a truck is given below.
[tex]\rm{Cost}=17x+1.75y[/tex]
Now, On one particular day, the driver drove an average of 40 miles per hour, and Luke's total expenses for the driver, gas and truck maintenance were $522.
Thus,
The total distance traveled by truck is 40x.
That is,
[tex]y=40x[/tex]
Substitute the values and solve them further.
[tex]522=17x+1.75y\\522=17x+1.75 \times 40x\\522=17x+70x\\522=87x\\x=6[/tex]
Thus, the truck is going for a run for 6 hours and the system of the equation to solve the further problems related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
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In accounting, a company's gross profit rate measures how well the company controls cost of goods sold to maximize gross profit. The gross profit rate, PPP, is calculated using the formula P = \dfrac{S - C}{S}P= S S−C P, equals, start fraction, S, minus, C, divided by, S, end fraction, where SSS is the net sales and CCC is the cost of goods sold. Rearrange the formula to solve for the cost of goods sold (C)(C)left parenthesis, C, right parenthesis. C=C=C, equals What is the cost of goods sold if the net sales is \$1{,}200{,}000$1,200,000dollar sign, 1, comma, 200, comma, 000 and the gross profit ratio is 0.20.20, point, 2? Round your answer, if necessary, to the nearest dollar. C=C=C, equals dollars
Answer:
$960,000Step-by-step explanation:
The gross profit rate of the company is expressed as [tex]P = \dfrac{S - C}{S}[/tex] where C is the cost of goods sold and S is the net sales. If the net sales S = $1,200,000, and gross profit ratio is 0.20, the cost of goods sold will be expressed as shown;
Making C the subject of the formula from the expression given.
[tex]P = \dfrac{S - C}{S}\\\\cross \ multiply\\\\SP = S-C\\\-C = SP-S\\\\C = S -SP\\[/tex]
Substituting P = 0.20 and S = $1,200,000 into the resulting equation, we will have;
[tex]C = $1,2000,000 - 0.2($1,2000,000)\\C = $1,2000,000- 240,000\\ C = 960,000[/tex]
Hence the cost of goods sold is $960,000
Will mark the brainliest i havent chosen an answer but I pressed accidentally
Answer:
The full answer is 4.40625 but rounded it would be 4.41
A recipe calls for 2 tablespoons of sugar for every 7 tablespoons of flour. If you plan on tripling the recipe what is the ratio of
sugar to flour?
-0)
A)
2 to 7
B)
2 to 21
5 to 10
DY
5 to 7
Answer:
It is still 2 to 7
Step-by-step explanation:
It is still 2 to 7 because if you triple the recipe, it will become 6 to 21 which still simplifies to 2 to 7.
A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 in. A bearing is acceptable if its diameter is within 0.004 in. of this target value. Suppose, however, that the setting has changed during the course of production, so that the bearings have normally distributed diameters with a mean 0.499 in. and standard deviation 0.002 in. What percentage of bearings will now not be acceptable
Answer:
the percentage of bearings that will not be acceptable = 7.3%
Step-by-step explanation:
Given that:
Mean = 0.499
standard deviation = 0.002
if the true average diameter of the bearings it produces is 0.500 in and bearing is acceptable if its diameter is within 0.004 in.
Then the ball bearing acceptable range = (0.500 - 0.004, 0.500 + 0.004 )
= ( 0.496 , 0.504)
If x represents the diameter of the bearing , then the probability for the z value for the random variable x with a mean and standard deviation can be computed as follows:
[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - \mu}{\sigma} \leq \dfrac{X -\mu}{\sigma} \leq \dfrac{0.504 - \mu}{\sigma})[/tex]
[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - 0.499}{0.002} \leq \dfrac{X -0.499}{0.002} \leq \dfrac{0.504 - 0.499}{0.002})[/tex]
[tex]P(0.496\leq X \leq 0.504) = (\dfrac{-0.003}{0.002} \leq Z \leq \dfrac{0.005}{0.002})[/tex]
[tex]P(0.496\leq X \leq 0.504) = (-1.5 \leq Z \leq 2.5)[/tex]
[tex]P(0.496\leq X \leq 0.504) = P (-1.5 \leq Z \leq 2.5)[/tex]
[tex]P(0.496\leq X \leq 0.504) = P(Z \leq 2.5) - P(Z \leq -1.5)[/tex]
From the standard normal tables
[tex]P(0.496\leq X \leq 0.504) = 0.9938-0.0668[/tex]
[tex]P(0.496\leq X \leq 0.504) = 0.927[/tex]
By applying the concept of probability of a complement , the percentage of bearings will now not be acceptable
P(not be acceptable) = 1 - P(acceptable)
P(not be acceptable) = 1 - 0.927
P(not be acceptable) = 0.073
Thus, the percentage of bearings that will not be acceptable = 7.3%
What is the approximate value of x in –2 ln (x + 1) − 3 = 7?
Answer:
x = 1/e^-5 - 1
Step-by-step explanation:
–2 ln (x + 1) − 3 = 7
–2 ln (x + 1) = 10
ln (x + 1) = –5
x + 1 = e^-5
x = e^-5 - 1
x = 1/e^-5 - 1
the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:
1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.
2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.
3. Simplify: -2 ln(x + 1) = 10.
4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.
5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.
6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.
7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.
8. Simplify: x ≈ -0.9933.
Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
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is -2.75 an integer?
Answer:
yes
Step-by-step explanation:
every negative any positive number is an integer
Answer:
Step-by-step explanation:
No. Integers do not have fractions in them.
-2.75 is equivalent to -275/100, which is a fraction that does not reduce to an integer
PLEASE HELPPPP
A standard I.Q. test produces normally distributed results with a mean of 100 and a standard deviation of 15 for the city of New York. Out of approximately 8,400,000 citizens, how many of these people would have I.Q.s below 67?
Answer:
approx 193200
Step-by-step explanation:
As known for normal distribution is correct the rule 95.4% of the results are situation within mean+-2*s ( where s is a standard deviation)
So the border is 100+-2*15=70 and that is approx=67.
95.4% of 84000000 citizens are= 8 400 000*0.954=8013600 persons
So the residual number of the citizens =8400000-8013600=386400 citizens
Because of the simmetry of normal distribution to find the number of the citizens that have IQ below 67 we have to divide 386400 by 2.
N=386000/2=193200
The lines below are parallel. If the slope of the green line is -4, what is the slope of the red line?
Answer:
-4
Step-by-step explanation:
Hey there!
Well the slopes of 2 parallel lines have the same slope,
meaning if the green line has a slope of -4 then the slope of the red line has a slope of -4.
Hope this helps :)
17. In figure, BAC -859, CA = CB and BD - CD. Find the measure of ZX, Zy and Zz. Give
reasons to support your answer.
A
85°
ب
B
H
V
Answer:
x = 10°, y = 10° and z = 160°
Step-by-step explanation:
Given : m∠BAC = 85°
CA ≅ CB and BD ≅ CD
In the given ΔABC,
Since, CA ≅ CB
Angles opposite to these equal sides will be equal in measure.
m∠BAC ≅ m∠ABC ≅ 85°
Since, sum of interior angles of a triangle = 180°
m∠BAC + m∠ABC + m∠BCA = 180°
85° + 85° + m∠BCA = 180°
m∠BCA = 180° - 170°
m∠BCA = 10°
x = 10°
In ΔBDC,
Since, BD ≅ DC [Given]
Opposite angles to these equal sides will be equal in measure.
Therefore, x° = z° = 10°
Since, x° + y° + z° = 180°
10° + y° + 10° = 180°
y = 180 - 20°
y = 160°
Solve for x -3x-3=-3(x+1)
Step-by-step explanation:
[tex] - 3x - 3 = - 3(x + 1) \\ - 3x - 3 = - 3x - 3 \\ - 3x + 3x = - 3 + 3 \\ 0 = 0[/tex]
Step 1: Use 3 to open the bracket
Step 2 : Collect like terms and simplify
Answer = 0
Which table represents a linear function?
x y
1 5
2 10
3 15
4 20
5 25
x y
1 5
2 20
3 45
4 80
5 125
x y
1 5
2 25
3 125
4 625
5 3125
x y
1 2
2 4
3 7
4 16
5 32
Answer:
The first table on the list:
x 1 2 3 4 5
y 5 10 15 20 25
Step-by-step explanation:
A linear equation is when the slope is the exact same between each point. The way we find slope is by finding the change in "y" over the change in "x".
x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5
x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5
x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5
x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5
The slope for each change in points is 5, which means that this table represents a linear function.
The only table that represents a linear function is; Table 1
Linear functionA linear function is one that has the same slope for every coordinate point.
Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;
At x = 1, y = 5 and;Slope = 5/1 = 5
At x = 2; y = 10 and;Slope = 10/2 = 5
At x = 3, y = 15 and;Slope = 15/3 = 5
At x = 4, y = 20 and;Slope = 20/4 = 5
At x = 5, y = 25 and;slope = 25/5 = 5
In conclusion, only table 1 represents a linear function.
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The sum of two polynomials is 10a^2b^2-8a^2b+6ab^2-4ab+2 if one addend is -5a^2b^2+12a^2b-5 what is the other addend
Answer:
The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].
Step-by-step explanation:
The other addend is determined by subtracting [tex]-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b-5[/tex] from [tex]10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a\cdot b^{2}-4\cdot a \cdot b + 2[/tex]:
[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b + 2 - (-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b -5)[/tex]
[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +2 +5\cdot a^{2}\cdot b^{2}-12\cdot a^{2}\cdot b+5[/tex]
[tex]x = (10\cdot a^{2}\cdot b^{2}+5\cdot a^{2}\cdot b^{2})-(8\cdot a^{2}\cdot b+12\cdot a^{2}\cdot b)+6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]
[tex]x = 15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]
The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].
Answer:
A
Step-by-step explanation:
During the school year, there were 315 total points scored between basketball, soccer, baseball, and football. The baseball team scored 55 points. The soccer team scored twice as much as the baseball team. The football team scored 0.5 more than 1.5 times as much as the baseball team. How many points did the basketball team score?
Answer:
67.5p.
Step-by-step explanation:
315p in total.
- Baseball has 55p.
- Soccer teams points = 55x2 = 110p.
- Football team points = 110 x 0.5 = 55 x 1.5 = 82.5p.
So then you just do 315p - 82.5p - 55p - 110p = 67.5p
a lottery offers one $1000 prize one $500 and two $50 prizes. one thousand tickets are sold at $2.50. what is the expectived profit
Answer:
$900
Step-by-step explanation:
To begin with let us estimate the total cash value of the prices
$1000 x 1= 1000
$500 x 1= 500
$50 x 2= 100
Total = $1600
Now let us calculate the total cost of tickets sold at $2.50 per tickets for 1000 tickets
2.5*1000= $2,500
Assuming worse case that the lottery had winners in all three categories and i.e the total prices given out is $1600
Then the expected profit is = $2,500-$1600= $900
1 liter of ink can print 5000 pages of text. If you had 100 gallons of ink then how many pages
could you print?
It keeps saying my answer is wrong after i identified the GCF as 3 but maybe I typed it wrong.
Answer:
3(9t^5-7p^4)(9t^5+7p^4)
Step-by-step explanation:
243 t^10 - 147 p^8
3 ( 81 t^10-49 p^8 )
Then we need to factor what is in the parentheses
3 ( ( 9t^5) ^2 - ( 7p^4) ^2)
This is the difference of squares ( a^2 -b^2) = ( a-b) (a+b)
3(9t^5-7p^4)(9t^5+7p^4)
A data set lists earthquake depths. The summary statistics are
nequals=400400,
x overbarxequals=6.866.86
km,
sequals=4.374.37
km. Use a
0.010.01
significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to
6.006.00.
Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses?
A.
Upper H 0H0:
muμequals=5.005.00
km
Upper H 1H1:
muμnot equals≠5.005.00
km
B.
Upper H 0H0:
muμnot equals≠5.005.00
km
Upper H 1H1:
muμequals=5.005.00
km
C.
Upper H 0H0:
muμequals=5.005.00
km
Upper H 1H1:
muμgreater than>5.005.00
km
D.
Upper H 0H0:
muμequals=5.005.00
km
Upper H 1H1:
muμless than<5.005.00
km
Determine the test statistic.
(Round to two decimal places as needed.)
Determine the P-value.
(Round to three decimal places as needed.)
State the final conclusion that addresses the original claim.
Fail to reject
Upper H 0H0.
There is
evidence to conclude that the original claim that the mean of the population of earthquake depths is
5.005.00
km
Answer:
Step-by-step explanation:
The summary of the given statistics data include:
sample size n = 400
sample mean [tex]\overline x[/tex] = 6.86
standard deviation = 4.37
Level of significance ∝ = 0.01
Population Mean [tex]\mu[/tex] = 6.00
Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
To start with the hypothesis;
The null and the alternative hypothesis can be computed as :
[tex]H_o: \mu = 6.00 \\ \\ H_1 : \mu \neq 6.00[/tex]
The test statistics for this two tailed test can be computed as:
[tex]z= \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt {n}}}[/tex]
[tex]z= \dfrac{6.86 - 6.00}{\dfrac{4.37}{\sqrt {400}}}[/tex]
[tex]z= \dfrac{0.86}{\dfrac{4.37}{20}}[/tex]
z = 3.936
degree of freedom = n - 1
degree of freedom = 400 - 1
degree of freedom = 399
At the level of significance ∝ = 0.01
P -value = 2 × (z < 3.936) since it is a two tailed test
P -value = 2 × ( 1 - P(z ≤ 3.936)
P -value = 2 × ( 1 -0.9999)
P -value = 2 × ( 0.0001)
P -value = 0.0002
Since the P-value is less than level of significance , we reject [tex]H_o[/tex] at level of significance 0.01
Conclusion: There is sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is 5.00 km.
Finding the perimeter or area of a rectangle given one of th
The length of a rectangle six times its width.
If the area of the rectangle is 150 cm”, find its perimeter.
Answer:
The answer is 70cmStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
Area of a rectangle = l × w
where
l is the length
w is the width
From the question
The length of a rectangle six times its width which is written as
l = 6w
Area = 150cm²
Substitute these values into the formula for finding the area
That's
150 = 6w²
Divide both sides by 6
w² = 25
Find the square root of both sides
width = 5cm
Substitute this value into l = 6w
That's
l = 6(5)
length = 30cm
So the perimeter of the rectangle is
2(30) + 2(5)
= 60 + 10
= 70cmHope this helps you
8) The perimeter of a rectangle is 20x2 + xy - 7y2 and one of it's sides is
7x2 - xy. Find the other side.
Answer:
3x^2 + 3xy/2 - 7xy^2/2
Step-by-step explanation:
So we know the perimeter is 20x^2 + xy - 7y^2,
To find any perimeter you need 2l + 2w = P so,
One of the sides is 7x^2 - xy
First plug in the values,
2(7x^2-xy) + 2w = 20x^2 + xy - 7y^2
Multiply,
14x^2-2xy + 2w = 20x^2 + xy - 7y^2
Subtract,
14x^2 - 2xy - 14x^2 + 2xy + 2w = 20x^2 + xy - 7y^2 - 14x^2 + 2xy
2w = 6x^2 + 3xy - 7y^2
w = 3x^2 + 3xy/2 - 7xy^2/2
If Tristan wants to stretch the spring by 9 inches, how many kilograms of weight must he apply to it? I need help with it please.
Answer:
9/3 = 3x/3
3 = x
The spring stretches 9 inches with 3 kilograms of weight attached to it
Step-by-step explanation:
Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:
y = 3x
9 = 3x.
Divide both sides of the equation by 3
Answer:The spring stretches 9 inches with 3 kilograms of weight attached to it.
Step-by-step explanation:
Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:
y = 3x
9 = 3x.
Divide both sides of the equation by 3:
The spring stretches 9 inches with 3 kilograms of weight attached to it.
The perpendicular bisectors of ΔKLM intersect at point A. If AK = 25 and AM = 3n - 2, then what is the value of n?
Answer:
n = 9 is the answer.
Step-by-step explanation:
Given a Triangle [tex]\triangle KLM[/tex] with its perpendicular bisectors intersecting at a point A.
AK = 25 units and
AM = 3n -2
To find:
Value of n = ?
Solution:
First of all, let us learn about perpendicular bisectors and their intersection points.
Perpendicular bisector of a line PQ is the line which divides the line PQ into two equal halves and is makes an angle of [tex]\bold{90^\circ}[/tex] with the line PQ.
And in a triangle, the perpendicular bisectors of 3 sides meet at one point and that point is called Circumcenter of the triangle.
We can draw a circle from circumcenter so that the circle passes from the three vertices of the triangle.
i.e.
Circumcenter of a triangle is equidistant from all the three vertices of the triangle.
In the given statement, we are given that A is the circumcenter of the [tex]\triangle KLM[/tex].
Please refer to the attached image for the given triangle and sides.
The distance of A from all the three vertices will be same.
i.e. AK = AM
[tex]\Rightarrow 25 = 3n-2\\\Rightarrow 3n =25+2\\\Rightarrow 3n =27\\\Rightarrow \bold{n = 9}[/tex]
Therefore, n = 9 is the answer.
The top speed of this coaster is
128 mph. What is the tallest peak
of this coaster?
** Hint... convert mph into m/s.*
To convert miles per hour to meters per second divide by 2.237
128 miles per hour / 2.237 = 57.22 meters per second.
Using the first equation:
57.22 = sqrt(2 x 9.81 x h)
Remove the sqrt by raising both sides to the second power:
57.22^2 = (2 x 9.81 x h)
Simplify Both sides:
3274.1284 = 19.62h
Divide both sides by 19.62:
H = 3274.1284/ 19.62
H = 166.88 meters
Suppose 65% of people in Georgia support a special transportation tax. Alejandro is not confident that this claim is correct. To investigate the claim, he surveys 150 people in his community and discovers that 78 people support a special transportation tax.
A. calculate sample proportion.
B. calculate standard error of the sample proportion, (SE). Give answer to three decimal places
C. Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.
Answer:
C
Step-by-step explanation:
Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.
A. The sample proportion is 0.52.
B. The standard error of the sample proportion is approximately 0.041.
C. The standard error of the sample proportion estimate is approximately 0.041.
A. To calculate the sample proportion, we divide the number of people who support the special transportation tax (78) by the total number of people surveyed (150):
Sample proportion = 78 / 150 = 0.52
B. To calculate the standard error of the sample proportion (SE), we use the formula:
[tex]SE = \sqrt{(p * (1 - p)) / n}[/tex]
where p is the sample proportion and n is the sample size. Substituting the values into the formula:
[tex]SE = \sqrt{(0.52 * (1 - 0.52)) / 150}\\\\SE = \sqrt{0.2496 / 150}\\\\SE = \sqrt{0.001664}\\\\SE = 0.0407[/tex]
Therefore, the standard error of the sample proportion is approximately 0.041 (rounded to three decimal places).
C. The standard error of the sample proportion estimate (SEest) is the same as the standard error of the sample proportion (SE) calculated in part B. Hence, the standard error of the sample proportion estimate is also approximately 0.041 (rounded to three decimal places).
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Jury Duty Three people are randomly selected from voter registration and driving records to report for jury duty. The gender of each person is noted by the county clerk.
a. Define the experiment.
b. List the simple events in S.
c. If each person is just as likely to be a man as a woman, what probability do you assign to each simple event?
d. What is the probability that only one of the three is a man?
e. What is the probability that all three are women?
Answer:
(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.
(b) The simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).
(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].
(d) The probability that only one of the three is a man is 0.375.
(e) The probability that all three are women is 0.125.
Step-by-step explanation:
We are given that three people are randomly selected from voter registration and driving records to report for jury duty. The gender of each person is noted by the county clerk.
(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.
(b) As we know that the gender of each person is noted by the county clerk, which means one is male and another female.
So, the simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).
Here, M is denoted for male and F for female.
(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].
Because there is 50-50 chance of selecting males or females.
(d) The probability that only one of the three is a man is given by;
The total cases in the sample space = 8
Number of cases of only one man out of three = 3
So, the required probability = [tex]\frac{3}{8}[/tex] = 0.375.
(e) The probability that all three are women is given by;
The total cases in the sample space = 8
Number of cases of all three are women = 1
So, the required probability = [tex]\frac{1}{8}[/tex] = 0.125.
How many variable terms are in the expression 3x3y + 5x2 − 4y + z + 9?
Answer:
4
Step-by-step explanation:
"4" is the number of variable terms that are in the expression 3x3y + 5x2 _ 4y + z + 9. The four variable terms in the expression are "xy", "x^2", "y" and "z". I hope that this is the answer that you were looking for and the answer has actually come to your desired help. If you need any clarification, you can always ask.
We have to accept or reject a large shipment of items. For quality control purposes, we collect a sample of 200 items and find 24 defective items. Construct a 95% percent confidence interval for the proportion of defective items in the whole shipment.
Answer:
A 95% confidence for the population proportion of defective items in the whole shipment is [0.075, 0.165] .
Step-by-step explanation:
We are given that for quality control purposes, we collect a sample of 200 items and find 24 defective items.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of defective items = [tex]\frac{24}{200}[/tex] = 0.12
n = sample of items = 200
p = population proportion of defective items
Here for constructing a 95% confidence interval we have used a One-sample z-test statistics for proportions.
So, 95% confidence interval for the population proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.12-1.96 \times {\sqrt{\frac{0.12(1-0.12)}{200} } }[/tex] , [tex]0.12+1.96 \times {\sqrt{\frac{0.12(1-0.12)}{200} } }[/tex] ]
= [0.075, 0.165]
Therefore, a 95% confidence for the population proportion of defective items in the whole shipment is [0.075, 0.165] .
PLEASE HELP ME ASAP On a test, the average score of 25 boys and 15 girls is 68 points. The average test score of the boys is 62 points. What is the average score of the girls? SHOW YOUR WORK
Answer:
74
Step-by-step explanation:
The average score of boys and girls is 68 and boys is 62
Think of it as an equation (62 + x)/2 = 68, where x is the average score of girls
First multiply each side by 2 making the equation 62 + x = 136
Now subtract each side by 62, which will make the average score for girls 74
(x = 74)
If a person earns $8.74 per hour, estimate how much the person would earn per year. Assume a person works 40 hours per week and 50 weeks per year.
Answer:
$17,480 per year.
Step-by-step explanation:
Amount earned per hour = $8.74
If a person works for 40 hours every week for 50 weeks in a year, number of hours worked in a year = [tex] 40hrs*50weeks = 2000 hrs [/tex]
Estimated amount earned per year by the person = [tex] 2000hrs * 8.74 dollars [/tex]
= $17,480 per year.
1. What is the difference between an exponential growth and exponential decay? 2. What is an example equation for expoential growth and an example equation for exponential decay?
Answer: see below
Step-by-step explanation:
The standard form of an exponential equation is: y = a(b)ˣ where
a is the initial valueb is the rateGrowth:
Exponential growth is where the final value (y) is greater than the initial value (a).
An example would be the spreading of a rumor:
You tell 1 person (a = 1) who then tells 2 people each minute (b = 2). How many people will they have spread the rumor to after 5 minutes (x = 5)?
y = 1(2)⁵
= 32
Decay:
Exponential decay is where the final value (y) is less than the initial value (a).
An example would be the decrease of bacteria in a person:
A person has 100 bacteria (a = 1) who takes a pill that is supposed to cut in half the number of bacteria each hour (b = 1/2). How many bacteria will the person have after 2 hours (x = 2)?
[tex]y=100\bigg(\dfrac{1}{2}\bigg)^2\\\\\\.\quad =100\bigg(\dfrac{1}{4}\bigg)\\\\\\.\quad = 25[/tex]
In the game plan for model building on your multiple regression project, which of the following is true about the test that determines whether the interaction term(s) is/are significant in predicting y?
A. It will definitely be a t-test
B. It will either be a t-test or a best subset for partial) F-test depending on whether we kept or dropped the quadratic terms
C. It will definitely be a partial F-test
D. It will definitely be a global
Answer:
A. It will definitely be a t-test
Step-by-step explanation:
T-test is a type of inferential statistic test which used to determine whether there is a significant difference between mean of two group sets or variables.The t-test technique is widely used in hypothesis testing in statistics. When the model building for game play is determine through regression analysis, it will require t-test to be conducted to reach a conclusion.
