Include all three indicator variables (A1, A2, and A3) in the model
To allow different slopes in the relationship between X and Y for each level of the categorical variable, the model should include terms A1X and A2X in A1 and A2 respectively. For example, the model can be expressed as:
Bo + B1X + B2A1X + B3A2X + B4A3
where B2 and B3 represent the slope of the relationship between X and Y for people at levels 1 and 2 of the categorical variable, respectively. represent. The value of X remains constant.
Include all three indicator variables (A1, A2, and A3) in the model. This allows to compare the effect of a given level of a categorical variable on the response variable while keeping the value of X constant. For example, if you include only A1 and A2 in your model, you cannot compare the effects of level 3 of the categorical variables on the response.
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A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples were obtained of 16 people who do not exercise regularly and 12 people who do exercise regularly. The resting pulse rate (in beats per minute) of each person was recorded. The summary statistics are as follows.
Do Not Exercise - Do Exercise
x1 = 73.4 beats/min - x2 = 69.7 beats/min
s1 = 10.3 beats/min - s2 = 8.6 beats/min
n1 = 16 - n2 = 12
test the claim that he difference between the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly.
We Reject H₀ if t calculated > t tabulated and hence the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly
We Reject H₀ if t calculated > t tabulated
But in this case,
0.83 is not greater than 2.056
Therefore, we failed to reject H₀
There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise
The Null and Alternate hypothesis is given by
Null hypotheses = H₀: μ₁ = μ₂
Alternate hypotheses = H₁: μ₁ ≠ μ₂
The test statistic is given by
Where is the sample mean of people who do not exercise regularly.
Where is the sample mean of people who do exercise regularly.
Where is the sample standard deviation of people who do not exercise regularly.
Where is the sample standard deviation of people who do exercise regularly.
Where is the sample size of people who do not exercise regularly.
Where is the sample size of people who do exercise regularly.
The given level of significance is
1 - 0.95 = 0.05
The degree of freedom is
df = 16 + 12 - 2 = 26
From the t-table, df = 26 and significance level 0.05,
t = 2.056 (two-tailed)
Conclusion:
We Reject H₀ if t calculated > t tabulated
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PLEASE ASAP 100 POITNS
a) Jill jumped 6 7/8 feet in the long-jump event. Jill’s best friend jumped 6 15/16 feet. How much farther did Jill’s best friend jump? Describe in words the process you used to solve the problem. (2 points)
b) If Jill’s best friend jumped farther than 6.5 feet, then she beat the school record and the seventh graders earn 50 points. If not, the eighth graders earn 50 points. Which grade should be awarded 50 points**? (1 point)
c) Claire and her partner, Grace, are throwing for the javelin event as a team. Claire threw the javelin 42 5/8 feet and Grace threw it 39 3/5 feet. If Claire and Grace combined their distances, what would their total feet thrown be? Show your work. (2 points)
d) If the total distance of Claire and Grace is greater than 83.7 feet, then the seventh graders earn 50 points. If not, then the eighth graders earn 50 points. Which grade should be awarded 50 points**? (1 point).
Answer:
Step-by-step explanation:
a) To find how much farther Jill's best friend jumped, we need to subtract Jill's distance from her best friend's distance. First, we need to convert both distances to the same unit, in this case inches. 6 7/8 feet is equal to 6 7/8 * 12 inches/foot = 82 7/8 inches. 6 15/16 feet is equal to 6 15/16 * 12 inches/foot = 83 16/16 inches. Now that both distances are in inches, we can subtract them: 83 16/16 inches - 82 7/8 inches = 1 9/16 inches. Therefore, Jill's best friend jumped 1 9/16 inches farther.
b) To determine if Jill's best friend beat the school record, we need to compare her distance to the record distance. The record distance for seventh graders is 6 feet 1 3/5 inches, which is equal to 6 1/5 * 12 inches/foot = 74 inches. Jill's best friend jumped 83 16/16 inches, which is greater than 74 inches. Therefore, Jill's best friend beat the school record and the seventh graders should be awarded 50 points.
c) To find the total distance thrown by Claire and Grace, we need to add their individual distances. First, we need to convert both distances to the same unit, in this case inches. 42 5/8 feet is equal to 42 5/8 * 12 inches/foot = 510 5/8 inches. 39 3/5 feet is equal to 39 3/5 * 12 inches/foot = 472 3/5 inches. Now that both distances are in inches, we can add them: 510 5/8 inches + 472 3/5 inches = 983 8/5 inches. Therefore, the total distance thrown by Claire and Grace is 983 8/5 inches.
d) To determine if the total distance thrown by Claire and Grace is greater than 83.7 feet, we need to compare their distance to the record distance. The record distance for seventh graders is 83.7 feet, which is equal to 83.7 * 12 inches/foot = 1004.4 inches. The total distance thrown by Claire and Grace is 983 8/5 inches, which is less than 1004.4 inches. Therefore, the total distance thrown by Claire and Grace is not greater than the record distance and the eighth graders should be awarded 50 points.
consider two medical tests, a and b, for a virus. test a is 90% effective at recognizing the virus when it is present, but has a 5% false positive rate (indicating that the virus is present, when it is not). test b is 95% effective at recognizing the virus, but has a 10% false positive rate. the two tests use independent methods of identifying the virus. the virus is carried by 2% of all people.Say that a person is tested for the virus using only one of the tests, and that test comes back positive for carrying the virus.Which test returning positive is more indicative of someone really carrying the virus? Justify your answer mathematically (i.e. writing down your calculations).
We observe, that P(V|B)>P(V|A), so the person is more likely to have virus, however is still very small probability (only 15%), so in order to confirm illness, he should make one more test.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
P(V/A) is not 0.95. It is opposite:
P(A/V)=0.95
From the text we can also conclude, that
P(A/∼V)=0.1
P(B/V)=0.9
P(B/∼V)=0.05
P(V)=0.01
P(∼V)=0.99
P(V/A) is not 0.95. It is opposite:
P(A/V)=0.95
From the text we can also conclude, that
P(A/∼V)=0.1
P(B/V)=0.9
P(B/∼V)=0.05
P(V)=0.01
P(∼V)=0.99
What we need to calculate and compare is P(V/A) and P(V/B)
P(V∩A)=P(A)⋅P(V/A)⇒P(V/A)=P(V∩A)/P(A)
P(V∩A) means, that person has a virus and it is detected, so
P(V∩A)=P(V)⋅P(A/V)
=0.01⋅0.95
=0.0095
P(A) is sum of two options: "Person has virus and it is detected" and "Person has no virus, but it was mistakenly detected", therefore:
P(A)=P(V)⋅P(A/V)+P(∼V)⋅P(A/∼V)=0.01⋅0.95+0.99⋅0.1=0.1085
Dividing those two numbers we obtain
P(V/A)=0.0095/0.1085=0.08755760368663594
Analogically,
P(V/B)=P(V∩B)/P(B)=P(V)⋅P(B/V)/P(V)⋅P(B/V)+P(∼V)⋅P(B/∼V)
=0.01⋅0.9/0.01⋅0.9+0.99⋅0.1
=0.1538461538461539
We see that P(V|B)>P(V|A), meaning the individual is more likely to have a virus, but is still very unlikely (only 15%), therefore person should perform another test to confirm illness.
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A horse owner needs to replace four sections of a coral for the horses. The first section
needs 26 yards of fencing, the second needs 10 3/5, the third, 10 1/5 yards, and the fourth,
8 3/10 yards. How many yards are needed to repair four sections of the fencing?
10
Answer:
55 1/10 yd
Step-by-step explanation:
26 + 10 + 3/5 + 10 + 1/5 + 8 + 3/10 =
= 54 + 4/5 + 3/10 =
= 54 + (8 + 3)/10 =
= 54 + 11/10 =
= 54 + 10/10 + 1/10 =
= 54 + 1 + 1/10 =
= 55 1/10
Answer:
55[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
Convert all the mixed numbers to fractions with a common denominator (10) then add them up:
26 + 53/5 + 51/5 + 83/10 =
26 + 106/10 + 102/10 + 83/10 =
26 + 291/10 =
26 + 29[tex]\frac{1}{10}[/tex] = 55[tex]\frac{1}{10}[/tex]
triangle p undergoes a sequence of transformations resulting in tringle q. which sequence of transformation could be used to show that triangle q is similar but not congruent to triangle P
The transformation could be used to show that triangle Q is similar but not congruent to triangle P is Dilation.
What is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given that, triangle P undergoes a transformations resulting in triangle Q.
We know, Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.
Hence, The transformation could be used to show that triangle Q is similar but not congruent to triangle P is Dilation.
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what is 13 -90
then 50/90=
then + together both answers and then multiply by 26 and what is the answer =
Answer: if there is an option for -1,989 then it would be that one
Step-by-step explanation:
13 - 90 would give you -77 and then 50/90 is would give you 0.5555555. -77 + 0.5 would be -76.5 which then you multiply by 26 gives you -1,989.
A soccer coach surveyed the players to determine the number who preferred selling coupon books, magazine subscriptions, or both for their fundraiser. The results are given in the Venn diagram. To the nearest whole percent, what is the value of a in the relative frequency table for the survey results? a = 27% a = 42% a = 81% a = 88%
The value of a in the relative frequency table for the survey results a = 27%
From the given Venn diagram, the total number of players = 11 + 3 + 7 + 5 = 26
The number of players preferred magazines books which are not coupon books = 7
The relative frequency for the players who preferred magazines books which are not coupon books (a)=
magazine books but not coupon books/ total player = 7 / 26 = 0.269
In percent,
7/26 x 100 = 26.9 = 27%
Hence, a = 27%
Therefore, the value of a in the relative frequency table for the survey results a = 27%
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Which ordered pair is a solution to the system of inequalities shown on the graph?
A)(3, 3)
B) (1,2)
C)(-3,-2)
D) (0, 1)
Answer:
C) (-3,-2)
Step-by-step explanation:
Solutions to the graphed system of inequalities are any points that are contained within the overlapping shaded region.
Plot the points on the given coordinate grid.
The only point that is contained with the overlapping shaded region is:
(-3, -2)Simplify for all questions.
Answer:
3y; -2a; -5y; 3c; -6-----------------------------------------
Question 1[tex]-\sqrt{9y^2}=-(-3y)= 3y, \ since\ y < 0[/tex]Question 2[tex]0.5\sqrt{16a^2} =0.5(-4a)=-2a,\ since\ a < 0[/tex]Question 3[tex]-5\sqrt{y^2} =-5y, since \ y > 0[/tex]Question 4[tex]3\sqrt{c^2} =3c,\ since \ c \geq 0[/tex]Question 5[tex]\sqrt{(3-\sqrt{15})^2 } -\sqrt{(3+\sqrt{15})^2 } =-(3-\sqrt{15}) -(3+\sqrt{15})=-6, since\ 3 < \sqrt{15}[/tex]Jacob's body metabolizes caffeine at a rate of 13.5% per hour (so the amount of caffeine in Jacob's body decreases by 13.5% each hour) a. If Jacob consumes a cup of coffee with 96 mg of caffeine in it, how long will it take for Jacob's body to metabolize half of the 96 mg of caffeine? hours Preview b. If Jacob consumes an energy drink with 212 mg of caffeine in it, how long will it take for Jacob's body to metabolize half of the 212 mg of caffeine? hours Preview c. If Jacob consumes a cup of coffee with c mg of caffeine in it, how long will it take for Jacob's body to metabolize half of the cmg of caffeine? (Hint: your answer will be a numerical value.) hours Preview Submit
Jacob's body metabolizes caffeine at a rate of 13.5% per hour.
a)Jacob's body will takes 4.77 ~5 hours to metabolize half of the 96 mg of caffeine.
b) If Jacob consumes an energy drink with 212 mg of caffeine in it, Jacob's body will take 4.77948 ~ 5 hours to metabolize half of the 212 mg of caffeine.
c) Jacob consumes a cup of coffee with c mg of caffeine in it. Jacob's body will take 4.77948~ 5 hours to metabolize half of the c mg of caffeine.
What is decay rate?The volume will slowly decrease at regular intervals and at a regular rate. This growth reduction is calculated using the exponential decay formula. The general form is y = a(1- r)ᵗ
We have, decay rate r = 13.5 % = 0.135
Initial value , a = 96 mg
plugging the value in formula we get,
y = 96(1 - 0.135)ᵗ --(1)
Now, Half of 96 is 48
so, 48 = 96(0.865)ᵗ --(2)
dividing equation by 96 we get
=> 48/96 = (0.865)ᵗ
taking natrual logarithm both sides,
=> ln(1/2) = ln ((0.865))
=> ln(1/2) = t In (0.865)
=> t = ln(1/2)/In (0.865)
=> t = 4.77948
Since, decay rate is constant so, half never changes for any .
a) 4.779~5 hours, long will it take for Jacob's body to metabolize half of the 96 mg of caffeine.
b) Jacob's body to metabolize half of the 212 mg of caffeine is 4.779~ 5 hours.
c) for Jacob's body to metabolize half of the cmg of caffeine is 4.77948.. So, we have 4.77948 ~ 5 hours is decay constant rate.
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Can someone explain what the rules are for division algorithm and what it means?
Answer:
The division algorithm says when a number is divided by a number gives the quotient
Step-by-step explanation:
Work out the value of d in the equality below. 0.0043 = 4.3 × 10d
Answer:
d= -3
Step-by-step explanation:
Rearrange variables to the left side of the equation: -4.3x 10d= -0.0043
Divide both sides of the equation by the coefficient of variable
Reduce the fraction
Convert fraction into negative exponential form
Convert both sides of the equation into terms with the same with same base
Simplify using exponent power rule
Based on the given conditions, corresponding exponents are equal
Determine the coordinates of the point shown.
Answer ASAP
A coordinate grid shown. There are increments of 0.5 for each grid line on each of the two axes. A point is located at 3 grid lines to the right and 1 grid line down from the origin.
(4 points)
(1.5, −0.5)
(−0.5, 1.5)
(3, −1)
(1, −1)
Answer:
(1.5, −0.5)
Step-by-step explanation:
Y=x^3-4x^2-20x+48 use the rational zero theorem
The roots of the given polynomial using the rational zero theorem are; 2, -4 and 6.
How to use the rational zero theorem?We are given the polynomial;
y = x³ - 4x² - 20x + 48
Since all coefficients are integers, we can apply the rational zeros theorem.
The trailing coefficient (the coefficient of the constant term) is 48
Find its factors (with the plus sign and the minus sign): ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.
These are the possible values for p.
The leading coefficient (the coefficient of the term with the highest degree) is 1.
These are the possible rational roots:
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.
Checking the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x - a should equal 0 (according to the remainder theorem, this means that P(a)=0
Plugging in those values, the only ones that yield P(a) = 0 are; 2, -4 and 6.
Thus, these are the roots of the given polynomial.
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Find all solutions of the equation 2sinx +√3 = 0
The answer is A+Bkπ and C+Dkπ where k is any integer, 0
Answer:
Step-by-step explanation:
2sin x=-√3
[tex]sin~x=-\frac{\sqrt{3} }{2} =-sin~\frac{\pi }{3} =sin (\pi +\frac{\pi }{3} ),sin(2\pi -\frac{\pi }{3} )\\=sin(\frac{4\pi }{3} +2k\pi ),sin (\frac{5\pi }{3} +2k\pi )\\=sin(A+Bk\pi ),sin(C+Dk\pi )\\x=A+Bk\pi ,C+Dk\pi \\where~A=\frac{4\pi }{3} ,B=2\\C=\frac{5\pi }{3} ,D=2[/tex]
3 1/2 + 4 3/4 + 5 3/10
Answer: 13.55 or 13 11/20.
Step-by-step explanation: First, you have to find a common denominator, in this case, it would be 20. 2 can go into 20 10 times, 4 can go into 20 5 times, and 10 can go into 20 2 times. Then, you would NOW have 3 10/20 + 4 15/20 + 5 6/20, to have all the equal denominators. When you add, you would get 12 31/20, but now you have to simplify. Now, you SHOULD get 13 11/20 after simplifying. As a decimal, it would be 13.55 I hoped this helped!
Allie had four and three-fourths tubes of purple paint. She used two and one-fourth tubes. Later, she found three and three-eighths more tubes. How many tubes of purple paint does she have now?
five and thirteen over twenty-four tubes
five and nine over twenty-four tubes
five and seven over eight tubes
five and one over eight tubes
By subtracting and adding mixed numbers, we can see that at the end she has (5 + 7/8) tubes of paint.
How many tubes of purple paint does she have now?We know that initially Allie had (4 + 3/4) tubes of purple paint, and she sed (2+ 1/4) tubes.
So at this point we need to take the difference between the two mixed numbers, we will get:
(4 + 3/4) - (2 + 1/4) = (4 - 2) + (3/4 - 1/4)
(4 - 2) + (3/4 - 1/4) = 2 + 2/4
2 + 2/4 = 2 + 1/2
Then she founds (3 + 3/8) more. Now we need to add that:
2 + 1/2 + (3 + 3/8) = (2 + 3) + (1/2 + 3/8)
(2 + 3) + (1/2 + 3/8) = 5 + (4/8 + 3/8)
5 + (4/8 + 3/8) = 5 + 7/8
She has 5 + 7/8 tubes of purple paint.
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Find the constant term in the expansion of (2x+1/x)8
Answer:
the constant term in this problem is 8
The original price of a scarf was $16, During a store closing sale, a shopper saved $12 on the scarf, What percentage discount did she receive? Explain or show your reasoning.
Answer:
The shopper received a 75% discount
Step-by-step explanation:
ok so first we turn it into an equation
let x=percentage discount
16(x)=12
x=.75
discount=75%
FIND THE COTANGENT! Help me pls.
Answer: 5/8
Step-by-step explanation:
For which values of x does each expression make sense?
Square root of x+5
Square root of |x|+1
Square root of (-2x)^2
Square root of (-5x)^3
The value of x that makes sense for the expression is the domain of the expression
The value of x makes sense for √-2x² is 0
The value of x must not exceed 0 for √(-2x)³ to make sense
What is Angle Sum Property?
The sum of all angles of a triangle is equal to the angle of a straight line i.e. 180°. If we have a triangle ABC, then the Sum of angles A , B, and angle C will be 180 ° and the value of the exterior angle is equal to the sum of two interior opposite angles.
√-2x²
For the above expression to have a defined value, the expression in the bracket must be positive.
However, x² will always be positive, and -2 will ensure that the expression is always negative, except when x = 0
Hence, the value of x makes sense for √-2x² is 0.
√(-2x)³
For the above expression to have a defined value, the expression in the square root must be positive.
However, the power of 3 will ensure that the expression is always positive only when x is less than or equal to 0
Hence, the value of x must not exceed 0 for √(-2x)³ to make sense.
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Find axis of symmetry
Answer:
Step-by-step explanation:
x=-4
a town's population was 7500 at the beginning of the year 2000 and has been decreasing by 3.2 % each year thereafter.
Answer:
In 2022, the town's population is 2220.
Step-by-step explanation:
It currently the year 2022. Hence, 22 years have passed since 2000.
2022 − 2000 = 22
To solve for the town's population today, first multiply the years passed since 2000 by the percent decrease each year.
[tex]22 \, \textrm{years} \times \dfrac{3.2 \, \%}{\textrm{year}} = 70.4 \, \%[/tex]
Then, subtract that percent of the population in 2000 from the population in 2000.
[tex]7500-(70.4 \,\% \cdot 7500)[/tex]
[tex]= 7500 - 5280[/tex]
[tex]=2220[/tex]
for cos(theta) = -3/5, and pi/2 < theta < pi, find the following trig values
sin theta
tan theta
csc theta
sec theta
cot theta
For the given range of theta, cos(theta) is negative, which means that theta is in the third or fourth quadrant. In these quadrants, the sine function is positive, the tangent function is negative, and the cotangent function is negative.
Since cos(theta) = -3/5, we can use the Pythagorean identity to find the value of sin(theta):
sin^2(theta) + cos^2(theta) = 1
sin^2(theta) = 1 - cos^2(theta)
sin^2(theta) = 1 - (-3/5)^2
sin^2(theta) = 1 - 9/25
sin^2(theta) = 16/25
sin(theta) = sqrt(16/25) = 4/5
Therefore, the value of sin(theta) is 4/5.
We can also use the identity cot(theta) = 1/tan(theta) to find the value of cot(theta):
cot(theta) = 1/tan(theta)
cot(theta) = 1/(sin(theta)/cos(theta))
cot(theta) = cos(theta)/sin(theta)
cot(theta) = (-3/5)/(4/5)
cot(theta) = -3/4
Therefore, the value of cot(theta) is -3/4.
The values of the other trigonometric functions can be found using the definitions of these functions:
tan(theta) = sin(theta)/cos(theta) = (4/5)/(-3/5) = -4/3
csc(theta) = 1/sin(theta) = 1/(4/5) = 5/4
sec(theta) = 1/cos(theta) = 1/(-3/5) = -5/3
Therefore, the values of the trigonometric functions for the given range of theta are:
sin(theta) = 4/5
tan(theta) = -4/3
csc(theta) = 5/4
sec(theta) = -5/3
cot(theta) = -3/4
a line with a y-intercept of 4 passes through the point (14, -3). it also passes through point (x, -8). what is the x coordinate for that point?: * a) 8 b) 24 c) -24 d) 6 e) -6
The x-coordinate for the point (x, -8), if Y-intercept is 4, and the coordinates of the point is (14, -3), is 24, so option B is correct.
What is line?
An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
Y-intercept = 4,
Coordinates of point = (14, -3), (x, -8)
Calculate the line equation as shown below,
y = m x + 4
Here, m is the slope,
Put point (14, -3) in the equation,
-3 = m × 14 + 4
m = -7 / 14
m = -1 / 2
Hence, the equation of a line is,
y = -1/2 x + 4
Put point (x, -8),
-8 = -1/2 x + 4,
-12 = -1/2x
x = 24
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James fenced in his backyard. The perimeter of his fence is 20 feet, and the width of his yard is 2 feet wide. Use the perimeter formula to find the length of his rectangular yard in inches: P = 2L + 2W. (1 foot = 12 inches)
The length of James's rectangular yard, given a fence perimeter of 20 feet and a width of 2 feet, is 8 feet, equivalent to 96 inches.
How to use the perimeter of a rectangle?Given: Perimeter (P) = 20 feet, Width (W) = 2 feet,
Conversion factor: 1 foot = 12 inches
Using the formula for perimeter: P = 2L + 2W
Substitute the given values: 20 = 2L + 2(2)
Simplify: 20 = 2L + 4
Subtract 4 from both sides: 16 = 2L
Divide by 2: L = 8 feet
Convert feet to inches: Length (in inches) = 8 feet * 12 inches/foot = 96 inches
So, the length of the rectangular yard is 96 inches.
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To find the length of James' rectangular yard in inches, we can use the perimeter formula P = 2L + 2W. Given that the perimeter is 20 feet and the width is 2 feet, we can substitute these values into the formula and solve for the length in inches. The length of James' rectangular yard is 108 inches.
Explanation:To find the length of James' rectangular yard in inches, we can use the perimeter formula P = 2L + 2W. Given that the perimeter is 20 feet and the width is 2 feet, we can substitute these values into the formula. However, since we need the length in inches, we will convert the feet to inches using the conversion factor of 1 foot = 12 inches.
Let's solve:
Convert the width from feet to inches: 2 feet * 12 inches/foot = 24 inchesSubstitute the values into the formula: 20 feet = 2L + 24 inchesSince the units don't match, we need to convert 20 feet to inches: 20 feet * 12 inches/foot = 240 inchesNow we have the equation: 240 inches = 2L + 24 inchesIsolate L by subtracting 24 inches from both sides: 240 inches - 24 inches = 2LSimplify: 216 inches = 2LDivide both sides by 2: 216 inches / 2 = LSolve: L = 108 inchesThe length of James' rectangular yard is 108 inches.
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Solve
16) -x<-x+7(x-2)
The solution of the given inequality -x < -x + 7 ( x - 2 ) is given by x > 2.
As given in the question,
Inequality is given by :
-x < -x + 7 ( x - 2 )
Open the parenthesis of the given inequality we have,
⇒ -x < -x + 7x - 14
Collect all the like terms on the same side we get,
⇒ - x < 6x - 14
Subtract 6x from both the side of the inequality we get,
⇒ - x - 6x < 6x - 6x - 14
⇒ -7x < -14
Divide both the side of the inequality by -7 we get,
⇒ -7x/ -7 > -14 / -7
⇒ x > 2
x has all the value greater than 2.
Therefore, for the given inequality the solution is given by x > 2.
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A systems analyst is testing the feasibility of using a new computer system. He wants to see if the new system uses less processing time than the old system. (Assume the original populations are normally distributed.) A sample of 25 jobs was selected and the processing time for each in seconds was recorded on each of the two systems. The results are as follows:Old System: mean = 27.2 seconds, s = 3.2 seconds, n - 25New System: mean = 24.3 seconds, s = 2.1 seconds, n = 25Difference (Old -New): mean = 2.9 seconds, s = 1.4 seconds, n = 25What is the alternative hypothesis for this problem?a. HA: µD≠0b. HA: µD>0c. HA: µD=0d. HA: µD<0
The alternative hypothesis for this problem b. HA: µD>0
What is meant by hypothesis?
In math, A hypothesis is an assumption made based on some evidence.
Here we have given that systems analyst is testing the feasibility of using a new computer system. He wants to see if the new system uses less processing time than the old system.
And we need to find the alternative hypothesis for this problem
While we looking into the given question we have identified the following values,
Old System: mean = 27.2 seconds, s = 3.2 seconds, n - 25
New System: mean = 24.3 seconds, s = 2.1 seconds, n = 25
Difference (Old -New): mean = 2.9 seconds, s = 1.4 seconds, n = 25
Basically, while written the hypothesis, we have to follow the order of the following,
=> (Old-New, Larger-Smaller>)
Therefore, the correct option is (B).
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Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right
Answer:
You've got it right
Step-by-step explanation:
If you want to get stellar communication on the question then maybe include a number line to visually represent why, but otherwise you have the answer right.
Identify the factors in the expression 3(m + 2).
A. 3 and (m + 2)
B. m and 2
OC. 3 and m
D. 3 and 2
The factors of the expression 3(m + 2) are 3 and (m + 2) and the correct option is A. 3 and (m + 2).
What is a factorA factor in an expression of number, variable, term or any other longer expression that is multiplied by another. In mathematics, a number or algebraic expression that divides another number or expression evenly without remainder is also called a factor.
The question have an algebraic expression; 3(m + 2)
considering the four options;
A. 3 and (m + 2)
B. m and 2
C. 3 and m
D. 3 and 2
Only option A. with 3 and (m + 2) can be said to be factors as multiplying them will give 3(m + 2) and can both divide the expression 3(m + 2) evenly without a remainder.
In conclusion, 3 and (m + 2) are factors for the given expression and option A. 3 and (m + 2) is correct.
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