To calculate the total time it takes to run 2 miles uphill at 4 mph and then 3 miles downhill at a speed that takes the same time as running 2 miles uphill, we find that the time for each is 0.5 hours, or 30 minutes, totaling 1 hour
The main question asks how long it would take for the runner to run 2 miles uphill and then 3 miles downhill, knowing that he jogs at a rate of 4 miles per hour uphill, and he can run 3 miles downhill in the same time it takes to run 2 miles uphill
First, let's find the time it takes to run 2 miles uphill. Since he runs at 4 miles per hour uphill, the time for 2 miles uphill is 2 miles divided by 4 miles per hour, which equals 0.5 hours or 30 minutes. Now, since it takes the same time to run 3 miles downhill, we know the downhill time is also 30 minutes
The total time taken for 2 miles uphill and 3 miles downhill is the sum of both, which is 30 minutes + 30 minutes = 60 minutes, or 1 hour. Thus, the answer to the student's question is 1 hour
Write the quadratic as a product of factors irreducible over the reals. x2 + 16
Answer:
The product of factors irreducible over the reals are [tex]x^2+16=(x+4i)(x-4i)[/tex]
Step-by-step explanation:
Given : Quadratic form [tex]x^2+16[/tex]
To find : Write the quadratic as a product of factors irreducible over the reals?
Solution :
To find the product first we have to find the roots of the quadratic.
[tex]x^2+16=0[/tex]
[tex]x^2=-16[/tex]
Root both side,
[tex]\sqrt{x^2}=\sqrt{-16}[/tex]
[tex]x=\pm 4i[/tex]
So,The factors of the quadratic equation is [tex](x+4i)(x-4i)[/tex] in the form of complex number.
Therefore, The product of factors irreducible over the reals are [tex]x^2+16=(x+4i)(x-4i)[/tex]
What is the most specific name that can be given to a figure with the following coordinates? (–10, 8), (–7, 13), (3, 7), and (0, 2)
What is the solution to the equation x + 7.5 = 21.5? A.x = 2.9 B.x = 7.8 C.x = 14 D.x = 29
Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Which equation shows p, the price in dollars that she paid for her previous car?
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Assume employees' weekly gross earnings are $80,000, federal income tax withholding is $22,634.50, and FICA taxes are $11,920 in total for the employee and the employer. Determine the net amount to be paid to employees.
Over a two-hour time period, a snail moved 72 inches. How far is this in yards?
A snail moved distance of 2 yards.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
Given that, over a two-hour time period, a snail moved 72 inches.
We know that, 1 yard = 36 inches
Now, distance in yards = 72/36
= 2 yards
Therefore, a snail moved 2 yards.
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Construct a 95% confidence interval estimate of the mean net change in ldl cholesterol after the garlic treatment. what does the confidence interval suggest about the effectiveness of garlic in reducing ldl cholesterol?
Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDLcholesterol?
sample mean = x-bar = 4.7
ME = 1.96*15.6/sqrt(43) = 4.663
95% CI: 4.7 - 4.663 < u < 4.7 + 4.663
The 95% confidence interval of (4.5, 9.5) suggests that the true average change in LDL cholesterol after the garlic treatment is likely to fall within this range. However, with a p-value of 0.1494, there isn't enough statistical evidence to conclusively affirm that the garlic treatment significantly reduces LDL cholesterol levels.
Explanation:To construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, you have to be given or calculate the sample mean, the standard error, and the degrees of freedom. These factors depend on the data provided.
In this scenario, using the pre-calculated confidence interval provided, we have it at (4.5, 9.5). This means that we are 95% confident that the true population mean net LDL cholesterol change after garlic treatment is somewhere between a 4.5 unit decrease and a 9.5 unit decrease.
The effectiveness of the garlic treatment cannot be determined solely by this confidence interval, but this range might suggest a possible decrease in LDL cholesterol levels.
However, keep in mind that the p-value signifies the strength of the evidence against the null hypothesis. A p-value of 0.1494, as stated in the problem, means there isn't enough evidence to significantly conclude that the garlic treatment reduced LDL cholesterol at the 5% significance level.
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Which expressions are equivalent to 6 +(–x) + 2x + (–7) + 2x? Check all that apply.
The correct options is 3. (3 - x + 2x - 4 + 2x) simplifies to (-1 + 3x ), which is equivalent.
The given expression is (6 + (-x) + 2x + (-7) + 2x). Simplifying this expression by combining like terms results in ( -1 + 3x). To check for equivalent expressions, we evaluate each option:
1. x + x + 6 - 7 + x simplifies to (3x - 1), which is not equivalent.
2. (2x + 2 + x) simplifies to (3x + 2), which is not equivalent.
3. (3 - x + 2x - 4 + 2x) simplifies to (-1 + 3x ), which is equivalent.
4. (x - 1) is not equivalent.
5. (x + 1) is not equivalent.
Therefore, only the expression (3 - x + 2x - 4 + 2x) is equivalent to the given expression. The simplified form of the original expression is ( -1 + 3x), and the equivalent expression confirms this result by matching the simplified terms.
Complete question:
Which expressions are equivalent to 6 +(–x) + 2x + (–7) + 2x? Check all that apply.
x + x + 6 – 7 + x2x + 2 + x3 – x + 2x – 4 + 2xx – 1x + 1The expressions that are equivalent to [tex]\(6 + x + 2x - 7 + 2x\)[/tex] are:
a. [tex]\(x + x + 6 - 7 + x\)[/tex]
c.[tex]\(3 - x + 2x - 4 + 2x\)[/tex]
The correct option is (a)&(c).
To find which expressions are equivalent to [tex]\(6 + x + 2x - 7 + 2x\)[/tex], let's simplify the given expression first:
[tex]\[6 + x + 2x - 7 + 2x\][/tex]
Combining like terms:
[tex]\[6 - 7 + x + 2x + 2x\][/tex]
[tex]\[(-1) + 5x\][/tex]
Now, let's check each option to see which ones are equivalent:
a.[tex]\(x + x + 6 - 7 + x\)[/tex]
Combine like terms:
[tex]\(3x - 1\)[/tex]
This expression is equivalent.
b. [tex]\(2x + 2 + x\)[/tex]
Combine like terms:
[tex]\(3x + 2\)[/tex]
This expression is not equivalent.
c. [tex]\(3 - x + 2x - 4 + 2x\)[/tex]
Combine like terms:
[tex]\(3 + 5x - 4\)[/tex]
[tex]\(5x - 1\)[/tex]
This expression is equivalent.
d. [tex]\(x - 1\)[/tex]
This expression is not equivalent.
e. [tex]\(x + 1\)[/tex]
This expression is not equivalent.
So, the expressions that are equivalent to [tex]\(6 + x + 2x - 7 + 2x\)[/tex] are:
a. [tex]\(x + x + 6 - 7 + x\)[/tex]
c.[tex]\(3 - x + 2x - 4 + 2x\)[/tex]
complete question given below:
Which expressions are equivalent to 6 +(x)+2x+(- 7) + 2x? Check all that apply.
a.x+x+6-7+x
b.2x+2+x
c.3-x+2x-4+2x
d.x-1
e.x+1.
Ralph has 957 race car stickers. He gave 10 to ken. He gave 100 to Matt. How many stickers does Ralph have left?
Which statements are true about the graph of the function f(x) = 6x – 4 + x2?
Check all that apply.
The vertex form of the function is f(x) = (x – 2)2 + 2.
The vertex of the function is (–3, –13).
The axis of symmetry for the function is x = 3.
The graph increases over the interval (–3, ).
The function does not cross the x-axis.v
Jan’s pencil is 8.5 cm long. Ted’s pencil is longer. Write a decimal that could represent the length of Tex’s pencil?
Dan bought 5 1/4 gallons of gas on Friday and 6 1/2 gallons of gas on Saturday. How many liters of gas did he buy? Assume 1 gallon = 3.8 liters.
Answer:
Dan bought 44.65 liters of gas.
Step-by-step explanation:
The gas Dan bought on Friday and Saturday in gallons is
[tex]5\frac{1}{4}+6\frac{1}{2}[/tex]
[tex]=\frac{21}{4} +\frac{13}{2}[/tex]
We collect LCM for the denominators,
[tex]=\frac{21+26}{4}[/tex]
[tex]=\frac{47}{4}[/tex]gallons
We now convert to liters using the relation,
[tex]1\:gallon=3.8\: liters[/tex]
Let [tex]\frac{47}{4}\:gallons=x\:liters[/tex]
Then,
[tex]x=3.8\times \frac{47}{4}[/tex]
[tex]x=\frac{38}{10}\times \frac{47}{4}[/tex]
[tex]x=\frac{19}{5}\times \frac{47}{4}[/tex]
[tex]x=\frac{893}{20}=44.65[/tex]
Therefore Dan bought 44.65 liters of gas.
Sean, a freelance editor, charges the rates shown in the table below to edit manuscripts. The cost per page increases as the quality of editing improves. Sean also gives a 5% discount if the entire amount is paid up front. A 2 column table with Type of Editing and Cost per page as the column headings. Express Proofreading costs 2 dollars, Basic Proofreading 2.95 dollars, Extended Proofreading 3.95 dollars, and Deep Editing 11 dollars Michelle has an 85-page manuscript. The equation below shows the relationship between the total cost of editing 85 pages, T, and the cost per page, c, if she gets the 5% discount: 85c − 0.05(85c) = T Using the equation, what is the best quality of editing that Michelle can get done for a maximum of $161.50? Express proofreading Basic proofreading Extended proofreading Deep editing
which expression shows how 6 times 45 can be written using the distributive property?
A.6 times 4 + 6 times 5
B.6 times 40 + 6 times 5
C.6 times 40 + 6
D, 20 times 6 + 20 Times 5
Write the fraction 14/16 in simplest form. If the fraction is in simplest form
The amount of time a bank teller spends with each customer has a population mean = 3.10 minutes and standard deviation = 0.40 minute. if a random sample of 16 customers is selected without replacement from a population of 500 customers,
a. what is the probability that the average time spent per customer will be at least 3 minutes?
b. there is an 85% chance that the sample mean will be below how many minutes?
a. First we solve the finite population correction factor σx from the formula:
σx = [s / sqrt(n)] * sqrt [(N – n) / (N – 1)]
σx = [0.40 / sqrt(16)] * sqrt[(500 – 16) / (500 – 1)]
σx = 0.0985
Then we compute for z score when x ≥ 3 minutes:
z = (x – m) / σx
z = (3 – 3.10) / 0.0985
z = -1.015
From the tables, the probability (p value) using right tailed test is:
P = 0.845 = 84.5%
b. At P = 0.85, the z score is z = 1.04
1.04 = (x – 3.10) / 0.0985
x = 3.20
Hence there is a 85% chance it will be below 3.20 minutes
Final answer:
The probability that the average time spent per customer will be at least 3 minutes is approximately 0.8413. There is an 85% chance that the sample mean will be below approximately 3.359 minutes.
Explanation:
a. To find the probability that the average time spent per customer will be at least 3 minutes, we need to find the probability that the sample mean is greater than or equal to 3 minutes. Since the population standard deviation is known and the sample size is large (n=16), we can use the z-score formula and the standard normal distribution to calculate the probability. The z-score is calculated as follows:
z = (x - µ) / (σ / √n)
where x is the sample mean, µ is the population mean, σ is the population standard deviation, and n is the sample size. Substituting the values into the formula:
z = (3 - 3.10) / (0.40 / √16) = -0.1 / (0.40 / 4) = -0.1 / 0.1 = -1
Looking up the corresponding area to the left of z=-1 in the standard normal distribution table, we find that the probability is approximately 0.1587. Therefore, the probability that the average time spent per customer will be at least 3 minutes is approximately 0.8413.
b. To find the value below which there is an 85% chance that the sample mean will be, we need to find the z-score that corresponds to the cumulative probability of 0.85. Using the standard normal distribution table, we find that the z-score is approximately 1.036. Substituting the values into the z-score formula:
1.036 = (x - 3.10) / (0.40 / √16)
Solving for x:
1.036 * (0.40 / √16) + 3.10 = x
x ≈ 0.259 + 3.10 ≈ 3.359
Therefore, there is an 85% chance that the sample mean will be below approximately 3.359 minutes.
A normal distribution in which approximately 68% of the data values fall within one standard deviation of the mean behaves according to
Final answer:
The normal distribution in question behaves according to the Empirical Rule, which states that about 68% of the data falls within one standard deviation of the mean in a bell-shaped, symmetric distribution. This percentage changes to about 95% within two standard deviations and over 99% within three standard deviations.
Explanation:
A normal distribution in which approximately 68% of the data values fall within one standard deviation of the mean behaves according to the Empirical Rule. This is a key concept of descriptive statistics that applies specifically to bell-shaped, symmetric distributions. According to the rule, about 68 percent of the data lies within one standard deviation of the mean, about 95 percent lies within two standard deviations, and over 99 percent lies within three standard deviations.
For example, if a distribution has a mean (μ) of 50 and a standard deviation (σ) of 6, then approximately 68 percent of the values (x) would lie between 44 (50 - 6) and 56 (50 + 6). These points are one standard deviation away from the mean and correspond to the z-scores of -1 and +1, respectively. It is important to remember that this rule only applies when the distribution is perfectly bell-shaped and symmetric.
What is the equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32)?
A)y = –x + 33
B)y = –x + 36
C)y = 4x − 16
D)y = 4x + 16
The equation of line that is parallel to the line [tex]y-1=4\left({x+3}\right)[/tex] and passes through the point [tex]\left({4,32}\right)[/tex] is [tex]\boxed{{\mathbf{y=4x+16}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION}}\,{\mathbf{D}}}[/tex] .
Further explanation:
It is given that the equation of line is [tex]y-1=4\left({x+3}\right)[/tex] and passes through point [tex]\left({4,32}\right)[/tex] .
Rewrite the given equation [tex]y-1=4\left({x+3}\right)[/tex] as follows:
[tex]\begin{aligned}y-1&=4\left({x+3}\right)\\y-1&=4x+12\\y&=4x+12+1\\y&=4x+13\\\end{aligned}[/tex]
Now, compare the obtained equation of line [tex]y=4x+13[/tex] with the standard equation of line [tex]y=mx+b[/tex] .
[tex]\begin{aligned}m&=4\\b&=13\\\end{aligned}[/tex]
Therefore, the slope is [tex]4[/tex] .
It is given that both lines are parallel to each other so the product of slope must be equal.
[tex]{m_1}={m_2}[/tex] …… (1)
Substitute [tex]4[/tex] for [tex]{m_1}[/tex] in equation (1) to obtain the value of slope [tex]{m_2}[/tex] .
[tex]{m_2}=4[/tex]
Therefore, the slope is [tex]4[/tex] .
It is given that the line passes through point [tex]\left({4,32}\right)[/tex] .
The point-slope form of the equation of a line with slope [tex]m[/tex] passes through point [tex]\left({{x_1},{y_1}}\right)[/tex] is represented as follows:
[tex]y-{y_1}=m\left({x-{x_1}}\right)[/tex] …… (2)
Substitute [tex]4[/tex] for [tex]{x_1}[/tex] , [tex]32[/tex] for [tex]{y_1}[/tex] and [tex]4[/tex] for [tex]m[/tex] in equation (2) to obtain the equation of line.
[tex]\begin{aligned}y-32&=4\left({x-4}\right)\\y-32&=4x-16\\y&=4x-16+32\\y&=4x+16\\\end{aligned}[/tex]
Therefore, the equation of line is [tex]y=4x+16[/tex] .
Now, the four options are given below.
[tex]\begin{gathered}{\text{OPTION A}}\to y=-x+33\hfill\\{\text{OPTION B}}\to y=-x+36\hfill\\{\text{OPTION C}}\to y=4x-16\hfill\\{\text{OPTION D}}\to y=4x+16\hfill\\\end{gathered}[/tex]
Since OPTION D matches the solution that is [tex]y=4x+16[/tex] .
Thus, the equation of line that is parallel to the line [tex]y-1=4\left({x+3}\right)[/tex] and passes through the point [tex]\left({4,32}\right)[/tex] is [tex]\boxed{{\mathbf{y=4x+16}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION}}\,{\mathbf{D}}}[/tex] .
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Answer Details:
Grade: Junior High School
Subject: Mathematics
Chapter: Coordinate Geometry
Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, equation of line, line, passes through point.
Which of the following expressions is in simplified form?
A) 1 1/2n + 2.9n
B) 4w - 5
C) -2 + 1.4m + 0.5
D) 9j - 3 - j
Answer:
B. Is the Answer Because its the only one that is simplified.
Step-by-step explanation:
Have A Nice Day!
Complete the following statement of congruence:
Answer:
(C) ΔABC
Step-by-step explanation:
Congruence: Two figures or shapes can be congruent if they have same dimensions and shape.
From the given information, ΔXYZ is congruent to ΔABC as when according to the respective angles of ΔXYZ, the respective angles of the ΔABC matches and this makes them congruent to eachother.
Rest other options fails to satisfy the congruence criteria, thus option C is correct.
Hence, ΔXYZ is congruent to ΔABC.
Julie is selling candy bars to raise money for new band uniforms. Candy bar X sells for $2 and candy bar Y sells for $3. Julie needs to sell at least three times more Y candy bars than X candy bars. She has at most 36 candy bars to sell. Which objective function can be used to find the profit P that Julie makes from selling the candy bars?
A) P = x + y
B) P = 36xy
C) P = 2x + 3y
D) P = 3x + 2y
Answer:
Answer is C [tex]P = 2x + 3y[/tex]
Step-by-step explanation:
Selling price of candy bar X =$2
Selling price of candy bar Y =$3
So if Julie sells x from X candy bars and y bars from Y candy bars,
Profit made from selling X candy bars = [tex]2\times x[/tex]
Profit made from selling Y candy bars = [tex]3\times y[/tex]
Therefore, assuming that there is no cost for the candy bars the profit by selling candy bars can be represented by the following objective function:
[tex]P = 2x + 3y[/tex]
Therefore, answer is C
Suppose that work hours in new zombie are 200 in year 1 and productivity is $8 per hour worked. what is new zombie's real gdp? if work hours increase to 210 in year 2 and productivity rises to $10 per hour, what is new zombie's rate of economic growth?
Final answer:
New Zombie's real GDP in year 1 is $1600 and in year 2 is $2100, resulting in a rate of economic growth of 31.25%.
Explanation:
To calculate the real GDP of New Zombie we must multiply the work hours by the productivity (value produced per hour).
For year 1, the real GDP is calculated as follows:
200 hours * $8 per hour = $1600.
For year 2, we calculate the real GDP as:
210 hours * $10 per hour = $2100.
Now, to find the rate of economic growth from year 1 to year 2, we use the formula:
((GDP in year 2 - GDP in year 1) / GDP in year 1) * 100
= (($2100 - $1600) / $1600) * 100
= 31.25%.
Thus, New Zombie's rate of economic growth is 31.25%.
Evaluate |2x+y-3z| for x=-2, y=10, and z=3
How to solve?
which property is illustrated by the following statement? 5g+7= 7 + 5g
Answer:
The property which is illustrated by the statement 5g+7= 7 + 5g is:
Commutative property
Step-by-step explanation:
Commutative property states that:
If a and b are two elements defined under the operation *
Then, a*b=b*a
Here, we are given
5g+7= 7 + 5g
i.e. a=5g, b=7 and * = +
Hence, the property which is illustrated by the statement 5g+7= 7 + 5g is:
Commutative property
name the numerator and the denominator in each fraction 11/12 7/512 12/10 0/78
We bought five 3 3/4 pound bags of bird seed. A. What is the total weight of the birdseed they bought? B. If each smaller bag contains 1 1/2 pounds, how many bags can they make? C. Will there be any birdseed
Left over? .
Answer:
We bought five 3 3/4 pound bags of bird seed.
A :
Total weight is = [tex]3\times(\frac{3}{4} )=\frac{9}{4}[/tex] pounds of bird seed.
In mixed fraction it is : [tex]2\frac{1}{4}[/tex] pounds
B :
As given, each smaller bag contains 1 1/2 pounds, so 9/4 pounds can make:
=[tex]\frac{\frac{9}{4}}{\frac{3}{2}}[/tex]= 18/12 = 3/2 bags
C :
We can make 1 full bag and will have left out enough for half of another bag. Half of a 3/2 pound is :
[tex]1/2(3/2)[/tex] = 3/4 of a pound.
Ken watches a marching band. He sees 2 rows of flute players. Six people are in each row . He sees 8 trombone players. How many flute players and trombone players does Ken see?
Use compatible numbers to find two estimates 336 divided by 12
The sum of two numbers is with a ratio of 15:10. Find the larger number.
1. which expression is equal to (f+g) (×) f (x)=x^2+3;g (x)=x-1
A. x^3-3
B.x^2-2x+4
C. x^2+x+2
D. x^3-x^2+3x-3
2. which expression is equal to (fog)(x)
f (x)=3x; g (x)=4x^2+1
A. 12x^3+3x
B. 4x^2+3x+1
C.12x^2+3
D. 36x^2+1
3. f (x)= 2x-8; g (x) = x-5
what is the value of (gof)(6)
a. -6
b. -1
c. 1
d. 6
4. f(x) =5x-10 what is the value of f^-1 (-3)
a. -5
b. 1.4
c. 9.4
d. -25