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
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.
A satellite 200 miles above the earth is orbiting the earth once every 4 hrs. How far does the satellite travel in 1 hr
Assume the radius of the the earth is ~4000 miles.
radius of orbit = 4000 +200 = 4200 miles
In 4 hrs it orbits 2Pi*r =2pi*4200= 8400pi miles
In 1 hr it would travel (8400pi/4 )
= 2100pi = 6597.3445 miles (exact value)
= 6597 miles ( approximate)
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
The sum of two numbers is with a ratio of 15:10. Find the larger number.
A contiguous subsequence of a list s is a subsequence made up of consecutive elements of s. for instance, if s is
A contiguous subsequence of a list is a subsequence made up of consecutive elements.
Explanation:A contiguous subsequence of a list s is a subsequence made up of consecutive elements of s. For example, if s is [1, 2, 3, 4, 5], a contiguous subsequence could be [2, 3, 4].
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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!
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
The volume of a cone is 62.8 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the nearest inch? Use pi = 3.14
2 inches
4 inches
8 inches
9 inches
Answer: 2inches
Step-by-step explanation:
Use compatible numbers to find two estimates 336 divided by 12
name the numerator and the denominator in each fraction 11/12 7/512 12/10 0/78
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)
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
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?
What is 7√27+5√48 in simplified radical form?
The expression 7√27+5√48 in simplified radical form is [tex]41 \sqrt{3}[/tex] and this can be determined by using the arithmetic operations.
Given :
Expression -- 7√27+5√48
The following steps can be used in order to determine the simplified radical form of the given expression:
Step 1 - The arithmetic operations can be used in order to determine the simplified radical form of the given expression.
Step 2 - Write the given expression.
= 7√27+5√48
Step 3 - Rewrite [tex]\sqrt{27}[/tex] as [tex]3\sqrt{3}[/tex] in the above expression.
[tex]= 7 \times 3 \sqrt{3}+ 5 \sqrt{48}[/tex]
Step 4 - Rewrite [tex]\sqrt{48}[/tex] as [tex]4\sqrt{3}[/tex] in the above expression.
[tex]= 21 \sqrt{3}+ 20\sqrt{3}[/tex]
Step 5 - Simplify the above expression.
[tex]= 41 \sqrt{3}[/tex]
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4 3/4 minus 5/8 in simplest form
Which problem can be solved using this inequality?
x + 5 ≤ 20
A) Beth is purchasing school supplies. She knows that the price for her pencil case is $5. She only has $20 to spend. How much money will she have left after buying the pencil case?
B) Beth is purchasing school supplies. She knows that the price for her pencil case is $5. She only has $20 to spend. What is the most amount of money she can spend on the remaining supplies?
C) Beth is purchasing school supplies. She knows that the price for her pencil case is less than $5. She only has $20 to spend. How much money will she have left to spend after buying the pencil case?
D) Beth is purchasing school supplies. She knows that the price for her pencil case is $5 more than the cost of a book bag. She only has $20 to spend. Does Beth have enough money to buy the pencil case and book bag?
Answer:
The answer would be b.
Step-by-step explanation:
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.
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
What value of n will make (-5) × (-8) = n × (-5) a TRUE statement?
A) (-8)
B) 8
C) (-3)
D) 3
to make the statement true, n need to equal the same as what is on the left side, so n = -8
correct answer is A
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
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.
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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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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Evaluate |2x+y-3z| for x=-2, y=10, and z=3
How to solve?
A car travels 2 1/3 miles in 3 1/2 minutes at a constant speed. Write an equation to represent the car travels in miles and minutes
Answer:
x = [tex]\frac{2}{3}\times t[/tex]
Step-by-step explanation:
We know the formula to represent the speed is,
Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
If a car travels the distance = [tex]\frac{7}{3}[/tex] miles in [tex]\frac{7}{2}[/tex] minutes then the speed will be
Speed = [tex]\frac{\frac{7}{3}}{\frac{7}{2}}[/tex]
= [tex]\frac{7}{3}\times \frac{2}{7}[/tex]
= [tex]\frac{2}{3}[/tex] miles per minute
If the car travels x miles in t minutes then the equation to calculate the distance will be
[tex]\frac{2}{3}=\frac{x}{t}[/tex]
x = [tex]\frac{2}{3}\times t[/tex]
Therefore, the equation that represents the distance in terms of time will be
x = [tex]\frac{2}{3}\times t[/tex]
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.
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.
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?