Answer:
(6 necklaces x $9 per necklace) - $14 spent on supplies = profit for Lola
or (6 x 9) - 14 = profit for Lola
The actual profit is $40.
Step-by-step explanation:
First, you need to calculate how much money Lola made from selling jewelry. She sold 6 necklaces, and each one was sold for $9, so you can calculate the total sale proceeds by multiplying 6 x $9 = $54.
However, you then have to subtract the cost of supplies that Lola had to buy to make the necklaces, in order to find out how much money Lola actually made. Therefore, subtract $14 from the calculation above.
Therefore the final expression is: (6 x 9) - 14 = profit
Make sure to take into account order of operations when solving the equation (it's important to multiply 6x9 before you subtract out the 14). The actual profit for Lola comes out to $40.
The number N of cars produced at a certain factory in 1 day after t hours of operation is given by Upper N (t )equals 800 t minus 5 t squared commaN(t)=800t−5t2, 0 less than or equals t less than or equals 10.0≤t≤10. If the cost C (in dollars) of producing N cars is Upper C (Upper N )equals 30 comma 000 plus 8000 Upper N commaC(N)=30,000+8000N, find the cost C as a function of the time of operation of the factory. What is the cost C as a function of the time t of operation of the factory?
Answer:
The cost C as a function of t is C(t) = 30,000 + 6,400,000 t - 40,000 t²
Step-by-step explanation:
The function N(t) = 800 t - 5t², represents the number of cars produced at a time t hours in a day, where 0 ≤ t ≤ 10
The function C(N) = 30,000 + 8,000 N, represents the cost C (in dollars) of producing N cars
We need to find The cost C as a function of the time t
That means Substitute N in C by its function by other word find the composite function (C о N)(t)
∵ C(N) = 30,000 + 8,000 N
∵ N(t) = 800 t - 5 t²
- Substitute N in C by 800 t - 5 t²
∴ C(N(t)) = 30,000 + 8000(800 t - 5 t²)
- Multiply the bracket by 8000
∴ C(N(t)) = 30,000 + 8000(800 t) - 8000(5 t²)
∴ C(N(t)) = 30,000 + 6,400,000 t - 40,000 t²
- C(N(t) = C(t)
∴ C(t) = 30,000 + 6,400,000 t - 40,000 t²
The cost C as a function of t is C(t) = 30,000 + 6,400,000 t - 40,000 t²
The cost C as a function of time t of operation is given by the equation C(t) = 30000 + 6400000t - 40000t^2. This equation factors in the initial costs, the revenue from the cars produced, and the costs per each additional hour of operation.
Explanation:To answer your question, we first need to find a relationship between the cost C(N) and the number of cars produced N(t) as a function of time. We know that N(t) = 800t - 5t2 and C(N) = 30000 + 8000N. We can substitute N(t) into C(N) to find C as a function of time t.
Therefore, the cost C as a function of time t, denoted as C(t), is C(t) = 30000 + 8000 * (800t - 5t2).
This simplifies further to C(t) = 30000 + 6400000t - 40000t2.
In other words, the cost of operations in the factory is a function of the time it operates, taking into account the initial costs, the revenue from the cars produced, and the cost associated with each additional hour of operation.
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Which graph represents this system?
2 x minus 5 y = negative 5. y = two-fifths x + 1.
Answer:
The answer is the first graph.
Step-by-step explanation:
I did it on edge. I got it wrong the first time because I used an answer from this question. Because of that, I reported it. Now I have the correct answer lol.
The slope and the intercept for the lines 2 x minus 5 y = negative 5 and y = two-fifths x + 1 are the same thus the line will coincide so, option A is the correct graph.
What is a graph?A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Given:
2 x minus 5 y = negative 5 and y = two-fifths x + 1,
Write the above phrase in mathematical form,
2x - 5y = -5 and y = 2 / 5 x + 1
5y = 2x + 5 and y = 2 / 5 x + 1
y = 2 / 5 x + 1 and y = 2 / 5 x + 1
As we can see here, the slope and the intercept are the same so, the lines are collinear.
Thus, the line will coincide.
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The parent function h(x)=log3(x) is transformed into j(x)=2log3(x+3)−7. Using complete sentences, describe ALL transformation that occurred.
Answer:
The function is vertically scaled (expanded) by a factor of 2.The scaled function is translated left 3 units and down 7 units.Step-by-step explanation:
When a function f(x) is transformed by ...
g(x) = a·f(x -h) +k
it has been vertically scaled by a factor of "a" and translated to the right and up by amounts h and k, respectively.
Here, we have a=2, h=-3, and k=-7. The means ...
The function has been vertically expanded by a factor of 2, translated left 3 units, and translated down 7 units.
Major arc JL measures 300°.
Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Major arc J L is 300 degrees.
Which describes triangle JLM?
right
obtuse
scalene
equilateral
Answer:
The answer is D. Equilateral
Step-by-step explanation:
Answer on edg
The triangle ΔJLM is an equilateral triangle. Then the correct option is D.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In an isosceles triangle, two angles and their opposite sides are equal.
In an equilateral triangle, all the angles and sides of the triangle are congruent.
Circle M is shown. Line segments MJ and ML are radii.
Tangents JK and LK intersect at point K outside the circle.
Major arc JL is 300 degrees.
Then the measure of the minor arc will be
Major arc + minor arc = 360°
300° + minor arc = 360°
Minor arc = 60°
Then the measure of angle ∠MLJ will be
Minor arc = ∠LMJ = 60°
Then the sides MJ and ML congruent, then their opposite angles are also congruent.
∠MJL = ∠MLJ
Then the measure of the angle ∠MLJ will be
∠MJL + ∠MLJ + ∠LMJ = 180
∠MLJ + ∠MLJ + 60° = 180°
2∠MLJ = 120°
∠MLJ = 60°
All the angles of the triangle are congruent.
Then the correct option is D.
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16.
(a)
Simply
3b + 5b - 2
Combine like terms
1. Add 3b and 5b (combine like terms)
2. After adding you are supposed to get 8b
3. The -2 would stay as it is because we can't add it to 8b
4. So the answer would be 8b-2
The trinomial x2+bx-c has factors of (x+m)(x-n) where m,n, and b are positive. What is the relationship between the values of m and n? Explain
Answer:
(m - n ) = b
mn = c
The relationship between m and n is such that their product is c and their difference is b
Step-by-step explanation:
roots are x = -m and x = n
-m = -b/2 - root(b*b + 4c)/2
n = -b/2 + root(b*b + 4c)/2
(x + m)(x -n) = x*x +(m - n)x - mn
(m - n ) = b
mn = c
Sample Answer: The value of m must be greater than the value of n. When you multiply the binomials, the middle term is the result of combining the outside and inside products. So, bx = –nx + mx, or bx = (–n + m)x. This means that b = –n + m. When adding numbers with opposite signs, you subtract their absolute values, and keep the sign of the number having the larger absolute value. Since b is positive, m must have the larger absolute value.
its right ur welcome
what dimension or dimensions do you need to know to find the volume of a sphere?
Answer:
the radius
Step-by-step explanation:
4/3*pi*r squared
Last week’s and this week’s low temperatures are shown in the table below. Low Temperatures for 5 Days This Week and Last Week Low Temperatures This Week (Degrees Fahrenheit) 4 10 6 9 6 Low Temperatures Last Week (Degrees Fahrenheit) 13 9 5 8 5 Which measures of center or variability are greater than 5 degrees? Select three choices. the mean of this week’s temperatures the mean of last week’s temperatures the range of this week’s temperatures the mean absolute deviation of this week’s temperatures the mean absolute deviation of last week’s temperatures
Question:
Temperatures for 5 Days This Week and Last Week
Low Temperatures This Week (Degrees Fahrenheit) 4 10 6 9 6 Low Temperatures Last Week (Degrees Fahrenheit) 13 9 5 8 5 Which measures of center or variability are greater than 5 degrees? Select three choices.
a) the mean of this week’s temperatures
b) the mean of last week’s temperatures
c) the range of this week’s temperatures
d)the mean absolute deviation of this week’s temperatures
e) the mean absolute deviation of last week’s temperatures
Answer:
a) the mean of this week’s temperatures
b) the mean of last week’s temperatures
c) the range of this week’s temperatures
Step-by-step explanation:
I would be verifying the options a, b, and c in my answer above through calculations which are shown below.
We were given the following data:
Low Temperatures This Week (Degrees Fahrenheit)
4, 10, 6, 9, 6
Low Temperatures Last Week (Degrees Fahrenheit)
13, 9, 5, 8, 5
We are to find which measures of center or variability are greater than 5 degrees.
Option a
The mean of this week’s temperatures
(4+ 10+ 6+9+ 6) °F ÷ 5 = 35 °F ÷5 = 7°F
Option a is correct because it measures of center or variability which is 7 °F is higher than 5°F
Option b
The mean of last week’s temperatures
(13+ 9 + 5 + 8 + 5) °F = 40°F ÷ 5 = 8°F
Option b is correct , because its measure of variability which is 8°F is greater than 5°F.
Option c
the range of this week’s temperatures
This week's temperature is given as
(4, 10, 6, 9, 6) °F
Range is defined as the difference between the highest number and the lowest number
Range of this week's temperature = (10 - 4) °F = 6°F
Hence Option c is correct because it measures of center or variability which is 6°F is greater than 5°F
From the above calculations we can accurately confirm that options a, b, and c are correct because the measures of their center or variability is greater than 5°F
Answer:
A,B,C
Step-by-step explanation:
Sharon bought a mixture of nuts that was made up of pecans, walnuts and cashews in a ratio by weight of $2:3:1$, respectively. If she bought $9$ pounds of nuts, how many pounds of walnuts were in the mixture? Express your answer as a decimal to the nearest tenth.
Answer:4.5
Step-by-step explanation:
2+3+1=6, 3 divided by 6 equals to 1/2. 1/2 times 9 equals 4.5 pounds of walnuts
Answer:
4.5
Step-by-step explanation:
Since the pecan to walnut to cashew ratio is 2:3:1, it follows that the walnut ratio to all of the nuts is equal to 3/2+3+1. Thus, there were 1/2 x 9 = 4.5 pounds of walnuts in the mixture.
it took a skydiver 15 to drop 450. What is the rate (in feet per/ seconds) of the skydivers drop?
Answer:
its 30
Step-by-step explanation:
you have to divide 450 by 15 to see what it takes
Use the spinner to identify the probability to the nearest hundredth of the pointer
landing on a shaded area.
The general manager of a fast food restaurant chain must select 6 restaurants from 11 for a promotional program. How many different possible ways can this selection be done?
Answer:
Step-by-step explanation:
This question will be solved using the combination formula which is nCr because the order is unimportant and we need the selection.
11C6
11!/(11-6)!*6!
= 462
Therefore the manager can select the restaurant in 462 ways.
Answer:
462
Step-by-step explanation:
There 6 slots available to fill in the restaurants options
- For the 1st slot, there are 11 ways to choose
- For the 2nd slot, there are 10 ways to choose
- For the 3rd slot, there are 9
- For the 4th slot, there are 8
- For the 5th slot, there are 7
- For the last 6th, there are 6 ways
So in total there would be 11*10*9*8*7*6 = 332640 ways to choose. But since the order of these 6 slots don't matter, there are actually 6! = 720 ways to order these 6 slots. So the actual number of possible ways is
332640 / 720 = 462
The Venn diagram shows the number of students playing instruments. How many students play either the guitar or tuba?
A) 7
B) 8
C) 15
D) 80
Answer:
B) 8
( I Hope this was helpful)
A class of 22 students is having a drawing. Each student's name is placed on a piece of paper and then placed in a hat. One name is randomly drawn from the hat.
If there are 11 boys in the class, what is the probability that the name drawn is a girl's?
A.
5/11
B.
6/11
C.
1/2
D.
10/11
Answer:C 1/2
Step-by-step explanation:
If 11 are boys that means the left over 11 from the 22 are girls.
22-11=11
11/22 simplified is 1/2 as you divide both sides by 11.
Hope this helps!
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What is:
a=sr (25²-25/2²)
Answer:
24.8746859277
Step-by-step explanation:
sqrt(625 - 25/4)
sqrt[(2500-25)/4]
sqrt(2475/4)
sqrt(618.75)
24.8746859277
Answer:
24.87
Step-by-step explanation:
(x^2−1)(3x−4)(3x+4) what is the product
Answer:
9x^4-25x^2+16
Step-by-step explanation:
(x^2−1)(3x−4)(3x+4)=(*)
(x^2−1)((3x)^2−4^2) =
(x^2 - 1)(9x^2-16)=
x^2*9x^2 - x^2*16 - 1*9x^2 +16=
9x^4-16x^2-9x^2+16=
9x^4-25x^2+16
(*) (A-B)(A+B) =A^2 - B^2
Lisa made 6 sandwiches in 15 minutes. At that rate, how long will it take her to make 15 sandwiches?
Ok, so we know she can make 6 sandwiches in 15 minutes. So, in 30 minutes she can make 12 sandwiches. It takes her 2.5 minutes to make one sandwhich. Therefore for another 3 sandwiches it would take 7.5 minutes.
Answer: 37.5 minutes to make 15 sandwiches
Answer:
37.5 minutes
Step-by-step explanation:
You must find the rate at which she can make sandwhiches and use that to find your answer
A cylindrical tank has a diameter of 10 and a height of 7 feet. If each cubic foot holds 7.48 gallons of water, how many gallons of water does the tank hold?
Answer:
The tank can hold 4110.26 gallons of water.
Step-by-step explanation:
In order to solve this question we need to compute the volume of this tank, the volume is given by:
V = (area of the base)*height
Since the base is circullar, it is given by:
area of the base = pi*r^2
So we have:
V = height*pi*r^2
The radius of circle is the diameter divided by 2, so in this case r = 10/2 = 5 ft. We can now use the values on the equations:
V = 7*3.14*(5)^2 = 549.5 ft^3
Since each cubic foot holds 7.48 gallons of water the volume in gallons is:
V = 549.5*7.48 = 4110.26 gallons
The tank can hold 4110.26 gallons of water.
To find the number of gallons a cylindrical tank can hold, calculate the volume in cubic feet using the formula V = πr^2h, where the diameter is 10 feet (radius is 5 feet) and the height is 7 feet, then multiply the volume by 7.48 gallons per cubic foot.
Explanation:To calculate the number of gallons a cylindrical tank can hold, we first need to find the volume of the cylinder in cubic feet and then convert that volume to gallons. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
Since the diameter of the tank is given as 10 feet, the radius (r) would be half of that, which is 5 feet. The height (h) is given as 7 feet. Plugging these values into the formula, we get:
V = π(5)^2(7) = π(25)(7) = π(175) cubic feet.
Using the conversion factor 7.48 gallons per cubic foot, we can find the total gallons the tank holds:
Gallons = Cubic feet × 7.48 gallons/cubic foot
Gallons = π(175) × 7.48 gallons/cubic foot
We thus calculate the total volume in gallons.
Problem: Construct a triangle with an interior angle measure of 110°. What type of triangle did you construct? Acute triangle Obtuse triangle Right triangle Scalene triangle
Answer:
it'd be an obtuse triangle. If any angle is greater than 90 degrees it makes it obtuse.
Step-by-step explanation:
Answer:
obtuse triangle
Step-by-step explanation:
Chocolate bars produced by a certain machine are labeled with 8.0 oz. The distribution of the acutal weights of these chocolates bars is Normal with a mean of 8.1 oz and a standard deviation of 0.1oz. A chocolate bar is considered underweight if it weighs less then 8.0 oz.
(A) What proportion of chocolate bars wieghs less then 8.0 oz?
(B) What propertion of chocolate bars weighs between 8.2 and 8.3 oz?
(C) How should the chocolate bar wrappers be labeled so that only 1% of such bars are underwight?
Answer:
[tex]a.\ P(C<8.0)=0.1587\\\\b. \ P(8.2<C<8.3)=0.1359\\\\c. 7.87\ oz[/tex]
Step-by-step explanation:
a. Let C be the normally distributed random variable.
-Given the chocolates is normally distributed with mean =8.1 oz and standard deviation =0.1 oz.
#The proportion of those less than 8.0 oz can be calculated as:
[tex]P(C<8.0)=P(Z<\frac{\bar X-\mu}{\sigma})\\\\\\=P(Z<\frac{8.0-8.1}{0.1})\\\\\\=P(Z<-1)=0.1587[/tex]
Hence, the proportion of bars weighing below 8 ounces is 0.1587 or 15.87%
b. We use the z-test to determine the probability or proportion of bars weighing between 8.2 and 8.3 ounces:
[tex]P(8.2<C<8.3)=P(\frac{\bar X-\mu}{\sigma}<Z<\frac{\bar X-\mu}{\sigma})\\\\\\=P(\frac{8.2-8.1}{0.1}<Z<\frac{8.3-8.1}{0.1})\\\\\\=P(1<Z<2)\\\\\\=0.9772-0.8413\\\\=0.1359[/tex]
Hence, the proportion of bars weighing between 8.2 and 8.3 ounces is 0.1359 or 13.59%
c. To label the wrappers such that only 1% are underweight.
#Find B such that
P(C<B)=0.01
#Now find z-value such that:
[tex]P(Z<B)=0.01[/tex]
Using the z-tables, z=-2.33
Therefore:
[tex]C=z\sigma +\mu\\\\=-2.333\times 0.1+8.1\\\\=7.8667\approx 7.87 \ oz[/tex]
Hence, the wrappers should be labelled as 7.87 ounces
Approximately 15.87% of the chocolate bars weigh less than 8.0 oz. Approximately 13.59% of the bars weigh between 8.2 and 8.3 oz. The wrappers should be labeled as 7.867 oz to ensure only 1% of the bars are considered underweight.
Explanation:In order to answer the student's questions, we have to find the Z-scores, which correspond to the given weights, in the standard normal distribution table.
(A) To find the proportion of chocolate bars that weigh less than 8.0 oz, we first find the Z-score using the formula Z = (X-μ)/σ, where X is the weight, μ is the mean, and σ is the standard deviation. Thus, Z = (8.0-8.1)/0.1 = -1, implying the bar is one standard deviation below the mean. Referring to the Z-table, Z = -1 corresponds to 0.1587, or 15.87% of the population. Therefore, approximately 15.87% of the chocolate bars weigh less than 8.0 oz.
(B) To find the proportion of chocolate bars weighing between 8.2 and 8.3 oz, find the Z-scores for 8.2 and 8.3 oz. Using the Z-score formula, Z_8.2 = (8.2-8.1)/0.1 = 1 and Z_8.3 = (8.3-8.1)/0.1 = 2. From the Z-table, the proportions corresponding to these Z-scores are 0.8413 and 0.9772 respectively. Thus, the proportion between these weights is 0.9772 - 0.8413 = 0.1359, or 13.59%.
(C) For only 1% of the bars to be underweight, we need a weight that is at the 1% mark in the standard normal distribution. Looking up the Z-table, Z = -2.33 corresponds with the lower 1%. Using the Z = (X-μ)/σ formula rearranged to X = Z*σ + μ, we get X = -2.33*0.1 + 8.1 = 7.867 oz. Therefore, to ensure only 1% of bars are underweight, the wrappers should be labeled as 7.867 oz.
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A survey of 480 high school students found that 37% had a pet. Find the margin of error. Round to the nearest percent. Use the margin of error to find an interval that is likely to contain the true population proportion.
Answer:
[tex] ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
And replacing we got:
[tex] ME= 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}= 0.0432[/tex]
And replacing into the confidence interval formula we got:
[tex]0.37 - 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.327[/tex]
[tex]0.37 + 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.413[/tex]
And the 95% confidence interval would be given (0.327;0.413).
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
The confidence interval would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Assuming a 95% of confidence. For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=1.96[/tex]
The margin of error would be:
[tex] ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
And replacing we got:
[tex] ME= 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}= 0.0432[/tex]
And replacing into the confidence interval formula we got:
[tex]0.37 - 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.327[/tex]
[tex]0.37 + 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.413[/tex]
And the 95% confidence interval would be given (0.327;0.413).
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The diameter of the steering wheel of a car is 15.5 inches.
a.If you turn the steering wheel through an arc of 90 degrees without taking your hands from the wheel, how far have your hands moved
b.If you move your hands 10 inches, what angle does the steering wheel pass through
Step-by-step explanation:
The diameter of the steering wheel of a car is 15.5 inches.
Circumference of the wheel = 15.5π = 48.6
If you turn the steering wheel through an arc of 90 degrees without taking your hands from the wheel,
The distance moved by hands = [tex]\frac{48.67}{4}[/tex] = 12 inches.
Answer:
12 inStep-by-step explanation:
About 32% of the population in a large region are between the ages of 40 and 65, according to the country's census. However, only 2% of the 2100 employees at a company in the region are between the ages of 40 and 65. Lawyers might argue that if the company hires people regardless of their ages, the distribution of ages would be the same as through they had hired people at random from the surrounding population. Check whether the condoms for using the one proportion z-test are met.
The conditions for using a one proportion z-test are likely met as the sample of 2100 employees is assumed to be randomly selected, independent, and satisfies the success-failure condition, allowing for comparison of the company's age distribution with the surrounding population.
To check whether the conditions for using a one proportion z-test are met, we need to ensure that the following conditions are satisfied:
1. **Random Sample**: The sample of 2100 employees should be selected randomly from the population.
2. **Independence**: The selection of one employee should not influence the selection of another. This condition is typically assumed to be met if the sample size is less than 10% of the population size.
3. **Success-Failure Condition**: The number of successes (employees aged between 40 and 65) and failures (employees not aged between 40 and 65) in the sample should each be at least 10.
Let's check each condition:
1. **Random Sample**: If the company's hiring process is unbiased and follows fair employment practices, then this condition is likely met.
2. **Independence**: With 2100 employees selected, it's reasonable to assume that this condition is met, especially if the population of potential employees is large.
3. **Success-Failure Condition**: We have:
- Number of successes: [tex]\(2100 \times 0.02 = 42\)[/tex]
- Number of failures: [tex]\(2100 - 42 = 2058\)[/tex]
Both 42 and 2058 are greater than 10, so the success-failure condition is met.
Since all three conditions are satisfied, the company's distribution of ages among its employees can be analyzed using a one proportion z-test to compare it with the population distribution.
The times a fire department takes to arrive at the scene of an emergency are normally distributed with a mean of 6 minutes and a standard deviation of 1 minute. For about what percent of emergencies does the fire department arrive at the scene in between 4 minutes and 8 minutes ?
Answer:
Step-by-step explanation:
Let x be the random variable representing the times a fire department takes to arrive at the scene of an emergency. Since the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 6 minutes
σ = 1 minute
the probability that fire department arrives at the scene in case of an emergency between 4 minutes and 8 minutes is expressed as
P(4 ≤ x ≤ 8)
For x = 4,
z = (4 - 6)/1 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.023
For x = 8
z = (8 - 6)/1 = 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.98
Therefore,
P(4 ≤ x ≤ 8) = 0.98 - 0.23 = 0.75
The percent of emergencies that the fire department arrive at the scene in between 4 minutes and 8 minutes is
0.75 × 100 = 75%
A cylinder is designing a new cylinder water bottle the volume of the bottle will be 299cm3 the height of the water bottle is 7.3cm what is the radius of the water bottle use 3.14 for pie
Answer: radius = 3.61 cm
Step-by-step explanation:
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
π is a constant whose value is 3.14
From the information given,
Volume = 299 cm³
Height = 7.3 cm
Therefore,
299 = 3.14 × r² × 7.3
299 = 22.922r²
r² = 299/22.922 = 13.044
Taking square root of the left hand side and the right hand side of the equation, it becomes
r = 3.61 cm
Evaluate 0.1m+8-12n0.1m+8−12n0, point, 1, m, plus, 8, minus, 12, n when m=30m=30m, equals, 30 and n=\dfrac14n= 4 1 n, equals, start fraction, 1, divided by, 4, end fraction
Answer:
8
Step-by-step explanation:
We are required to evaluate:
0.1m+8-12n
When [tex]m=30, n=\frac{1}{4}[/tex]
Substituting these values into the expression, we have:
[tex]0.1m+8-12n=0.1(30)+8-12(\frac{1}{4})\\=3+8-\frac{12}{4}\\=3+8-3\\=8[/tex]
After evaluating the expression the value is 8.
Evaluating the Expression
To evaluate the expression 0.1m + 8 - 12n when m = 30 and n = \frac{1}{4}, we need to follow these steps:
Substitute m and n into the expression:
0.1(30) + 8 - 12 [tex]\left(\frac{1}{4}\right)[/tex]
Calculate 0.1(30):
0.1 [tex]\times[/tex] 30 = 3
Calculate 12[tex]\left(\frac{1}{4}\right):[/tex]
12 [tex]\times \frac{1}{4}[/tex] = 3
Substitute these values back into the expression:
3 + 8 - 3
Simplify the expression:
3 + 8 = 11
11 - 3 = 8
Thus, the value of the expression is 8.
Researchers are investigating whether people who exercise with a training partner have a greater increase, on average, in targeted exercise intensity compared with people who exercise alone. Two methods of collecting data have been proposed.
Method I: Recruit volunteers who are willing to participate. Randomly assign each participant to exercise with a training partner or to exercise alone.
Method II: Select a random sample of people from all the people who exercise at a community fitness center. Ask each person in the sample whether they use a training partner, and use the response to create the two groups.
(a) For each method, the researchers will record the change in targeted exercise intensity for each person in the investigation. They will compare the mean change in intensity between those who exercise with a training partner and those who do not.
(i) Describe the population of generalization if method I is used. Explain your answer.
(ii) Describe the population of generalization if method II is used. Explain your answer.
(b) Suppose the investigation produces a result that is statistically significant using both methods. What can be concluded if method I is used that cannot be concluded if method II is used? Explain your answer.
Answer:
1 - If method I is used, population of generalization will include all those people who may have varying exercising habits or routines. They may or may not have a regular excersing habit. In his case sample is taken from a more diverse population
2 - Population of generalization will include people who will have similar excersing routines and habits if method II is used since sample is choosen from a specific population
Step-by-step explanation:
Past excercising habits may affect the change in intensity to a targeted excersise in different manner. So in method I a greater diversity is included and result of excersing with or without a trainer will account for greater number of variables than method II.
Method I involves randomized assignment and its generalization population is those willing to participate in such a study. Method II samples a fitness center population and cannot isolate causality.
Explanation:(i) Method I uses a randomized control trial, where volunteers are randomly assigned to exercise either with a partner or alone. The population of generalization is all people willing to participate in such a study, which likely skews towards those who are more interested in exercise and possibly more health-conscious.
(ii) Method II uses a random sample from a community fitness center, allowing the researchers to control less for participant choice as they directly ask each person about their workout habits. The population of generalization is all people who exercise at a community fitness center.
(b) If the results of the investigation are statistically significant using method I, we can conclude that exercising with a training partner causes a greater increase in targeted exercise intensity, due to the random assignment removing confounding variables. This conclusion can not be drawn using method II because it is observational and not experimental.
Learn more about Experimental Methods in Statistics here:https://brainly.com/question/34295952
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A certain shade of light blue is made byixing 1 1/2 quarts of blue paint with 5 quarts of white paint. How much white paint would you need to mix with 4 quarts of blue paint?
Answer:
We will need [tex]13\frac{1}{3}[/tex] quarts of white paint to mix with 4 quarts of blue paint to make the required shade of blue.
Step-by-step explanation:
A certain shade of blue is made by mixing [tex]1\frac{1}{2}[/tex] quarts of blue paint with 5 quarts of white paint. This means the ratio of quantity of blue paint to white paint is:
[tex]1\frac{1}{2}:5\\\\ \frac{3}{2}:5\\\\ 3:10[/tex]
If we want to prepare this certain shade then we have to maintain this ratio of blue paint to white paint. We have 4 quarts of blue paint and we need to find how many quarts of white paint we need. Let the amount of white paint needed be x quarts. So ratio of blue to white will be 4 : x
Since, this ratio must be equal to 3 : 10, we can set both ratios equal and find the value of x
[tex]3:10 = 4:x\\\\\frac{3}{10}=\frac{4}{x}\\\\ 3x=40\\\\ x=\frac{40}{3}\\\\ x=13\frac{1}{3}[/tex]
This mean we will need [tex]13\frac{1}{3}[/tex] quarts of white paint to mix with 4 quarts of blue paint to make the required shade of blue.
6/5
Step-by-step explanation:
If tan A = 4/5; what does CSC A =?
Round to nearest tenth.
Answer:
1.6
Step-by-step explanation:
[tex] \tan \: A = \frac{4}{5} \\ \\ \cot \: A = \frac{1}{ \tan \: A } = \frac{1}{ \frac{4}{5} } = \frac{5}{4} \\ \\ csc\: A = \sqrt{1 + {cot}^{2}\: A} \\ = \sqrt{1 + { \bigg( \frac{5}{4} \bigg)}^{2} } \\ = \sqrt{1 + \frac{25}{16} } \\ = \sqrt{\frac{16 + 25}{16} } \\ = \sqrt{\frac{41}{16}} \\ = \frac{ \sqrt{41} }{4} \\ = \frac{6.40312424}{4} \\ = 1.60078106 \\ \therefore \: csc \: A =1.6[/tex]
Help number 8 Please help
Answer: V = 97.08 or B.
Step-by-step explanation: Hope this helps.
Answer:
its answer is 30.9[tex]\pi inch^{3}[/tex]
Step-by-step explanation:
given
radius (r) = 3 inch
height (h) =10.3 inch
Now
Volume of cone
= 1/3 * [tex]\pi[/tex]* [tex]r^{2} *h[/tex]
= 0.33 * 3 * 3 * 10.3 [tex]\pi[/tex]
= 30. 9[tex]\pi[/tex] inch ^3