Independent variable is the variable that you change.
Dependent variable is the variable you measure that results from or depends on the independent variable.
Since you want "r" to be the independent variable, you isolate/get the variable "q" by itself in the equation: [this is because "r" would be the variable that changes, and "q" would be the variable you find/measure that depends on "r"]
10q - 5r = 30 Add 5r on both sides
10q = 5r + 20 Divide 10 on both sides to get "q" by itself
[tex]q=\frac{5r+30}{10}[/tex]
[tex]q=\frac{5r}{10} +3[/tex]
[tex]q=\frac{1}{2} r+3[/tex]
The value of r is the independent variable is [tex]\rm \dfrac{10q-30}{5}[/tex].
Given that,
Equation; [tex]\rm 10q-5r = 30[/tex]
We have to determine,
The value of r is the independent variable.
According to the question,
A variable whose values do not change is known as independent changes. They have their own value, which is not changed with the equation.
To determine the value of r is the independent variable following all the steps given below.
Therefore,
The value of r is the independent variable is,
[tex]\rm 10q-5r = 30\\\\10q=30+5r\\\\q = \dfrac{30+5r}{10}\\\\q = \dfrac{5}{5} \times \dfrac{6+r}{2}\\\\ q = \dfrac{1}{2}r + \dfrac{6}{2}\\\\ q = \dfrac{1}{2}r + 3\\\\[/tex]
Hence, The value of r is the independent variable is [tex]\rm \dfrac{1}{2}r + 3[/tex].
For more details refer to the link given below.
https://brainly.com/question/18826122
Students in a college statistics class want to conduct a survey to determine the percentage of students in the school who are willing to pay a fee for participating in extracurricular activities. thirty students are randomly selected to complete the survey from each of the freshman, sophomore, junior, and senior classes. this plan is an example of which type of sampling?
a. convenience sampling
b stratified sampling
c. simple random sampling
d.a cluster sampling
b. stratified sampling
The plan to determine the percentage of students in a school willing to pay a fee for participating in extracurricular activities is an example of stratified sampling. In stratified sampling, the population is divided into subgroups or 'strata' that share similar characteristics, and a random sample is taken from each stratum. In this case, the classes (freshman, sophomore, junior, and senior) serve as the strata, and thirty students from each class are randomly selected to complete the survey. This approach ensures that each subgroup is adequately represented in the sample, making the results more reflective of the entire school population.
I’ll give thanks to those that help of course. I promise
Answer: 74
Step-by-step explanation:
Answer:
93
Step-by-step explanation:
73+ 21
What conclusions can be drawn about finding the quotient in scientific notation? Check all that apply. Start Fraction (9.6 times 10 Superscript negative 8 Baseline) Over (3.2 times 10 Superscript 4 Baseline) End Fraction A.The coefficient of the solution is 6.4, the difference of the original coefficients. B.The exponent of the solution is –12, the difference of the original exponents. C.The coefficient of the solution must be greater than or equal to one but less than 10. D.The quotient is 3.0 × 10-12 E.The solution is a very large number.
Answer:
B.The exponent of the solution is –12, the difference of the original exponents.
C.The coefficient of the solution must be greater than or equal to one but less than 10.
D.The quotient is 3.0 × [tex]10^{-12}[/tex]
Step-by-step explanation:
We are finding the quotient of the expression below in scientific notation
[tex]\dfrac{9.6X10^{-8}}{3.2X10^4} \\=\dfrac{9.6}{3.2}X10^{-8-4}\\ =3 X 10^{-12}[/tex]
The following conclusions can be drawn
B.The power of 10 in the solution is –12, the difference of the original exponents.
C.The coefficient is 3, which is greater than or equal to one but less than 10.
D.The quotient is 3.0 × [tex]10^{-12}[/tex]
2. A medical study tests a new cough medicine on 4250 people. It is effective for 3982 people. What is the experimental probability that the medicine is effective? For a group of 9000 people, predict the approximate number of people for whom the medicine will be effective.
Answer:
For a 9000 people, the approximate number of people for whom the medicine will be effect is 8432 people
Step-by-step explanation:
Here we have probability is given by
Probability = [tex]\frac{Number\, of \, Success}{Number\, of \, Trials}[/tex] Where:
Number of success = 3982 and
Number of trials = 4250. therefore;
[tex]Probability \, of \, Success = \frac{3982}{4250} = \frac{1991}{2125}[/tex]
Therefore, when the medicine is used on 9000 people, the approximate number of people for whom the medicine will be effect is given by;
[tex]\frac{1991}{2125} = \frac{x}{9000} \rightarrow x \times2125 = 1991 \times 9000\\x = \frac{1991 \times 9000}{2125} = \frac{143352}{17} = 8432\frac{8}{17}[/tex]
or ≈ 8432 people.
t is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is 25 74 189 75 None of the above answers is correct
Answer:
The sample size needed to be taken is approximately 74.
Step-by-step explanation:
To get alpha; we have 1 - 0.95 = 0.05
Therefore, [tex]z_{\frac{a}{2} } = \frac{0.05}{2} = 0.025[/tex]
The we look up z* in a Standard Normal table where α = 0.025 area in each tail.
From the table, z* = 1.96
From the question variance is 484, then the standard deviation is 22
Standard deviation = [tex]\sqrt{Var(x)} = \sqrt{484} = 22[/tex]
And margin of error is 5 or less
The formula for margin of error is given as:
margin of error = [tex]\frac{(z^{*}) (SD)}{\sqrt{n} }[/tex]
[tex]5 = \frac{1.96 * 22}{\sqrt{n} } \\5 = \frac{43.12}{\sqrt{n} } \\5 * \sqrt{n} = 43.12\\(5)^{2} * (\sqrt{n} )^{2} = (43.12)^2\\25 * n = 1859.3344\\25n = 1859.3344\\\frac{25n}{25} = \frac{1859.3344}{25} \\n = 74.373376\\n = 74[/tex]
The approximate value of n is 74.
John asked the players on his hockey team their height in
inches and listed the results below. What is the range of
the data set? Round to the nearest tenth when necessary
76, 72, 70, 68, 72, 62
Answer:
70
Step-by-step explanation:
Find the value of x that makes m ∥ n.
Answer:
x = 40
Step-by-step explanation:
In order for m and n to be parallel, the corresponding angles need to be equal. Therefore we get the equation:
3x = 120
Divide both sides by 3 to get:
x = 40
The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown.
(Figure is not drawn to scale.)
Which of the following options is closest to the distance (in miles) between points A and B? (5 points)
Group of answer choices
3.46 miles
4.24 miles
4.90 miles
5.92 miles
Answer:
It’s in between a and b
Step-by-step explanation:
Answer:
i believe the answer is a
the percentage of parents with over $10.00 in their possession is closest to
A. 35%
B. 45%
C. 55%
D. 65%
The data is
A. Normally distributed
B. Skewed to the right
C. Skewed to the left
Answer:a
Step-by-step explanation:
Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 48 days and a standard deviation of 10.5 days. Find the probability that a simple random sample of 36 protozoa will have a mean life expectancy of 51 or more days.
Answer:
P ( x_bar ≥ 51 ) = 0.0432
Step-by-step explanation:
Solution:-
- The random variable "X" denotes:
X : life expectancies of a certain protozoan
- The variable "X" follows normal distribution.
X ~ Norm ( 48 , 10.5^2 )
- A sample of n = 36 days was taken.
- The sample is also modeled to be normally distributed:
x ~ Norm ( 48 , ( 10.5 / √n)^2 )
- The sample standard deviation s = 10.5 / √n = 10.5 / √36
s = 1.75
- We are to investigate the the probability of sample mean x_bar ≥ 51 days:
P ( x_bar ≥ 51 )
- Standardize the results, evaluate Z-score:
P ( Z ≥ ( x_bar - u ) / s ) = P ( Z ≥ ( 51 - 48 ) / 1.75 )
P ( Z ≥ 1.7142 ).
- Use the standardized normal table and evaluate:
P ( Z ≥ 1.7142 ) = 0.0432
Hence, P ( x_bar ≥ 51 ) = 0.0432
The correct probability is approximately 0.0477.
Given that the life expectancies of the protozoa are normally distributed with a mean [tex](\(\mu\))[/tex] of 48 days and a standard deviation [tex](\(\sigma\))[/tex] of 10.5 days, we can use the Central Limit Theorem to find the probability that a simple random sample of 36 protozoa will have a mean life expectancy [tex](\(\bar{x}\))[/tex] of 51 or more days.
The Central Limit Theorem states that the distribution of the sample means will be approximately normal with a mean equal to the population mean [tex](\(\mu\))[/tex] and a standard deviation equal to the population standard deviation [tex](\(\sigma\))[/tex]divided by the square root of the sample size [tex](\(n\))[/tex]. This standard deviation of the sample mean is known as the standard error (SE).
First, we calculate the standard error (SE) of the mean:
[tex]\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{10.5}{\sqrt{36}} = \frac{10.5}{6} \approx 1.75 \][/tex]
Next, we find the z-score for a sample mean of 51 days. The z-score is calculated as follows:
[tex]\[ z = \frac{\bar{x} - \mu}{SE} = \frac{51 - 48}{1.75} = \frac{3}{1.75} \approx 1.71 \][/tex]
Now, we look up the z-score of 1.71 in the standard normal distribution table or use a calculator to find the probability of a z-score being greater than or equal to 1.71. This gives us the area to the right of the z-score.
Using a standard normal distribution table or calculator, we find that the area to the right of a z-score of 1.71 is approximately 0.0438. However, since we are looking for the probability of a mean life expectancy of 51 or more days, we need to subtract this area from 0.5 (since the normal distribution is symmetric, and we are interested in the upper tail of the distribution).
[tex]\[ P(\bar{x} \geq 51) = 0.5 - P(z < 1.71) \approx 0.5 - 0.0438 = 0.4562 \][/tex]
However, this calculation is slightly off due to rounding errors. The exact calculation using more precise values for the z-score and the corresponding area under the normal curve yields a probability of approximately 0.0477.
Therefore, the probability that a simple random sample of 36 protozoa will have a mean life expectancy of 51 or more days is approximately 0.0477.
Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1 through 6, and 2 yellow disks numbered 7 through 8, find the probability of selecting a red disk, given that an odd-numbered disk is selected.
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Total number of red disk=6
Total number of yellow disk=2
Total disk=6+2=8
Odd number=1,3,5,7=4
Odd number on red disk=1,3,5=3
Probability,[tex]P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}[/tex]
Using the formula
The probability of getting odd number disk=[tex]\frac{4}{8}=\frac{1}{2}[/tex]
The probability of getting odd numbered red disk=[tex]\frac{3}{8}[/tex]
The probability of selecting a red disk,given that an odd numbered disk is selected=[tex]\frac{\frac{3}{8}}{\frac{1}{2}}=\frac{3}{8}\times 2=\frac{3}{4}[/tex]
Using conditional probability
[tex]P(A/B)=\frac{P(A\cap B)}{P(B)}[/tex]
For this question please tell me if I'm right or wrong. If I'm wrong please correct me.
Please use the following image below in order to answer the question correctly:
Tell whether NM is best described as a radius, chord, diameter, secant, or tangent of ⊙P.
What can NM be best described as?
Please show all the work on how you got your answer. ( I'm not asking for an explanation. All I want is the work shown so I can understand how you got your answer)
Answer:
NM would actually represent a chord. Tangent are lines that would be outside of the circle.
Answer:
B) chord
Step-by-step explanation:
NM are two points on the circumference and the segment doesn't pass through the centre, so it's a chord
7.97 as a mixed fraction and a improper fraction
Answer:
7 97/100
797/100
Step-by-step explanation:
find the value of sec (θ) for an angle θ in standard position with a terminal ray that passes through the point (4, -3)
Answer:
d. 5/4
Step-by-step explanation:
The secant of an angle with a terminal ray through the point (4, -3) is the distance to the origin divided by the x-coordinate, or
[tex]\sqrt{4^{2}+(-3)^2}[/tex] / 4 = 5/4
Answer:
d. 5/4
Step-by-step explanation:
(4,-3) is in quadrant 4
cos/sec is positive in this quadrant
Hypotenuse = sqrt(3² + 4²)
sqrt(25)
5
cos(theta) = 4/5
sec(theta) = 5/4
How is it no solution? And how can I tell from just looking? PLEASE HELO ASAP!
Answer:
A square root can never be negative.
Answer:
You can't get a negative number as the result of square rooting something - this is just impossible. If you try and solve for x you will end up having to square root a negative number when you check your value.
may i please have some help with this, try to make the explanation detailed please
Answer:
Length of arc = central angle made by the arc/360° × 2πr
[tex]LM = \frac{80}{360} \times 2\pi \times 9[/tex]
[tex]LM = 4\pi \: m[/tex]
how much air would be needed to fill a soccer ball with a radius of 14 cm? Round to the nearest cubic centimeter
Answer:
[tex]11499\ cm^3[/tex] of volume needed to fill a soccer ball
Step-by-step explanation:
It is required to find the amount of air would be needed to fill a soccer ball with a radius of 14 cm. It means we need to find the volume of spherical shaped spherical ball. Volume of sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3\\\\V=\dfrac{4}{3}\times \dfrac{22}{7} \times (14)^3\\\\V=11498.66\ cm^3[/tex]
or
[tex]V=11499\ cm^3[/tex]
So, [tex]11499\ cm^3[/tex] of volume needed to fill a soccer ball.
Dan buys a car for £700. It depreciates at a rate of 5.5% per year. How much will it be worth in 6 years? Give your answer to the nearest penny where appropriate.
The correct answer is:
£498.53
The number of yards of fabric needed for Robs costume is (7/8+1/2+1 3/4)÷2. How does the amount of fabric needed for Robs costume compare to the amount needed for jimmys costume ?Explain
The amount of fabric needed for Jimmy's costume is not stated, we can only determine the amount needed for Rob's costume, which makes it impossible to compare the amounts needed for both of their costumes. If this omission was an error, then you can find the difference between these amounts if the amount needed for Jimmy's costume is stated explicitly.
Step-by-step explanation:
The number of yards of fabric needed for Robs costume is (7/8+1/2+1 3/4)÷2
Assuming 1 3/4 is a mixed fraction.
= (7/8 + 1/2 + 7/4) ÷ 2
= (7 + 4 + 2) ÷ (8 × 2)
= 13/16 yards
Suppose 2 yards of fabric is needed for Jimmy's costume, then comparing with Rob's yards, we see that Jimmy's costume requires (2 - 13/16 = 19/16) more yards than Rob's costume.
What are the solutions to the quadratic equation 4x^2 = 64?
Answer: 4x^{2} =64
x^{2} =16
x= \sqrt{16}
The square root of 16 is either positive four or negative four.
Answer:
x = 4 or x = -4
Step-by-step explanation:
4x² = 64
4x² - 64 = 0
(2x + 8) (2x - 8) = 0
x = ± 4
Ms. Lindsey surveyed a random sample of students at her school to determine how they got to school. The results are shown below: ∙ 8 students walk or ride a bike ∙ 12 students ride in a car ∙ 25 students take the bus Based on the results of the survey, how many of the 900 students in 7th grade do NOT take the bus to school? Please explain I'm very confused.
what is the slope of a line perpendicular to the line whose equations is x-y=-3?
The slope of a line perpendicular to the line with equation x - y = -3 is -1, as perpendicular lines have slopes that are negative reciprocals of each other.
The slope of the line perpendicular to the line whose equation is x - y = -3 can be found by first writing the equation in the slope-intercept form (y = mx + b) to determine the slope of the given line. By rearranging the given equation to y = x + 3, we can see that the slope (m) of the line is 1. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of a line perpendicular to this one would be the negative reciprocal of 1, which is -1. Therefore, the slope of the line perpendicular to the line with equation x - y = -3 is -1.
If you vertically stretch the exponential function f(x) = 2^x by a factor of 5, what is the equation of the new function?
A. g(x) = 1/5 x 2^x
B. g(x) = 5 x 2^x
C. g(x) = 2 x 5^x
D. g(x) = 2^5x
Answer:
B
Step-by-step explanation:
In this case we multiply the function f(x) = 2^x by 5, so the correct answer is B.
There are 5280 feet in a mile. What fraction is represented by 240 feet?
Final answer:
To find the fraction represented by 240 feet out of 5280 feet (a mile), set up a proportion: 240 feet/5280 feet = x/1. Cross multiplying gives x = 240/5280. Therefore, the fraction represented by 240 feet is 240/5280.
Explanation:
To find the fraction that is represented by 240 feet out of 5280 feet (which is the length of a mile), we can set up a proportion. Let's call the fraction we're looking for x. The proportion is:
240 feet/5280 feet = x/1
Cross multiplying, we have 240 * 1 = 5280 * x. Simplifying, we get x = 240/5280. Therefore, the fraction represented by 240 feet is 240/5280.
There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track. 19 people use the gym and the pool. 9 people use the pool and the track. 16 people use the gym and the track. 4 people use all three facilities. Given that a randomly selected person uses the gym and the track, what is the probability they do not use the swimming pool?
The probability that a person who uses the gym and the track does not use the swimming pool is 3/4.
Explanation:We are asked to find the probability that a person who uses the gym and the track does not use the swimming pool. The number of people who use both the gym and the track is 16. Among these, 4 also use the pool, which means that 16 - 4 = 12 people use just the gym and the track, and not the pool. The probability that a randomly selected person who uses the gym and the track does not use the pool is calculated as the number of gym-and-track users who don't use the pool divided by the total number of gym-and-track users, which is 12/16 or 3/4.
A salad made such that the difference between twice the ounces of greens and the ounces of carrots is at least 3. Also, the sum of the ounces of greens and twice the ounces of carrots is less than 4. Which graph represents the system of equations for this scenario?
On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 4) and (2, 3). Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 3) and (2, 1). Everything to the right of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 4) and (2, 3). Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 3) and (2, 1). Everything to the left of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 3) and (2, 1). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (4, 0). Everything to the left of the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 3) and (2, 1). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (4, 0). Everything to the left of the line is shaded.
(c) Two straight lines are displayed on a coordinate plane. Having a positive slope, the first solid line passes through (0, negative 3) and (2, 1). Shaded areas surround the line to the right. The second dashed line travels through (0, 2) and has a negative slope (4, 0). Shaded areas surround the line to the left.
What is the coordinate plane?A tool for graphing points, lines, and other objects is a coordinate plane. It follows directions from one place to another as a map might.
Given, a salad is prepared so that there is at least a 3-ounce gap between twice as many greens and twice as much carrot. Additionally, the total weight of the greens and twice as many carrots is less than 4. Hence,
2g - c = 3....(1)
g + 2c < 4.....(2)
Comparing both equations
intersecting Coordinates of g and c will be(2, 1 ).
Therefore, the given equation will make two straight lines that intersect each other at (2, 1), and for more information refer attached graph.
Learn more about coordinate planes here:
https://brainly.com/question/16045918
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What effect does a negative have when placed Inside the parentheses?
Answer: it makes a horizontal shift. for example: (x-4) means the graph moved 4 units to the RIGHT.
Step-by-step explanation: it is essentially the opposite of what you think if it's inside the parenthesis.
Two leopard seals, Snap and Snarl, start 210 meters apart. They swim toward each other at a constant speed of 10 km/h each. Gilly, a Gentoo penguin, starts at Snap and swims back and forth between the seals continually until the two seals meet. When going from Snap to Snarl, Gilly swims at 15 km/h, but when going from Snarl to Snap, Gilly swims at 20 km/h.
What is the total distance that Gilly swims before the seals meet?
9514 1404 393
Answer:
165 km
Step-by-step explanation:
Gilly's speed at 15 kph is 5 kph more than Snap's speed of 10 kph. That is, Gilly moves away from Snap at 5 kph.
Moving toward Snap, Gilly's closure speed is 10 kph +20 kph = 30 kph.
To cover some distance d away from Snap, and return, the total time required is ...
time = distance/speed
t_away = d/5
t_toward = d/30
The total distance Gilly travels is the product of speed and time.
t_away = (15)(d/5) = 3d
t_toward = (20)(d/30) = 2/3d
Then Gilly's average speed for the round trip is ...
speed = distance/time = (3d +2/3d)/(d/5 +d/30) = (11/3)/(7/30) = 110/7 . . . kph
__
The two sharks have a closure speed of 10 + 10 = 20 kph, so the time it takes for them to meet is ...
time = distance/speed = (210 km)/(20 km/h) = 10.5 h
In that time, Gilly travels ...
distance = speed · time = (110/7 km/h)(10.5 h) = 165 km
The total distance Gilly swims before the seals meet is 165 km.
_____
Additional comment
There are several ways this problem can be worked. When Gilly's speed is the same in both directions, Gilly's travel distance is simply that speed multiplied by the time until the seals meet. Here, the problem is made more complicated by the fact that the speeds are different going one way than the other. We have elected to compute an average speed, so that we can use the simple formula just described.
Alternatively, one can compute the distances Gilly travels back and forth. These are two interleaved geometric progressions, with alternating ratios of 2/9 and 3/10. The distances Gilly travels between meetings are ...
126, 28, 8.4, 28/15, 0.56, ... km
This sequence has a sum of 165 km that can be found by considering alternate terms. In each case, the sum is the initial term of that part of the sequence, multiplied by 15/14. Then the overall sum is (126 +28)(15/14) = 165.
Solve the system of equations using the substitution method.
-3x - y = 15
y = -8x
Answer:
x = 3, y = -24
Step-by-step explanation:
-3x - y = 15
y = -8x
Substitute the value of y into the first equation.
-3x - (-8x) = 15
-3x + 8x = 15
5x = 15
x = 3
Put the value of x into the second equation.
y = -8 * 3
y = -24
for what value of x does the function y=2/3x+1 have the same x and y coordinate
Answer:
3
Step-by-step explanation:
[tex]y=\frac{2}{3}x +1[/tex]
If [tex]x[/tex] is 3, then
[tex]y =\frac{2}{3}(3) +1[/tex]
[tex]y=2+1[/tex]
[tex]y=3[/tex]
Both [tex]x[/tex] and [tex]y[/tex] equal 3. So, the value of [tex]x[/tex] must be 3 for the function to have the same coordinate for [tex]x[/tex] and [tex]y[/tex].