If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.
What is hypothesis testing?
A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters through hypothesis testing.
Here,
We have to find the correct statement about hypothesis testing.
We concluded that If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.
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Answer:
In this case, B is true.
Whether to use a one-sided or a two-sided test is typically decided BEFORE the data are gathered, not after.
Be careful while reading the options on the quiz, because depending on the question you get, the options may be worded slightly differently. Because of the wording, the answer may be different as well (on the FLVS quiz, I got different answer choices for this question). Be careful and read cautiously!
Have a great day.
A standardized exam's scores are normally distributed. In a recent year, the mean test score was1479 and the standard deviation was 317 The test scores of four students selected at random are 1910, 1220, 2160, and 1370. Find the z-scores that correspond to each value and determine whether any of the values are unusual
For the first student with a score of 1910, the z-score is: 1.34 ,For the second student with a score of 1220, the z-score is: 0.81 , For the third student with a score of 2160, the z-score is:2.14 , For the fourth student with a score of 1370, the z-score is: -0.34 and , out of the four students, only the one with the test score of 2160 is considered an unusual score based on the z-score.
To find the z-score for a given data point, we use the formula:
z = (x - μ) / σ
where x is the data point, μ is the mean, and σ is the standard deviation.
For the first student with a score of 1910, the z-score is:
z = (1910 - 1479) / 317 = 1.34
For the second student with a score of 1220, the z-score is:
z = (1220 - 1479) / 317 = -0.81
For the third student with a score of 2160, the z-score is:
z = (2160 - 1479) / 317 = 2.14
For the fourth student with a score of 1370, the z-score is:
z = (1370 - 1479) / 317 = -0.34
Now, we need to determine whether any of these z-scores are unusual. One way to do this is to use the rule of thumb for normal distributions, which states that about 68% of the data falls within one standard deviation of the mean, about 95% of the data falls within two standard deviations of the mean, and about 99.7% of the data falls within three standard deviations of the mean.
Using this rule, we can say that a z-score greater than 2 or less than -2 is unusual, since it corresponds to data that falls more than two standard deviations from the mean.
From the z-scores we calculated, only the third student with a z-score of 2.14 falls outside of this range and can be considered an unusual score.
Therefore, out of the four students, only the one with the test score of 2160 is considered an unusual score based on the z-score.
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Identify the equation for a circle with its center at (-10, 4) and a radius length of 2.
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-10}{h}~~,~~\underset{4}{k})}\qquad \stackrel{radius}{\underset{2}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-10) ~~ )^2 ~~ + ~~ ( ~~ y-4 ~~ )^2~~ = ~~2^2\implies (x+10)^2+(y-4)^2=4[/tex]
each year, francesca earns a salary that is 2 % 2%2, percent higher than her previous year's salary. in her first 5 55 years at this job, she earned a total of $ 187 , 345 $187,345dollar sign, 187, comma, 345. what was francesca's salary in her 1 st 1 st 1, start superscript, start text, s, t, end text, end superscript year at this job? round your final answer to the nearest thousand.
Francesca salary in the first year is $169684.14
Let us assume that P be the first salary of Francesca.
The salary increases by 2% every year.
Let A be the amount she earns after n years at a rate of r.
Using the formula for the compound interest is:
A = P (1 + r)ⁿ
Here, A = $187345
n = 5 years
R = 2%
So, r = 0.02
We need to find the value of P
substituting these values in above equation we get,
187345 = P (1.02)⁵
187345 = 1.10408 × P
P = $169684.14
Therefore,her salary in the first year is $169684.14
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The complete question is:
Each year, Francesca earns a salary that is 2 percent higher than her previous year's salary. In her first 5 years at this job, she earned a total of $187,345. What was Francesca's salary in her 1st year at this job?
the mean difference equals 1.2, the standard deviation of the difference equals 1.5, and n equals 25. what does t equal?
The value of t according to the given conditions equals 4.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
The t-value can be calculated by dividing the mean difference by the standard error of the mean difference.
The formula for calculating t is:
t = (mean difference) / (standard deviation / sqrt(n))
Given that the mean difference equals 1.2, the standard deviation of the difference equals 1.5, and n equals 25.
Therefore the t-value can be calculated as follows:
t = (1.2) / (1.5 / sqrt(25)) = (1.2) / (1.5 / 5)= (1.2) / (0.3)= 4
Therefore, t equals 4.
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What is the volume of a hemisphere with a radius of 7.1 in, rounded to the nearest tenth of a cubic inch?
A hemisphere with a 7.1-inch radius has a volume of 2478.8 cubic inches.
To calculate a hemisphere's volume, use the following formula:
V = (2/3) × π × r³
where r is the radius of the hemisphere, and π (pi) is a mathematical constant approximately equal to 3.14159.
Substituting the given value of the radius, r = 7.1 inches, into the formula, we get:
V = (2/3) × π × 7.1³
V ≈ 2.094 × π × 7.1³ (rounded to three decimal places)
V ≈ 2.094 × 3.141 × 357.911
V ≈ 2478.796 cubic inches
Therefore, the volume of the hemisphere with a radius of 7.1 inches is approximately 2478.796 cubic inches. Rounded to the nearest tenth of a cubic inch, the volume is 2478.8 cubic inches.
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Find the thirty-fourth term of the sequence defined by a = 146, a₁ = an-1+ 36.
The thirty-fourth term of the sequence is 1282.
How to find the nth term of any sequence?First, we can find the second term of the ap series as follows:
a₂ = a₁ + 36 = a₄₃ + 36
Similarly, we can find the third term of the sequence as:
a₃ = a₂ + 36 = a₄₄ + 36
Continuing this pattern, we can find the thirty-fourth term of the sequence as:
a₃₄ = a₃₃ + 36 = (a₃₂ + 36) + 36 = ((a₃₁ + 36) + 36) + 36 = so on = a + 33(36)
Substituting the given value of a = 146, we get:
a₃₄ = 146 + 33(36) = 1282
a₃₄ = 1282
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A stop sign casts a shadow as shown in the
figure. How tall is the light pole to the nearest
tenth of a foot?
The answer of the given question based on the right angle triangle is , the height of the light pole to the nearest tenth of a foot is 9.3 feet.
What is Right angle triangle?A right-angled triangle, also known as a right triangle, is a triangle that has one angle equal to 90 degrees. The side opposite right angle is called hypotenuse, and other two sides is called legs. The leg opposite to a particular acute angle is known as the opposite side, and the leg adjacent to it is known as the adjacent side.
The Pythagorean theorem is a fundamental theorem that applies to all right-angled triangles. It states that square of hypotenuse of right-angled triangle is equal to sum of squares of its two legs
To determine the height of the light pole, we can use similar triangles.
Let's call height of light pole be "x". Then we have:
(height of stop sign) / (length of stop sign's shadow) = (height of light pole)/(length of light pole's shadow)
Substituting the given values, we have:
8/12 = x/14
Simplifying this equation, we get:
x = (8/12) * 14 = 9.33 feet
Therefore, the height of the light pole to the nearest tenth of a foot is 9.3 feet.
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Ian scores 44 out of 60 marks in a Maths test
What is his score as a percentage to 1 decimal place?
Ian's score as a percentage is 73.3%, rounded to one decimal place. This means that he obtained 73.3% of the total marks possible in the test.
The percentages are a useful way to express scores or quantities relative to the whole. In this case, Ian's percentage score indicates how well he performed on the test compared to the maximum score possible.
To calculate Ian's score as a percentage, we can use the formula:
percentage score = (marks obtained / total marks) x 100
In this case, Ian scored 44 out of a total of 60 marks. Plugging these values into the formula, we get:
percentage score = (44 / 60) x 100 = 73.3%
Therefore, Ian's score as a percentage is 73.3%, rounded to one decimal place. This means that he obtained 73.3% of the total marks possible in the test.
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help!!!!
the possible answers are below:
a: x=-1/4, y=-1/2
b: x=-1/2, y= -1/4
c: x=1/2, y=1/4
d: x= 1/4, y= 1/2
Answer: Based on the graph, I believe that the answer is a. x = -1/4, y = -1/2
Step-by-step explanation:
if a person 12 ft above water is pulling a rope 6 ft per minture how fast is the boat moving when 16 ft from the pier
If person is standing at the end of a pier 12 ft above the water, then the velocity of the boat when it is 16 ft from the pier is 7.5 ft/min.
The distance between the person and the water (y) = 12 ft,
The distance between the boat and the pier is (x) = 16 ft,
So, p = √(12² + 16²) = 20 ft,
From the triangle given below,
⇒ x² + y² = p²,
taking "derivative" with respect to "x",
We get,
⇒ 2x(dx/dt) + 2y(dy/dt) = 2p(dp/dt);
⇒ dy/dt = 0 ..because height is constant,
The water is pulling on a rope at speed of (dp/dt) = 6 ft/min,
⇒ 2x(dx/dt) = 2p(dp/dt),
⇒ 2×16×(dx/dt) = 2×20×6,
⇒ dx/dt = 7.5 ft/min.
Therefore, the velocity of the boat is 7.5ft/min.
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The given question is incomplete, the complete question is
A person is standing at the end of a pier 12 ft above the water and is pulling on a rope attached to a rowboat at the waterline at a rate of 6 ft per minute. What is the velocity of the boat when it is 16 ft from the pier?
What are the solutions of the equation 3x² – 5x + 2 = 0? U C D 1 and 2 1 and Homb -1 and -2 -1 and -2
Answer:
1and 2/3
Step-by-step explanation:
using the factorization method
the product of the equation is positive 6(3×2)
then we find the factors of 6 which give us the product 6 and the sum of-5
the factors are-3 and -2
we then substitute negative 5 with these factors
it then be 3x^2-3x-2x+2=0
then we group factorise
we will have 3x(x-1)-2(x-1)=0
we find the common factors of the 2 groups
we will then have (x-1)(3x-2)=0
then we equate the both brackets to 0
(x-1)=0 and(3x-2)=0
for the first bracket add 1 both sidesand the second add 2 both sides and divide by 3
Which are real zeroes of this function?
x3 + 2x2 – 9x – 18
given 20% chance that any given person walks in the door is wearing N95 mask what is the probability that the first person walk in wearing N95 is the third person
The probability that the first person who walks in wearing an N95 mask is the third person is 0.128 or 12.8%. The probability that the first person who walks in wearing an N95 mask is the third person can be found using the geometric probability distribution formula.
The formula for the probability of the first success occurring on the kth trial is:
P(k) = (1 - p)^(k-1) * p
Where p is the probability of success (in this case, 20% or 0.2), and k is the number of trials.
In this case, we want to find the probability that the third person who walks in is wearing an N95 mask, so k = 3.
Substituting the values, we get:
P(3) = (1 - 0.2)^(3-1) * 0.2
P(3) = 0.64 * 0.2
P(3) = 0.128
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If three coins are flipped, what is the probability of two heads and a tail coming up in any
order? Justify your answer by constructing a sample space using an organized list or a tree
diagram (or both).
The probability of getting two heads and one tail in any order is 3/8.
What is probability ?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a coin and it landing heads up is 0.5, because there are two equally likely outcomes (heads or tails) and one of them is heads.
Probabilities can also be expressed as percentages or fractions. For instance, a probability of 0.25 can be expressed as a percentage of 25%, or as a fraction of 1/4.
According to the question:
The sample space for flipping three coins is:
HHH
HHT
HTH
THH
HTT
THT
TTH
TTT
where H represents heads and T represents tails.
Out of these eight outcomes, there are three outcomes in which two heads and one tail come up in any order: HHT, HTH, and THH. Therefore, the probability of getting two heads and one tail in any order is 3/8, or 0.375, which can also be written as a fraction.
To see why this is the case, you can also use a tree diagram to represent the sample space:
H T
/ \ / \
H T H T
/ \ / \ / \ / \
H T H T H T H T
Each branch represents the outcome of one coin flip, and the branches lead to the possible outcomes of flipping three coins. The outcomes with two heads and one tail are HHT, HTH, and THH, which occur in three out of the eight possible outcomes, as previously stated. Therefore, the probability of getting two heads and one tail in any order is 3/8.
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point P has coordinate (-9,10) what will the coordinates of P be after translation 1 up and 3left ?
How do you simplify 16/24
Answer:
2/3
Step-by-step explanation:
1) find the gcf of 16 and 24.
Method 1: By Listing Factors
List the factors of each number.
Factors of 16 : 1, 2, 4, 8, 16
Factors of 24 : 1, 2, 3, 4, 6, 8, 12, 24
Find the largest number that is shared by all rows above. This is the GCF.
GCF = 8
Method 2: By Prime Factors
List the prime factors of each number.
Prime Factors of 16 : 2, 2, 2, 2
Prime Factors of 24 : 2, 2, 2, 3
Find the intersection of these primes.
2,2,2
Multiply these numbers: 2x2x2=8. this is the gcf.
gcf = 8
2) Divide both the numerator and the denominator by the GCF.
16/8 / 24/8
3)simplify
2/3
The number of home runs a baseball player earned each season in his career are listed. 12, 14, 20, 21, 25, 29, 30, 30, 31, 32, 32, 39, 46 Which of the following box plots best represents the data given?
option (C) is the box plot that best represents the given data set.
Based on the given data set, the box plot that best represents the data is (C). Here are the reasons:
The median of the data set is 30, and this is represented by the line inside the box in all four options.
The box in option (C) ranges from 22.5 to 33.5, which includes the interquartile range (IQR) of the data set, which is from 16 to 37. This means that 50% of the data falls within this range, and the box in option (C) represents this well.
The whiskers in option (C) extend to the minimum and maximum values in the data set, which are 9 and 39 respectively. This means that none of the data points fall outside the whiskers.
The range of the number line in option (C) (7 to 46) and the tick marks (every one unit) also match the range and increments of the given data set.
Therefore, option (C) is the box plot that best represents the given data set.
Here is the visual representation of option (C):
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PLEASE ANSWER I HAVE 10 MINS
What is the mean of this data set?
A set of data showing the lengths of string in inches. The data includes the following values: 6, 5, 8, 4, 9, 7, 5, 7, 4, 8, 7, 6.
5
five and three fourths
6
six and four-twelfths
(Mean means the average value in a data set; found by adding all numbers in the set and dividing by the number of values in the set)
A set of information displaying string lengths in inches. The values in the data are as follows: 6, 5, 8, 4, 9, 7, 5, 7, 4, 8, 7, 6. This data set's mean is 6.
To find the mean of the data set, we need to add up all the values and then divide by the total number of values.
Adding up all the values:
[tex]6 + 5 + 8 + 4 + 9 + 7 + 5 + 7 + 4 + 8 + 7 + 6 = 76[/tex]
There are 12 values in the data set, so we divide the sum by 12:
76/12 = 6.33 (rounded to two decimal places)
Therefore, the mean of the data set is 6.33.
Therefore the correct answer is thus 6.
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the objective of statistical process control (spc) is to question 38 options: 1) determine whether a batch of raw materials should be accepted or rejected 2) determine whether a batch of finished goods should be accepted or rejected 3) detect assignable cause variations versus normal random variations in the process 4) identify variable versus attribute measures
From the following option given, the correct option is option (3) - detect assignable cause variations versus normal random variations in the process.
The objective of statistical process control (SPC) is to monitor and control a process to ensure that it operates within its specifications and meets the desired quality level. One of the main goals of SPC is to distinguish between normal random variation in the process and variation that is caused by assignable or special causes.
By identifying and eliminating the assignable causes of variation, the process can be improved and the quality of the output can be maintained or improved over time. Therefore, the primary objective of SPC is to detect assignable cause variations versus normal random variations in the process.
Options 1, 2, and 4 are related to quality control and monitoring, but they do not capture the essence of what SPC is trying to achieve. SPC is focused on monitoring and improving the process, rather than simply accepting or rejecting batches of raw materials or finished goods or identifying variable versus attribute measures.
Therefore, the correct option is '3' - detect assignable cause variations versus normal random variations in the process.
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Help me please asappppp
Answer:
To fine mean (average) you add up all the numbers and divide it by the amount of numbers. there are 8 scores
Step-by-step explanation:
55+60+65+70+75+80+85+90
=580
580/8=72.5
the mean is 72.5
There are 16 tablespoons in one cup. Which table correctly relates the number of cups to the number of tablespoons?
A 2-column table with 4 rows. Column 1 is labeled cups with entries 1, 2, 4, 8. Column 2 is labeled tablespoons with entries 16, 32, 64, 128.
A 2-column table with 4 rows. Column 1 is labeled cups with entries 16, 32, 64, 128. Column 2 is labeled tablespoons with entries 1, 2, 4, 8.
A 2-column table with 4 rows. Column 1 is labeled cups with entries 32, 48, 80, 144. Column 2 is labeled tablespoons with entries 16, 32, 64, 128.
A 2-column table with 4 rows. Column 1 is labeled cups with entries 16, 32, 64, 128. Column 2 is labeled tablespoons with entries 32, 48, 80, 144.
The correct table is:
A 2-column table with 4 rows. Column 1 is labeled cups with entries 1, 2, 4, 8. Column 2 is labeled tablespoons with entries 16, 32, 64, 128 which is option first.
EquationsThis is because we know that there are 16 tablespoons in one cup. So, if we multiply the number of cups by 16, we get the corresponding number of tablespoons forming a geometric sequence. For example, 2 cups is equal to 2 x 16 = 32 tablespoons. This relationship is correctly shown in the first table where each entry in the second column is obtained by multiplying the corresponding entry in the first column by 16.
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The correct table that relates the number of cups to the number of tablespoons is:
A 2-column table with 4 rows.
- Column 1 is labeled cups with entries 1, 2, 4, 8.
- Column 2 is labeled tablespoons with entries 16, 32, 64, 128.
In this table, the first row tells us that there is 1 cup which is equivalent to 16 tablespoons. The second row shows that 2 cups is equal to 32 tablespoons. The third row indicates that 4 cups is equal to 64 tablespoons. And finally, the fourth row states that 8 cups is equal to 128 tablespoons.
This table follows the relationship where for every 1 cup, there are 16 tablespoons. So, to find the number of tablespoons for a given number of cups, you can use this table as a reference.
For example, if you have 3 cups, you can find the number of tablespoons by looking at the table. Since there is no row for 3 cups in the given table, you can approximate it by knowing that 2 cups is equal to 32 tablespoons, and 4 cups is equal to 64 tablespoons. Therefore, 3 cups would be somewhere between 32 and 64 tablespoons.
EXPONENTS AND SCIENTIFIC NOTATION Name:
Date:
Pd:
MAZE #1 Instructions: Simplify each expression using properties of exponents to make it correctly through
the maze. Shade or color your path as you go 8th grade math
Each of the expressions has been simplified by using properties of exponents as shown below.
What is an exponent?In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:
(1.25 × 10⁷) + 63,000,000 = (1.25 × 10⁷) + (6.3 × 10⁷) = (1.25 + 6.3) × 10⁷ = 7.55 × 10⁷
12,000 + 7 × 10⁴ = 1.2 × 10⁴ + 7 × 10⁴ = (1.2 + 7) × 10⁴ = 8.2 × 10⁴
5.88 × 10⁵ - 3.44 × 10⁵ = (5.88 - 3.44) × 10⁵ = 2.44 × 10⁵
6 × 10⁸ ÷ 120 = 6 × 10⁸ ÷ 1.2 × 10² = (6 ÷ 1.2) × 10⁸⁻² = 5 × 10⁶
9 × 10¹² ÷ 4.5 × 10⁴ = (9 ÷ 4.5) × 10¹²⁻⁴ = 2 × 10⁸
1.3 × 10³ · 2,200 = 1.3 × 10³ × 2.2 × 10³ = (1.3 × 2.2) × 10³⁺³ = 2.86 × 10⁶
(6.3 × 10⁴) + 1.3 × 10⁴ = (6.3 + 1.3) × 10⁴ = 7.6 × 10⁴
3,400 · 2 × 10⁴ = 3.4 × 10³ × 2 × 10⁴ = (3.4 × 2) × 10³⁺⁴ = 6.8 × 10⁷
9.78 × 10⁵ - 732,000 = (9.78 - 7.32) × 10⁵ = 2.46 × 10⁵
3.5 × 10² · 2 × 10⁴ = (3.5 × 2) × 10²⁺⁴ = 7 × 10⁶
1.1 × 10⁸ ÷ 22,000 = 1.1 × 10⁸ ÷ 2.2 × 10⁴ = (1.1 ÷ 2.2) × 10⁸⁻⁴ = 0.5 × 10⁴ = 5 × 10³.
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Which function is represented by the graph below?
24
3+
101
O f(x) = e.x O f(x) = log x ○ f(x) = e) Of(x) = lnx
The graph below is a graph of a function in the form of f(x) = eˣ,
where ‘e’ is the mathematical constant known as Euler's number and is approximately equal to 2.718.
What is a exponential function?An exponential function has an output that increases rapidly with increasing inputs.
This function is an exponential function, which means that the output increases at an exponential rate as the input increases.
The graph shows that the output, which is represented by the y-axis, increases rapidly as the input, which is represented by the x-axis, increases.
This is a characteristic of an exponential function, which is why this graph is a representation of the function f(x) = eˣ.
The other three functions, f(x) = e.x, f(x) = log x and f(x) = ln x, do not represent the graph as they are not exponential functions.
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First, rewrite 19/21 and 8/9 so that they have a common denominator.
we can simply do that by multiplying each by the other's denominator.
[tex]\cfrac{19}{21}\hspace{9em}\cfrac{8}{9} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{19}{21}\cdot \cfrac{9}{9}\implies \boxed{\cfrac{171}{189}}\hspace{9em}\cfrac{8}{9}\cdot \cfrac{21}{21}\implies \boxed{\cfrac{168}{189}}[/tex]
3 extra squares can be shaded on this grid so that the resulting pattern has 4 lines of symmetry and rotational symmetry of order 4. Which 3 squares should be shaded?
The three extra squares that should be shaded to have a pattern with 4 lines of symmetry and a rotational symmetry of order 4 are E, H, N.
What requirements should be met?It is required for the new shape to have four lines of symmetry, which means that if the new shape is divided we can obtain four identical lines; moreover, it should have a rotational symmetry of order 4, which means that if we rotate the shape it will coincide with the original shape four times. Based on this, the squares that should be shaded are E, H, N.
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Can someone help Asap
Step-by-step explanation:
I answered this on the other question
The center is (1,-4)
The new center is
(-4,-6)
The equation of the center is
[tex](x + 4) {}^{2} + (y + 6) {}^{2} = 16[/tex]
the equation
-8x-y=3
8x+y=-3
have the same/different what slopes and the same/different what y-intercepts?
Step-by-step explanation:
Arrange each of the equations into y = mx+ b to compare....m is the slope and b is the y -axis intercept
- 8x - y = 3 ======> y = -8x -3
8x + y = - 3 ======> y = - 8x -3
These are equations of the SAME LINE with slope = -8 intercept = -3
Answer:
The equations have the same slopes and the same y-intercepts.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Rearrange both equations so that they are in slope-intercept form.
[tex]\underline{\sf Equation\;1}\\\\\begin{aligned}-8x-y&=3\\-8x-y+8x&=8x+3\\-y&=8x+3\\y&=-8x-3\end{aligned}[/tex]
[tex]\underline{\sf Equation\;2}\\\\\begin{aligned}8x+y&=-3\\8x+y-8x&=-8x-3\\y&=-8x-3\end{aligned}[/tex]
Therefore, the equations have the same slopes and the same y-intercepts.
The volume of a right cylinder is V = πr²h, where r is the
radius of the base and h is the height of the cylinder. If the
volume of a cylinder is 48π cubic inches and the height of the
cylinder is 3 inches, then what is the radius of the cylinder in
inches?
The requried radius of the cylinder is 4 inches.
We are given the volume of the cylinder as 48π cubic inches and the height as 3 inches. So we can use the formula V = πr²h to solve for the radius.
48π = πr²(3)
16 = r²
r = ±4
Since the radius of a cylinder cannot be negative, we take the positive value of r, which is 4.
Therefore, the radius of the cylinder is 4 inches.
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Find the value of x.
The value of x from the triangle using the triangle proportionality theorem is 8.4
Calculating the values of x from the triangleGiven that we have the triangle
Using the triangle proportionality theorem, we have the following equivalent ratio
3.5 : 5 = x : 12
When this ratio is represented as a fraction, we have
3.5/5 = x/12
So, we have
x = 12 * 3.5/5
Evaluate the products
This gives
x = 8.4
Hence. the solution for x is 8.4
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write a equation of a line that goes through (1,2) that is perpendicular to y=-4x+6
Answer:
4y = x + 7.
Step-by-step explanation:
The slope of a line perpendicular to a line of slope m = -1/m
So the slope of the required line = -1/ (-4) = 1/4.
y - y1 = m(x - x1)
y - 2 = 1/4(x - 1)
y = 1/4(x - 1) + 2
y = 1/4x - 1/4 + 2
y = 1/4x + 7/4
4y = x + 7