The central angle of the arc in degree is 48° when a circle has a circumference of 12 units and it has an arc of length 8/5 units.
Given that,
A circle has a circumference of 12 units and it has an arc of length 8/5 units.
We have to find what is the central angle of the arc in degree.
We know that,
Circumference =12 units
Arc length =8/5= 1.6 units
If the central angle is "θ" then the length of the arc is given by
Arc length= θ/360°×circumference
Substituting values,
1.6=θ/360°×12
θ=48°
Therefore, The central angle of the arc in degree is 48° when a circle has a circumference of 12 units and it has an arc of length 8/5 units.
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Find the midpoint of PQ. SEE17. P(3, 5), Q(-2, 13) 18. P(-2, 2.5), Q(1.4, 4) 19. P(4 1/3, 3 1/6), 0(-2 1/5, 3 2/3)
Therefore, The necessary midpoints are Mz(1 1/5, 3 1/4), My (-0.3, 3.25), and Mx(1/2, 9).
Where does the middle point lie?Sometimes you have to locate the precise midpoint between two other plane point. You might, for instance, wish to locate a line that divides a given line segment into two equal halves. The "halfway" is the name given to this midpoint.
Here,
M can be used to indicate where two coordinates (x, y) and (a, b) meet in the middle (s, t)
s = x +a/2; t = y +b/2
Mid points
For P(3, 5), Q (-2, 13)
s = 3 - 2 / 2 ; t = 5 + 13 /2
1 / 2 =s ;
t= 9
Mx(1/2, 9) is a midpoint.
For P(-2, 2.5), Q (1.4, 4)
s = -2 + 1.4 / 2 ; t = 2.5 + 4 / 2
s = -0.3 ; t = 3.25
My middle (-0.3, 3.25)
For P(4 1/3, 3 1/6), Q (-2 1/5, 3 2/3)
s = (4 1 / 3 - 2 1/5 ) / 2 ; t = (3 1/6 + 3 2/3) / 2
s = 1 1/15 : t = 3 1/4
Midpoints Mz(1 1/5, 3 1/4)
Thus, the required midpoints are Mx(1/2, 9), My (-0.3, 3.25) and Mz(1 1/5, 3 1/4).
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The diagonals of an isosceles trapezoid are congruent. TRUE or FALSE
Answer: True.
Because the trapezoid is isosceles, the base angles are congruent by default.
Given isosceles trapezoid ABCD
Sides AB and DC are congruent
By the SAS postulate, triangles ABC and DCB are congruent
Therefore, segment AC is congruent to segment DB
samuel used 1/5 of an ounce of butter; jacob used 1/7 of a liter; mason used 1/6 of a gram; michael plays 1/5 of a song in 1/15 of a minute
The ounces of butter that are needed to make a pound of jelly is 3 ounce .
In the question ,
it is given that ,
Samuel is using 1/5 of an ounce of butter to make 1/15 of a pound of jelly.
let the number of ounces of butter needed to make a pound of jelly be "x" .
So , the equation for the situation can be represented as
( 1/5 ounce butter)/(1/15 pound jelly) = x/( 1 pound jelly)
So ,after cross multiplication ,
we get ,
15/5 = x/1
So , x = 3 .
Therefore , the ounces of butter needed is 3 ounce .
The given question is incomplete , the complete question is
Samuel used 1/5 of an ounce of butter to make 1/15 of a pound of jelly. How many ounces of butter are needed to make a pound of jelly ?
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dy is perpendicular to ac, xf is perpendicular to bc, ze is perpendicular to ab. prove triangle abc is similar to triangle yzx
Triangle ABC and triangle XYZ are congruent thus ∆ABC and XYZ are similar
What are similar trianglesSimilar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects.
if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
line DY bisects AC and line ZE bisects line AB.
Therefore line AD is congruent to line AE and line CD is congruent to line EB.
therefore AB = CD and similar XY = YZ
therefore ∆ABC and ∆XYZ are similar
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stirling's approximation is an incredibly accurate approximation of factorials using a continuous and differentiable function.
In mathematics, Stirling's approximation (or Stirling's formula) is a factorial approximation. A good approximation that gives accurate results even for small values of n. It is named after James Stirling and was first given by Abraham de Moivre, although relevant but less accurate.
Factorial is one of thein mathematics. It is also an important mathematical concept ubiquitous concepts used in data science. Factors are used to model probability distributions in Poisson processes. The probability mass function of the Poisson distribution has a factorial formula in the denominator. You can't find the probability of a Poisson random variable without a way to compute the factorial.
Factorials are also related to combinatorics. For example, hmm! is the number of permutations of n unique objects. From the point of view of statistical mechanics, entropy is defined as a combinatorial problem. Entropy also has its own definition in information theory. Comparing the two alternative definitions, they are identical.
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Use the equations for the total cost C and total revenue R to find the number x of units a company must sell to break even. (Round to the nearest whole unit.)
C = 2.5
x
+ 14,000, R = 6.23x
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The number of units to sell to break even is 3753.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
C = 2.5x + 14,000
R = 6.23x
Where,
C is the total cost.
R is the total revenue.
Now,
The number of x units a company must sell to break even.
2.5x + 14,000 = 6.23x
14000 = 6.23x - 2.5x
14000 = 3.73x
x = 14000 / 3.73
x = 3753
Thus,
The number of units to sell to break even is 3753.
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30/4+5•3-9
help me please!! ;)
Answer:
30/4+5•3-9
= 7.5+15-9
= 22.5-9
= 13.5
Step-by-step explanation:
Solve the equation 2y+5=y-7
Answer: -12
Step-by-step explanation:
Find the Slope:
A. 2
B. -2
C. 1/2
D. -1/2
If a number is added to the numerator of 1/7 and twice the number is subtracted from the denominator, the result is 4. Find the number.
Answer:
2
Step-by-step explanation:
Please tell me ALL the partial products of 3.4 times 1.2
Answer:
34
× 12
---------
8
60
40
+ 300
----------
= 408
Use a graph to show the relationship between the time and the distance traveled
Answer:
I don't know the answer of this questions
Find the area of this circle. Use 3.14 for π.
a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5. in the last year for standard deviation seems to have changed she bases this on a random sample of 25 students whose final exam had a mean a 80 with a standard deviation of 4.2 test the professor's claim that the current mean is different from 82.4. use a equals 0.05 Assume that o is known to be 6.5
Express the claim in symbolic form. Express the claim in symbolic form. Group of answer choices A )σ > 6.5 B) σ = 6.5 C) σ < 6.5 D) σ ≠ 6.5 E) σ ≥ 6.5 F) σ ≤ 6.5 28) What is the alternative hypothesis, H1? Group of answer choices A) σ < 6.5 B) σ ≤ 6.5 C) σ ≠ 6.5 D) σ = 6.5 E) σ > 6.5 F) σ ≥ 6.5 29) Find the critical value(s). (Round to the nearest thousandth. If more than one value is found, enter the smallest critical value.) 30) Find the value of the test statistic. (Round to the nearest ten-thousandth.) 31) What is the statistical conclusion? Group of answer choices A)Fail to reject H0 B) Reject H0 32) State the conclusion in words. Group of answer choices A) There is not sufficient sample evidence to support the claim that the current standard deviation is different from 6.5 . B) The sample data support the claim that the current standard deviation is different from 6.5 . C) There is not sufficient evidence to warrant rejection of the claim that the current standard deviation is different from 6.5 . D) There is sufficient evidence to warrant rejection of the claim that the current standard deviation is different from 6.5 .
The value of the standard deviation does not change and remains the same.
Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.
The mean μ = 82.4
The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]
we have to find the variance,
We now add a constant k to each data value and calculate the new mean μ'.
μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k
We now calculate the new mean standard deviation σ'.
σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]
Note that x + k - μ' = x + k - μ - k = x - μ
also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ
Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ
If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.
Hence, the standard deviation does not change.
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5 Barb has 8 white balls, Tom has 3 white balls and 9 blue balls, Clare has 2 green balls and 1 blue ball. How many blue balls do Barb, Tom
and Clare have?
1 blue ball
O9 blue balls
7 blue balls
10 blue balls
Skip
4/6 complete
Type A: f(x)= 10 + 8x Type B: g(x)= 17 + 7x Two types of generators each require a fixed amount of fuel to start. After starting, each generator produces a constant amount of energy per ounce of fuel used. The functions fand g above represent the amount of fuel, in ounces, that each type of generator requires to produce x units of energy when started once. 29 A type A generator was used to produce units of energy, and a type B generator was used to produce k units of energy. Each generator-was started once, and a combined total of 100 ounces of fuel was used. Which of the following equations represents the relationship between n and k? A) 8n+7k 100 B) 8m+7k-73 C) 8n+7k=127 8n 7k D) +7 100 100 30 A type A and a type B generator were started and operated until they ran out of fuel. The two generators combined used 216 ounces of fuel to produce 25 units of energy. How many more units of energy were produced by the type A generator than by the type B generator? A) 0.2 B) 3.0 C) 11.0 D) 12.6
Answer:
The relationship between n and k represent by 8n+7k=73 (option B) when 100 ounces of fuel are used in total
11 more units of energy were produced by the type A generator than by the type B generator
Step-by-step explanation:
Type A generate produces n units of energy so,f(n)=10+8n
Type B generate produces k units of energy so,g(k)=17+7k
f(x) and g(x) represent amounts of fuel used.
Total ounces of fuel used = 100
f(x)+g(x) = 100
f(n)+g(k)=100
10+8n+17+7k=100
8n+7k=100-10-17
8n+7k=73
The relationship between n and k represent by 8n+7k=73(option B)
Total ounces of fuel used = 216
f(x)+g(x) = 216
f(n)+g(k)=216
10+8n+17+7k=216
8n+7k=216-10-17
8n+7k=189
n+7n+7k=189
n+7(n+k)=189
Total energy produced = n + k = 25
n+7(n+k)=189
n=189-7(n+k)
n=189-(7 ✕ 25)
n=189-175
n=14 units
Total energy produced = n + k = 25
Substitute n = 14 in n + k = 25,we get
14+k =25
k=25-14=11
k=11 units
11 more units of energy were produced by the type A generator than by the type B generator
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a study was conducted to determine if drinking a cup of tea before bedtime helped with falling asleep faster. after randomly assigning 50 people to one group that received tea before bedtime and 50 other people to a group that did not receive tea before bedtime, the researcher then compared the amount of time it took for each person to fall asleep.
According to the given hypothesis, the experiment was conducted based on the observational study.
Hypothesis:
in statistics, the statement of expectation or prediction that will be tested by research is known as hypothesis.
Given,
Here we have a study was conducted to determine if drinking a cup of tea before bedtime helped with falling asleep faster. after randomly assigning 50 people to one group that received tea before bedtime and 50 other people to a group that did not receive tea before bedtime, the researcher then compared the amount of time it took for each person to fall asleep.
Now, we need to find the type of study used in the given study.
While we looking into the given question, we know that they researchers must study the group of 100 people sleeping patter.
Here the total amount is divided into two parts, the first group who is taken tea before bed and the second one is not.
Here the researchers observe the behavior of the people. So, these type of research fall under the observational study concept.
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Tell whether the table of values represents a linear, exponential, or quadratic function.
The rate of decrease of this function is constant so it is a linear function.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
From the given table we can observe or conclude that the as x coordinate is increasing by 1 unit y coordinate is decreasing by 2 units.
So this is a linear function as the rate of increase or decrease is the same.
The points are (1, 1), (2, - 1), (3, - 3), (4, - 5), (5, - 7), and (6, - 9).
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Samuel is buying a pair of boots with an original price of $80 ...
Based on the information , the store that gives the best deal is Store A .
Inn the question ,
it is given that ,
the original price for the shoes that Samuel is buying is = $80 .
the discount offered by Store A is = 25% ,
So , the effective price is = 80 - 0.25 of original price
Substituting the values ,
we get ,
= 80 - 20
= $60
the discount offered by Store B is = $10
So , the effective price is = 80 - 10 = $70 .
So , the price of shoe is less in store A in comparison to store B .
Therefore , the best deal is given by Store A .
The given question is incomplete , the complete question is
Samuel is buying a pair of boots with an original price of $80. Store A is offering a 25% discount off the original price of all boots. Store B is offering a $10 discount off the original price of all boots .
Based on this information, which store gave the best deal ?
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Convert \large \frac{5\pi}{7}radians to degrees.
(Use \large \pi = 3.14 when necessary and round your final answer to the hundredths place.)
\large \frac{5\pi}{7}radians= degrees
The equivalent measure of the angle when converted from radians to degrees is 128.57 degrees
How can the angle be converted from radians to degrees?From the question, we have the following parameters that can be used in our computation:
Angle = \large \frac{5\pi}{7}radians to degrees.
This angle can be properly expressed
So, we have the following representation
Angle = 5π/7 radians
Also, the angle can be further expressed
So, we have the following representation
Angle = 5/7 π radians
As a general rule of angle conversion, we have
π radians = 180 degrees
Substitute the known values in the above equation, so, we have the following representation
Angle = 5/7 * 180 degrees
Evaluate the products
Angle = 128.57 degrees
Hence, the measure of the angle in degrees is 128.57 degrees
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Answer the angle when converted from radians to degrees is 128.57 degrees
Angle = 5π/7 radians
Angle = 5/7 π radians
π radians = 180 degrees
Angle = 5/7 * 180 degrees
Evaluate the products
Angle = 128.57 degrees
7. Segment A'B' is parallel to
segment AB. (Lesson 3-11)
a. What is the length of
segment A'B'?
2
B'
b. What is the length of C 3
segment B'B?
A'
B
6
12
A
a) The length of segment A'B' is given as follows: 4 units.
b) The length of segment B'B is given as follows: 4 units.
How to obtain the missing lenghts?The two similar triangles in this problem are given as follows:
ABC and A'B'C'.
Then side lengths of ABC are given as follows:
12, 9 and 2 + x.
The equivalent side lengths on triangle A'B'C' are given as follows:
y, 3 and 2.
When the triangles are similar, the side lengths are proportional, hence the following equation is built:
12/y = 9/3 = 2+x/2.
Then the length of segment A'B' is obtained as follows:
12/y = 9/3
12/y = 3
3y = 12
y = 12/3
y = 4.
The length of segment B'B is x, hence it is obtained as follows:
9/3 = 2+x/2.
2 + x = 6
x = 4 units.
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Trinagle ABC has vertices at A(0,5), B(-3,3), and C(0,-5) Classify the triangle according to the side lengths
The classification of the triangle according to its side lengths and vertices would be scalene triangle.
How to classify the triangle?To classify the triangle, you first need to find the lengths of the sides of the triangle. You can do this by finding the distance between the vertices given.
To find the vertices, the formula is:
= √ ( ( x₂ - x₁ ) ² + ( y ₂ - y ₁) ² )
The length of AB is therefore 3.61 units
The length of BC is 8.54 units
The length of AC is 10 units.
None of the side lengths of this triangle are the same so it is a scalene triangle.
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Which of the following refers to a set of procedures in which the sample size and sample statistics are used to make estimates of population values or facts?
A) sample logic
B) deductive statistics
C) statistical deduction
D) generalization
E) deductive logic
A set of procedures in which the sample size and sample statistics are used to make estimates of population values or facts is generalization. (Option D)
Statistical generalization refers to the inference of the results from a sample and applying it to a population. It involves statistically calculating the likely parameters of a population using data from a random sample of that population i.e., the sample must be selected randomly, and sample size must be large enough to be considered a representative of the population. Generalization is an essential component of the wider scientific process where researchers evaluate how well researchers consider their experimental results i.e., sample statistics from a sample can be extended to the population as a whole. Hence, generalization is used to make estimates of population values or facts.
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Solve 19 - 4x = 2x + 1
Answer: The answer is 3
Step-by-step explanation: I’m smart.
x= 3.
Step-by-step explanation:1. Write the expression.[tex]19 - 4x = 2x + 1[/tex]
2. Subtract 19 from both sides of the equation.[tex]19 - 4x-19 = 2x + 1-19\\ \\-4x=2x-18[/tex]
3. Subtract 2 from both sides of the equation.[tex]-4x-2x=2x-18-2x\\ \\-6x=-18[/tex]
4. Divide both sides by "-6".[tex]\frac{-6x}{-6} =\frac{-18}{-6} \\ \\x=3[/tex]
5. Verify the answer by substituting the calculated value of m into the original equation and simplifying.[tex]19 - 4(3) = 2(3) + 1\\ \\19-12=6+1\\ \\7=7[/tex]
That's correct. Therefore, x= 3 is the correct answer!
A dessert recipe calls for 2 cups of milk and makes 5 servings. How many cups of milk are needed for 8 servings?
5 servings = 2 cups of milk
1 serving = 2/5 cups of milk
do not worry about the fraction of milk for now!!
8 servings = 2/5 × 8 cups of milk
= 3.2 cups of milk
= 3 cups (rounded down)
I dont know how to get it. Anything helps
Answer:
25. y = 36
26. w = -4
Explanation:
25.
74 + 74 = 148
360 - 148 = 212
212 ÷ 2 = 106
106 = 2y + 34
106 - 34 = 2y
72 = 2y
72 ÷ 2 = (2y) ÷ 2
y = 36
26.
72 = 2w + 80
72 - 80 = 2w
-8 = 2w
-8 ÷ 2 = (2w) ÷ 2
w = -4
a researcher wants to discover if age has any influence on how many hours a person spends doing/reading/answering emails in a week. they collect the following data, where there are 2 categories of age and the number of hours per week someone spends on email: 36 and under
over 36
28
0
4
2
2
0
25
1
15
5
3
2
15
4
20
8
10
5
1
10
What is the t statistic?
From given data we can conclude that there is no influence of age on how many hours a person spends doing/reading/answering emails in a week.
In this question, the given data has 2 categories of age and the number of hours per week someone spends on email.
Let H0(null hypothesis): age has any influence on how many hours a person spends doing/reading/answering emails in a week.
Ha = age has no influence on how many hours a person spends doing/reading/answering emails in a week.
36 and under over 36 x - y (x - y)²
28 0 28 784
4 2 2 4
2 0 2 4
25 1 24 576
15 5 10 200
3 2 1 1
15 4 11 121
20 8 12 144
10 5 5 25
1 10 -9 81
Total : 86 1940
Using the formula for t-score:
t = (∑D / N)/[√(∑D² - (∑D)²/N)/(N-1)N]
where
∑D = sum of differences
∑D² = sum of squared differences
(∑D)² = square of sum of differences
t = (86 / 10)/[√(1940 - 7396/10)/(10-1)10]
t = 8.6/√((1940 - 739.6)/90)
t = 8.6 /√(1200.4/90)
t = 8.6 /√13.34
t = 2.35
The p-value with degree of freedom = 9 and alpha-level = 0.05 is 0.021653
Since calculated value is greater than the p-value, we reject the null hypothesis.
Therefore, age has no influence on how many hours a person spends doing/reading/answering emails in a week.
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Allison had a birthday on Saturday she set up six tables and had 5 friends sitting at each table. How many people were at Allison’s birthday?
Answer:
there was 30 people at her birthday party
when vector vector a is added to vector vector b, the resultant is a vector vector r such that vector r is equal to vector a plus vector b. this resultant vector has component rx
a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.
b. ∅ = (Rx/Ry)
Vectors are used to represent physical quantities in terms of magnitude and direction. Vectors can be added using the parallelogram method or the triangle addition method. The magnitude and direction of the resulting vector are generally proportional to the magnitude and direction of the component vectors.
I have every vector in 2D that has both vertical and horizontal components.
There are vectors say: A = xi + yj
and, B =zi + wj
For example, adding two vectors gives the result
R = (x +z)i + (y + w) j.
The - component has y +w as z and the y component as w. The sum has the horizontal component as x + z and the vertical component as y + w. So we get the y component of the resulting vector R = A+ y component of B
The direction of the angle is found as
tan∅ = Rx/Ry
∅ = (Rx/Ry)
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Which of the following is coterminal to 500 degrees in radians?
5pi/6
8pi/9
2pi/3
7pi/9
Answer:
7pi/9
Step-by-step explanation:
subtract 360 from 500 as many times as you can
number left should be converted to radians
500 - 360 = 140
140 * (pi/180) =
140Pi/180 =
simplify by dividing by 20 top & bottom
7Pi/9
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