Consider the figure shown below. Find the value of each variable mentioned in the figure below
Answers
-------------------
The measure of an inscribed angle is half the measure of the intercepted arc:
a = 52/2 = 26,c = 84/2 = 42.Angles a and b sum to a right angle since inscribed between the tangent and diameter.
Then we have:
a + b = 9026 + b = 90b = 90 - 26b = 64Related Questions
Please show all work. Show the steps in transforming the expression on the right into the one on the left. (Verifying identities - this is precalc.)
(1+3cosx-4cos²x)/sin²x = (1-4cosx)/(1-cosx)
Answers
(1 – 3cosx – 4cos^2x) / sin^2x =
(1+cos x)(1-4cos x) /(1-cos^2 x) =
(1+cos x)(1-4cos x) /[(1-cos x)(1+cos x)] =
(1-4cos x) /(1-cos x)
Factor:
1+cos(x))(1 – 4cos(x)) / (1 + cos(x))(1 – cos(x)) =
RHSCancel:(1 – 4cos(x)) / (1 – cos(x)) = RHSQED
the scores on a standardized test have an average of 1200 with a standard deviation of 60. a sample of 50 scores is selected. what is the probability that the sample mean will be between 1195 and 1205? round your answer to three decimal places.
Answers
The probability that the sample mean will be between 1195 and 1205 is 0.445
What is a probability distribution?
In mathematics, a probability distribution is a function that expresses the likelihood of many possible values for a variable. Graphs and probability tables are common ways of displaying probability distributions.
Given, mean = [tex]\mu[/tex] = 1200
standard deviation = [tex]\sigma[/tex] = 60
n = 50
[tex]\mu_{\bar x} = 1200\\\sigma_{\bar x} =\sigma / \sqrt(n) = 60/ \sqrt50=8.485[/tex]
[tex]P(1195 < \bar x < 1205 ) = P[(1195-1200) / 8.485 < (\bar x - \mu\bar x ) / \sigma\bar x < (1205-1200) / 8.485)][/tex]
= P(-0.59 < Z <0.59 )
= P(Z <0.59 ) - P(Z <-0.59 )
Using the z table, we get
=0.7224-0.2776
=0.4448 = 0.445 ( rounded to 3 decimal places)
Hence, the probability that the sample mean will be between 1195 and 1205 is 0.445
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Find the complex zeros of each polynomial function. Use your results to write the polynomial as a product of linear factors. Thanks! :)
Answers
here you are the answer.
-0.8x - 2.14 = -6.2 all my points
Answers
Answer: 5.072
Step-by-step explanation: -0.8-2.14=-6.2
+2.14 | +2.14
-----------------------------------------------------------------------------------------------
-4.06/-0.8=5.072
please help me now, much appreciated! I'll give brainliest if you answer!
Answers
By evaluating the piecewise function we will see that the difference is:
f(1) - f(-7) = 3
How to find f(1) - f(-7)?Here we have a piecewise function defined on the image, and we want to find the difference:
f(1) - f(-7).
First, let's find these values.
f(1) means that we need to evaluate the function in x = 1.
Notice that the second piece can be used on the domain 4 < x ≤ 1, so we need to use that part.
f(1) = -(1)^2 - 3*1
f(1) =-1 - 3 = -4
To evaluate in x = -7 we need to use the first piece of the function:
f(-7) = |-7 + 5| - 9
f(-7) = |-2| - 9 = -7
Then the difference is:
f(1) - f(-7) = -4 - (-7) = -4 + 7 = 3
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. There are 976 people working in an office. On a particular day, 61
people were absent. What percentage of the workforce did not show
up for work that day?
Answers
Answer: 6.25%
Step-by-step explanation:
To find what percent 61 is of 976, we divide 61/976. This comes out to be 0.0625. Multiply by 100 to get your percentage, and it's 6.25%.
80 points!! PLS HELP! look at picture. this is geometry and has to do with similar triangles.
Answers
The sum of DE+FG+HI=90 if DE, FG, HI are all parallel to BC and BC=60.
What is meant by trapezium?Quadrilaterals with at least one set of parallel sides are referred to as "trapezoid" quadrilaterals. In British and other dialects of English, the word "trapezium" is used.
Euclidean geometry dictates that a trapezoid must be a convex quadrilateral. The base of the trapezoid is referred to by its parallel sides. If the other two sides are parallel, the trapezoid is a parallelogram, and there are two pairs of bases. If not, the other two sides are known as the legs (or lateral sides). Unlike the specific situations below, a scalene trapezoid is a trapezoid where none of the sides have equal lengths.
Given,
ΔABC is a scalene triangle.
And BC=60
DE, FG, HI are all parallel to BC.
From the midpoint-theorem,
DE||BC then,
DE=(1/2)BC
FG||BC
FG=(1/2)BC
HI ||BC
HI=(1/2)BC
DE+FG+HI=(1/2BC+1/2BC+1/2BC)
=(1/2(3BC))
1/2(3(60))
=90
Therefore,
The sum of DE+FG+HI=90
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I need help with this one please
Answers
Answer:
A
Step-by-step explanation:
3 - (-1.5)
when you open the backet it will be 3 - - 1.5
minus and minus makes plus
therefore it will be 3+1.5
so the answer is 4.5
amc 12a 2014] let a < b < c be three integers such that a, b, c is an arithmetic progression and a, c, b is a geometric progression. what is the smallest possible value of c?
Answers
The smallest possible value of c is 1 in this case.
If the integer a, b and c are in arithmetic progression.
Then we can write,
b = (a+c)/2
If the integer a, b and c are in geometric progression,
Then, we can write,
b = √(ac)
Now, we can write,
a+b = 2√(ac)
Squaring both sides,
a²+c²+2ac = 4ac
(a-c)² = 0
So,
a = c.
If a = c.
Then,
b = (a+a)/2
b = a
So, a = b = c.
Smallest possible positive integer is 1.
So, the smallest possible value of c is 1.
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help me rq pls it wont take long
Answers
Answer:
52[tex]a^{2}[/tex] + 26
A company manufactures and sells shirts. The daily profit the company makes depends on how many shirts they sell. The profit, in dollars, when the company sells xx shirts can be found using the function f(x) = 6x - 70. Find and interpret the given function values and determine an appropriate domain for the function.
Answers
The numeric values of the function are given as follows:
f(-2) = -82, meaning that if the company sells -2 shirts, it would have a profit of -82 dollars. This interpretation does not make sense in the context of the problem.f(12) = 2, meaning that if the company sells 12 shirts, it would have a profit of 2 dollars. This interpretation makes sense in the context of the problem.f(17.5) = 35, meaning that if the company sells 17.5 shirts, it would have a profit of 36 dollars. This interpretation does not make sense in the context of the problem.An appropriate domain for the situation is of:
{x ∈ N | x ≥ 0.}
What are the numeric values of the function?The function in this problem is defined as follows:
f(x) = 6x - 70.
In which the variables are given as follows:
x is the number of shirts sold.f(x) is the profit when x shirts are sold.Hence when x = -2, the numeric value is given as follows:
f(-2) = 6(-2) - 70 = -82.
This point is outside of the domain, as the number of shirts cannot be negative, hence an appropriate domain for the function is of:
{x ∈ N | x ≥ 0.}
As the number of shirts is also a countable amount.
When x = 12, the numeric value is given as follows:
f(12) = 6(12) - 70 = 72 - 70 = 2.
When x = 17.5, the numeric value is given as follows:
f(17.5) = 6(17.5) - 70 = 35.
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Look at this table:
X Y
-4 7
-3 5
-2 3
-1 1
0 -1
Write a linear function (y = mx + b) or an exponential function (y = a(b)*) that models the
data.
Answers
Answer:
y= -2x -1
Step-by-step explanation:
m= (5-7)/(-3- -4) = -2/1 = -2
y-intercept = -1
y= -2x -1
Solve while using the Pythagorean theorem! Please help
Answers
Answer:
Step-by-step explanation:
a^2 +b^2 =c^2
8^2 +14^2=y^2
64+196 =y^2
260=y^2
(260)^1/2 =y
Simplified: 4^1/2 * 65^1/2= 2(65^1/2)
29x + 3 (5 – 35x) = −119 - 9x
Answers
Answer:
The answer is x=2
Step-by-step explanation:
1. Rearrange terms-
29x + 3 ( 5 - 35x) = - 119 - 9x
29x + 3 ( - 35x + 5) = - 119 - 9x
2. Distribute-
29x + 3 ( - 35x + 5) = - 119 - 9x
29x - 105x + 15 = - 119 - 9x
3. Combine like terms-
29x - 105x + 15 = - 119 - 9x
- 76x + 15 = -119 -9x
4. Rearrange terms-
- 76x + 15 = - 119 - 9x
- 76x + 15 = - 9x - 119
5. Subtract 15 from both sides-
- 76x + 15 = - 9x - 119
- 76x +15 -15 = -9x - 119 - 15
6. Simplify-
- 76x = - 9x - 134
7. Add 9x to both sides-
- 76x + 9x = - 9x - 134 + 9x
8. simplify-
- 67x = - 134
9. Divide both sides by the same factor-
[tex]\frac{-67x}{-67} = \frac{-134}{-67}[/tex]
10. Simplify-
x = 2
suppose a sample of bone fossil contains 5.2% of the carbon-14 found in an equal amount of carbon in present-day bone. estimate the age of the fossil, assuming an exponential decay model. the half-life of carbon-14 is approximately 5700 years.
Answers
The age of the fossil is 24, 312 years assuming an exponential decay model.
Exponential decay model refers to model in which the amount of something decreases at a rate proportional to the amount left and this rate is given by a constant ratio k. The formula for remaining quantities of a substance is given by:
P = 100 e^(-kt)
Where P is the remaining quantity, k is the constant of decay, and t is time.
As the half life of the carbon 14 is 5700, when 50% of the substance remains,
50 = 100 e^(-5700k)
1/2 = e^(-5700k)
In(1/2) = In(e^(-5700k))
- In (2) = -5700k
k = In(2)/5700 = 0.0001216
Since, 5.2% carbon-14 remains,
5.2 = 100 e^(-0.0001216t)
0.052 = e^(-0.0001216t)
In(0.0052) = - 0.0001216
t = In(0.052) * - 0.0001216
t ≈ 24, 312 years.
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we are given a bag of 35 different colored chips. there are 20 black chips and 15 white chips. you draw 11 chips at random, what is the probability of getting 5 black chips and 6 white chips1 ?
Answers
The probability of getting 5 black chips and 6 white chips is [tex]\frac{7}{22}[/tex].
What do you mean by probability?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
According to data in the given question,
We have the given information:
Total number of different colored chips = 35
Number of black chips = 20
Number of white chips = 15
And you draw 11 chips at random.
Now, we will calculate the probability of getting 5 black chips and 6 white chips,
[tex]P(B) = \frac{5}{20} =\frac{1}{4} \\P(W) = \frac{6}{15} =\frac{2}{5} \\P( black and white ) = \frac{\frac{1}{4}*\frac{2}{5}}{\frac{11}{35} } \\=\frac{\frac{1}{2}*\frac{1}{5}}{\frac{11}{35} }\\=\frac{1}{10}*\frac{35}{11}=\frac{7}{22}[/tex]
Therefore, the probability of getting 5 black chips and 6 white chips is 7/22.
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Find the cube roots of i. Round all numbers to 3 decimal places. Enter 0s or 1s in the appropriate boxes to answer 0 + i, 1+0i, etc.
Answers
The cube root of unity are found to be 1, -1±i√3/2 and -1±i√3/2.
In order to find the cube root of unity let us say,
x³ = 1
Solving further,
x³-1 = 0
Now,
(x-1)(x²+x+1)=0
For, x-1=0
x = 1.
And,
For, (x²+x+1)
Solving by using quadratic formula,
x = -1±√(-3)/2.
x = -1±i√3/2
x = -1+i√3/2 and,
x = -1-i√3/2
also, x = 1.
So that cube root of unity are 1, -1±i√3/2 and -1±i√3/2.
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A pharmacist asserts that more than 40% of prescribed medicines are derived from plants. They decide to test this assertion by computing the sample proportion for a random sample. The data results in a test statistic of z = 2.14 and a P- value of .0162. Test at a 5% significance level. a. State the hypotheses for their test. I b. Briefly describe what the P-value is. c. Using the test statistic, how was the P-value found? d. Based on the P-value what conclusion should the pharmacist make? In particular, do they have enough evidence in support of their claim?
Answers
We reject the null hypothesis and come to the conclusion that their argument is adequately supported.
Given that,
z = 2.14 and p value = 0.0162
a) Hypotheses are
H₀ : p≤ 0.40
H₀ : p > 0.40 (claim)
This is right tailed test.
b) p value = 0.0162
c) Test statistic Z =2.14
P(Z>2.14) = 1 - P(Z≤2.14)
= 1 - 0.98382
= 0.01618
P value ≈ 0.01618
d) P value is less than α = 5% = 0.05
So, we reject the null hypothesis and conclude that they have enough evidence in support of their claim
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what is the formula for square of a circle?
Answers
The formula for the area of a circle is pi times the radius squared (A = π r²)
What is a circle?A circle is a two-dimensional closed figure in which the set of all points in the plane is equidistant from a given point known as the "centre." The line of reflection symmetry is formed by every line that passes through the circle. It also has rotational symmetry around the center for all angles.
It is a curved portion of its circumference. A semicircle is an arc that connects the endpoints of the diameter and has a measure of 180°. The circle is divided into two parts by an arc. The minor arc is the smaller part, and the major arc is the larger part.
To find the area goes thus;
Identify the radius of a circle.
Square the radius.
Multiply by pi. Pi.
In conclusion, the formula is πr².
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Complete question
what is the formula for the area of a circle?
a cone has volume of 98cm the radius of the cone is 5.13 what is the hight of the cone
Answers
Step-by-step explanation:
v=1/3πr²h
98=1/3×22/7×(5.13)²×h
98=1/3×22/7×(27.2403)×h
98=28.537×h
h=28.537/98
h=0.291m
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Answer:
Answer to your question is in the attachment
What type of variable is required to construct a confidence interval for a population​ proportion?.
Answers
A variable which is required to construct a confidence interval for population proportion is qualitative variable with two possible outcomes. So the correct option is D.
In the given question we have to find what type of variable is required to construct a confidence interval for a population proportion.
As we know that;
Population proportion is the percentage of the entire population that possesses the given quality (which is qualitative in nature). The confidence interval for the population proportion must thus be constructed using a qualitative variable with two possible outcomes.
So, the correct option is identified from nature of different type of the variables. A variable which is required to construct a confidence interval for population proportion is qualitative variable with two possible outcomes.
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The right question is:
What type of variable is required to construct a confidence interval for a population proportion?
A. Quantitative
B. Qualitative with any number of possible outcomes
C. Continuous
D. Qualitative with 2 possible outcomes
E. Discrete
F. Qualitative with 3 or more possible outcomes
In MNO, O≈ N, MN = 20 and NO = 14. Find OM.
Answers
The length of OM is 20 if MN=20 and N0=14
What is meant by an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.
To find the length of OM
Given,
MN=20
ON=14
∠O≅∠N
Since, ∠O≅∠N
ΔMNO is isosceles triangle with
OM=MN=20
Hence, the length of OM is 20.
Therefore, The length of OM is 20 if MN=20 and N0=14
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Which is the solution for the system of
linear equations graphed below?
A. (-4,3)
B. (0, 1)
C. (0, 3)
D. (-3, 4)
Answers
Answer:
D. (-3, 4)
Step-by-step explanation:
Hope it helps!
Can you guys help me with this thanksss!!
Answers
Answer:
Step-by-step explanation:
What are you supposed to do
Lola has a collection of 432 trading cards, and Joel has a collection of 505
trading cards.
At the end of each month, Lola buys a box of 40 trading cards and Joel
buys a box of 32 trading cards.
After how many months will Lola have more trading cards than Joel?
Answers
Answer: 10 months
Step-by-step explanation:
432 + 40x >505 + 32x
40x >32x + 73
8x > 73
8x/8 > 73/8
x > 73/8 = 9.125
Round 9.125 to 10
The number of months that will take Lola to have more trading cards is obtained as 8.
What is linear inequality?Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.
Unlike a linear equation it can have a range of values inside an interval.
The number of cards with Lola and Joel are 432 and 505 respectively.
Suppose the number of required month be x.
Then, the inequality expression can be written for the given case as,
432 + 40x > 505 + 32x
⇒ 40x - 32x > 505 - 432
⇒ 8x > 63
⇒ x > 63/8
The number of months should be an integer value.
And, the nearest integer value of the greater than 63/8 is 8.
Hence, the number of months required for the given case is 8.
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compare using >, =, or <. 3 _____ -3
Answers
Answer:
=
Step-by-step explanation:
consider a trial in which a jury must decide between the hypothesis that the defendant is guilty and the hypothesis that the defendant is innocent. in the framework of hypothesis testing and the u.s. legal system, which of the hypotheses should be the null hypothesis?
Answers
The null hypothesis is
H₀:The defendant is innocent
The alternative hypothesis or research hypothesis is
H₁ : The defendant is guilty
Which of the two hypotheses is correct is unknown to the jury.
Given that,
Think about a case where a jury must choose between the hypotheses that the defendant is guilty and the defendant is innocent.
We have to find which of the hypotheses ought to be the null hypothesis in the context of hypothesis testing and the American legal system.
We know that,
A jury in a trial must choose between two hypotheses. The null hypothesis is
H₀:The defendant is innocent
The alternative hypothesis or research hypothesis is
H₁ : The defendant is guilty
Which of the two hypotheses is correct is unknown to the jury. They must decide based on the information provided.
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HELP I WILL GIVE BRAINLIEST!!!
Answers
Answer:
ITS B
Step-by-step explanation:
Todd's living room is rectangular and measures 9 meters by 3 meters. Beginning in one corner, Todd walks the length of his living room and then turns and walks the width. Finally, Todd walks back to the corner he started in. How far has he walked? If necessary, round to the nearest tenth.
Answers
Rank the population sizes (N) from fastest to slowest growth. If two population sizes have the same growth, overlap them.
Answers
The rank of population size from fastest to slowest growth is N = 1250, N = 1500, N = 1000, N = 750, N = 500, and N = 250.
The population growth rate is the measure that helps to determine how much the population size changes over time. The population growth rate shows either logistic growth or exponential growth. The formula for logistic population growth is given by [tex]\frac{dN}{dt}=r_{\text{max}}N\left(\frac{K-N}{N}\right)[/tex]. Here, N is the population size, t is time, r (max) is the maximum rate of increase, and K is the carrying capacity.
The one that grows fast will have a large population size, and the one that grows slowly will have a small population size. To rank the population size, arrange the given population size from the largest to the smallest. As a result, we get,
Fastest growth rate N=1250, N=1500 , N=1000, N= 750, N= 500, N= 250 Slowest growth rate
The complete question is -
Arrange the following population sizes in the order of decreasing growth rate. Rank the population sizes (N) from fastest to slowest growth. If two population sizes have the same growth, overlap them.
N = 1250, N = 1500, N = 1000, N = 750, N = 500, N = 250
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