Answers
a. Central angle: Angle BAC
b. A major arc is: Arc BEC
c. A minor arc is: Arc BC
d. Measure of arc BEC in circle A = 260°
e. Measure of arc BC = 100°
What is the Central Angle Theorem?According to the central angle theorem the measure of central angle (i.e. angle BAC in circle A) is the same as the measure of the intercepted arc (i.e. arc BC in circle A).
What is a Central Angle?Referring to the image given, a central angle (i.e. angle BAC) is formed by two radii of a circle (i.e. AB and AC in circle A), where the vertex of the angle (i.e. vertex A in circle A) is at the center of the circle.
What is a Major Arc?An arc that is bigger than a semicircle (half a circle) or with a measure greater than 180 degrees is called a major arc of a circle.
What is a Minor Arc?An arc that is smaller than a semicircle (half a circle) or with a measure less than 180 degrees is called a minor arc of a circle.
a. Central angle in circle A is: ∠BAC
b. Major arc in circle A is: Arc BEC
c. Minor arc in circle A is: Arc BC.
d. Based on the central angle theorem, we have:
Measure of arc BEC in circle A = 360 - 100
Measure of arc BEC in circle A = 260°
e. m∠BAC = 100° [given]
Based on the central angle theorem, we have:
m(arc BC) = m∠BAC
Measure of arc BC = 100°
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Related Questions
f(x)=x3 −4x even odd or neither
Answers
Answer:
The function would be odd
The answer is neither.
Let's take an odd number and substitute.
f(3) = 3³ - 4(3)f(3) = 27 - 12f(3) = 15 (odd)Now, let's take an even number.
f(4) = 4³ - 4(4)f(4) = 64 - 16f(4) = 48 (even)Since both even and odd numbers are possible, it is neither.
Can u guys please give me the correct answe
Answers
Answer:
35
Step-by-step explanation:
Since the two sides are equal in a parallelogram angle B = y ,so we have angle to be equal to 145°
We sum both angles and divide from
360° - [145° +145°]
360° - 290° = 70
Since the left sides( X And Z) are equal then we divide what we got into 2
70 ÷ 2 = 35
therefore angle X equals 35
a) Find the perimeter of a rectangle whose length is 10 10²/3 cm and breadth is 6 cm.
please need fast I will make brilliant
Answers
Answer:
40
Step-by-step explanation:
P=2(l+w)
2·(10+10)
=40
Suppose 45% of the population has a college degree.
If a random sample of size 437 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%? Round your answer to four decimal places.
Answers
Using the normal distribution, there is a 0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The proportion estimate and the sample size are given as follows:
p = 0.45, n = 437.
Hence the mean and the standard error are:
[tex]\mu = p = 0.45[/tex][tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.45(0.55)}{437}} = 0.0238[/tex]The probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3% is 2 multiplied by the p-value of Z when X = 0.45 - 0.03 = 0.42.
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (0.42 - 0.45)/0.0238
Z = -1.26
Z = -1.26 has a p-value of 0.1038.
2 x 0.1038 = 0.2076.
0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.
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Add 10/12 and 6/10 as a mixed number
Answers
Answer:
1 13/30
Step-by-step explanation:
10/12 + 6/10 =
= 5/6 + 3/5
= 25/30 + 18/30
= 43/30
= 30/30 + 13/30
= 1 13/30
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Equation:}[/tex]
[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]
[tex]\huge\textsf{Solving:}[/tex]
[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]
[tex]\mathsf{= \dfrac{10\div2}{12\div2} + \dfrac{6\div2}{10\div2}}[/tex]
[tex]\mathsf{= \dfrac{5}{6} + \dfrac{3}{5}}[/tex]
[tex]\mathsf{= \dfrac{5\times5}{6\times5} + \dfrac{3\times6}{5\times6}}[/tex]
[tex]\mathsf{= \dfrac{25}{30} + \dfrac{18}{30}}[/tex]
[tex]\mathsf{= \dfrac{25 + 18}{30-0}}[/tex]
[tex]\mathsf{= \dfrac{25 + 18}{30}}[/tex]
[tex]\mathsf{= \dfrac{43}{30}}[/tex]
[tex]\approx\mathsf{1\dfrac{13}{30}}[/tex]
[tex]\huge\textsf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{1\dfrac{13}{30}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The points
(−1.2,2.9) and (2.9,9.46) are on the graph of a linear relationship between two variables, x and y
Write a formula that expresses
y in terms of x
What is the value of y when x=115
Answers
[tex](\stackrel{x_1}{-1.2}~,~\stackrel{y_1}{2.9})\qquad (\stackrel{x_2}{2.9}~,~\stackrel{y_2}{9.46}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9.46}-\stackrel{y1}{2.9}}}{\underset{run} {\underset{x_2}{2.9}-\underset{x_1}{(-1.2)}}}\implies \cfrac{6.56}{2.9+1.2}\implies \cfrac{6.56}{4.1}\implies 1.6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2.9}=\stackrel{m}{1.6}(x-\stackrel{x_1}{(-1.2)}) \\\\\\ y-2.9=1.6(x+1.2)\implies y-2.9=1.6x+1.92\implies \boxed{y=1.6x+4.82} \\\\\\ \textit{when x = 115, what is "y"?}\qquad y=1.6(115)+4.82\implies y=188.82[/tex]
Find the difference. Enter your answer in lowest terms in the box below as a
fraction, using the slash mark (/) for the fraction bar. 8/11 - 4/15
Answers
Answer:
76/165
Step-by-step explanation:
The difference of fractions can be found using the formula ...
a/b -c/d = (ad -bc)/(bd)
DifferenceUsing the given values in the formula, we have ...
[tex]\dfrac{8}{11}-\dfrac{4}{15}=\dfrac{8(15)-11(4)}{11\cdot15}=\dfrac{120-44}{165}=\boxed{\dfrac{76}{165}}[/tex]
Here, the difference fraction does not need to be reduced. Many calculators and spreadsheets can do this arithmetic for you.
The above formula can also be used for sums of fractions. In that case, the sign changes from minus to plus.
Answer:
Step-by-step explanation:
76/165 is the answer
What form is 950,000 in
Answers
Answer:
standard form
hope this helps! <3
Enter the letter for the function graphed
below.
1
a) y = √x - 5
b) y = √x-5
c)y = 5-√√x
d) y = √x + 5
e) y = √x + 5
Answers
The letter for the graphed function is y = √(x) - 5
How to determine the letter for the graphed function?The parent function is given as:
y = √x
From the graph, we can see that the function is shifted downwards by 5 unts
This is represented as:
y = √(x) - h
Where h = 5
Substitute the known values in the above equation
y = √(x) - 5
This means that the letter for the graphed function is y = √(x) - 5
Hence, the letter for the graphed function is y = √(x) - 5
So, the complete functions are
Parent function is given as: y = √xTransformed function is y = √(x) - 5Read more about function transformation at:
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NO LINKS! Help me with this problem
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Equation of directrix is : y = 1, so we can say that it's a parabola of form : -
[tex]\qquad \sf \dashrightarrow \: (x - h) {}^{2} = 4a(y - k)[/tex]
h = x - coordinate of focus = -4k = y - coordinate of focus = 5a = half the perpendicular distance between directrix and focus = 1/2(5 - 1) = 1/2(4) = 2and since the focus is above the directrix, it's a parabola with upward opening.
[tex]\qquad \sf \dashrightarrow \: (x - ( - 4)) {}^{2} = 4(2)(y - 5)[/tex]
[tex]\qquad \sf \dashrightarrow \: (x + 4) {}^{2} = 8(y - 5)[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 8x + 16 = 8y - 40[/tex]
[tex]\qquad \sf \dashrightarrow \: 8y = {x}^{2} + 8x + 56[/tex]
[tex]\qquad \sf \dashrightarrow \: y = \cfrac{1}{8} {x}^{2} + x + 7[/tex]
Directrix
y=1Focus
(h,k)=(-4,5)Focus lies in Q3 and above y=1
Parabola is opening upwardsThen
Perpendicular distance
(5-1)=4Find a for the equation
a=4/2=2Now the equation is
[tex]\\ \rm\dashrightarrow 4a(y-k)=(x-h)^2[/tex]
[tex]\\ \rm\dashrightarrow 4(2)(y-5)=(x+4)^2[/tex]
[tex]\\ \rm\dashrightarrow 8(y-5)=x^2+8x+16[/tex]
[tex]\\ \rm\dashrightarrow 8y-40=x^2+8x+16[/tex]
[tex]\\ \rm\dashrightarrow 8y=x^2+8x+16+40[/tex]
[tex]\\ \rm\dashrightarrow 8y=x^2+8x+56[/tex]
[tex]\\ \rm\dashrightarrow y=\dfrac{x^2}{8}+x+7[/tex]
Captain's Autos sells 22 used cars on
Monday, and 18 cars on Tuesday. This was
25% of the number of sales for the week.
How many cars did they sell altogether that
week?
Answers
Answer:
160
Step-by-step explanation:
22+18=40, and this was 25% of the cars.
So, 40(4)=160 cars were sold that week.
The number of cars Captain's Autos sold in total that week is 160.
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Number of used car on monday= 22
Number of cars on tuesday= 18
Now,
Let's call the total number of cars sold during the week "x".
We know that the number of cars sold on Monday and Tuesday is 25% of the total number of cars sold during the week. So we can write:
22 + 18 = 0.25x
Simplifying, we get:
40 = 0.25x
Dividing both sides by 0.25, we get:
x = 160
Therefore, by the unitary method the answer will be 160.
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Could you please help me solve this question?
Answers
Find the common ratio: 64, -16, 4, -1, ...
Answers
The common ratio of the given sequence is -1/4. In a geometric sequence, the common ratio is the value that is in between each number in the sequence.
What is the common ratio?The ratio of the value of a term in the sequence to the value of the previous term in the sequence is said to be the common ratio. I.e.,
C.R = (nth term)/(n - 1)th term
Calculation:The given sequence is 64, -16, 4, -1, ...
Taking the ratio of the second term to the first term, we get
-16/64 = -1/4
Similarly, the ratio of the third term to the second term,
4/16 = -1/4
Since the ratios are equal, then the common ratio of the sequence is -1/4.
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19. At a boardroom meeting, the sales manager is happy to announce that sales have risen from $850,000 to $1,750,000 at a
rate of 4.931998% per year. How many years did it take for the sales to reach $1,750,000?
Answers
The number of years it would take sales to reach $1,750,000 is 14.65 years.
What is the number of years?The formula that can be used to determine the number of years it would take for the sales to reach $1,750,000 is:
Number of years : In (FV / PV) / r
Where:
FV = future level of sales - $1,750,000PV = present level of sales = 850,000r = rate of growth - 4.931998%Number of years : In ($1,750,000 / 850,000) / 0.04931998
Number of years : In (2.06) / 0.04931998
Number of years : 14.65 years
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If A= {1,2,3,4,5},B= {1,3,5,7}and C= {2,4,6,8}
Answers
Step-by-step explanation:
Intersection of A and B={1,3,5}Intersection of B and C={ }B - A={1,3,5,7} - {1,2,3,4,5} ={1,7}A cereal box filling machine is designed to release an amount of 16 ounces of cereal into each box, and the machine’s manufacturer wants to know of any departure from this setting. The engineers at the factory randomly sample 150 boxes of cereal and find a sample mean of 15.75 ounces. If we know from previous research that the population is normally distributed with a standard deviation of 1.46 ounces, is there evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance? State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.
Answers
Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is not different to 16 ounces, that is:
[tex]H_0: \mu = 16[/tex]
At the alternative hypothesis, it is tested if the mean is different, hence:
[tex]H_1: \mu \neq 16[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are:
[tex]\overline{x} = 15.75, \mu = 16, \sigma = 1.46, n = 150[/tex].
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{15.75 - 16}{\frac{1.46}{\sqrt{150}}}[/tex]
z = -2.1
What is the p-value and the conclusion?Using a z-distribution calculator, for a two-tailed test, as we are testing if the mean is different of a value, with z = -2.1, the p-value is of 0.0357.
Since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.
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A drink bottle is 3/8 full. It contains 240 millilitres of water. How much water does the bottle contain when it is half-full?
Answers
Answer: 320 mL
Step-by-step explanation:
Given information
The bottle is currently 3/8 full
Current Volume = 240 mL
Concept:
Imagine the water in the bottle being separated into 8 parts
Currently, 3 parts are being occupied
Determine the volume for 1 part
3 parts = 240 mL
1 part = 240 / 3 = 80 mL
Determine the volume for half-full (4 parts)
1 part = 80 mL
4 parts = 80 × 4 = [tex]\Large\boxed{320~mL}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Please help!
Express the area of the region bounded by the x-axis, y = 1/2x - 2 and y equals the cubed root of x, using definite integrals.
Answers
The integral which expresses the area of the region bounded by y = ¹/₂x - 2 and y = ∛x is; ∫⁸₀((x^(1/3)) - ¹/₂x + 2
How to integrate between two curves?
We are given the functions as;
y = ¹/₂x - 2
y = ∛x
Now, from the graph the coordinate of the point where both curves intersect is at; (8, 2)
Thus, the x-coordinate here is x = 8
∛x - (¹/₂x - 2)
∛x - ¹/₂x + 2
Similarly, another point of intersection of both curves is at the coordinate (0, -2). Thus, the x-coordinate here is; x = 0
Thus, the integral which expresses the area of the region bounded by y = ¹/₂x - 2 and y = ∛x is; ∫⁸₀((x^(1/3)) - ¹/₂x + 2
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An older person is 9 years older than four times the age of a younger person the sum of their ages is 24 find their ages
Answers
Step-by-step explanation:
let the younger person be x and older be y
4x + 9 = 24
4x = 15
x = 3.75
y = 24 - 3.75
y = 20.25
The sum of three numbers is 100. The second number is 2 times the third. The third number is 8 less than the first. What are the numbers?
Answers
Answer:
Step-by-step explanation:x+y+z=100(let x ,y,z represent the first second and third numbers respectively)
Therefore,y=2z
z=x-8
y=2x-16
substituting the values of x,y and z into the question,we have
x+(2x-16)+(x-8)=100
Simplifying,we have
4x-24=100
adding 24 to both sides of the equation,
4x=100+24
4x=124
dividing both sides of the equation by the co-efficient of x,we have
4x/4=124/4
4.31=124
therefore,x=31.
Please help solve this equation?
Answers
[tex]{ \red{ \bold{cos \: y \: }}}[/tex]
Step-by-step explanation:
[tex]{ \green{ \tt{ \frac{1 \: + \: \cos \: y \: }{1 \: + \: \sec \: y \: }}}} \: → {eq}^{n} (1)[/tex]
But, as you know that
[tex]{ \blue{ \tt{sec \: y \:}}} = { \green{ \tt{\frac{1}{ \ \cos \: y }}}} [/tex]
Then the equation (1) becomes
[tex]{ \green{ \tt{ \frac{1 \: + \: cos \: y }{1 \: + \: \frac{1}{cos \: y} }}}} \: [/tex]
Multiply Numerator and Denominator by [tex] \frac{cos \: y}{cos \: y} [/tex]
then,
[tex]{ \green{ \tt{( \frac{cos \: y}{cos \: y})}}} \: { \green{ \tt{ \frac{1 \: + \: cos \: y}{1 \: + \: \frac{1}{cos \: y}}}}} [/tex]
[tex] = { \green{ \tt{ \frac{cos \: y \: + \: {cos}^{2} \: y }{cos \: y \: + \: 1 }}}}[/tex]
take cos y as common, then
[tex]{ \green{ \tt{cos \: y}}} \: { \green{ \tt( \frac{1 \: + \: cos \: y}{cos \: y \: + \: 1} )}}[/tex]
Here, (1+cos y/cos y + 1) gets cancelled.
Then the remaining answer is cos y.
Please help me I’m stuck
Answers
Answer:
-1/3
5
Step-by-step explanation:
We need to complete
y = mx + b
with a slope, m, and with the y-intercept, b.
From the graph, we see that the line intersects the y-axis at y = 5, so the y-intercept, b, is 5.
We now have y = mx + 5.
Now we need the slope.
We pick two points that are easy to read, (0, 5) and (3, 4).
m = slope = rise/run
To go from (3, 4) to (0, 5), we go up vertically 1 unit. The rise is 1.
Then we go left horizontally 3 units. The run is -3.
m = slope = rise/run = 1/(-3) = -1/3
Now we have the slope, so we can finish.
y = -1/3 x + 5
Answer:
-1/3
5
f(x)=2x-6 Match each transformation of f(x) with its description
Answers
The transformation of the function is illustrated below
How to match the transformation?Parent function is: f(x) = 2x - 6
Transformations are:
shifts f(x) 4 units down
f(x) → f(x) - 4 ⇒ g(x)= 2x - 6 - 4 = 2x - 10
stretches f(x) by a factor of 4 away from the x-axis
f(x) → 4*f(x) ⇒ g(x) = 4(2x - 6) = 8x - 24
shifts f(x) 4 units right
f(x) → f(x - 4) ⇒ g(x) = 2(x - 4) - 6 = 2x - 14
compresses f(x) by a factor of toward the y-axis (must be 4)
f(x) → f(4x) ⇒ g(x) = 2*4x - 6 = 8x - 6
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What percent of 50 is 15?
A. 0.3%
B. 7.5%
C. 30%
D. 35%
Answers
Answer:30%
Step-by-step explanation:
10% of 50 is 50/10 so 10% is 5
15/5=3 so its three lots of 10%
3*10%=30%
Step by step.
What percent of 50 is 15?
So
what percent of (means multiply)
50 is (means equal) 15.
So
50x = 15
Solve for “x” by dividing both sides by 50.
X= .30
To turn a decimal into a percent, multiply by 100 = 30%.
Researchers wanted to study if having a long beak is related to flight and birds they surveyed a total of 34 birds the data are shown in the contingency table below what is the relative risk of flying for those birds that have long beaks
Answers
The odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76.
What is an odds ratio?An odds ratio is a measure of the strength of an association with the exposure and outcome.
The odds ratio can be calculated by dividing the odds of the first group (exposure) by the odds of the second group (outcome).
Flies Does not fly Total
Long beak 11 7 19
Not a long beak 3 13 15
Total 14 20 34
Probability of long beaks flying = 0.79 (1/14)
Probability of not having long beaks flying = 0.21 (3/14)
Odds ratio = 3.76 (0.79/0.21)
Thus, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76, showing greater odds of association.
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Complete question
Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly? Round your answer to two decimal places.
Long beakNot a long beakTotalFlies11719Does not fly31315Total142034
A glass inform of frustrum of cone
Answers
The volume of the cone illustrated will be 117.2 unit³.
How to illustrate the information?From the information illustrated, the glass inform of a the frustrum of a cone has the dimensions: radius 4cm and a height of 7cm.
It should be noted that the volume of a cone is calculated as:
= 1/3 πr²h.
where,
π = 3.142
r = radius = 4cm
h = height = 7cm
In this case, since we know the values of the dimensions, then we can calculate the volume. This will be:
= 1/3πr²h
= 1/3 × 3.14 × 4² × 7
= 117.2 unit³
Therefore, the volume of the shape is 117.2 unit³.
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Complete question:
A glass inform of a the frustrum of a cone has the following dimensions: radius 4cm and a height of 7cm. Calculate the volume of the shape.
A metallurgist has one alloy containing 26% copper and another containing 69% copper. How many pounds of each alloy must he use to make 53 pounds of a third alloy containing 50% copper?
Answers
The pounds of alloy that contains 26% copper that would be used is 23.42 pounds.
The pounds of alloy that contains 69% copper that would be used is 29.58 pounds.
What are the linear equations that represent the question0.26a + 0.69b = (53 x 0.5)
0.26a + 0.69b = 26.50 equation 1
a + b = 53 equation 2
Where:
a =pounds of alloy that contains 26% copperb = pounds of alloy that contains 69% copperHow many pounds of each alloy should be in the third alloy?Multiply equation 2 by 0.26
0.26a + 0.26b = 13.78 equation 3
Subtract equation 3 from equation 2
12.72 = 0.43b
b = 12.72 / 0.43
b = 29.58 pounds
a = 53 - 29.58 = 23.42 pounds
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Suppose you are in charge of setting up tables and ordering
appetizers and cookies for an awards dinner. The principal
expects 168 seventh-graders and 112 eighth-graders to attend
the dinner. Each grade will have dinner in a separate room.
1. Decide how many tables and how many chairs per table you will need, based on
the following criteria:
• No more than 15 tables in each room, and no more than 15
chairs per table.
• All tables in both rooms must have the same number of chairs.
Only 280 chairs can be ordered.
●
Answers
Answer: 10 tables in each room 14 kids at each table
Derive Integral equation for dy/dv
Answers
By the fundamental theorem of calculus,
[tex]\displaystyle y = \int_0^v \sqrt{3+4t^2} \, dt \implies \boxed{\frac{dy}{dv} = \sqrt{3+4v^2}}[/tex]
In general,
[tex]\displaystyle \frac{d}{dx} \int_0^{g(x)} f(u) \, du = f(g(x)) \frac{dg}{dx}[/tex]
Thirty-two percent of workers in Troberca City are college graduates. You randomly select 50 workers and ask them is he or she is a
college graduate. Find the probability that less than 18 workers are college graduate. (Approximating a Binomial Distribution)
(A) 32.6%
B 67.4%
64.0%
36.0%
Answers
The correct option is B) 67.4%
What is the z- score table?A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution. Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.
Given here, P(probability that a worker is a college graduate) = 32%
= 0.32
q (probability that a worker is not a college graduate) is 1-0.32 = 0.68
now μ(mean) = n×p
= 50×0.32
= 16
Again standard deviation σ = [tex]\sqrt{npq\\}[/tex]
σ = [tex]\sqrt{50\cdot 0.32\cdot 0.68}[/tex]
σ = 3.2985
now P(x<17.5) = P((x-μ)/σ <(17.5-16)/3.2985)
= P(z<0.45)
= 0.674 [using z table]
= 67.4%
Hence option 2 is the correct answer
Learn more about z-table here:
https://brainly.com/question/29283457
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