Answer:
The smallest sample size to satisfy the conditions is n=500.
Step-by-step explanation:
The condition for performing the inference related to the sample size is that, for all the categories, the expected success and failures in the sample are at least 10:
[tex]np\geq10\\\\n(1-p)\geq10[/tex]
The largest sample size required will be for the minimum p or (1-p).
This happens to be the proportion that can play other instruments: 2%.
Then, we can calculate the minimum sample size as:
[tex]np\geq10\\\\n(0.02)\geq10\\\\n\geq(10/0.02)\\\\n\geq500[/tex]
250
Step-by-step explanation:Remember there are 2 conditions to perform a goodness of fit chi-test:
Simple random sample: The data must come from a random sample or a randomized experiment.
Expected counts: All expected counts are at least five. You must state the expected counts.
To explain expected counts a bit better, imagine I surveyed 100 people about their ice cream preferences. Before beginning it is believed that 50% like chocolate, 47% like vanilla, and 3% like strawberry.
That means our expected counts are:
100(.50) = 50
100(.47) = 47
100(.03) = 3
This is a problem, because 3 < 5 and so we can not perform a goodness of fit chi-test.
So how do you find the minimum sample size? Use this formula:
sample size (n) * smallest proportion (p) = 5
In the context of ice cream:
n*.03 = 5
n = 5 / .03
n = 167 (because you can't interview 2/3s of a person)
In the context of the problem:
n* .02 = 5
n = 5 / 0.02
n = 250
This means we need to sample at least 250 people to meet our expected count condition.
What is 3/4 divided by 1/6
Answer:
[tex]\frac{9}{2}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{6}[/tex]
Multiply and flip
[tex]\frac{3}{4}[/tex] x [tex]\frac{6}{1}[/tex]
= [tex]\frac{18}{4}[/tex]
= [tex]\frac{9}{2}[/tex]
The value of the division of the two numbers 3/4 and 1/6 results in an improper fraction of 9/2.
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.
In this case, we want to divide 3/4 by 1/6, so we multiply 3/4 by the reciprocal of 1/6.
The reciprocal of a fraction is obtained by flipping the fraction upside down. The reciprocal of 1/6 is 6/1 or simply 6.
Therefore, to solve 3/4 divided by 1/6, we can multiply 3/4 by 6:
(3/4) x 6
= (3 x 6) / 4
= 18/4
To simplify the result, we can divide the numerator and denominator by their greatest common divisor, which is 2:
18/4
= (18/2) / (4/2)
= 9/2
So, the division of 3/4 by 1/6 is equal to 9/2.
In mixed number form, 9/2 can be expressed as 4 1/2, meaning there are 4 whole units and 1/2 unit remaining.
Therefore, 3/4 divided by 1/6 is equal to 4 1/2.
To learn more about the division;
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An animal shelter has 5 times as many cats as it has dogs. There are 75cats at the shelter
Answer: 15 dogs
Step-by-step explanation:
75 / 5 = 15
Answer:
15 dogs
Step-by-step explanation:
Let the number of dogs be x
number of cats be y
5 times the number of cats = number of dogs
y = x*5
Since y = 75
75 = 5x
Bring 5 to the other side n divide
x= 75/5
= 15
Mary pays income tax according to the graduated schedule shown below. A 3-column table with 6 rows. Column 1 is labeled If taxable income is over with entries 0 dollars, 7,825 dollars, 31,850 dollars, 77,100 dollars, 160,850 dollars, 349,700 dollars. Column 2 is labeled but not over with entries 7,825 dollars, 31,850 dollars, 77,100 dollars, 160,850 dollars, 349,700 dollars, no limit. Column 3 is labeled the tax is with entries 10 percent of the amount of 0 dollars, 782 dollars and 50 cents plus 15 percent of the amount of 7,825 dollars, 4,386 dollars and 25 cents plus 25 percent of the amount of 31,850 dollars, 15,698 dollars and 75 cents plus 28 percent of the amount over 77,100 dollars, 39,148 dollars and 75 cents plus 33 percent of the amount of 160,850 dollars, 101,469 dollars and 25 cents plus 35 percent of the amount over 349,700 dollars. If Mary’s taxable income is $68,562, how much income tax does she owe, rounded to the nearest dollar?
Answer:
$13564
Step-by-step explanation:
[tex]\left|\begin{array}{c|c|c}$If taxable&& \\$income&&\\$ is over&$but not over&$the tax is\\---&---&---\\$0 &7,825 &$10\% of the amount over 0\\7,825 &31,850 &$782.50 plus $15\% $ of the amount over 7,825$ \end{array}\right|[/tex][tex]\left|\begin{array}{c|c|c}31,850 &77,100 &$4,386.25 plus 25\% of the amount over 31,850 \\77,100 &160,850 &$15,698.75 plus 28\% of the amount over 77,100\end{array}\right|[/tex]
[tex]\left|\begin{array}{c|c|c}160,850 &349,700 &$39,148.75 plus 33\% of the amount over 160,850 \\349,700 &$no limit&$101,469.25 plus 35\% of the amount over 349,700\end{array}\right|[/tex]
Mary’s taxable income= $68,562
From the table, If taxable income is over $31,850 but not over $77,100
The tax = $4386.25 + 25% of the amount over 31,850
Amount over $31,850=$68,562-$31,850
=$36,712
Therefore:
Mary's tax = $4386.25 + (25% of $36,712)
=$4386.25 +9,178
=$13564.25
=$13564 (to the nearest dollar)
Income tax is the tax charged on individual's or entities' income
Mary owes $13564 income tax
Given that the taxable income is $68,562.
Using the table as a guide, $68,562 falls within the income range $31,850 - $77,100
So, the tax is $4386 added to 25% of the excess over $31850
This is calculated as:
[tex]Tax = \$4386 + 25\% \times (Income -\$31850)[/tex]
Substitute $68,562 for income
[tex]Tax = \$4386 + 25\% \times (\$68562 -\$31850)[/tex]
Solve the expression in the bracket
[tex]Tax = \$4386 + 25\% \times \$36712[/tex]
Evaluate the product
[tex]Tax = \$4386 + \$9178[/tex]
Add the terms of the expression
[tex]Tax = \$13564[/tex]
Hence, Mary owes $13564 income tax
Read more about income tax at:
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A pound contains 9.4 cubic yards of water. What is
the volume of the water in cubic meters to the nearest
tenth?
A. 12.3
B. 8.6
C. 10.3
D. 7.2
Answer:
the answer is 7.2
Step-by-step explanation:
Please answer this correctly.
Answer:
m=(3+f)/(f-4)
Step-by-step explanation:
To make m the subject of the formula, we want to isolate m. That is, we want to move m to one side of the equation.
First, the fractions need to be taken away. Multiply both sides by m-1 to get: f(m-1)=4m+3.
The distributive property of subtraction tells us a(b-c)=ab-ac. Thus, from this equation we have fm-f=4m+3.
Subtracting 4m, we have fm-4m-f=3
Now, we work the distributive property backwards, where we have ab-ac=a(b-c). Rearrange the terms of fm and 4m, to get mf, and m4. Thus, this can be simplified to m(f-4).
Going back to the equation, we have m(f-4)-f=3.
Add f on both sides, so we have m(f-4)=3+f.
Divide by f-4, so we have m=(3+f)/(f-4)
Last month Maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. Let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. If she hiked a total of 90 miles, which equation can be used to find the number of times Maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x
Answer:
(C)90 – 10y = 5x
Step-by-step explanation:
Given:
x = number of times she hiked the 5-mile trail
Then, total Distance covered on the 5-mile trail =5xy = number of times she hiked the 10-mile trail
Then, total Distance covered on the 10-mile trail =10yMaria hikes a total of 90 miles
Therefore, total distance hiked can be represented by the equation:
5x+10y=90
Subtract 10y from both sides, we have:
5x=90-10y
This is option C.
Answer:
C
Step-by-step explanation:
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
[tex] \frac{4 {x }^{2} - 17x - 9 }{ {x}^{3} - 7 {x}^{2} + 7x + 15 } [/tex]
Step-by-step explanation:
In the picture.
I hope I am correct
I hope it helps :)
Find the length of side x in simplest radical form with a rational denominator.
PLZZZHELPPPPPPP
Step-by-step explanation:
sin60°=opposite/adjacent sin60°=x/7 √3/2=X/7 u will crisscross it here 7√3/2=XX=7√3/2Write the equation of the line that is parallel to the x-axis and goes through the point (1, 4).
Answer:
y=4
Step-by-step explanation:
A line that is parallel to the x-axis would have an equation of y= ______.
This is because a horizontal graph has a gradient of zero, thus the value of m in y=mx+c is zero.
y=0x +c
y= c
Since it passed through the point (1,4):
When x=1, y=4,
4= 0(1) +c
c= 4
Thus, the equation of the line is y=4.
Answer:
y =4
Step-by-step explanation:
Parallel to x axis means a horizontal line
Horizontal lines are of the form
y =
Since it goes through the point (1,4)
y =4
two technicians regularly make repairs when breakdowns occur on an automated production line. the first technican, who services 40% of the breakdowns, has 5% chance of making incomplete repair. the second technican, who services 60% of the breakdowns, has 3% chance of making an incomplete repair. given that there is a problem with the production line due to an incomplete repair, what is the probability that thids intial repair was made by the first technican
Answer:
52.63% probability that thids intial repair was made by the first technican
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Incomplete repair
Event B: Made by the first technican.
The first technican, who services 40% of the breakdowns, has 5% chance of making incomplete repair.
This means that [tex]P(B) = 0.4, P(A|B) = 0.05[/tex].
Probability of an incomplete repair:
5% of 40%(first technican) or 3% of 60%(second technican). So
[tex]P(A) = 0.05*0.4 + 0.03*0.6 = 0.038[/tex]
Given that there is a problem with the production line due to an incomplete repair, what is the probability that thids intial repair was made by the first technican
[tex]P(B|A) = \frac{0.4*0.05}{0.038} = 0.5263[/tex]
52.63% probability that thids intial repair was made by the first technican
A multiple-choice examination has 20 questions, each with five possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that he answers at least seventeen questions correctly? (Round your answer to three decimal places.)
Answer:
The probability that the student answers at least seventeen questions correctly is [tex]8.03\times 10^{-10}[/tex].
Step-by-step explanation:
Let the random variable X represent the number of correctly answered questions.
It is provided all the questions have five options with only one correct option.
Then the probability of selecting the correct option is,
[tex]P(X)=p=\frac{1}{5}=0.20[/tex]
There are n = 20 question in the exam.
It is also provided that a student taking the examination answers each of the questions with an independent random guess.
Then the random variable can be modeled by the Binomial distribution with parameters n = 20 and p = 0.20.
The probability mass function of X is:
[tex]P(X=x)={20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x};\ x =0,1,2,3...[/tex]
Compute the probability that the student answers at least seventeen questions correctly as follows:
[tex]P(X\geq 17)=P (X=17)+P (X=18)+P (X=19)+P (X=20)[/tex]
[tex]=\sum\limits^{20}_{x=17}{{20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x}}\\\\=0.00000000077+0.000000000032+0.00000000000084+0.000000000000042\\\\=0.000000000802882\\\\=8.03\times10^{-10}[/tex]
Thus, the probability that the student answers at least seventeen questions correctly is [tex]8.03\times 10^{-10}[/tex].
If three times a number, added to 2 is divided by the number plus 5, the result is eight thirds.
Answer:
Number = 34
Step-by-step explanation:
We are looking for our mystery "number". I will call this number N.
We can find out what our equation looks like based on what the question tells us.
"three times a number" is 3N
"added to 2" is + 2
Which so far is 3N + 2
"divided by the number plus 5" is ÷ [tex]{N+5}[/tex]
Combined with the first two parts to give us (3N + 2) ÷ (N + 5)
"the result is eight third" So the above equation is equal to 8/3
Combining all these comments together to get the following equation
(3N + 2) ÷ (N + 5) = 8/3
Rearrange by multiplying both sides of the = by (N+5)
3N + 2 ÷ (N + 5) × (N + 5) = 8/3 × (N + 5)
Simplify
3N + 2 = 8/3 × (N + 5)
3N + 2 = 8N/3 + 40/3
Bring the N numbers to one side and the non N numbers to the other side, by subtracting 2 from both sides of the =
3N + 2 - 2 = 8N/3 + 40/3 - 2
Simplify
3N = 8N/3 + 34/3
and then subtracting 8N/3 from both sides
3N - 8N/3 = 8N/3 - 8N/3 + 34/3
Simplify
1N/3 = 34/3
Simplify for our final answer by multiplying both sides of the = by 3
1N/3 x 3 = 34/3 x 3
N = 34
Many of these steps can be skipped when solving for yourself but I wanted to be thorough
A consumer group surveyed 146 airplane travelers after a flight and found that 132 of them would fly that airline again. Find the standard error for the sample proportion of airline travelers who would fly on that airline again. Enter your answer as a decimal rounded to three decimal places.
Answer:
[tex]\hat p =\frac{X}{n}[/tex]
And replacing we got:
[tex]\hat p =\frac{132}{146}= 0.904[/tex]
And for this case the standard error assuming normality would be given by:
[tex] SE= \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
And replacing we got:
[tex]SE= \sqrt{\frac{0.904*(1-0.904)}{146}}= 0.024[/tex]
Step-by-step explanation:
For this problem we know the following notation:
[tex] n= 146 [/tex] represent the sample size selected
[tex] X= 132[/tex] represent the number of airplane travelers who after a flight would fly that airline again
The estimated proportion for this case would be:
[tex]\hat p =\frac{X}{n}[/tex]
And replacing we got:
[tex]\hat p =\frac{132}{146}= 0.904[/tex]
And for this case the standard error assuming normality would be given by:
[tex] SE= \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
And replacing we got:
[tex]SE= \sqrt{\frac{0.904*(1-0.904)}{146}}= 0.024[/tex]
Solve for x. whats the solutions from least to greatest. 4x^2 + 48x + 128 = 0
Answer:
[tex]\boxed{\sf \ \ \ x = -8 \ or \ x = -4 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]4x^2+48x+128=0\\<=> 4(x^2+12x+32)=0\\<=> x^2+12x+32=0\\<=> (x+6)^2 - 36 + 32= 0\\\\<=> (x+6)^2-4=0\\<=> (x+6+2)(x+6-2)=0\\<=> (x+8)(x+4) = 0\\<=> x = -8 \ or \ x = -4[/tex]
vouch, i confirm that -8, -4 are the answers
explain why the solution to the absolute value inequality |4x-9|>-12 is all real numbers
Answer:
Step-by-step explanation:
Hello,
by definition the absolute value is always positive
so |4x-9| >= 0
so the equation |4x-9| > -12 is always true
so all real numbers are solution of this equation
hope this helps
In our decimal system, we distinguish odd and even numbers by looking at their ones (or units) digits. If the ones digit is even (0, 2, 4, 6, 8), the number is even. If the ones digit is odd (1, 3, 5, 7, 9), the number is odd. Determine whether this same criterion works for numbers expressed in base four
Answer:
Yes. In base 4 numbers if a number ends with 0 or 2 then it is an even number. If it ends with 1 or 3 then it is an odd number.
Step-by-step explanation:
The first 13 numbers in base 4 are written in brackets next to their corrsponding decimal number below
decimal number 0(0) ,1 (1) ,2(2), 3(3), 4(10), 5(11), 6(12), 7(13), 8,(20), 9(21), 10(22), 11(23), 12(30), 13(31) and so on
From above we can deduce that in base-4 any number ending with 0 or 2 is an even nmuber and any number ending with 1 or 3 is an odd number
Find the exact value of each of the following under the given conditions.
a. cosine left parenthesis alpha plus beta right parenthesis b. sine left parenthesis alpha plus beta right parenthesis c. tangent left parenthesis alpha plus beta right parenthesis
tangent alpha equals one half
, pi less than alpha less than StartFraction 3 pi Over 2 EndFraction
, and cosine beta equals three fifths
, StartFraction 3 pi Over 2 EndFraction less than beta less than 2 pi
Answer:
[tex](a)-\dfrac{11\sqrt{5}}{25} \\(b) -\dfrac{2\sqrt{5}}{25} \\(c)\dfrac{11}{2}[/tex]
Step-by-step explanation:
[tex]\tan \alpha =\dfrac12, \pi < \alpha< \dfrac{3 \pi}{2}[/tex]
Therefore:
[tex]\alpha$ is in Quadrant III[/tex]
Opposite = -1
Adjacent =-2
Using Pythagoras Theorem
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\=(-1)^2+(-2)^2=5\\Hypotenuse=\sqrt{5}[/tex]
Therefore:
[tex]\sin \alpha =-\dfrac{1}{\sqrt{5}}\\\cos \alpha =-\dfrac{2}{\sqrt{5}}[/tex]
Similarly
[tex]\cos \beta =\dfrac35, \dfrac{3 \pi}{2}<\beta<2\pi\\\beta $ is in Quadrant IV (x is negative, y is positive), therefore:\\Adjacent=$-3\\$Hypotenuse=5\\Opposite=4 (Using Pythagoras Theorem)[/tex]
[tex]\sin \beta =\dfrac{4}{5}\\\tan \beta =-\dfrac{4}{3}[/tex]
(a)
[tex]\cos(\alpha + \beta)=\cos\alpha\cos\beta-\sin \alpha\sin \beta\\[/tex]
[tex]=-\dfrac{2}{\sqrt{5}}\cdot \dfrac{3}{5}-(-\dfrac{1}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{2\sqrt{5}}{5}\cdot \dfrac{3}{5}+\dfrac{\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{2\sqrt{5}}{25}[/tex]
(b)
[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta[/tex]
[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta\\=-\dfrac{1}{\sqrt{5}}\cdot\dfrac35+(-\dfrac{2}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{\sqrt{5}}{5}\cdot\dfrac35-\dfrac{2\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{11\sqrt{5}}{25}[/tex]
(c)
[tex]\tan(\alpha + \beta)=\dfrac{\sin(\alpha + \beta)}{\sin(\alpha + \beta)}=-\dfrac{11\sqrt{5}}{25} \div -\dfrac{2\sqrt{5}}{25} =\dfrac{11}{2}[/tex]
WORK OUT THE VALUE of 19+7⌹2-5
Answer:
17.5
Step-by-step explanation:
Remember PEMDAS
step 1 : divide 7 by 2
7 ÷ 2 = 3.5
step 2 : rewrite the equation
19 + 3.5 - 5
step 3 : add 19 + 3.5
19 + 3.5 = 22.5
step 4 : subtract 22.5 - 5
22.5 - 5 = 17.5
Choose the correct simplification of a to the 5th power times b to the 6th power all over a to the 4th power times b to the 4th power. a9b10 ab2 1 over a times b to the 2nd power 1 over a to the 9th power times b to the 10th power
Answer:
ab²
Step-by-step explanation:
Step 1: Write out the expression
[tex]\frac{a^5b^6}{a^4b^4}[/tex]
Step 2: Cross out like terms
The a's cancel out, leaving a in the numerator
The b's cancel out, leaving b² in the numerator
Step 3: Finalize
ab²
And you have your final answer!
Answer:
the answer is ab^2
Step-by-step explanation:
hope this helps
PLEASE HELP MEH RN!!!
Answer:
its 4x
Step-by-step explanation:
Answer:
4x
Step-by-step explanation:
Please answer this correctly
Answer:
1-5: Make it 5 units tall
6-10: Make it 4 units tall
11-15: Make it 2 units tall
16-20: Make it 0 units tall (Don't do anything to it)
21-25: Make it 4 units tall
Step-by-step explanation:
1-5: 2, 3, 3, 3, 5 (5 numbers)
6-10: 6, 6, 8, 10 (4 numbers)
11-15: 11, 13 (2 numbers)
16-20: (0 numbers)
21-25: 22, 23, 24, 24 (4 numbers)
Answer:
The heights of the missing bars are the following:
1- 5 ⇒ 5
6-10 ⇒ 4
11-15 ⇒ 2
16-20 ⇒ 0
21-25 ⇒ 4
The endpoints of the directed line segment AB are A(−7, 4) and B(8, 9). Find the coordinates of point P along line segment AB so that the ratio of AP to PB is 2 to 3. pls help
Answer:
(-1,5)
Step-by-step explanation:
When a line segment is divided in the ratio m:n, we use the section formula to determine the point P which divides the line segment:
The coordinates of x and y are:
[tex](x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)[/tex]
Given:
[tex]A(x_1,y_1)=(-7, 4)\\B(x_2,y_2)=(8, 9)\\AP:PB=m:n=2:3[/tex]
The coordinates of P is:
[tex](x,y)=\left(\dfrac{2*8+3*-7}{2+3}, \dfrac{2*9+3*4}{2+3}\right)\\=\left(\dfrac{-5}{5}, \dfrac{25}{5}\right)\\\\=(-1,5)[/tex]
Please answer this correctly
Answer:
The range will decrease by 1
Step-by-step explanation:
Range: Largest no. - Smallest no.
The range with the original numbers is 7 -1 =6
The range when 1 is replaced by 6,the smallest no. becomes 2 which makes the range 7-2= 5
So 1st range - 2nd range =6 - 5 = 1
[ASAP] Which table represents the graph of a logarithmic function in the form y=log _(b)x when b>1
Answer:
the first table
Step-by-step explanation:
We see that the first table represents the logarithmic function [tex]y = \log_2x[/tex], so it's the first table.
The first table represents the graph of a logarithmic function in the form y=log _(b)x.
What is a logarithm?Exponentiation's inverse function is the logarithm. That is, the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised in order to obtain that number x.
The given table has data where y is a function of x;
y=F(x)
[tex]y=log _{b}x \\\\ -2 = log _{b}\frac{1}{4} \\\\ \frac{1}{4} = log _{b}{-2} \\\\ -1= log _{b}\frac{1}{2} \\\\ 0=log _{b}1 \\\\ 1=log _{b}2[/tex]
Hence the first table represents the graph of a logarithmic function in the form y=log _(b)x.
To learn more about the logarithm refer to the link;
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PLZZZZ HELPPP FOR BRAINLIEST! COMPARING EXPONENTIAL FUNCTIONS WHICH STATEMENT CORRECTLY COMPARES FUNCTIONS F AND G
Answer:
B. Left limits are the same; right limits are different.
Step-by-step explanation:
When we talk about "end behavior," we are generally concerned with the limiting behavior of the function for x-values of large magnitude. Decreasing exponential functions all have the same end behavior: they approach infinity on the left (for large negative values of x), and they approach a horizontal asymptote on the right (for large positive values of x).
If we are to write the end behavior in terms of specific limiting values, we would have to say that ...
as x → -∞, f(x) → ∞
as x → -∞, g(x) → ∞ . . . . . . the same end behavior as f(x)
__
and ...
as x → ∞, f(x) → -4
as x → ∞, g(x) → (some constant between 0 and 5) . . . . . different from f(x)
__
So, in terms of these limiting values, the left-end behavior is the same; the right-end behavior is different for the two functions, matching choice B.
A builder was paid £550 for the work he did. He spent 35% of the money on materials how much did the materials cost
Answer: £192.50
Step-by-step explanation:
550 x 0.35 = 192.50
a realtor uses a lock box to store the keys to a house that is for sale. the access code for the lock consist of five digits. the first digit cannot be 1 and the last digit must be even. how many different codes are avaible
Answer:
45,000 codes
Step-by-step explanation:
Given:
Code of 5 digits
Condition
First digit can't be 1Last digit must be evenRequired
Calculate the number of codes available
Digits = {0,1,2....9}
n(Digits) = 10
Let the format of the code be represented as follows;
ABCDE
From the conditions given
A can't be 1;
This means that A can be any of 0,2,3,4....9
This implies that A can be any of the above 9 digits
n(A) = 9
There's no condition attached to BCD;
This means that B can be any of 10 digits
This means that C can be any of 10 digits
This means that D can be any of 10 digits
n(B) = n(C) = n(D) = 10
Lastly, E must be an even number;
This means that E can be any of 0,2,4,6,8
This implies that E can be any of the above 5 digits
n(E) = 5
So,
Number of available codes = n(A) * n(B) * n(C) * n(D) * n(E)
Number of available codes = 9 * 10 * 10 * 10 *5
Number of available codes = 45,000
Hence, there are 45,000 available codes
Identify the polygon that has vertices A(−10,−1), P(−7,3), E(−3,0), and X(−6,−4), and then find the perimeter and area of the polygon.
Answer:
square; perimeter 20 units; area 25 square units.
Step-by-step explanation:
As the attachment shows, each side of the polygon is the hypotenuse of a 3-4-5 right triangle, so has length 5 units. The perimeter is the sum of those lengths, 4×5 = 20; the area is the product of the lengths of adjacent sides, 5×5 = 25.
The figure is a square of side length 5 units.
The perimeter is 20 units; the area is 25 square units.
For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent Mercer survey showed that 52% of U.S. employers were likely to require higher employee contributions for health care coverage. Suppose the survey was based on a sample of 700 companies. Compute the margin of error and a 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage. If required, round your answer to four decimal places. Round intermediate calculations to four decimal places. Margin of Error: Confidence Interval: to
Answer:
The 95% confidence interval estimate of the true population proportion of U.S. employers that were likely to require higher employee contributions for health care coverage is 0.52 +/- 0.0370
= (0.4830, 0.5570)
The margin of error M.E = 0.0370
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
p+/-z√(p(1-p)/n)
p+/-M.E
Given that;
M.E = margin of error
Proportion p = 52% = 0.52
Number of samples n = 700
Confidence interval = 95%
z value (at 95% confidence) = 1.96
Substituting the values we have;
0.52 +/- 1.96√(0.52(1-0.52)/700)
0.52 +/- 1.96(0.0189)
0.52 +/- 0.0370
( 0.4830, 0.5570)
The 95% confidence interval estimate of the true population proportion of U.S. employers that were likely to require higher employee contributions for health care coverage is 0.52 +/- 0.0370
= (0.4830, 0.5570)
The margin of error M.E = 0.0370
Quadrilateral J K L M is shown. A diagonal is drawn from point J to point L. Sides K L and J M are parallel. Sides J K and L M are congruent. The length of J L is 18, the length of J K is 16, and the length of J M is 40. Angle M is 45 degrees.
If KM is drawn on this quadrilateral, what will be its length?
Answer:
KM is 52.55
Step-by-step explanation:
Given that JKLM is a quadrilateral with a diagonal drawn from J to L, we have;
Sides KL is parallel to side JM
Side JK is congruent to side LM
Therefore, sides JK and LM are parallel being the equal distances between two parallel lines
JL = 18, JK = 16, therefore, LM = 16, JM = 40 therefore, KL = 40 (equal distances between parallel lines JK and LM)
∠M = 45° ∴ ∠L = 180° - 45° = 135° (sum of adjacent interior angles of a parallelogram)
By cosine rule, we have;
KM² = LM² + KL² - 2×KL×LM×cos(∠M) = 16² + 40² - 2×16×40×cos(135°)
KM² = 2761.0967
KM = √(2761.0967) = 52.55 units.
Answer:
18
Step-by-step explanation:
Edg 2021