Answer:
14 and 9
Step-by-step explanation:
Y values are always the second number in the parenthesis. The X value is the first one. I like to think of Y being dependent on X, so X goes first, then Y.
Which of the following points is a solution of y > Ixl + 5?
A. (0, 5)
B. (1, 7)
C. (7, 1)
Answer:
B. (1,7)
Step-by-step explanation:
We can substitute the x and y values of each coordinate into the inequality and test if they work.
Let's start with A, 5 being y and 0 being x .
[tex]5 > |0|+5\\5> 0+5\\5 > 5[/tex]
5 IS NOT greater than 5, they are the exact same, so A is out.
Let's try B, 1 being x and 7 being y.
[tex]7 > |1| + 5\\7 > 1 + 5\\7 > 6[/tex]
7 IS greater than 6, so B. (1,7) does work for this inequality!
Let's do C for fun, when 7 is x and 1 is y.
[tex]1 > |7| + 5\\1>7+5\\1>12[/tex]
1 IS NOT greater than 12, it is quite less than 12, so C doesn't work.
Therefore B. (1,7) works for the inequality of [tex]y > |x|+5[/tex].
Hope this helped!
[PLEASE HELP] in the function above, the slope of it will be multiplied by -4, and it’s y value of the y intercept will be decreased by only 1 units, which of these following graphs best represent the new function???
Answer:
Z (The one on the bottom right)
Step-by-step explanation:
You said that the y intercept goes down by 1 unit which makes only W and Z possible.
The slope is 1/2 and if you multiply that by -4 the new slope is -2 which means the change in y is -2 every time the change in x is 1. Which perfectly fits Z and if you have any questions please ask me with the comments!
What is the missing term in this arithmetic sequence? 9, 14, 19, __, 29, 34, …
Answer: 24 because you add 5 for every number ex: 9+5=14
Answer:
24
Step-by-step explanation:
The difference can be calculated by subtracting the second term with the first term.
d = 14 - 9
d = 5
The difference is 5.
Add 5 to 19.
19 + 5 = 24
A necklace was on sale for 20% discount off the original price of
$1250.00. What was the final sale price if 12.5% VAT has to be
paid?
Answer:
= $ [tex] \mathsf{1125}[/tex]Step-by-step explanation:
[tex] \mathrm{Given}[/tex],
[tex] \mathrm{Discount\% = 20\%}[/tex]
[tex] \mathrm{Marked \: price = 1250}[/tex]
[tex] \mathrm{Now \: let's \: find \: the \: discount \: amount}[/tex]
[tex] \mathrm{discount \: amount = dis\% \: of \: MP}[/tex]
[tex] \mathrm { = 20\% \: of \: 1250}[/tex]
[tex] \mathrm{ = 250}[/tex]
[tex] \mathrm{let's \: find \: the \: selling \: price}[/tex]
[tex] \mathrm{ = MP \: - \: discount \: amount}[/tex]
[tex] \mathrm{ = 1250 - 250}[/tex]
= $ [tex] \mathrm{1000}[/tex]
[tex] \mathrm{lets \: find \: the \: Vat \: amount}[/tex]
[tex] \mathrm{vat \: amount = vat\% \: of \: sp}[/tex]
[tex] \mathrm{ = 12.5\% \: of \: 1000}[/tex]
= $ [tex] \mathrm{ 125}[/tex]
[tex] \mathrm{Now \: finally \: let's \: find \: the \: selling \: price \: with \: vat}[/tex]
[tex] \mathrm{selling \: price \: + \: vat \: amount}[/tex]
[tex] \mathrm{ = 1000 + 125}[/tex]
= $ [tex] \mathrm{1125}[/tex]
Therefore, The final sale of the necklace is $ 1125
Hope I helped
Best regards!
When josh borrowed money, he originally agreed to repay the loan by making three equal payments of $1500, with a payment due now, another payment due two years from now, and the final payment due four years from now. Instead of the original payments, he plans to pay off the loan by making a single payment of 5010. If interest is 10%, compounded annually, when will he make the single payment?
Answer:
5 years
Step-by-step explanation:
Principal Amount to be paid=$4500
Interest rate = 2%
Number if Times compounded= number of years
Number of years = x
Among total= $5010
A= p(1+r/n)^(nt)
But n= t =x
A= p(1+r/x)^(x²)
5010=4500(1+0.02/x)^(x²)
5010/4500 = (1+0.02/x)^(x²)
1.11333=( 1+0.02/x)^(x²)
Using trial and error method the number of years maximum to give approximately $5010 is 5 years
The mean rate for cable with Internet from a sample of households was $106.50 per month with a standard deviation of $3.85 per month. Assuming the data set has a normal distribution, estimate the percent of households with rates from $100 to $115.
Answer:
The percent of households with rates from $100 to $115. is [tex]P(100 < x < 115) =[/tex]94.1%
Step-by-step explanation:
From the question we are told that
The mean rate is [tex]\mu =[/tex]$ 106.50 per month
The standard deviation is [tex]\sigma =[/tex]$3.85
Let the lower rate be [tex]a =[/tex]$100
Let the higher rate be [tex]b =[/tex]$ 115
Assumed from the question that the data set is normally
The estimate of the percent of households with rates from $100 to $115. is mathematically represented as
[tex]P(a < x < b) = P[ \frac{a -\mu}{\sigma } } < \frac{x- \mu}{\sigma} < \frac{b - \mu }{\sigma } ][/tex]
here x is a random value rate which lies between the higher rate and the lower rate so
[tex]P(100 < x < 115) = P[ \frac{100 -106.50}{3.85} } < \frac{x- \mu}{\sigma} < \frac{115 - 106.50 }{3.85 } ][/tex]
[tex]P(100 < x < 115) = P[ -1.688< \frac{x- \mu}{\sigma} < 2.208 ][/tex]
Where
[tex]z = \frac{x- \mu}{\sigma}[/tex]
Where z is the standardized value of x
So
[tex]P(100 < x < 115) = P[ -1.688< z < 2.208 ][/tex]
[tex]P(100 < x < 115) = P(z< 2.208 ) - P(z< -1.69 )[/tex]
Now from the z table we obtain that
[tex]P(100 < x < 115) = 0.9864 - 0.0455[/tex]
[tex]P(100 < x < 115) = 0.941[/tex]
[tex]P(100 < x < 115) =[/tex]94.1%
6th grade math, help me pleasee:)
Answer:
8 pounds
Step-by-step explanation:
2 x 3 = 6 tb of chili powder in pot 2
find pounds per tablespoon: 48 / 6 = 8 pounds
Answer:
1/2 pound per tablespoon
Step-by-step explanation:
Jaden sure does like his chili!
In the first and second pot, he uses 3 pounds worth of ground beef, which means, 12 ounces of something is a pound. And because Jaden had used 3 times the amount of chili powder in the second pot, he used 6 tablespoons worth of powder. 3 pounds divided by 6 equals 1/2.
3.01)Which statement best describes the area of the triangle shown below?
9
It is one-half the area of a rectangle of length 4 units and width 2 units.
It is twice the area of a rectangle of length 4 units and width 2 units.
O It is one-half the area of a square of side length 4 units.
Ont is twice the area of a square of side length 4 units.
Answer:
C. It is one-half the area of a square of side length 4 units.
Step-by-step explanation:
Hey there!
Well if a square has side lengths of 4 units,
the area would be 16 because of l*w.
Now the formula for the area of a triangle is,
b*h/2
b = 4
h = 4
4*4=16
16 ÷ 2 = 8
So the area of a square is 16 units^2 whereas the area of a triangle with the same dimensions is 8 units^2,
meaning the area of a triangle is one-half the area of a square.
Hope this helps :)
Does anyone know the answers to these?
Step-by-step explanation:
a. The point estimate is the mean, 47 days.
b. The margin of error is the critical value times the standard error.
At 31 degrees of freedom and 98% confidence, t = 2.453.
The margin of error is therefore:
MoE = 2.453 × 10.2 / √32
MoE = 4.42
c. The confidence interval is:
CI = 47 ± 4.42
CI = (42.58, 51.42)
d. We can conclude with 98% confidence that the true mean is between 42.58 days and 51.42 days.
e. We can reduce the margin of error by either increasing the sample size, or using a lower confidence level.
Efficiency is the ratio of output work to input work, expressed as a percentage. Light bulbs put out less light energy than the amount of electrical energy that is put into the bulb. An illustration of a wide arrow with a light bulb at the tail of it labeled electrical energy 100 J, breaks into a small arrow going forward labeled light 10 J and a larger curling away labeled heat 90 J. The goal of the bulb is to produce light. What is the efficiency of this bulb as it works to put out light? 10% 80% 90% 100%
Answer:
10%
Step-by-step explanation:
Using the given formula with the given data, we have ...
efficiency = output work / input work
= (10 J)/(100 J) = 0.10 = 10%
Answer:
A) 10%
Step-by-step explanation:
10/100=10
3^x = 27^a+b and a^2-b^2/(a-b)=5 What is x?
Probability of landing on even # on a spinner; probability of rolling an odd # on a die
Answer:
Spinner: 50%
Die: 50%
Step-by-step explanation:
Well for the spinner it depends on the amount of numbers it has,
in this case we’ll use 6.
So The probability of landing on the even numbers in a 6 numbered spinner.
2, 4, 6
3/6
50%
Your average die has 6 sides so the odd numbers are,
1, 3, 5
3/6
50%
[PLEASE HELP] in the function above, the slope of it will be multiplied by 1/2 and it’s y value of its y intercept will be increased by 3 units, which of the graphs below best shows the new function???
Answer:
The graph at the bottom left in your group of possible answers.
Step-by-step explanation:
Notice that the original given graph corresponds to the equation:
[tex]y=2x+1[/tex]
since the line's slope is 2/1 = 2 and the y-intercept is at the point (0, 1).
So if one modifies the equation multiplying the current slope by 1/2, and the y intercept increased by 3 units, Then the new function would be:
[tex]y=x+4[/tex]
A line of slope 1 and y-intercept at (0, 4)
Notice that the graph at the bottom left in your possible answers is representing such function.
Answer:
Answer Y: or Bottom Left of Given Answers
Step-by-step explanation:
x varies directly as y, when x=4,y=3. find Y when x=5
Answer:
Y =4
Step-by-step explanation:
Hope it helps
In △ABC, m∠A=27 °, c=14 , and m∠B=25 °. Find a to the nearest tenth.
Answer:
a = 8.1
Step-by-step explanation:
Firstly, since we have a triangle, automatically, we have 3 interior angles
Mathematically the sum of these angles = 180
A + B + C = 180
27 + 25 + C = 180
52 + C = 180
C = 180-52
C = 128
We use the sine rule to find a
The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle
Thus, mathematically according to the sine rule;
c/Sin C = a/Sin A
14/sin 128 = a/sin 27
a = 14sin27/sin 128 = 8.0657
which to the nearest tenth is 8.1
Arrange the cards below to show the solution to 40.091 x 10³
Answer:
40091.
Step-by-step explanation:
Multiply 40.091 by 10 three times to get the answer.
40.091 * 10 = 400.91
400.91 * 10 = 4009.1
4009.1 * 10 = 40091.
The expression 40.091 x 10³ can be represented as 40091.
What are exponents?The term xⁿ, read as x to the power n, shows an exponent n, which implies x is multiplied by itself n times.
How to solve the given question?In the question, we are asked to arrange the cards showing '.', '0', '0', '1', '4', and '9', to show the solution to the expression 40.091 x 10³.
Now, 10³ is 10 to the power 3, where 3 is the exponent, so 10 is multiplied by itself 3 times = 10*10*10 = 1000.
Now, the expression 40.091 x 10³ = 40.091 * 1000 = 40091.
∴ The expression 40.091 x 10³ can be represented as 40091.
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Determine which of the sets of vectors is linearly independent. A: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t B: The set where p1(t) = t, p2(t) = t2, p3(t) = 2t + 3t2 C: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t + t2
Answer:
The set of vectors A and C are linearly independent.
Step-by-step explanation:
A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:
[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)= t^{2}[/tex] and [tex]p_{3}(t) = 3 + 3\cdot t[/tex]:
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0[/tex]
[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1} + 3\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2} = 0[/tex]
[tex]\alpha_{3} = 0[/tex]
Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.
[tex]p_{1}(t) = t[/tex], [tex]p_{2}(t) = t^{2}[/tex] and [tex]p_{3}(t) = 2\cdot t + 3\cdot t^{2}[/tex]
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0[/tex]
[tex](\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1}+2\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2}+3\cdot \alpha_{3} = 0[/tex]
Since the number of variables is greater than the number of equations, let suppose that [tex]\alpha_{3} = k[/tex], where [tex]k\in\mathbb{R}[/tex]. Then, the following relationships are consequently found:
[tex]\alpha_{1} = -2\cdot \alpha_{3}[/tex]
[tex]\alpha_{1} = -2\cdot k[/tex]
[tex]\alpha_{2}= -2\cdot \alpha_{3}[/tex]
[tex]\alpha_{2} = -3\cdot k[/tex]
It is evident that [tex]\alpha_{1}[/tex] and [tex]\alpha_{2}[/tex] are multiples of [tex]\alpha_{3}[/tex], which means that the set of vector are linearly dependent.
[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)=t^{2}[/tex] and [tex]p_{3}(t) = 3+3\cdot t +t^{2}[/tex]
[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]
[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2}+ \alpha_{3}\cdot (3+3\cdot t+t^{2}) = 0[/tex]
[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1+(\alpha_{2}+\alpha_{3})\cdot t^{2}+3\cdot \alpha_{3}\cdot t = 0[/tex]
The following system of linear equations is obtained:
[tex]\alpha_{1}+3\cdot \alpha_{3} = 0[/tex]
[tex]\alpha_{2} + \alpha_{3} = 0[/tex]
[tex]3\cdot \alpha_{3} = 0[/tex]
Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.
The set of vectors A and C are linearly independent.
Statistics students in Oxnard College sampled 10 textbooks in the Condor bookstore, and recorded number of pages in each textbook and its cost. The bivariate data is shown below, Number of Pages ( x ) Cost( y ) 526 52.08 625 59 589 56.12 409 25.72 489 34.12 500 53 906 78.48 251 26.08 595 50.6 719 68.52 A student calculates a linear model y = x + . (Please show your answers to two decimal places) Use the model above to estimate the cost when number of pages is 563 Cost = $ (Please show your answer to 2 decimal places.)
Answer:
y = -0.85 + 0.09x; $49.82
Step-by-step explanation:
1. Calculate Σx, Σy, Σxy, and Σx²
The calculation is tedious but not difficult.
[tex]\begin{array}{rrrr}\mathbf{x} & \mathbf{y} & \mathbf{xy} & \mathbf{x^{2}}\\526 & 52.08 & 27394.08 & 276676\\625& 59.00 & 36875.00 &390625\\589 & 56.12 & 33054.68 & 346921\\409 & 25.72 & 10519.48 & 167281\\489 & 34.12& 16684.68 & 293121\\500 & 53.00 & 26500.00 &250000\\906 & 76.48 & 71102.88 & 820836\\251 &26.08 & 6546.08 & 63001\\595 & 50.60 & 30107.00 & 354025\\719 & 68.52 & 49265.88 & 516961\\\mathbf{5609} & \mathbf{503.72} &\mathbf{308049.76} & \mathbf{3425447}\\\end{array}[/tex]
2. Calculate the coefficients in the regression equation
[tex]a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}} = \dfrac{503.7 \times 3425447 - 5609 \times 308049.76}{10 \times 3425447- 5609^{2}}\\\\= \dfrac{1725466163 - 1727851103.84}{34254470 - 31460881} = -\dfrac{2384941}{2793589}= \mathbf{-0.8537}[/tex]
[tex]b = \dfrac{n\sumx y - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}} = \dfrac{3080498 - 2825365.48}{2793589} = \dfrac{255132}{2793589} = \mathbf{0.09133}[/tex]
To two decimal places, the regression equation is
y = -0.85 + 0.09x
3. Prediction
If x = 563,
y = -0.85 + 0.09x = -0.85 + 0.09 × 563 = -0.85 + 50.67 = $49.82
(If we don't round the regression equation to two decimal places, the predicted value is $50.56.)
What is the missing side lenght in the triangle below?
Answer:
45
Step-by-step explanation:
Let's call the missing side x
This is a right triangle and in right triangles the square length of hypotenuse is equal to sum of square length of base and side lengths
53^2 = 28^2 + x^2
x = 45
PLZ help me !!!!!! QUICKLY
What is the solution to the inequality −1/6e ≥ 2 ?
Answer:
e < -12Step-by-step explanation:
In algebra, we always need to follow a set of steps that involve undoing the operations that led to the equation to reveal the value of x.
Step 1: Divide by -1/6e < -12
(Since we divided by a negative number, we must reverse the inequality sign.)
Step 2: Check(-1/6)(-12) > 2
2 > 2 ✅
Now we check a number less than -12, such as -14.
(-1/6)(-14) > 2
2 1/3 > 2 ✅
The correct answer is: e < -12I'm always happy to help :)We draw a random sample of size 25 from a normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?
Answer:
11.2≤[tex]\mu[/tex]12.8Step-by-step explanation:
Confidence interval for the population mean is expressed by the formula;
CI = xbar ± Z(S/√n) where;
xbar is the sample mean = 12.5
Z is the z score at 99% confidence = 2.576
S is the standard deviation = √variance
S = √2.4 = 1.5492
n is the sample size = 25
Substituting the given values into the formula given above,
CI = 12.5 ± 2.576(1.5492/√25)
CI = 12.5 ± 2.576(0.30984)
CI = 12.5 ± 0.7981
CI = (12.5-0.7981, 12.5+0.7981)
CI = (11.2019, 12.7981)
Hence the 99% confidence interval for the population mean is 11.2≤[tex]\mu[/tex]12.8 (to 1 decimal place)
A 99% confidence interval for the population mean will be "11.2 [tex]\leq[/tex] 12.8".
StatisticsAccording to the question,
Sample mean, [tex]\bar x[/tex] = 12.5
Z score at 99%, Z = 2.576
Standard deviation, S = √Variance
= √2.4
= 1.5492
Sample size, n = 25
We know the formula,
Confidence interval, CI = [tex]\bar x \ \pm[/tex] Z ([tex]\frac{S}{\sqrt{n} }[/tex])
By substituting the given values, we get
= 12.5 [tex]\pm[/tex] 2.576 ([tex]\frac{1.5492}{\sqrt{25} }[/tex])
= 12.5 [tex]\pm[/tex] 2.576 (0.30984)
= 12.5 [tex]\pm[/tex] 0.7981
Now,
Cl = (12.5 - 0.7981, 12.5 + 0.7981)
= (11.2019, 12.7981) or,
= (11.2, 12.8)
Thus the above answer is appropriate.
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What is ∛2197? Explain how you got your answer.
Answer:
13
Step-by-step explanation:
We need to write our answer in exponential form. Ask yourself the question, "What times itself 3 times will give you 2197?" Your answer is [tex]13^{3}[/tex]. This will go inside of your cube root. You now have [tex]\sqrt[3]{13^{3} }[/tex]. Since there's a power of 3 and a cube root, those cancel each other out, and your answer is 13.
Answer:
[tex]\boxed{13}[/tex]
Step-by-step explanation:
=> [tex]\sqrt[3]{2197}[/tex]
Factorizing 2197 gives 13 * 13 * 13
=> [tex]\sqrt[3]{13*13*13}[/tex]
=> [tex]\sqrt[3]{13^3}[/tex]
We know that [tex]\sqrt[3]{} = ^{1/3}[/tex]
=> [tex]13^{3 * 1/3}[/tex]
=> [tex]13^1[/tex]
=> 13
The ratio of oranges in a fruit salad to people it will serve is 9/40, or 9:40. If Lisa wants to serve 800 people, how many oranges will Lisa use?
The correct answer is 180 oranges
Explanation:
In mathematics, a ratio expresses two or more numbers that are related. In the case fo the ration 9: 40 this expresses 9 oranges are used to serve fruit salad for 40 people. Now, if you need to determine what is the number of oranges not for 40 people but for 800 people you can use cross multiplication. This process is explained below:
[tex]\frac{9}{40} = \frac{x}{800}[/tex] - 1. Multiply 9 x 800 and 40 x x (cross multiplication)
[tex]7200 = 40x[/tex] - 2. Solve the equation by diving 7200 into 40
[tex]\frac{7200}{40} = x[/tex]
[tex]x = 180[/tex] - 3. 180 represents the number of oranges to serve 800 people, which can be expressed as 180: 800
Louden County Wildlife Conservancy counts butterflies each year. Data over the last three years regarding four types
of butterflies are shown below. What is the average number of Variegated Fritillaries for all three samples?
A. 55 B.83 C.106 D.165
Answer:
A). 55
Step-by-step explanation:
Number of Variegated Fritillaries for each year is
2009 = 7
2010= 95
2011= 63
The sum total of the samples= 7+95+63
The sum total of the samples= 165
Number of years= 3
The average= total/number of years
The average= 165/3
The average= 55
Answer: A
Step-by-step explanation: I have a massive brain (•-*•)
The product of 6 and a number (n) is 48 . Which equation shows this relationship? ANSWER CHOICES: 6n=48 n+6=48 48n=6 n-6=48
Answer:
6n=48
Step-by-step explanation:
product means multiplication
6×n=48
6n=48
An equation that shows this relationship is: A. 6n = 48.
How to determine the equation representing the product?In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:
Let the variable n represent the unknown number.
Based on the statement "The product of 6 and a number is 48," we can logically deduce the following algebraic equation;
6 × n = 48
6n = 48
n = 48/6
n = 8.
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A sample of 4 different calculators is randomly selected from a group containing 42 that are defective and 20 that have no defects. What is the probability that all four of the calculators selected are defective? No replacement. Round to four decimal places.
Answer: = approx 0.2006
Step-by-step explanation:
The probability that first 1 randomly selected calculator is defective is
P(1st defect)= 42/(42+20)=42/62=21/31
If the first calculator is defective the residual number of defective calculators is 42-1=41. The residual total number number of calculators is 62-1=61
So the probability that second calculator is defected
P(2nd defective)=41/61
If both previous calculators are defective the residual number of defective calculators is 42-2=40. Total residual number of calculators is 62-2=60
So the probability that third calculator is defected
P(3rd defective)=40/60=2/3
Finally the probability that also fourth calculator is defective is 39/59
P(4th defective)=39/59
The resulted probability that all 4 calculators are defective is
P(all 4 are defective)= P(1st defect)* P(2nd defect) * P(3rd defect)* P(4th defect)=21*41*2*39/(31*61*3*59)=67158/334707=0.200647... = approx 0.2006
From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ).
a. The normal distribution can be used.
b. The t distribution with 6 degrees of freedom must be used.
c. The sample size must be increased.
d. The t distribution with 5 degrees of freedom must be used.
Answer:
d) The t-distribution with 5 degrees of freedom must be used
Step-by-step explanation:
For cases of Normal Distribution where the variance is unknown and the sample size n is smaller than 30, we must use the t-student distribution.
The shape of the curve for t-student is bell-shape (flatter and with wider tails than the bell shape of normal distribution.
Actually, when we deal with t-student distribution we are dealing with a family of curves that will become closer and closer to the bell shape of the normal distribution as the degree of freedom increases. From values of n =30( and bigger), we can assume that the curve of t-student is the same as for normal distribution
omplete)
HWS
X 3.3.13-BE
The manufacturer's suggested retail price (MSRP) for a particular car is $25,495, and it is expected to be worth $20,081 in 2 years.
(a) Find a linear depreciation function for this car.
(b) Estimate the value of the car 4 years from now.
(c) At what rate is the car depreciating?
(a) What is the linear depreciation function for this car?
f(x) =
(Simplify your answer. Do not include the $ symbol in your answer.)
Answer:
a) y = 25495 - 2707x
b) y = 25495 - 2707(4) = 14,667
c) $2,707 per year
Step-by-step explanation:
Value now: $25,495
Value in 2 years: $20,081
Loss of value in 2 years: $25,495 - $20,081 = $5,414
Loss of value per year: $5,414/2 = $2,707
a) y = 25495 - 2707x
b) y = 25495 - 2707(4) = 14,667
c) $2,707 per year
According to the National Health Statistics Reports, the standard deviation of the weights of all one-year-old baby boys born in the U.S. is 5.3 pounds. A random sample of 360 one-year-old baby boys born in the U.S. had a mean weight of 25.5 pounds.
a) Construct a 90% confidence interval for the mean weight of all one-year-old baby boys in the U.S. Write a sentence that interprets this interval.
b) Should this confidence interval be used to estimate the mean weights of all one-year-old babies in the U.S.? Explain.
Answer: A) At 90% confidence interval estimate of the population mean
is,( 25.0405 , 25.9595 )
B) YES
Step-by-step explanation:
Given that,
Point estimate = sample mean Ж = 25.5
Population standard deviation α = 5.3
Sample size = n =360
At 90% confidence level the z is ,
∝ = 1 - 90% = 1 - 0.90 = 0.1
∝ / 2 = 0.1 / 2 = 0.05
Z∝/2 = Z0.05 = 1.645 ( WHEN WE USE THE Z TABLE )
Margin of error E = Z∝/2 * ( α/√n)
E = 1.645 * (5.3 / √360 ) = 0.4595
At 90% confidence interval estimate of the population mean
is
Ж - E < ц < Ж + E
25.5 - 0.4595 < ц < 25.5 + 0.4595
25.0405 < ц < 25.9595
( 25.0405 , 25.9595 )
At 90% confidence interval estimate of the population mean
is,( 25.0405 , 25.9595 )
B) This confidence interval can be used to estimate the mean weight of all one - year old babies in the US since the mean value of 25.5 falls within the confidence values, we have sufficient evidence to
conclude that the mean weight of all one-year-old boys is 25.5
Which is hyperplane is better between B1 and B2? a. B1 is better than B2 b. B2 is better than B1 c. Both B1 and B2 are the same d. Neither B1 nor B2
Answer:
a. B1 is better than B2.
Step-by-step explanation:
Hyperplane is a geometric shape which has subspace whose dimension is one less than ambient space. Hyperplane that maximizes the margin it will have better generalization. Margin is calculated by [tex]\frac{2}{||W||}[/tex]. The correct option is a.
Answer:
A
Step-by-step explanation: