Answer:
[tex]-2[/tex]
Step-by-step explanation:
Just substitute -3 for all instances of x.
[tex](-3)^{2} + 4(-3) + 1\\\\[/tex]
[tex]9 - 12 + 1[/tex]
[tex]-2[/tex]
14 Calculate the mode from the following data: 7,8, 6, 5, 10, 11, 4, 5,2 b. 5: а. 3.' 4 6 с. d: 6
MODE IS THE NUMBER THAT IS REPEATED THE HIGHEST TIME..
HERE, IN YOUR QUESTION 5CAME 2 TIMES i.e. it is repeated highest time .so mode=5....
Enunciate demerits of classical probability.
Answer:
Some demerits of classical probability are provided throughout the following portion.
Step-by-step explanation:
This could only be utilized if somehow the occurrences are fairly probable as well as predictable. Such supposition is established far in advance of the investigation or testing.This only applies whereas if an overall number of occurrences seems to be limited, one such term has quite a restricted scope, such as coins tossing, picking card numbers, etc.A rectangular garden is 5 ft longer than it is wide. Its area is 1800ft^2. What are its dimensions?
Answer:
The dimensions are 45 feet by 40 feet.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A=w\ell[/tex]
Where w is the width and l is the length.
The length is five feet longer than the width. Thus, we can write that:
[tex]\ell = w+5[/tex]
The total area is 1800 square feet. Substitute:
[tex]1800=w(w+5)[/tex]
Solve for w. Distribute:
[tex]w^2+5w=1800[/tex]
Subtract 1800 from both sides:
[tex]w^2+5w-1800=0[/tex]
Factor. We can use 45 and -40. Hence:
[tex]\displaystyle (w+45)(w-40)=0[/tex]
Zero Product Property:
[tex]w+45=0\text{ or } w-40=0[/tex]
Solve for each case:
[tex]\displaystyle w=-45\text{ or } w=40[/tex]
Since the width cannot be negative, we can ignore the first solution.
So, the width is 40 feet. Since the length is five feet longer, the length is 45 feet.
The dimensions are 45 feet by 40 feet.
indicate the following pairs of lines are coinciding, parallel ,perpendicular or neither
You are planning to buy a house for $800,000. City bank offers a 30 year loan at 4.9 % apr ( Annual percentage interest rate) if you put 20 % down. Calculate your expected monthly payment.
Answer:
3396.65
Step-by-step explanation:
Let's start by cacluating the amount the bank is loaning us
800000*.8=640000
Let's now calculate the effective rate: .049/12= .004083333333
let x= payment
[tex]640000=x\frac{1-(1+.004083333333)^{-30*12}}{.004083333333}\\x=3396.651012[/tex]
Solve the system of equations using the elimination method 5x+10y = 3
10x + 20y = 8
Answer:
No solution
Step-by-step explanation:
5x+10y=3 equation 1
10x+20y=8 equation 2
-2(5x+10y)=-2(3) multiply equation 1 by -2 to eliminate x
-10x-20y=-6 equation 1 multiplied by -2
10x+20y=8 equation 2
0 + 0 =2. Add above equations
0 =2
no solution
Help me on this please
Answer:
x = 3.5
Step-by-step explanation:
Triangle to the right:
4^2 + x^2 = 8^2
16 + x^2 = 64
y^2 = 48
Triangle to the left:
x^2 + 6^2 = 48
x^2 + 36 = 48
x^2 = 12
x = sqrt(12)
x = 3.5
i need helpp pleaseee
A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 82 months with a standard deviation of 7 months. If the claim is true, what is the probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
Answer:
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean life of 82 months with a standard deviation of 7 months.
This means that [tex]\mu = 82, \sigma = 7[/tex]
Sample of 71
This means that [tex]n = 71, s = \frac{7}{\sqrt{71}}[/tex]
What is the probability that the mean monitor life would be greater than 83.8 months?
1 subtracted by the p-value of Z when X = 83.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{83.8 - 82}{\frac{7}{\sqrt{71}}}[/tex]
[tex]Z = 2.17[/tex]
[tex]Z = 2.17[/tex] has a p-value of 0.985.
1 - 0.985 = 0.015
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
A survey found that the median number of calories consumed per day in a certain country was 3,304 and the mean was 3,204.9 calories. If a histogram were constructed for the data, would you expect it to be skewed to the right, to the left, or approximately symmetric
Answer:
Skewed to the left
Step-by-step explanation:
Given
[tex]Median = 3304[/tex]
[tex]Mean = 3204.9[/tex]
Required
The type of distribution
From the given data, we have:
[tex]Median \ne Mean[/tex] --- Mean and Median are not equal
and
[tex]Median > Mean[/tex] --- Median is greater than mean
When the median is greater than the mean; the histogram is expected to be left skewed
Which description of the graph of the linear inequality y > 3x – 8 is correct?
Options :
A.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below the line
B.The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the line.
C. The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the line.
D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line
Answer:
D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line
Step-by-step explanation:
The equation y > 3x – 8
Interpreting as a linear relation :
y > ax + b
Where, a = slope ; b = intercept
a = 3 ; that is a slope value of 3
b = -8 ; that is an intercept value of - 8
Since the inequality is >, a dashed line is used (dashed like is used for > and <) ; since we a have a greater than sign, the graph will be shaded above the dashed line.
Answer: The answer is D on edu 2021
Step-by-step explanation:
D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line
Graph g(x)=-8|x |+1.
Answer:
[tex] g(x)=-8|x |+1. = 9552815 \geqslant 6[/tex]
what's the answer to this
Answer:
the volume = 1152cm^2
Step-by-step explanation:
> The volume of cylinder =4 spheres
> Volume of sphere = v= 4/3πr³
> radius =6cm
volume of 4 spheres =
[tex]v \: = 4 \times \frac{4}{3} \times \pi \times {6}^{3} \\ \\ v = 1152cm {2} [/tex]
Answer:
the unused volume is 18095,57cm cubed
Mr johnson sells erasers for $3 each. He sold 96 erasers last week and he sold 204 erasers this week.
A. $300 B $600 C $100 D $900
I believe your answer is D.) $900
204 + 96 = 300
300 x 3 = 900
I hope this is correct and helps!
A Line passes through the .4 -6 and has a slope of -3 and four which is the equation of the line
Answer:
(in the image)
Step-by-step explanation:
I'm not sure I understood your question completely but I hope this helps.
A rare baseball card just sold for $12,000. Sports experts anticipate this baseball card to increase in value by 9% each decade.
According to the experts, about how much should the baseball card be worth in 30 years?
Hint: A decade is equal to 10 years.
$15,540.35
$159,212.14
$83,614.45
$9042.85
Answer:
$15,540
Step-by-step explanation:
I DONT KNOW IF ITS RIGHT THO BUT
9% = 1,800
The original price of a set lunch was 30 dollars. It is now sold at a 20%
discount. There is an extra discount of 10% for students. How much
should a student pay to order a set lunch?
The table shows the relationship between the number of faculty members and the number of students at a local school. What is the missing value?
Faculty
Students
1
17
2
34
3
51
4
?
17
68
85
102
Answer:
68
Step-by-step explanation:
I did it on my test
The missing value in the table is 68. The correct answer would be option (B).
What is the linear relationship?A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.
The table shows the relationship between the number of faculty members and the number of students at a local school.
Faculty Students
1 17
2 34
3 51
4 ?
The relationship between the number of faculty members and the number of students at the local school is that for every faculty member, there are 17 students.
Therefore, if there are 4 faculty members, we can find the number of students by multiplying 4 by 17, which gives us 68.
Thus, the missing value in the table is B. 68.
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When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M|B) represent? Is P(M|B) the same as P(B|M)?
Answer:
See explanation
Step-by-step explanation:
Given
[tex]M \to[/tex] randomly selecting a male
[tex]B \to[/tex] randomly selecting someone with blue eyes
Solving (a): Interpret P(M|B)
The above implies conditional probability
The interpretation is: the probability of selecting a male provided that a person with blue eyes has been selected
Solving (b): is (a) the same as P(B|M)
No, they are not the same.
The interpretation of P(B|M) is: the probability of selecting a person with blue eyes provided that a male has been selected
William invested $12,000 in a bank account that pays 9 percent simple interest. His friend invested the same amount at another bank that pays 8 percent interest compounded quarterly. These two functions, where t is time in years, represent the value of the investments: f(t) = 12(1.02)4t g(t) = 12(1.09)t The functions are graphed, and the point of intersection lies between 0.5 and 1.2. Based on the table, approximately how long will it be until both investments have the same value? Value of t f(t) = 12(1.02)4t g(t) = 12(1.09)t 0.5 12.48 6.54 0.6 12.58 7.84 0.7 12.68 9.16 0.8 12.79 10.46 0.9 12.89 11.87 1.0 12.99 13.08 1.1 13.09 14.39 1.2 13.20 15.70 A. 0.9 year B. 1.0 year C. 1.1 years D. 1.2 years
===========================================================
Explanation:
We have these two functions
f(t) = 12(1.02)^(4t)g(t) = 12(1.09)twhich represent the amounts for his friend and William in that order. Strangely your teacher mentions William first, but then swaps the order when listing the exponential function as the first. This might be slightly confusing.
The table of values is shown below. We have t represent the number of years and t starts at 0.5. It increments by 0.1
The f(t) and g(t) columns represent the outputs for those mentioned values of t. For example, if t = 0.5 years (aka 6 months) then f(t) = 12.48 and that indicates his friend has 12,480 dollars in the account.
I've added a fourth column labeled |f - g| which represents the absolute value of the difference of the f and g columns. If f = g, then f-g = 0. The goal is to see if we get 0 in this column or try to get as close as possible. This occurs when we get 0.09 when t = 1.0
So we don't exactly get f(t) and g(t) perfectly equal, but they get very close when t = 1.0
It turns out that the more accurate solution is roughly t = 0.9925 which is close enough. I used a graphing calculator to find this approximate solution.
It takes about a year for the two accounts to have the same approximate amount of money.
Answer:
B
Step-by-step explanation:
A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 volt, and the manufacturer wishes to test volts against volts, using units. In your intermediate calculations, use z-scores rounded to two decimal places (e.g. 98.76).
(a) The acceptance region is_____. Find the value of a.
(b) Find the power of the test for detecting a true mean output voltage of 5.1 volts.
Answer: hello your question was poorly written but i was able to the get missing parts online which enabled me resolve your question
answer:
a) a = 0.1096
b) 1.89 watts
Step-by-step explanation:
Std of output voltage = 0.25 volt
H0 : μ = 5 volts
Ha : μ ≠ 5 volts
n = 16
a) Acceptance region = 4.9 ≤ X ≤ 5.1
Determine the value of a
value of a = 0.0548 + 0.0548
= 0.1096
attached below is the reaming solution
note : a is a type 1 error
b) power of test
True mean output voltage = 5.1 volts
P = - 1.89 watts
power cant be negative hence the power of the test = 1.89 watts
in the pair of triangle, write the similarity statement and identify the postulate of theorem that justifies the similarity.
Answer:
ΔEFG ~ ΔRPQ - Angle Angle Angle Theorem
ΔEFG ~ ΔRFQ - Side Side Side Proportional Theorem
Step-by-step explanation:
First set : using triangle sum theory to find missing angle. Letters should match congruent angles when creating statement.
Second set :
[tex]\frac{EG}{RQ}[/tex] = [tex]\frac{10}{12}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{EF}{RF}[/tex] = [tex]\frac{15}{18}[/tex] = [tex]\frac{5}{6}[/tex]
[tex]\frac{FG}{FQ}[/tex] = [tex]\frac{20}{24}[/tex] = [tex]\frac{5}{6}[/tex]
Suppose 58% of the population has a retirement account. If a random sample of size 570 is selected, what is the probability that the proportion of persons with a retirement account will be less than 57%
Answer:
The probability that the proportion of persons with a retirement account will be less than 57%=31.561%
Step-by-step explanation:
We are given that
n=570
p=58%=0.58
We have to find the probability that the proportion of persons with a retirement account will be less than 57%.
q=1-p=1-0.58=0.42
By takin normal approximation to binomial then sampling distribution of sample proportion follow normal distribution.
Therefore,[tex]\hat{p}\sim N(\mu,\sigma^2)[/tex]
[tex]\mu_{\hat{p}}=p=0.58[/tex]
[tex]\sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]\sigma_{\hat{p}}=\sqrt{\frac{0.58\times 0.42}{570}}[/tex]
[tex]\sigma_{\hat{p}}=0.02067[/tex]
Now,
[tex]P(\hat{p}<0.57)=P(\frac{\hat{p}-\mu_{\hat{p}}}{\sigma_{\hat{p}}}<\frac{0.57-0.58}{0.02067})[/tex]
[tex]P(\hat{p}<0.57)=P(Z<-0.483)[/tex]
[tex]P(\hat{p}<0.57)=0.31561\times 100[/tex]
[tex]P(\hat{p}<0.57)[/tex]=31.561%
Hence, the probability that the proportion of persons with a retirement account will be less than 57%=31.561%
Use the completing the square to solve x^2+6x=12.
Answer:
x= -3 ± [tex]\sqrt{21}[/tex]
Step-by-step explanation:
[tex]x^{2}[/tex]+6x=12
We add 9 [[tex](6/2)^{2}[/tex]] to both sides to complete the square as [tex]x^{2}[/tex]+6x+9 = [tex](x+3)^{2}[/tex].
[tex](x+3)^{2}[/tex]=21
Now we take the square root of both sides:
x+3=±[tex]\sqrt{21}[/tex]
x= -3 ± [tex]\sqrt{21}[/tex]
Answer:
x = -3 ± [tex]\sqrt{21}[/tex]
Step-by-step explanation:
[tex]x^2+6x=12[/tex]
[tex](\frac{b}{2} )^{2}[/tex] = 9
[tex]x^2+6x + 9 =12 + 9[/tex]
[tex](x+3)^{2} =21[/tex]
x + 3 = [tex]\sqrt{21}[/tex]
x = -3 ± [tex]\sqrt{21}[/tex]
1. What is the area of the figure below? (1 point)
5 in.
3 in.
12 in
O 18 in.2
O 30 in.2
O 36 in.2
O 60 in.2
Answer: 36in2
Step-by-step explanation:
A= base *height
=12*3
=36
The Area of the figure is 36 in².
What is Area of parallelogram?The area of a parallelogram refers to the total number of unit squares that can fit into it and it is measured in square units (like cm2, m2, in2, etc). It is the region enclosed or encompassed by a parallelogram in two-dimensional space.
two equal, opposite sides,two intersecting and non-equal diagonals, andopposite angles that are equalThe area of a parallelogram can be calculated by multiplying its base with the altitude. The base and altitude of a parallelogram are perpendicular to each other. The formula to calculate the area of a parallelogram can thus be given as,
Area of parallelogram = b × h square units
where,
b is the length of the base
h is the height or altitude
Given:
base= 12 in
height= 3 in
Area of parallelogram,
= base * height
=12* 3
= 36 in²
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Which of the following consists of discrete data?
A. Number of suitcases on a plane.
B. Amount of rainfall.
C. Hair color.
D. Tree height.
Answer:
A
Step-by-step explanation:
Number of suitcases on a plane is discrete because you can only have an integer amount. You can't have a fraction of a suitcase on a plane.
round 3,236 to the nearest hundred
Answer:
3,200
Step-by-step explanation:
3 is less than 5 so you round down to 3,200
Which ordered pair is a solution of the equation?
y=-2x+5y=−2x+5y, equals, minus, 2, x, plus, 5
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Only (2,-9)(2,−9)left parenthesis, 2, comma, minus, 9, right parenthesis
(Choice B)
B
Only (-2,9)(−2,9)left parenthesis, minus, 2, comma, 9, right parenthesis
(Choice C)
C
Both (2,-9)(2,−9)left parenthesis, 2, comma, minus, 9, right parenthesis and (-2,9)(−2,9)left parenthesis, minus, 2, comma, 9, right parenthesis
(Choice D)
D
Neither
9514 1404 393
Answer:
B. only (-2, 9)
Step-by-step explanation:
A graph of the equation makes it easy to see that (-2, 9) is a solution and (2, -9) is not.
You can try these values of x in the equation to see what the corresponding y-values are.
y = -2{-2, 2} +5 = {4, -4} +5 = {9, 1}
Points on the line are (-2, 9) and (2, 1).
(2, -9) is not a solution.
Answer:
B
Step-by-step explanation:
I know it is B. I know it because I put b in and I got it right on khan academy
The slope of diagonal OA is ? and its equation is ?
Answer:
Slope = [tex]\frac{4}{3}[/tex]
Equation of the line → [tex]y=\frac{4}{3}x[/tex]
Step-by-step explanation:
Let the equation of diagonal OA is,
y = mx + b
Here, m = Slope of the line OA
b = y-intercept
Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through O(0, 0) and A(3, 4) will be,
m = [tex]\frac{4-0}{3-0}[/tex]
m = [tex]\frac{4}{3}[/tex]
Since, line OA is passing through the origin, y-intercept will be 0.
Therefore, equation of OA will be,
[tex]y=\frac{4}{3}x[/tex]
sec x tanx( 1- sin^2 x) = __x
Answer:
sin(x)
Step-by-step explanation:
sec x tanx(1 - sin^2 x)
1 - sin^2 x = cos^2 x
sec(x)tan(x)cos^2(x)
[tex]\frac{1}{cos(x)}[/tex] * [tex]\frac{sin(x)}{cos(x)}[/tex] * cos^2(x)
[tex]\frac{sin(x)cos^2(x)}{cos^2(x)}[/tex]
sin(x)
