Answer:
0.0035289
Step-by-step explanation:
From the question;
mean annual salary = $63,500
n = sample size = 31
Standard deviation = $6,200
Firstly, we calculate the z-score of $60,500
Mathematically;
z-score = x-mean/SD/√n = (60500-63500)/6200/√(31) = -2.6941
So we want to find the probability that P(z < -2.6941)
We can get this from the standard normal table
P( z < -2.6941) = 0.0035289
Find the equation, in standard form, of the line passing through the points
(2,-3) and (4,2).
Answer:
Standard form = y = mx + c
m = Δy/Δx
m = 5/2
y = 5/2 x + c
Sub in (4,2)
2 = 10 + c
c = -8
y = 5/2 x - 8
Step-by-step explanation:
The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by σ = 14.7. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
Answer:
There is sufficient evidence to support the claim that the standard deviation is less than 14.7.
Step-by-step explanation:
From the question we are told that that the null hypothesis is
[tex]H_o : \sigma < 14.7[/tex]
Now given from the question that this null hypothesis was rejected, it mean, in non technical term that there is sufficient evidence to support the claim that the standard deviation is less than 14.7.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each sequence to its appropriate recursively defined function. f(1) = 13 f(n) = f(n - 1) + 26 for n ≥ 2 f(1) = 13 f(n) = 3 · f(n - 1) for n ≥ 2 f(1) = -24 f(n) = -4 · f(n - 1) for n ≥ 2 f(1) = 28 f(n) = f(n - 1) - 84 for n ≥ 2 f(1) = 28 f(n) = -4 · f(n - 1) for n ≥ 2 f(1) = -24 f(n) = 4 · f(n - 1) for n ≥ 2 Sequence Recursively Defined Function -24, -96, -384, -1,536, ... 28, -112, 448, -1,792, ... 13, 39, 65, 91, ...
Answer:
sequence 3no matching sequenceno matching sequenceno matching sequencesequence 2sequence 1Step-by-step explanation:
Recursively Defined Function Sequence
f(1) = 13 f(n) = f(n - 1) + 26 for n ≥ 2 13, 39, 65, 91, ...
f(1) = 13 f(n) = 3 · f(n - 1) for n ≥ 2
f(1) = -24 f(n) = -4 · f(n - 1) for n ≥ 2
f(1) = 28 f(n) = f(n - 1) - 84 for n ≥ 2
f(1) = 28 f(n) = -4 · f(n - 1) for n ≥ 2 28, -112, 448, -1,792, ...
f(1) = -24 f(n) = 4 · f(n - 1) for n ≥ 2 -24, -96, -384, -1,536, ...
__
The initial values are easily seen. They match f(1). The recursive functions can be tested to see if they match the offered sequences.
sequence 1 has a common ratio of 4 (not -4)
sequence 2 has a common ratio of -4 (it is not arithmetic)
sequence 3 has a common difference of 26 (it is not geometric)
Answer:
1 is sequence 3
5 is sequence 2
6 is sequence 1
(These r not included in the test, so don't use them)
|
\ /
2 is no matching sequence
3 is no matching sequence
4 is no matching sequence
Step-by-step explanation:
PLATO
This table shows values that represent an exponential function.
What is the average rate of change for this function for the interval from x = 1
to x = 3?
Answer:
B. 3
Step-by-step Explanation:
To find the average rate of change of the exponential function represented by the table of values above can be calculated using the general formula for average rate of change of a function, which is given as [tex] m = \frac{f(b) - f(a)}{b - a} [/tex]
Where,
[tex] a = 1, f(1) = 7 [/tex]
[tex] b = 3, f(3) = 13 [/tex]
Plug in the above values in the average rate of change formula:
[tex] m = \frac{13 - 7}{3 - 1} [/tex]
[tex] m = \frac{6}{2} [/tex]
[tex] m = 3 [/tex]
Average rate of change is B. 3
Answer:
3
Step-by-step explanation:
I hope u can understand help asap
i think u can see sho T=5n+20
Answer:
T(n) = 5n + 20
Step-by-step explanation:
1 candy has a mass of 5 g.
n candies have a mass of 5n grams.
The box has a mass of 20 grams.
total mass = mass of candies + mass of box
T(n) = 5n + 20
n T(n)
0 20
25 145
50 270
75 395
100 520
x-5y=-15x−5 Complete the missing value in the solution to the equation. (-5, )
Answer:
y = -15
Step-by-step explanation:
x-5y=-15x−5
Let x = -5
-5 -5y = -15 * -5 -5
Combine like terms
-5 -5y = 75-5
-5 -5y = 70
Add 5 to each side
-5y = 75
Divide by -5
y = -15
In △ABC,a=11 , b=20 , and c=28 . Find m∠A .
Answer:
18.4°
Step-by-step explanation:
Use law of cosine.
a² = b² + c² − 2bc cos A
11² = 20² + 28² − 2(20)(28) cos A
121 = 1184 − 1120 cos A
cos A = 0.949
A = 18.4°
Different hotels in a certain area are randomly selected, and their ratings and prices were obtained online. Using technology, with x representing the ratings and y representing price, we find that the regression equation has a slope of 130 and a y-intercept of 350. Complete parts (a) and (b) below.
a. What is the equation of the regression line?
b. What does the symbol y represent?
A. The symbol y represents the average price of hotels in the area.
B. The symbol ý represents the amount that price increases with a 1-point increase in rating.
C. The symbol y represents the predicted value of price
D. The symbol y represents the expected price when the hotel's rating is 0
Answer:
a) Y = 350 + 130X
b) C. The symbol [tex]\hat {y}[/tex] represents the predicted value of price.
Step-by-step explanation:
The equation of a regression line is given as:
Y = a + bX
Where Y is the dependent variable, X is the independent variable, a is the intercept on the y axis when X = 0 and b is the slope of the regression line.
a) The regression equation has a slope of 130 and a y-intercept of 350. From Y = a + bX, the equation of the regression line is:
Y = 350 + 130X
b) From the question x represents the ratings of different hotels in a certain area and [tex]\hat {y}[/tex] represents the price of the different hotels based on their ratings. Since a regression line is drawn, y represents the predicted value of price
What is 3/4 improper or proper or mixed
Answer:
proper because the numerator is lower than the denominator
Question 10 of 10
Which set of polar coordinates are plotted in the graph below?
Answer:
(-2, -(2pi)/3)
Step-by-step explanation:
a p ex
In da pic :)))))))))
Nearsightedness: It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.
(a) What proportion of children in this sample are nearsighted?
(b) Construct hypotheses appropriate for the following question: do these data provide evidence that the 8% value is inaccurate?
(c) Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (the Z statistic).
(d) What is the p-value for this hypothesis test?
(e) What is the conclusion of the hypothesis test?
Answer:
a)the proportion of student is 0.1082
b)
H1: p = .08
H2: p not equal to 0.08
H1: p =0 .08
H2: p < .08
H1: p =0 .08
H2: p >0 .08
c)z=1.45
d) the p value is 0.1470
e)null hypothesis cannot be accepted,There is no enough evidence to reject the null hypothesis.
Step-by-step explanation:
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
A pair of linear equations which has a unique solution x = 2, y = –3 is
a) x – 4y –14 = 0
5x – y – 13 = 0
b) 2x – y = 1
3x + 2y = 0
c) x + y = –1
2x – 3y = –5
d) 2x + 5y = –11
4x + 10y = –22
Answer:
a)x - 4y -14 =0
5x - y - 13 =0
Step-by-step explanation:
Using substitution method to solve equation above gives:
x - 4y - 14 =0 ....eq1
5x - y -13 =0 ....eqn2
From eqn1, making x the subject formula:
x - 4y - 14 =0
x - 4y =14
x = 14+4y ...eqn3
From eqn2, substitute value of x and solve for y:
5(14+4y)-y-13 =0
70+20y-y-13 =0
70+19y-13 =0
70 - 13 = -19y
57 = -19y
divide both sides by -19
-57/19 = -19y/-19, then
y = -3
From eqn1:
x = 14 + 4y
substitute the value of y in the expression above
x = 14 + 4(-3)
x = 14 + (-12)
x = 14 - 12
x = 2
Solve this inequality. -9x - 3 > 51 A. x -392 C. x -6
Answer:
The answer is option C.
Step-by-step explanation:
- 9x - 3 > 51
Group like terms
- 9x > 51 + 3
- 9x > 54
Divide both sides by -9
x < - 6
Hope this helps you
how do I simplify this (sinx)/(secx+1)
Answer:
Step-by-step explanation:
[tex]\frac{sin~x}{sec~x+1} =\frac{sin~x}{\frac{1}{cos~x}+1 } =\frac{sin~x~cos~x}{1+cos~x} \\=\frac{sin~x~cos~x}{1+cos~x} \times \frac{1-cos~x}{1-cos~x} \\=\frac{sin~x~cos~x(1-cos~x)}{1-cos^2 x} \\=\frac{sin~x~cos~x(1-cos~x)}{sin^2x} \\=\frac{cos~x(1-cos~x)}{sin~x} \\=cos ~x(csc~x-cot~x)\\or\\=cot~x(1-cos~x)[/tex]
may someone assist me?
Answer:
15 is the answer.Step-by-step explanation:
The side lengths are equal - supposedly
30 25
? ?
25 + ? = 45
-25 - 25
? = 20
45 - 30 = 15
The question mark should be equal to 15.
Hope this helps,
Kavitha
The graph below shows a line of best fit for data collected on the number of students who wear a jacket to school and the average daily temperature in degrees Fahrenheit.
Based on the line of best fit, how many students wear a jacket to school when the temperature is 50°F?
A.) 240
B.) 210
C.) 300
D.) 180
Answer:
240
Step-by-step explanation:
You should go to the value 50 °F and see the value that match it
here it's 240 students
Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F is 240.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
Given that The graph shows a line of best fit for data collected on the number of students who wear a jacket to school and the average daily temperature in degrees Fahrenheit.
Now, Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F can be found by simply observing the graph when the average daily temperature is 50°F as shown below, and then looking the value of y at that temperature.
Hence, Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F is 240.
Learn more about Graph:
https://brainly.com/question/21608293
#SPJ5
What type of model best fits the height of a tree increases by 2.5 feet each growing season
Answer:
Step-by-step explanation:
A linear graph with y values (height of tree) going up 2.5 with each increase of x (growing season)
This is the model that best fits the graph describing a growth of a plant
Sixty percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 20 of them have looked at their score in the past six months
Answer:
The probability is [tex]P(X \ge 20 ) = 0.3707[/tex]
Step-by-step explanation:
From the the question we are told that
The population proportion is p = 0.60
The sample size is n = 31
The mean is evaluated as
[tex]\mu = n * p[/tex]
substituting values
[tex]\mu = 31 *0.60[/tex]
[tex]\mu = 18.6[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{n * p * (1- p )}[/tex]
substituting values
[tex]\sigma = \sqrt{31 * 0.6 * (1- 0.6 )}[/tex]
[tex]\sigma = 2.73[/tex]
The the probability that at least 20 of them have looked at their score in the past six months is mathematically represented as
[tex]P(X \ge 20) = 1- P(X < 20)[/tex]
applying normal approximation we have that
[tex]P(X \ge 20) = 1- P(X < (20-0.5))[/tex]
Standardizing
[tex]1 - P(X < 20) = 1 - P(\frac{X - \mu }{\sigma} < \frac{19.5 - \mu }{\sigma } )[/tex]
[tex]1 - P(X < 20) = 1 - P(Z < \frac{19.5 - 18.6 }{2.73 } )[/tex]
[tex]1 - P(X < 20) = 1 - P(Z < 0.33)[/tex]
Form the standardized normal distribution table we have that
[tex]P(Z < 0.0512)[/tex] = 0.6293
=> [tex]P(X \ge 20 ) = 1- 0.6293[/tex]
=> [tex]P(X \ge 20 ) = 0.3707[/tex]
Write an expression:
a) 4 less than twice a
number
11
Gra
ine
a)
e
Answer:
2x - 4.
Step-by-step explanation:
4 less than twice a number is the same thing as a number times 2 minus 4. Let's say that the number is represented by x.
2 * x - 4 = 2x - 4.
Hope this helps!
The following sample was obtained from a population with unknown parameters.
Scores: 13, 7, 6, 12, 0, 4
a. Compute the sample mean and standard deviation. (Note that these are descriptive values that summarize the sample data.)
b. Compute the estimated standard error for M. (Note that this is an inferential value that describes how accurately the sample mean represents the unknown population mean.)
Answer:
i think is 7
Step-by-step explanation:
Solve for x : 2^x+4^x+8^x=−14
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
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Let's solve this step by step.
[tex]2^x + 4^x + 8^x = -14[/tex]
↓
In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).
The number of times that each prime divides the original integer becomes its exponent in the final result.
Prime number 2 to the power of 2 = 4
[tex]2^x + (2^2)^x + (2^3) ^x = -14[/tex]
↓
Prime number 2 to the power of 3 = 8
[tex]2^x + 2^2x + 2^3x = -14[/tex]
↓
We need to exponentiate the power.
The following rule is applied:
[tex](A^B) ^C = A^BC[/tex]
In our example,
A is equal to 2,
B is equal to 2 and
C is equal to x.
[tex]( 2^x + 2^2x + 2^3x ) + 14 = -14 + 14[/tex]
↑
In order to solve this non-linear equation, we need to move all the terms to the left side.
In our example,
- term −14, will be moved to the left side.
Notice that a term changes sign when it 'moves' from one side of the equation to the other.
___________________
We need to get rid of expression parentheses.
If there is a negative sign in front of it, each term within the expression changes sign.
Otherwise, the expression remains unchanged.
In our example, there are no negative expressions.
↓
[tex]2^x + 2^2x + 2^3x + 14 = 0[/tex]
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Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Find the distance between the points by filling in the steps. The first one is done for you.
Answer:
Q.2 [tex]4\sqrt2[/tex] units
Q.3 [tex]10\sqrt2[/tex] units
Step-by-step explanation:
Given that points:
C(-1, 3) and D (-5, 7)
E(0, -5) and F(10, -15)
To find:
Q.2. Distance between C and D
Q.3. Distance between E and F
Solution:
First of all, let us solve the question marked as number 2 in the attached image.
C(-1, 3) and D (-5, 7)
[tex]x_2 = -5\\x_1 = -1\\y_2 = 7\\y_1 = 3[/tex]
To find the distance 'd' between the points, we can use distance formula:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d = \sqrt{(-5-(-1))^2+(7-3)^2}\\\Rightarrow d = \sqrt{(-4)^2+(4)^2}\\\Rightarrow d =\sqrt{16+16}\\\Rightarrow d =\sqrt{32} = 4\sqrt2\ units[/tex]
First of all, let us solve the question marked as number 3 in the attached image.
E(0, -5) and F(10, -15)
[tex]x_2 = 10\\x_1 = 0\\y_2 = -15\\y_1 = -5[/tex]
To find the distance 'd' between the points, we can use distance formula:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d = \sqrt{(10-0)^2+(-15-(-5))^2}\\\Rightarrow d = \sqrt{10^2+(-10)^2}\\\Rightarrow d =\sqrt{100+100}\\\Rightarrow d =\sqrt{200} = 10\sqrt2\ units[/tex]
Please find attached image for the answers filled in the boxes.
-s^2+2s=0 Separate the two values with a comma.
Answer:
s = 0 OR s = 2
Step-by-step explanation:
=> [tex]-s^2+2s = 0[/tex]
=> [tex]-s(s-2)=0[/tex]
So, Either:
=> -s = 0 OR s-2 = 0
=> s = 0 OR s = 2
Answer:
s=0,2
Step-by-step explanation:
-s^2+2s=0
Factor out -s
-s ( s-2) =0
Using the zero product property
-s =0 s-2 =0
s=0 s=2
Compute the least-squares regression line for predicting y from a given the following summary statistics. Round final answers to four decimal places, as needed.
xbar = 8.8 sx = 1.5 sy = 1.8 ybar = 30.3
r = -0.84
Download data
Regression line equation: y = ______ + _______ x
Answer: Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
Step-by-step explanation:
Equation of least-squares regression line for predicting y :
[tex]\hat{y}=b_1x+b_o[/tex]
, where [tex]\text{Slope} (b_1)=r\dfrac{s_y}{s_x}[/tex] , [tex]\text{intercept}(b_0)=\bar{y}-b_1\bar{x}[/tex]
Given: [tex]\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84[/tex]
Then,
[tex]b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008[/tex]
Now,
[tex]b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704[/tex]
Then, Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
A quality control inspector has determined that 0.25% of all parts manufactured by a particular machine are defective. If 50 parts are randomly selected, find the probability that there will be at most one defective part.
Answer:
9.941*10^-6
Step-by-step explanation:
Probability of at most 1 means not more than 1 defective= probability of 1 or probability of 0
Probability of 1 = 50C1(0.25)(0.75)^49
Probability= 50(0.25)*7.55*10^-7
Probability= 9.375*10^-6
Probability of 0
= 50C0(0.25)^0(0.75)^50
= 1(1)(0.566*10^-6)
= 0.566*10^-6
Total probability
= 9.375*10^-6+ 0.566*10^-6
= 9.941*10^-6
Find the slope of the line passing through the points (-5, 3) and (7,9).
Answer:
[tex]\huge\boxed{slope=\dfrac{1}{2}=0.5}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points
[tex](-5;\ 3)\to x_1=-5;\ y_1=3\\(7;\ 9)\to x_2=7;\ y_2=9[/tex]
Substitute:
[tex]m=\dfrac{9-3}{7-(-5)}=\dfrac{6}{7+5}=\dfrac{6}{12}=\dfrac{6:6}{12:6}=\dfrac{1}{2}[/tex]
Answer:
1/2
Step-by-step explanation:
We can use the slope formula since we have 2 points
m = ( y2-y1)/(x2-x1)
= (9-3)/( 7 - -5)
= (9-3) /( 7+5)
= 6/ 12
= 1/2
An investigation of a number of automobile accidents revealed the following information:
18 accidents involved alcohol and excessive speed.
26 involved alcohol.
12 accidents involved excessive speed but not alcohol.
21 accidents involved neither alcohol nor excessive speed.
How many accidents were investigated?
Answer:
59 accidents were investigated.
Step-by-step explanation:
The question above is a probability question that involves 2 elements: causes of accidents.
Let
A = Alcohol
E = Excessive speed
In the question, we are given the following information:
18 accidents involved Alcohol and Excessive speed =P(A ∩ E)
26 involved Alcohol = P(A)
12 accidents involved excessive speed but not alcohol = P( E ) Only
21 accidents involved neither alcohol nor excessive speed = neither A U B
We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)
P(A Only) = 26 - 18
= 8
So, only 8 accident involved Alcohol but not excessive speed.
The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)
= 8 + 12 + 18 + 21
= 59
Therefore, 59 accidents were investigated.
Which of the following is best described as all the points on a plane that are the same distance from a single point called a center?
A.
Ellipse
B.
Circle
C.
Diameter
D.
Chord
Answer:
It would be B. Circle
keith rented a truck for one day. There was a base fee of $15.95, there was an additional charge of 95 cents for each mile driven . keith had to pay $206.90 when he rented his truck. for how many miles did he drive the truck
Answer:
201 miles
Step-by-step explanation:
Base fee = $15.95
Mileage fee = $ 0.95 per/mile
Paid = $206.90
Distance= ?
--------------
Equation to calculate miles:
(206.90 - 15.95)/0.95= 201 milesAn amount of $21,000 is borrowed for 15 years at 7.75% Interest, compounded annually. If the loan is paid in full at the end of that period, how much must be
paid back?
round your answer to the nearest dollar.
Answer:
A=64340 dollars
Step-by-step explanation:
A=p(1+r)^t p principal, t= time period, r is the rate
A=21000(1+0.0775)^15= 64339.61
A=64340 dollars