Answer:
Step-by-step explanation:
Let us assume that x is normally distributed. The sample size is greater than 30. Since the the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = standard deviation
n = number of samples
From the information given,
µ = 50
σ = 7
n = 36
If x is within 0.5 of the population mean, it means that x is between (50 - 0.5) and (50 + 0.5)
the probability is expressed as
P(49.5 ≤ x ≤ 50.5)
For x = 49.5
z = (49.5 - 50)/(7/√36) = - 0.43
Looking at the normal distribution table, the probability corresponding to the z score is 0.334
For x = 49.5
z = (50.5 - 50)/(7/√36) = 0.43
Looking at the normal distribution table, the probability corresponding to the z score is 0.666
Therefore,
P(49.5 ≤ x ≤ 50.5) = 0.666 - 0.334 = 0.332
Mathematics
ose the correct answer:
. What number should be added to (-5/16) to get ( 7/24)?
Answer:
0.6042 or 29/48
Step-by-step explanation:
-5/16 = -0.3125
7/24 = 0.2917
0.2917 - -0.3125 = 0.6042
0.6042 ≅ 29/48
Answer:
29/48
Step-by-step explanation:
-5/16 + x= 7/24
x= 7/24-(-5/16)
x=7/24+5/16
x= 2*7/2*24+ 3*5/3*16
x=29/48
During the late 1980s and the early 1990s the Pepsi Challenge was in full swing. During the challenge, participants were asked to taste cola from both Coke and Pepsi. Once they had tasted both drinks, the participants were asked to report which was better tasting. The results indicated that participants found Pepsi products to be better tasting. What is the dependent variable in this study? coruse hero psyc 255
Answer:
Taste
Step-by-step explanation:
In the challenge, participants were asked to taste cola from both Coke and Pepsi. They were to give a report on which of the two drinks tasted better.
The taste reported by the participants is dependent on the type of cola taken (either Coke or Pepsi).
Therefore, the taste is the dependent variable while the types of cola are the independent variables.
A 50 ft kite string is flying on the beach above an umbrella. You are holding the end
of the string and are 12 feet from the umbrella. How high in the air is the kite flying?
Round to the nearest degree.
Answer:
The height of the kite is 48.54 feet
The angle of elevation is 76.11°
Step-by-step explanation:
To find the height of the kite, we can use the Pythagoras' theorem in the triangle created by the length of the string (hypotenuse), the height of the kite and the distance to the umbrella (catheti).
Then, we have:
50^2 = 12^2 + height^2
height^2 = 2500 - 144
height^2 = 2356
height = 48.54 ft
So the kite is 48.54 feet high in the air.
The angle of elevation can be calculated using the cosine relation:
cos(angle) = 12 / 50
cos(angle) = 0.24
angle = 76.11°
Complete the point-slope equation of the line through (− 2 ,6 ) ( 1 , 1 )
Answer:
y=-5/3x+8/3
Step-by-step explanation:
You want to find the equation for a line that passes through the two points:
(-2,6) and (1,1).
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-2,6), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-2 and y1=6.
Also, let's call the second point you gave, (1,1), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=1 and y2=1.
Now, just plug the numbers into the formula for m above, like this:
m=
1 - 6
1 - -2
or...
m=
-5
3
or...
m=-5/3
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=-5/3x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(-2,6). When x of the line is -2, y of the line must be 6.
(1,1). When x of the line is 1, y of the line must be 1.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=-5/3x+b. b is what we want, the -5/3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-2,6) and (1,1).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(-2,6). y=mx+b or 6=-5/3 × -2+b, or solving for b: b=6-(-5/3)(-2). b=8/3.
(1,1). y=mx+b or 1=-5/3 × 1+b, or solving for b: b=1-(-5/3)(1). b=8/3.
Consider a value to be significantly low if its z score less than or equal to minus2 or consider a value to be significantly high if its z score is greater than or equal to 2. A data set lists weights (grams) of a type of coin. Those weights have a mean of 5.45961 g and a standard deviation of 0.05215 g. Identify the weights that are significantly low or significantly high. What weights are significantly low? Select the correct answer below and fill in the answer box(es) to complete your choice.
Answer:
lowest score is 5.35531
highest score is x=5.45961
Step by step Explanation:
· A Z-score reffered to as a numerical measurement that identifies a value's relationship to the mean of a group of values. Z-score is usually measured in terms of standard deviations from the mean.
We were to Consider a value to be significantly low if its z score less than or equal to minus2 or consider a value to be significantly high if its z score is greater than or equal to 2
the z-score is given by:
z-score=(x-μ)/σ
where:
x=score
μ=mean=5.45961
σ=std deviation=0.05215
To calculate the lowest cost when the the z-score is -2, we have
[tex]-2=(x-5.45961)/0.05215[/tex]
To get the value of x then we collect like terms
-0.1043 = =(x-5.45961)
x=-0.1043 + 5.45961
[tex]X=5.35531[/tex]
therefore, the lowest score is 5.35531
Let us calculate the highest score when the z-score is 2 ,
then highest score will be:
[tex]2=(x-5.45961)/0.05215[/tex]
To get the value of x then we collect like terms
0.1043 = =(x-5.45961)
x=0.1043 + 5.45961
[tex]X=5.45961[/tex]
therefore the highest score is x=5.45961
p(x) is a polynomial with integer coefficients and p(-3) = 0. Which statements must be true? Choose all that apply. x - 3 is a factor of the polynomial. -3 is the constant term of the polynomial. p( x) can have at most 3 linear factors. x + 3 is a factor of the polynomial.
Answer:
yes all that apply to this q9
Eli uses 1/4 pound of apples to make 4 servings of fruit salad. He uses the same amount of apples for each serving. What amount of apples does he use for each serving of fruit salad?
Answer:
1/16 pound
Step-by-step explanation:
1/4 ÷ 4 = 1/4 x 1/4 = 1/16
3. In 28 days, a person saved $42. What was this person's
average daily savings?
Answer:
The average would be 42 / 28 = $1.50 / day.
Answer:
$1.50 per day
Step-by-step explanation:
Take the dollar amount and divide by the number of days
42 dollars / 28 days
1.50 dollars per day
$1.50 per day
Maria, Daniel, Stephanie, Michael, Elena, Tyler, Sue, and Dimitri have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if Maria and Daniel are to sit next to each other?
Answer:
1x1x6x5x4x3x2x1 = 720 also they can sit in:
6x1x1x5x4x3x2x1 = 720
6x5x1x1x4x3x2x1 = 720
6x5x4x1x1x3x2x1 = 720
6x5x4x3x1x1x2x1 = 720
6x5x4x3x2x1x1x1 = 720
6x5x4x3x2x1x1x1 = 720 or you could have gone 720 x 7
If the measure of angle 2 is (5 x + 14) degrees and angle 3 is (7 x minus 14) degrees, what is the measure of angle 1 in degrees?
2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 2, 3, 4.
88 degrees
89 degrees
90 degrees
91 degrees
Answer:
89 degrees
Step-by-step explanation:
The angle 1 is the same as angle 3.
Angle 2 is the same as angle 4.
The sum of these four angles is 360 degrees.
We have that:
Angle 2 = Angle 4 = 7x - 14
Angle 3 = Angle 1 = 5x + 14
Finding x:
Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360
2*(5x + 14) + 2*(7x - 14) = 360
10x + 28 + 14x - 28 = 360
24x = 360
x = 15
Angle 1:
5x + 14 = 5*15 + 14 = 89 degrees
Answer:
I think it is B
Step-by-step explanation:
Please answer this correctly
Answer:
326
Step-by-step explanation:
l x w
7x8
25x6
4x30
326
Quadrilateral BCDE is a kite. What is BF?
B
20
С
12
E
F
D
Answer:
32
Step-by-step explanation:
if u do pythagoras, sq root of 20^2-12^2=16
16x2=32
What is 11/12 divided 1/3
Answer:
2.75 or 2 3/4
Step-by-step explanation:
so here you use the recipricle of 1/3. so you would do 11/12 X 3/1 =33/12= 2 3/4
Answer: 11/4
Step-by-step explanation:
to divide a fraction by another, you multiply by the reciprocal(the opposite of a certain fraction). the reciprocal of 1/3 is 3/1. so:
[tex]\frac{11}{12} / \frac{1}{3} = \frac{11}{12} * \frac{3}{1} = \frac{33}{12} = \frac{11}{4}[/tex] (divide both sides by 3 to simplify for the last one)
Type your answers into the boxes.
There are 36 students in a class. The pie chart shows the colour of their hair.
Students' Hair Colours
40°
Red
Blonde
Dark
240°
How many students have blonde hair?
How many students have dark hair?
How many students have red hair?
Answer:
(a)24
(b)8
(c)4
Step-by-step explanation:
Number of STudents in the Class = 36
Angle representing Students with Red Hair =40 degrees
Angle representing Students with Blonde Hair =240 degrees
Therefore:
(a)Number of Students with Blonde Hair
[tex]=\dfrac{240^\circ}{360^\circ} \times 36\\\\ =24$ students[/tex]
(b)Number of Students with Dark Hair
Angle representing students with dark hair = 360-(240+40)=80 degrees
Therefore:
Number of Students with Dark Hair
[tex]=\dfrac{80^\circ}{360^\circ} \times 36\\\\ =8$ students[/tex]
(c)Number of Students with Blonde Hair
[tex]=\dfrac{40^\circ}{360^\circ} \times 36\\\\ =4$ students[/tex]
There are 8 students that have blond hair
There are 24 students that have dark hair
There are 4 students that have red hair
Please find attached the pie chart used in answering this question
A pie chart is a graph that displays information in a circle. The circle is divided into slices which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees
To determine the number of students with a type of hair, use this formula :
(degree of the slice that represents the hair type / 360) x total number of students in the class
Degree of the slice that represents blond hair = 360 - (240 + 40) = 80
Students that have blonde hair = [tex]\frac{80}{360}[/tex] x 36 = 8
Students that have dark hair = [tex]\frac{240}{360}[/tex] x 36 = 24
Students that have red hair = [tex]\frac{40}{360}[/tex] x 36 = 4
To learn more about pie charts, please check : https://brainly.com/question/11433309?referrer=searchResults
Ten teaching assistants are available for grading papers in a particular course. The first exam consists of four questions, and the professor wishes to select a different assistant to grade each question (only one assistant per question). In how many ways can assistants be chosen to grade the exam
Answer:
There are 210 ways
Step-by-step explanation:
The number of ways or combinations in which we can select x elements from a group of n elements where the order doesn't matter can be calculated as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, we have 10 teaching assistants and we need to choose 4 (one assistant per question) to grade each question. It means that n is equal to 10 and x is equal to 4.
Therefore, the number of ways that the assistants can be chosen to grade the exam are calculated as:
[tex]10C4=\frac{10!}{4!(10-4)!}=210[/tex]
Of the mathematics degrees awarded in recent years, 76% were bachelor’s degrees, 21% were master’s degrees and the remaining 3% were doctorates. Moreover, women earned 52% of bachelors, 40% of masters and 22% of doctorates. What is the probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman? Give your answer to 4 decimal places.
Answer:
0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman
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: Given to a woman.
Event B: Masters degree.
21% were master’s degrees
This means that [tex]P(B) = 0.21[/tex]
Women earned 40% of masters
This means that [tex]P(A|B) = 0.4[/tex]
Probability of the degree being given to a women:
52% of 76%, 40% of 21% and 22% of 3%. So
[tex]P(A) = 0.52*0.76 + 0.4*0.21 + 0.22*0.03 = 0.4858[/tex]
What is the probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman?
[tex]P(B|A) = \frac{0.21*0.4}{0.4858} = 0.1729[/tex]
0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman
At the neighborhood block party, John noticed that every 5 minutes, the
shadow of a nearby pine tree got six inches longer. The shadow was 12
feet long at 4:15pm. How long was the shadow at 5:00pm?
Answer:
7
Step-by-step explanation:
I think because at if you divide 45 by 6 because its 45 minutes from 4:15 to 5:00 and it grows 6 inches longer every five min
Mariah spent $9.50 on 9 pounds of limes and pears. Limes cost $0.50 per pound and pears cost $1.50 per pound. Let l be the number of pounds of limes and let p be the number of pounds of pears.
The system of linear equations that models this scenario is:
l + p = 9
0.5l + 1.5p = 9.5
How many pounds of each type of fruit did she buy?
Answer:
4 pounds of lime and 5 pounds of pears
Step-by-step explanation:
I + P = 9
0.5l + 1.5P = 9.5
I = 9 - P
0.5(9 - P) + 1.5P = 9.5
4.5-0.5P + 1.5P = 9.5
4.5 + P (1P) = 9.5
P = 9.5-4.5 = 5
I = 9 - 5 = 4
Answer: 4 pounds of lime and 5 pounds of pears
Which of the following is(are) the solution(s) to | x-1|-8?
A. X= 7.-9
B. X = 9
C. X = -79
D. X = 7
Answer:
Step-by-step explanation:
|x-1|=8
if (x-1) >= 0 meaning x >= 1
then |x-1| = x-1
and then the solution of the equation is
x-1=8
<=> x = 9
if (x-1) <= 0 meaning x <= 1
then |x-1| = -(x-1) = -x+1
so the solution of the equation is
-x+1=8
<=> -x = 7
<=> x = -7
so the solutions are -7 and 9
answer C
do no hesitate if you need further explanation
thank you
The circular area covered by a cell phone tower can be represented by the expression 225π miles2. What is the approximate length of the diameter of this circular area
Answer:
The length of the diameter of this circular area is of 30 miles.
Step-by-step explanation:
The area of a circular region can be represented by the following equation:
[tex]A = \pi r^{2}[/tex]
In which r is the radius. The diameter is twice the radius.
In this question:
[tex]A = 225\pi[/tex]
So
[tex]A = \pi r^{2}[/tex]
[tex]225\pi = \pi r^{2}[/tex]
[tex]r^{2} = 225[/tex]
[tex]r = \pm \sqrt{225}[/tex]
The radius is a positive measure, so
[tex]r = 15[/tex]
Area in squared miles, so the radius in miles.
What is the approximate length of the diameter of this circular area
D = 2r = 2*15 = 30 miles
The length of the diameter of this circular area is of 30 miles.
Tori needs to make some house repairs in three years that will cost $9,000. She has some money in an account earning 9% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs
Answer:
She needs to have approximately $6950 on that account.
Step-by-step explanation:
Since the account has an interest rate of 9% annually, then it's compounded and the earnings can be found by the following expression:
[tex]M = C*(1 + r)^t[/tex]
Where M is the final amount, C is the initial amount, r is the interest rate and t is the time elapsed in years.
She needs the money in 3 years, therefore t = 3. Applying this to the problem we have:
[tex]9000 = C*(1 + 0.09)^3\\9000 = C*(1.09)^3\\C*1.295 = 9000\\C = \frac{9000}{1.295}\\C = 6949.81[/tex]
She needs to have approximately $6950 on that account.
Which choice is equivalent to the expression below?
root-81
A. 9i
B. i root9
C. root9i
D. -9
E. -root9
Answer: B
Step-by-step explanation:
A stack of 4 identical books is 6.28 high. What is the heigh of 30 of these books?
Answer:47.1
Step-by-step explanation:6.28/4=x/30
188.4=4x
47.1=x
Answer:
47.1
Step-by-step explanation:
height of 1 book=6.28÷4=1.57
height of 30 books=1.57×30=47.1
A commuter train travels 65 kilometers in 27 minutes. What is it’s speed in kilometers per hour?
Answer:
Per hour: 2.40740740741
Step-by-step explanation:
you have to divided 65 and 27 so
65/27
which is 2.40740740741
What’s the correct answer for this question?
Answer:
C:
Step-by-step explanation:
Both angles add up to 180°
<BCG + <BFG = 180°
2x+146+4x+238=180
6x+384 = 180°
6x = 180-384
6x = -204
Dividing both sides by 6
x = -34
You are a medical assistant in a pediatrician’s office and one of your responsibilities is evaluating the growth of newborns and infants. Your first patient, a baby girl named Ivy Smith, was 21.5 inches long at 3 months old. At 8 months, you measure her at 24 inches long. For your medical records, all measurements must be given both in inches and in centimeters: 1 inch = 2.54 cm
I need to come up with an equation for this.
ACB = DCE
A = 3x-10, C = 45°, D = 2x+10
Please help confused
Answer:
x = 20
Step-by-step explanation:
The congruence statement tells you that angle A is congruent to angle D. (Both are listed first in the triangle names.) This means ...
∠A = ∠D
3x -10 = 2x +10
x = 20 . . . . . . . . . . add 10-2x to both sides
What is the answerrrrrrrrrrrr :(((((((((((
Answer: The answer is choice 3
Step-by-step explanation:
i think the answer is c
Step-by-step explanation:
i don't think u would want a whole explanation
in a survey of more than 3000 people 93% of the respondents claimed to prefer Isaac's immaculate ice cream over any other brand of ice cream. which of the folloling groups were surveyed.
Answer:
The answer is 2,790.
Step-by-step explanation:
Here's a handy tool.
93% of 1 = 0.93 93% of 131 = 121.83 93% of 261 = 242.73 93% of 391 = 363.63
93% of 2 = 1.86 93% of 132 = 122.76 93% of 262 = 243.66 93% of 392 = 364.56
93% of 3 = 2.79 93% of 133 = 123.69 93% of 263 = 244.59 93% of 393 = 365.49
93% of 4 = 3.72 93% of 134 = 124.62 93% of 264 = 245.52 93% of 394 = 366.42
93% of 5 = 4.65 93% of 135 = 125.55 93% of 265 = 246.45 93% of 395 = 367.35
93% of 6 = 5.58 93% of 136 = 126.48 93% of 266 = 247.38 93% of 396 = 368.28
93% of 7 = 6.51 93% of 137 = 127.41 93% of 267 = 248.31 93% of 397 = 369.21
93% of 8 = 7.44 93% of 138 = 128.34 93% of 268 = 249.24 93% of 398 = 370.14
93% of 9 = 8.37 93% of 139 = 129.27 93% of 269 = 250.17 93% of 399 = 371.07
93% of 10 = 9.30 93% of 140 = 130.20 93% of 270 = 251.10 93% of 400 = 372.00
Please answer I need help!
Answer:
c & d
Step-by-step explanation:
the description matches the information in the table
Answer: A, B, C
Step-by-step explanation:
domain = x
range = y
