Answer:
1/2
Step-by-step explanation:
The possible outcomes are
1,2,3,4,5,6,7,8,9,10
Factors of 6 are 1,2,3,6
or a 4
1,2,3,4,6 are the outcomes we want
There are 5 "good" outcomes
P( 4 or a factor of 6) = "good" outcomes/ total
= 5/10
=1/2
Answer:
[tex]\boxed{\frac{1}{2} }[/tex]
Step-by-step explanation:
There are total 10 outcomes.
[tex]1,2,3,4,5,6,7,8,9,10[/tex]
The probability of selecting 4 is 1 outcome out of total 10 outcomes.
Factors of 6 are [tex]1,2,3,6[/tex].
These are 4 outcomes out of total 10 outcomes.
The probability of selecting 4 or a factor of 6 is:
[tex]\displaystyle \frac{1}{10} +\frac{4}{10} =\frac{5}{10} =\frac{1}{2}[/tex]
Open the graphing tool. Move the slider for the equation y = kx3 to a position of your choice, where k ≠ 1. Next, move the slider of y = (kx)3 so the two graphs lie on top of one another. How do the values of k compare with one another in this situation? Why do you think that is?
Answer:
For the functions to coincide, the value of k in y = (kx)3 must be smaller than in y = kx3. This is because the value of y changes more rapidly when k is cubed inside the parentheses. The behavior of the functions is similar since a vertical stretch is similar to a horizontal compression.
Step-by-step explanation:
PLATO
If the bathtub holds a total of 46.2 gallons, how many minutes would it take to fill the entire tub? Write an equation in one variable to help you solve the problem. The variable represents the unknown time in minutes.
Answer:
46.2÷m=x
Step-by-step explanation:
u divide the amount of water by the time it takes to fill up(m). Witch will equal the amount per minute (x).
16.5/min
time = m
gallons / minutes = rate
46.2 = 16.5 (m)
46.2 / 16.5 = 16.5 (m) / 16.5
2.8 = minutes
3. A medical devices company wants to know the number of MRI machines needed per day. A previous study found a standard deviation of four hours. How many MRI machines must the company study in order to have a margin of error of 0.5 hours when calculating a 90% confidence interval
Answer:
173 MRI machines
Step-by-step explanation:
Margin of error E = 0.5
Confidence interval 90% = 1-0.9 = 0.1
Standard deviation = 4 hours
Number of MRI machines needed per day n, = [(z alpha/2 * SD)/E]²
Z alpha/2 = 1.645 at alpha = 0.1
Inputting these values into n we have that
[(1.645*4)/0.5]²
= 13.16²
= 173.18 is approximately equal to 173
The company has to study 173 machines.
What is the value of the mean from the following set of data: 12,10, 11, 8, 6, 5, 3, 7, 9. Round to the nearest hundredth.
Answer:
7.88 or 7.9
Step-by-step explanation:
To find the mean, we need to do:
=> (12 + 10 + 11 + 8 + 6 + 5 + 3 + 7 + 9) / 9
=> 71/9
=> 7.88 or 7.9
I divided the sum of all numbers by 9 because we added 9 numbers.
Please help. I’ll mark you as brainliest if correct!
Answer:
9 3 -7 -13
4 -4 11 8
0 9 2 -4
Step-by-step explanation:
9 3 -7 -13
4 -4 11 8
0 9 2 -4
Answer: 9 3 -7 -13
4 -4 11 8
0 9 2 -4
Step-by-step explanation:
1. Peyton has a credit card with an annual rate of 24.7% compounded monthly. She used the credit card to purchase cleaning supplies in the amount of $189.56. She can pay up to $72 on the
credit card each month. How much total interest will she pay?
Answer:
Total interest = $3.41
Step-by-step explanation:
Since she can pay $72 each month we can divide the payments on monthly basis till all the money is paid.
The annual interest rate is 24.7%, so the monthly rate will be 24.7 ÷ 12= 2.058%
For the first month
With payment of $72 the remaining amount will be 189.56 - 72 = $117.56
Interest paid will be 0.02058 * 117.56 = $2.42
Total amount owed now will be 117.56 + 2.42 = $119.98
For the second month another payment of $72 is made
The remaining will be 119.98 - 72 = $47.98
Interest charged will be 0.02058 * 47.98 = $0.99
The amount owed will be 47.98 + 0.99 = $48.97
In the third month she will pay the remaining $47.98 which is within her monthly limit
Total interest paid = Sum of Amount paid each month - Initial amount spent
Total interest = {(72 * 2) +48.97} - 189.56 = $3.41
Find the slope of a line perpendicular to the line defined by the equation 3x-5y=12
Answer:
-5/3
Step-by-step explanation:
Note the slope intercept form: y = mx + b
Note that:
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
Isolate the variable, y. First, Subtract 3x from both sides:
3x (-3x) - 5y = 12 (-3x)
-5y = -3x + 12
Next, divide -5 from both sides. Remember to divide from all terms within the equation:
(-5y)/-5 = (-3x + 12)/-5
y = (-3x/-5) + (-12/5)
Simplify.
y = (3x/5) - 12/5
y = (3/5)x - 12/5
You are trying to find the perpendicular slope to this line. To do so, simply flip the slope (m) as well as the sign:
Original m = 3/5
Flipped m = -5/3
-5/3 is your perpendicular slope.
Answer:
5
m = - ---- perpendicular slope
3
Step-by-step explanation:
3x - 5y = 12 -------->> convert to y = mx + b
- 5y = - 3x + 12
- 5y = - (3x + 12) --- eliminate the negative
5y = 3x + 12
3x + 12
y = -------------
5
3 12
y = -----x + -----
5 5
the above equation is the form of y = mx + b
where m is the slope and b is the intercept
5
therefore, m = - ---- perpendicular slope
3
ASAP Two points ___________ create a line. A. sometimes B. always C. never D. not enough information
Answer: B. Always
Explanation:
Two points always create a line. The correct answer is option B.
What is a line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.
If there are two points A(x₁,y₁) and B(x₂,y₂) then the distance between the two points will be the length of the line. The formula to calculate the distance is given as below:-
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore, the two points always create a line. The correct answer is option B.
To know more about lines follow
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Consider population data with μ = 30 and σ = 3. (a) Compute the coefficient of variation. (b) Compute an 88.9% Chebyshev interval around the population mean. Lower Limit Upper Limit
Answer:
A. 10%
B. Lower limit= 21
Upper limit = 39
Step-by-step explanation:
Mean = 30
SD = 3
a. COV = SD/|x| × 100
= 3/30 × 100
= 10%
= 0.1
B. For 88.9 chevbychev interval:
= (1 - 1/K²) = 0.889
= 1/K² = 1 - 0.889
= 1/K² = 0.111
= K² = 1/0.111
= K² = 9
= K = √9
K = 3
Lower limit = 30 - 3(3)
Lower limit = 21
Upper limit = 30 + 3(3)
Upper limit = 39
Therefore lower limit is 21 and upper limit is 39
2/3a - 1/6 =1/3 please help me
Answer:
[tex]a = \frac{3}{4}[/tex]
Step-by-step explanation:
Let's convert everything to sixths to make it easier to work with.
[tex]\frac{4}{6}a - \frac{1}{6} = \frac{2}{6}[/tex]
Add 1/6 to both sides:
[tex]\frac{4}{6}a = \frac{3}{6}[/tex].
Dividing both sides by 4/6:
[tex]a = \frac{3}{6} \div \frac{4}{6}\\\\a = \frac{3}{6} \cdot \frac{6}{4}\\\\a = \frac{18}{24}\\\\a = \frac{3}{4}[/tex]
Hope this helped!
The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 356 cubic inches under a pressure of 6 pounds per square inch, what will be its volume if the pressure is increased to 7 pounds per square inch? Round your answer to the nearest integer if necessary.
Answer:
[tex]V_2=305.14\ \text{inch}^3[/tex]
Step-by-step explanation:
The volume of a gas in a container varies inversely as the pressure on the gas.
[tex]V\propto \dfrac{1}{P}\\\\V_1P_1=V_2P_2[/tex]
If V₁ = 356 inch³, P₁ = 6 pounds/in², P₂ = 7 pounds/in², V₂ = ?
So, using the above relation.
So,
[tex]V_2=\dfrac{V_1P_1}{P_2}\\\\V_2=\dfrac{356\times 6}{7}\\\\V_2=305.14\ \text{inch}^3[/tex]
So, the new volume is [tex]305.14\ \text{inch}^3[/tex].
John painted his most famous work, in his country, in 1930 on composition board with perimeter 101.14 in. If the rectangular painting is 5.43 in. taller than it is wide, find the dimensions of the painting.
Answer:
22.57 x 28
Step-by-step explanation:
10.86 + 4x = 101.14
-10.86 -10.86
4x = 90.28
/4 /4
x = 22.57
5.43 + 22.57 = 28
22.57
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with mean 100 lb and 5 lb and standard deviation 1 lb and 0.5 lb, respectively. What percent of filled boxes weighing between 104 lb and 106 lb are to be expected?
a. 67%
b. None
c. 37%
d. 57%
Answer:
Option b. None is the correct option.
The Answer is 63%
Step-by-step explanation:
To solve for this question, we would be using the z score formula
The formula for calculating a z-score is given as:
z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
We have boxes X and Y. So we will be combining both boxes
Mean of X = 100 lb
Mean of Y = 5 lb
Total mean = 100 + 5 = 105lb
Standard deviation for X = 1 lb
Standard deviation for Y = 0.5 lb
Remember Variance = Standard deviation ²
Variance for X = 1lb² = 1
Variance for Y = 0.5² = 0.25
Total variance = 1 + 0.25 = 1.25
Total standard deviation = √Total variance
= √1.25
Solving our question, we were asked to find the percent of filled boxes weighing between 104 lb and 106 lb are to be expected. Hence,
For 104lb
z = (x-μ)/σ,
z = 104 - 105 / √25
z = -0.89443
Using z score table ,
P( x = z)
P ( x = 104) = P( z = -0.89443) = 0.18555
For 1061b
z = (x-μ)/σ,
z = 106 - 105 / √25
z = 0.89443
Using z score table ,
P( x = z)
P ( x = 106) = P( z = 0.89443) = 0.81445
P(104 ≤ Z ≤ 106) = 0.81445 - 0.18555
= 0.6289
Converting to percentage, we have :
0.6289 × 100 = 62.89%
Approximately = 63 %
Therefore, the percent of filled boxes weighing between 104 lb and 106 lb that are to be expected is 63%
Since there is no 63% in the option, the correct answer is Option b. None.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be 63%.
What is a normal distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with a mean of 100 lb and 5 lb and standard deviation of 1 lb and 0.5 lb, respectively.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be
Then the Variance will be
[tex]Var = \sigma ^2[/tex]
Then for X, we have
[tex]Var (X) = 1^2 = 1[/tex]
Then for Y, we have
[tex]Var (Y) = 0.5^2 = 0.25[/tex]
Then the total variance will be
[tex]Total \ Var (X+Y) = 1 + 0.25 = 1.25[/tex]
The total standard deviation will be
[tex]\sigma _T = \sqrt{Var(X+Y)}\\\\\sigma _T = \sqrt{1.25}[/tex]
For 104 lb, then
[tex]z = \dfrac{104-105}{\sqrt{25}} = -0.89443\\\\P(x = 104) = 0.18555[/tex]
For 106 lb, then
[tex]z = \dfrac{106-105}{\sqrt{25}} = 0.89443\\\\P(x = 106) = 0.81445[/tex]
Then
[tex]P(104 \leq Z \leq 106) = 0.81445 - 0.18555 = 0.6289 \ or \ 62.89\%[/tex]
Approximately, 63%.
More about the normal distribution link is given below.
https://brainly.com/question/12421652
What does it mean when the resulting temperature is above 0 on the number line? What does it mean when a temperature is below 0?
Answer:
It means that above 0 degrees Celsius the water does not freeze, whereas 0 degrees are freezing teperatures of water.
Step-by-step explanation:
Water freezes at 0 degrees Celsius, but the freezing temperature can be lowered by adding salt to the water. A student discovered that adding half a cup of salt to a gallon of water lowers its freezing temperature by 7 degrees Celsius. What is the freezing temperature of the gallon of salt water?
0° - 7° = -7°
What is the correct alternate hypothesis if the pilots' average gain score due to alcohol is indicated in the hypothesis statement by
Answer:
Ha : Pilots average gain score not due to alcohol.
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. Here the null hypothesis is that pilots average gain due to alcohol. Then if there is no alcohol what is pilots average gain. This thing will be tested as alternative hypothesis.
Help me please thank you
Answer: 60°
Step-by-step explanation:
apply concept: the interior angle sum of triangle is 180°
x+x+x=180
3x=180
x=60
---------------
this is also an equilateral triangle which if you know it, you will know that each angles are all 60°
Answer: x=60°
Step-by-step explanation:
We know that the sum of the angles in a triangle is 180°. Since all of the angles are x°, we know that they are equal in degrees. Since there are 3x, we can use that to solve for x.
3x=180 [divide both sides by 3]
x=60°
Find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area. z -2.13 0 A normal curve is over a horizontal z-axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at negative 2.13 and 0. The area under the curve between negative 2.13 and 0 is shaded. The area of the shaded region is nothing.(Round to four decimal places as needed.)
Answer:
The area of the shaded region under the standard normal curve is 0.4834.
Step-by-step explanation:
A random variable X is said to have a normal distribution with mean, µ and variance σ².
Then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z [tex]\sim[/tex] N (0, 1).
The distribution of these z-variates is known as the standard normal distribution.
Compute the area under the curve between -2.13 and 0 as follows:
[tex]P(-2.13<Z<0)=P(Z<0)-P(Z<-2.13)[/tex]
[tex]=0.50-0.01659\\=0.48341\\\approx 0.4834[/tex]
Thus, the area of the shaded region under the standard normal curve is 0.4834.
Using the normal distribution, it is found that the area of the shaded region is of 0.4833.
In a normal distribution, our test statistic is the z-score, which measures how many standard deviations a measure is from the mean. Each z-score has an associated p-value, which is given at the z-table, and represents the percentile of a measure or or the z-score, which is the area to the left under the normal curve.The area between two z-scores is the subtraction of their p-values.In this problem, we want the area between Z = -2.13 and Z = 0.
Z = 0 has a p-value of 0.5.Z = -2.13 has a p-value of 0.0166.0.5 - 0.0166 = 0.4833
The area of the shaded region is of 0.4833.
A similar problem is given at https://brainly.com/question/22940416
Hi I need help with 800×200= 8 × ______ hundreds=_____ Hundreds = _______ plz help me
Answer:
800×200= 8 × 200 hundreds= 1600 Hundreds = 160000
Complete the point-slope equation of the line through (2,3)(7,4). Use exact numbers. y-4=
Please help me, I would really appreciate it!
Answer:
The answer is
[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]Step-by-step explanation:
To find the equation of a line given two points first find the slope and use the formula
[tex] y - y_{1} = m(x - x_{1})[/tex]Where m is the slope
To find the slope we use the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]The slope of the line using points
(2,3)(7,4) is
[tex]m = \frac{4 - 3}{7 - 2} = \frac{1}{5} [/tex]Equation of the line using point (7,4) and slope 1/5 is
[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]Hope this helps you
Answer:
y-4=1/5(x-3)
Step-by-step explanation:
We plug in the x's and the y's and find the slope with:
[tex](y-y_{1} )/ x-x_{1})=m[/tex]
How many solutions does 2−9x=−6x+5−3x have?
Answer:
There are no values of x that make the equation true.
No solution
Step-by-step
hope it help
Hi
2-9x = -6x+5-3x
-9x+6x+3x = 5-2
0x = 3
as 0 ≠ 3 , there is no answer possible to your equation.
Find a linear inequality with the following solution set. Each grid line represents one unit. (Give your answer in the form ax+by+c>0 or ax+by+c>=0 where a, b, and c are integers with no common factor greater than 1.) Help please!! I have to finish it by tonight!! Thank you!!
Answer:
Below
Step-by-step explanation:
First let's find the equation of the doted line.
Notice that the line is crossing these points:
● (0,1)
● (1,2)
The equation of the line has the following form:
● y = ax+c
C is the y-intercept wich is given by the output of 0.
Notice that the output of 0 is 1.
● y = ax+1
● a = rise / run = (2-1)/(1-0) = 1
So y = x + 1
■■■■■■■■■■■■■■■■■■■■■■■■■■
Notice that the line divide the plan into 2 areas.
● y > x+1 => x+1-y < 0
● y < x+1 => x+1 -y > 0
To khwo wich one that represent the shaded area take a point and replace x and y by its coordinates
● (-1,2)
● -1+1-2 = 0-2 = -2
It is a negative value so the inequality is
● y > x+1
A person tosses a fair coin until a tail appears for the first time. If the tail appearson thenth flip, the person winsndollars. LetXdenote the player’s winnings.ComputeE(X).
Answer: The answer in a is No while the answer in b is Yes
Step-by-step explanation:
Find the explanation in the attached file.
g If A and B are disjoint events, with P( A) = 0.20 and P( B) = 0.30. Then P( A and B) is: a. .00 b. .10 c. .50 d. 0.06
Answer: A) 0
P(A and B) = 0 when events A and B are disjoint, aka mutually exclusive.
We say that two events are mutually exclusive if they cannot happen at the same time. An example would be flipping a coin to have it land on heads and tails at the same time.
15. What is the next number in this series?
6, 11, 9, 14, 12,
a. 17
b. 10
C. 18
d. 16
Answer:
a. 17
Step-by-step explanation:
The pattern is add 5 then subtract 2
A lottery exists where balls numbered 1 to "20" are placed in an urn. To win, you must match the balls chosen in the correct order. How many possible outcomes are there for this game?
Answer: 1860480
Step-by-step explanation:
Initially, there are 20 balls where 5 must be chosen in order.
The number of possible outcomes may be calculated using the concept of permutations.
The formula for permutations is:
nPr =n!/(n−r)!
where n represents the number of items and r represents the number of items to be selected.
The number of ways of selecting 5 balls in order out of 20 is:
20P5 = 20!/15!
= 1860480
To conclude, there are 1860480 possible outcomes.
"Julien is trying to determine his variable type in order to select the proper statistical tests. He is measuring the height of a part. What type of variable is this"
Answer:
Quantitative
Step-by-step explanation: Quantitative or numerical variable are statistical or measured variables which involves numbers. Numerical variables allows for mathematical operations such as addition, subtraction and so on to be performed in them. Quantitative variables include height, age, weight, population and other measured variable with have numerical attributes. They can be measured on either ordinal, ratio or interval scales. Hence, since Julien is trying to determine height, the variable is a quantitative or numeric variable.
PLEASE HURRY! i walked north 8 miles, the west 4 miles, and finally south 5 miles, at the end how far was i from where i started
Answer:
5 miles away
Step-by-step explanation:
If you walked north 8 miles, then west 4 miles, then south 5 miles, you have, in total, travelled 4 miles west and [tex]8-5=3[/tex] miles north.
This creates a triangle, in which we can find the the length of the hypotenuse to find how far away you are now.
We can use the Pythagorean theorem since this is a right triangle.
[tex]a^2+b^2=c^2\\3^2+4^2=c^2\\9+16=c^2\\25=c^2\\c=5[/tex]
Hope this helped!
Answer:
5 miles away
Step-by-step explanation:
Lines a and b are parallel. If the slope of line a is , what is the slope of line b?
A.
-
B.
4
C.
D.
-4
Answer:
C. 1/4
Step-by-step explanation:
Parallel lines always have the same slope.
Answer:
C. 1/4
Step-by-step explanation:
Parallel lines have the same slope. If line b is parallel to line a, and line a has slope 1/4, then line b has slope 1/4.
93/28=15/4n-5+4 4/7 i NEED this answer
Answer:
n=1
Step-by-step explanation:
93/28=15/4n-5+4 4/7
93/28=15/4n-5+32/7
93/28=15/4n-35+32/7
93/28=15/4n-3/7
93/28+3/7=15/4n
15/4n=93*7+28*3/28*7
15/4n= 651+84/196
15/4n=735/196
15/4n*4/15=753/196*4/15
n=49/49
n=1
I need help ASAP THANK YOU
Answer:
174 cm²
Step-by-step explanation:
The figure given is a prism with isosceles trapezoid as base.
Its surface area can be calculating the area of each face that makes up the prism, and summing all together.
There are 6 faces. Their dimensions and areas can be calculated as follows:
2 isosceles trapezium:
It has 2 parallel bases, (a and b), of 4cm and 6cm,
Height (h) = 2.8cm
Area = ½(a+b)*h
Area = ½(4+6)*2.8
Area = ½(10)*2.8 = 5*2.8 = 14 cm²
4 rectangles of different dimensions:
Rectangle 1 (down face): l = 10cm, b = 4cm
Area = 10*4 = 40 cm²
Rectangle 2 and 3 (side faces): l = 10cm, b = 3cm
Area = 2(l*b) = 2(10*3) = 60cm²
Rectangle 4 (top face) = l = 10cm, b = 6cm
Area = 10*6 = 60cm²
Surface area of the figure = 14 + 40 + 60 + 60 = 174 cm²
