Answer:
0.16
Step-by-step explanation:
81 is 1 standard deviation below the mean. According to the empirical rule, 68% of data lies within 1 standard deviation of the mean; here the equivalent statement would be that half of that, or 34%, lies within 1 standard deviation below the mean. Half of the area under the standard normal curve, less this 0.34, is the probability that the random variable is below 1 standard deviation beneath the mean. That comes to 0.16.
On a calculator, you might enter the command normalcdf(-100,81,85,4); on my old TI-83 Plus I get 0.1587, which rounds off to 0.16.
Final answer:
The z-score of -1 corresponds to a probability of approximately 0.1587, therefore P(x < 81) is approximately 0.1587, or 15.87%.
Explanation:
To find the probability that a normally distributed random variable x is less than 81, P(x < 81), when the mean μ is 85 and the standard deviation σ is 4, we need to use the properties of the normal distribution.
First, we convert the raw score of 81 into a z-score. The formula for calculating a z-score is:
[tex]z = (x - μ) / σ[/tex]
For x = 81, the z-score would be:
z = (81 - 85) / 4
z = -1
Next, we use a standard normal distribution table, a calculator, or software to find the probability that correlates with this z-score. The table lists probabilities to the left of z-scores.
The z-score of -1 corresponds to a probability of approximately 0.1587, therefore P(x < 81) is approximately 0.1587, or 15.87%.
GEOMETRY Please help me!!!!
Answer:
The correct answer is first option
512 cubic mm
Step-by-step explanation:
Points to remember
Volume of hexagonal pyramid = Base area * height
To find the volume of hexagonal pyramid
It is given that, base area = 64 square mm and
height = 8 mm
Volume = Base area * Height
= 64 * 8
= 512 cubic mm
Therefore the correct answer is first option
512 cubic mm
Estimate the x-coordinates at which the relative maxima and relative minima occur for the function.
f(x) = 3x3 + 9x2 – 1
ANSWER
Relative minimum occurs at x=0
Relative maximum occurs at x=-2
EXPLANATION
The given function is;
[tex]f(x) = 3 {x}^{3} + 9 {x}^{2} - 1[/tex]
We take the first derivative to get:
[tex]f'(x) = 9 {x}^{2} + 18x[/tex]
At turning point f'(x)=0
[tex] 9 {x}^{2} + 18x = 0[/tex]
[tex] 9x(x + 2) = 0[/tex]
[tex]x = 0 \: or \: x = - 2[/tex]
We take the second derivative to get
[tex]f''(x) = 18x + 18
[/tex]
[tex]f''(0) = 18(0) + 18 = 18 \: > \: 0[/tex]
Relative minimum occurs at x=0
[tex]f''( - 2) = 18( - 2)+ 18 = - 18 \: < \: 0[/tex]
Relative maximum occurs at x=-2
Answer:
Relative minimum occurs at x=0
Relative maximum occurs at x=-2
Step-by-step explanation:
The transitive property of equality states that:
O if a = b, then bra
O if a = b, then ac = bc
O if a = b and b= c, then a =
if a = b and c= C, then a + b = b + c
Answer: If [tex]a=b[/tex] and [tex]b=c[/tex], then [tex]a=c[/tex]
Step-by-step explanation:
Let be "a", "b", and "c" all real numbers, the Transitive property of equalities states that :
If [tex]a=b[/tex] and [tex]b=c[/tex], then [tex]a=c[/tex]
You can observe that if two numbers are equal to the same number, then all this numbers are equal to each other.
For example, applying the Transitive property of equalities to:
[tex]x+3=5[/tex] and [tex]2x+1=5[/tex]
You can equate them:
[tex]x+3=2x+1[/tex]
And solve for "x":
[tex]3-1=2x-x\\\\x=2[/tex]
Answer:
The correct answer option is: If a = b and b = c, then a = c.
Step-by-step explanation:
The Transitive Property of Equality states that if one value, lets say [tex] a [/tex] is equal to another value, call it [tex] b [/tex], which is equal to another value, call it [tex] c [/tex], then the very first value [tex] a [/tex] would be equal to the third value [tex] c [/tex].
So from the given answer options, the correct option is: If a = b and b = c, then a = c.
What factor is used to convert feet per minute into miles per hour?
To convert feet per minute into miles per hour, use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Divide the given value by 5280 to get the number of miles, then divide the result by 60 to convert minutes to hours.
Explanation:To convert feet per minute into miles per hour, you need to use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Here's the step-by-step calculation:
First, determine the number of miles in the given feet per minute by dividing the given value by 5280.Next, divide the result by 60 to convert minutes to hours.The final result will be the given value in feet per minute converted to miles per hour.For example, if you have a speed of 300 feet per minute:
300 feet per minute / 5280 feet per mile = 0.056818 miles per minute.0.056818 miles per minute / 60 minutes per hour = 0.000947 miles per hour.Therefore, 300 feet per minute is equal to 0.000947 miles per hour.Learn more about Unit Conversion here:https://brainly.com/question/19420601
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An artist makes a scale drawing of a building he likes. The building is 90 feet tall and 45 feet wide.If this picture is 3 feet wide how tall will this picture be?
Answer:
The Building's tall and wide ratio is 90 : 45 = 2 : 1
now the wide is 3, let's say that tall is a.
2 / 1 = a / 3
a = 2 x 3
a = 6
So the picture will be 6 feet tall.
Given the following similar triangles, find x.
Simplify the expression. –16 • 1/8 • 4 + 32 ÷ 2
Answer:
8
Step-by-step explanation:
–16 • 1/8 • 4 + 32 ÷ 2
Using PEMDAS, we multiply and divide from left to right since there are no parentheses or exponents.
-2 • 4 + 32 ÷ 2
-8 +32 ÷ 2
-8 + 16
Now we add and subtract from left to right
8
1. On delivery, eggs should be rejected if:
A. There is only one USDA inspection stamp on each carton
B. The shells of the eggs have cracks in them
c. The shells vary in color
D. The eggs are odorless
When eggs are delivered, if one notices that B. The shells of the eggs have cracks in them, the eggs should be rejected.
Eggs that have cracks in them can be potentially dangerous to people because microorganisms like bacteria can enter through those cracks and either spoil the egg or make it harmful for consumption.
It is therefore best that an egg that has a crack, be rejected upon delivery.
Other options are incorrect because:
One USDA inspection stamp is good enough proof that the eggs are good Shell color has no effect on whether an egg is bad or not Eggs are supposed to be odorlessIn conclusion, if an egg has a crack in it upon delivery, it should be rejected.
Find out more at https://brainly.com/question/17894532.
WILL GIVE BRAINLIEST What it the value of y?
Answer:
C 40
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
y+10 + 2y + 50 = 180
Combine like terms
3y + 60 =180
Subtract 60 from each side
3y+60-60 = 180-60
3y = 120
Divide by 3
3y/3 = 120/3
y = 40
The sum of all the angles of a triangle is 180 degrees. To solve for y you can make a formula of the sum of the angles equal to 180 like so...
y + 10 + 2y + 50 = 180
Now you must combine like terms. This means that first numbers with the same variables (y) must be combined...
(y + 2y) + 10 + 50 = 180
3y + 10 + 50 = 180
Combine like terms 10 and 50...
3y + 60 = 180
Now bring 60 to the left side by subtracting 60 to both sides (what you do on one side you must do to the other). Since 60 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.
3y + 60 - 60 = 180 - 60
3y + 0 = 120
3y = 120
Next divide 3 to both sides to finish isolating x. Since 3 is being multiplied by x, division (the opposite of multiplication) will cancel 3 out (in this case it will make 3 one) from the left side and bring it over to the right side.
3y / 3 = 120 / 3
y = 40
C. 40
Hope this helped!
~Just a girl in love with Shawn Mendes
716,773 rounded to the nearest thousand
Answer: 717,000
Step-by-step explanation:
716,773 rounded to the nearest thousand is 717000 because the 7 is closer to 10 than it is to 0
Hello There!
716,772 rounded to the nearest thousand would be 717,000
772 is closer to 717,000 than 716,000
What is the pattern in the values as the exponents increase?
Answer:
Option D is correct.
Step-by-step explanation:
We need to find the pattern in the values as the exponents increase.
First value is 1/3
if we multiply 3 with 1/3 i.e. 1/3*3 we get 1
The next value is 1 in the table.
Now, if we multiply 1 with 3 i.e. 1*3 we get 3
The next value is 3 in the table.
Now, if we multiply 3 with 3 i.e 3*3 we get 9
So, the next value is 9 in the table.
So, if we multiply 3 with the previous value we get the next value in the table.
Hence Option D multiply the previous value by 3 is correct.
12 one third minus 6 9/10
[tex]12\dfrac{1}{3}-6\dfrac{9}{10}=12\dfrac{10}{30}-6\dfrac{27}{30}=6+\left(-\dfrac{17}{30}\right)=5\dfrac{13}{30}[/tex]
Suppose f(x) = x. Find the graph of f(x+2).
Click on the correct answer.
graph 1
graph 2
Click on each graph to enlarge it.
graph 3
graph 4
The answer is:
The fourth graph.
Why?We are given the following equation:
[tex]f(x)=x[/tex]
Then, we need to find the graph of f(x+2) that will be equal to:
[tex]f(x+2)=x+2[/tex]
[tex]y=x+2[/tex]
Now, finding the x-axis interception, making "y" equal to 0, we have:
[tex]0=x+2[/tex]
[tex]-2=x[/tex]
Therefore, the x-axis interception point is located at (-2,0), it matches with the fourth graph.
Now, finding the y-axis interception, making "x" equal to 0, we have:
[tex]y=x+2[/tex]
[tex]y=0+2=2[/tex]
Therefore, the y-axis interception point is located at (0,2), it matches with the fourth graph.
Hence, we have that the graph of f(x+2) is the fourth graph since the second graph function cuts the x-axis at -2 and the y-axis at 2.
Have a nice day!
Write a function for p(x), the profit from selling x necklaces.
The revenue from selling x necklaces is r(x) = 10x. The cost of buying x necklaces is c(x) = 4x + 15. The profit from selling x necklaces is p(x) = r(x) – c(x)
ANSWER
[tex]p(x) = 6x - 15[/tex]
EXPLANATION
The revenue from selling x necklaces is
[tex]r(x) = 10x[/tex]
The cost of buying x necklaces is
[tex]c(x) = 4x + 15[/tex]
The profit from selling x necklaces is
[tex]p(x) = r(x) - c(x)[/tex]
We substitute the functions to get;
[tex]p(x) = 10x- (4x + 15)[/tex]
[tex]p(x) = 10x- 4x - 15[/tex]
[tex]p(x) = 6x - 15[/tex]
Therefore the function for the profit is
[tex]p(x) = 6x - 15[/tex]
What is f(3) for the quadratic function
f(x)=2x2 + x – 12?
F -3
G 3
H 6
I. 9
Answer:
f(3) = 9
Step-by-step explanation:
Wherever you see an x on the right, put a 3 in for that x
f(x) = 2x^2 + x - 12
f(3) = 2*(3)^2 + 3 - 12
f(3) = 2*9 + 3 - 12
f(3) = 18 + 3 - 12
f(3) = 9
Answer plz ASAP!!!!!!!
Let the base = x
Then the height would be 2x ( twice the length of the base.
Now using the given formula you get:
25 = 1/2 * 2x *x
Multiply 2x by 1/2:
1/2 * 2x = 2x/2
25 = 2x/2 * x
2x/2 = 1x, now you have:
25 = x *x
Multiply x by x:
25 = x^2
Take the square root of both sides:
x = √25
x = 5
when solving the equation which is the best first step to begin to simplify the equation? -2(x+3)=-10
Answer:
c
Step-by-step explanation:
The best first step to solve the equation -2(x+3)=-10 is to distribute the -2 across the parentheses, simplify the equation, and then solve for x.
Checking the answer by substituting the value of x back into the original equation ensures the solution is correct.
Explanation:When solving the equation -2(x+3)=-10, the best first step to simplify the equation is to distribute the multiplication of -2 across the parentheses.
This is done to eliminate the parentheses and simplify the equation into its simplest form. After distribution, you would then have the simplified equation -2x - 6 = -10.
From there, you can proceed to solve for x by adding 6 to both sides of the equation to isolate the term with x, then dividing both sides by -2 to find the value of x.
Here are the basic problem-solving steps:
Distribute the -2 across the parentheses: -2(x+3) becomes -2x - 6.Isolate the variable 'x' by adding 6 to both sides to get -2x = -4.Divide both sides by -2 to find x: x = 2.Once you've calculated the value of x, it's important to check the answer to ensure it is reasonable.
You can do this by substituting the value of x back into the original equation.
if you shift the linear parent function, f(x)=x, up 13 units, what is the equation of the new function?
Answer:
f(x) = x + 13
Step-by-step explanation:
Given f(x) then f(x) + c represents a vertical translation
• If c > 0 then vertical shift up ↑ of c units
• If c < 0 then vertical shift down ↓ of c units
here c = + 13, hence
f(x) = x + 13
What is the simplified form expression 2(x-5)?
Answer:
2x-10
Step-by-step explanation:
original equation: 2(×-5)
distributive property: 2(x) 2(-5) =2x-10
Answer:
2x-10
2(x-5)
2*x=2x
2*5=10
Evaluate 48/6-10/3 please and thank you :)))
Answer:
14/3
Step-by-step explanation:
Simplify the following:
48/6 - 10/3
Hint: | Reduce 48/6 to lowest terms. Start by finding the GCD of 48 and 6.
The gcd of 48 and 6 is 6, so 48/6 = (6×8)/(6×1) = 6/6×8 = 8:
8 - 10/3
Hint: | Put the fractions in 8 - 10/3 over a common denominator.
Put 8 - 10/3 over the common denominator 3. 8 - 10/3 = (3×8)/3 - 10/3:
(3×8)/3 - 10/3
Hint: | Multiply 3 and 8 together.
3×8 = 24:
24/3 - 10/3
Hint: | Subtract the fractions over a common denominator to a single fraction.
24/3 - 10/3 = (24 - 10)/3:
(24 - 10)/3
Hint: | Subtract 10 from 24.
| 2 | 4
- | 1 | 0
| 1 | 4:
Answer: 14/3
Answer:
Your answer is 4 and 2/3
Step-by-step explanation:
Hope this helps have a good day!
what is the y-interceptof the line shown?
Answer:
y- intercept = 4
Step-by-step explanation:
The y- intercept is the value of the y- coordinate where the line crosses the y- axis.
Here the y- intercept = 4 or (0, 4) ← coordinates of point
Answer:
( 0 , 4 )
Step-by-step explanation:
The y - intercept of the line is where the line hit's or crosses the y - axis and in the case since the line goes through 4 on the y - axis
The number of potato chips in a bag is normally distributed with a mean of 71 and a standard deviation of 2. Approximately what percent of bags contain between 69 and 73 potato chips?
Approximately 68%
Approximately 71%
Approximately 95%
Approximately 99.7%
Answer:
Approximately 68%
Step-by-step explanation:
The number of potato chips in a bag is normally distributed with a mean of 71 and a standard deviation of 2, that is to say:
X ∼ N(µ, σ2) ⇒ X ∼ N(71, 4).
Now, to find the percentage of bags that contain between 69 and 73 potatos we need the help of a calculator.
Pluging the data into a calculator we get that the percentage of bags that contain between 69 and 73 potatos is 68.27% ≈ 68%.
The solution is: Approximately 68%
Answer:
Approximately 68% percent of bags contain between 69 and 73 potato chips.
Step-by-step explanation:
Number of chips in a bag is normally distributed.
Mean = 71
Standard deviation = 2
We know that in normal distribution, 34.1% of bags will fall with in one standard deviation on one side. On both sides within the range of 1 standard deviation, 34.1 + 34.1 = 68.2 % of bags will fall.
A table of normal distribution about mean is attached for better understanding.
Our range is:
69 to 73
71 - 2 to 71 + 2
71 ± 2
mean ± standard deviation
Our range is within 1 standard deviation. Hence, Approximately 68% of bags contain between 69 and 73 potato chips.
Help me out uwu and I will give u 25
points
Answer:
it is the second one because 1/2 divided by 3 equals 1/6 3 times
What is the answer to this question
1.2 Puzzle Time
Why Did The Muffler Quit The Car Business?
Write the letter of each answer in the box containing the exercise number
Find the value of the variable which satisfies the equation,
1. 4a - 5 = 11
2. 16 = 17 - 1
Answers
E
-7
3. 8 =
-2
4, 647=9
T.1
5. 12c + 6c = 36
L
6
6. 14x + 11x + 10 = 85
7. 19w - 13 - 6w = -39
E. 2
in
T
8. -4(2n – 5) = -28
9. 85 + 3(12 – 73) = 49
10. -18 = 15z - 9(22 – 2)
H. -2
Solve an equation to find the number.
11. The difference of six times a number and 7 is -49,
W. 12
T. -52
12. Negative sixteen plus the quotient of a number and
-4 is –3.
13. The sum of two times a number and 11 is -7,
U.
-9
14. The total cost for a week at camp is $220. You have
$140. You earn $16 for every item you sell in a
fundraiser. How many items do you need to sell to
pay for a week at camp?
Answer:
B is le answer
Step-by-step explanation:
To find the values of the variables in each equation, isolate the variable on one side by performing operations. The solutions for the variables are 4, -1, 2, 6, no solution, and 10.8 for the respective equations.
Explanation:To find the value of the variable in each equation, we need to isolate the variable on one side of the equation. Let's solve each equation step by step:
4a - 5 = 11
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Combine the radicals -2/13 + 19/13
Answer:
17/13
Step-by-step explanation:
Answer:
Step-by-step explanation:
" / " indicates "division" and should not be used in this context.
If you meant: -2 square root 13 plus 19 square root 13, the simplest result would be 17 square root 13.
Note that if you click on the "omega" symbol (below), a menu of symbols will appear, including the square root symbol √.
Then: -2√13 + 19√13 = 17√13.
What is the solution of log2 (3x - 7) = 3?
4
5
Answer:
x = 5
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{2}[/tex](3x - 7) = 3, then
3x - 7 = 2³ = 8 ( add 7 to both sides )
3x = 15 ( divide both sides by 3 )
x = 5
The required solution of logarithmic expression log2 (3x - 7) = 3 is x = 5. Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
To solve for x in the equation log2 (3x - 7) = 3, we first use the definition of a logarithm to change the logarithmic form to the exponential form.
log2 (3x - 7) = 3
2³ = 3x - 7
Next, we solve for x by adding 7 to both sides of the equation:
8 + 7= 3x - 7 + 7
15 = 3x
Finally, we divide both sides of the equation by 3:
x = 5
So, the solution of log2 (3x - 7) = 3 is x = 5.
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helpp me plz respond
An unknown number x is at most 10. Which graph best represents all the values of x? Number line graph with closed circle on 10 and shading to the right. Number line graph with open circle on 10 and shading to the right. Number line graph with open circle on 10 and shading to the left. Number line graph with closed circle on 10 and shading to the left.
Answer:
Step-by-step explanation:
The question does say at most 10. That includes 10. So the circle on 10 should indicate it is closed or fully filled in.
The shading should go left. It should indicate less than 10.
2x + 3y = 17
5x + 6y = 32
Usibg method if elimination
Answer:
Solution (-2, 7)
Step-by-step explanation:
2x + 3y = 17 (1)
5x + 6y = 32 (2)
Using elimination method
Multiply (-2) to the equation (1)
-4x - 6y = -34
Now you have 2 new equations
-4x - 6y = -34
5x + 6y = 32
----------------------------Add
x = -2
Substitute x = -2 into 2x + 3y = 17
2(-2) + 3y = 17
- 4 + 3y = 17
3y = 21
y = 7
Solution (-2, 7)
Final answer:
The solution to the system of equations 2x + 3y = 17 and 5x + 6y = 32 using the elimination method is x = -2 and y = 7.
Explanation:
To solve the system of equations using the method of elimination, we manipulate the equations to make the coefficients of either x or y the same, and then subtract one equation from the other to eliminate that variable. Let's consider the given equations:
2x + 3y = 17 (Equation 1)
5x + 6y = 32 (Equation 2)
We can see that the coefficients of y are in the ratio of 3:6 or 1:2. To use elimination, we want the coefficients to match, so we can multiply Equation 1 by 2:
(2)(2x) + (2)(3y) = (2)(17)
4x + 6y = 34 (New Equation 1)
Now we can subtract the new Equation 1 from Equation 2:
(5x + 6y) - (4x + 6y) = 32 - 34
5x - 4x + 6y - 6y = -2
x = -2
Now that we have a value for x, we can substitute it back into one of the original equations to solve for y. Let's substitute x into Equation 1:
2(-2) + 3y = 17
-4 + 3y = 17
3y = 17 + 4
3y = 21
y = 7
The solution to the system of equations is x = -2 and y = 7.