Answer:
25
Step-by-step explanation:
Let's break this down step by step:
"2 digit positive odd integers greater than 50"
So we start at 50
Don't exceed 99 since 2-digit limit
Any 2-digit integer greater than 50 will be positive (So that's a redundant statement)
Well...we know that from 50-99, is 50 integers counting by ones.
We know that half will be even and half will be odd.
With this we can say 50/2 == 25
Hence, there are 25 2 digit positive odd integers greater than 50.
Cheers.
In a certain lake, trout average 12 in. in length with standard deviation 2.75 in. and the bass average 4 lb. in weight with standard deviation 0.8 lb. If Deion caught an 18-in trout and Keri caught a 6-lb bass, which fish was the better catch?
Answer:
The bass fish was the better catch
Step-by-step explanation:
From the question we are told that
The population mean for trout is [tex]\mu_1 = 12 \ in[/tex]
The standard deviation is [tex]\sigma_1 = 2.75 \ in[/tex]
The population mean for base is [tex]\mu _2 = 4 \ lb[/tex]
The standard deviation is [tex]\sigma_2 = 0.8 \ lb[/tex]
The number of trout caught [tex]x_1 = 18[/tex]
The number of bass caught [tex]x_2 = 6[/tex]
Generally z-value(standardized value ) for the of number trout caught is mathematically represented as
[tex]z_1 = \frac{x_1 - \mu_1}{\sigma_1 }[/tex]
substituting value
[tex]z_1 = \frac{18 - 12}{2.75 }[/tex]
[tex]z_1 = 2.18[/tex]
Generally z-value(standardized value ) for the of number bass caught is mathematically represented as
[tex]z_2 = \frac{x_2 - \mu_2}{\sigma_2 }[/tex]
substituting value
[tex]z_2 = \frac{6 - 4}{0.8 }[/tex]
[tex]z_2 = 2.5[/tex]
From our calculation we see that [tex]z_2 > z_1[/tex]
The fish that was the better catch is the bass fish
Solve the System of equations.
Answer:
x=9y=12Step-by-step explanation:
Plug x as 2y-15 in the first equation and solve for y.
-5(2y-15)+4y=3
-10y+75+4y=3
-6y+75=3
-6y=-72
y=12
Plug y as 12 in the second equation and solve for x.
x=2(12)-15
x=24-15
x=9
Which of the following is an example of a quadratic equation?
Answer:
C. x^2 - 64 = 0
hope this helps :)
Answer:
It's C
Step-by-step explanation:
It has a variable being squared
EXAMPLE 4 Find ∂z/∂x and ∂z/∂y if z is defined implicitly as a function of x and y by the equation x6 + y6 + z6 + 18xyz = 1. SOLUTION To find ∂z/∂x, we differentiate implicitly with respect to x, being careful to treat y as a constant:
Answer:
see attachment
Step-by-step explanation:
We differentiate implicitly with respect to x taking y as a constant and we differentiate implicitly with respect to y taking x as a constant.
[tex]\rm \dfrac{\partial z}{\partial x} = - \dfrac{(x^5 + 3yz)}{z^5 + x} \ \ and \ \ \dfrac{\partial z}{\partial y} &= - \dfrac{(y^5 + 3xz)}{z^5 + y}[/tex]
What is an implicit function?When in a function the dependent variable is not explicitly isolated on either side of the equation then the function becomes an implicit function.
The equation is given as [tex]\rm x^6 + y^6 + z^6 + 18xyz = 1.[/tex]
Differentiate partially the function with respect to x treating y as a constant.
[tex]\begin{aligned} \dfrac{\partial}{\partial x} x^6 + y^6 + z^6 + 18xyz &= 0\\\\6x^5 + 0 + 6z^5 \dfrac{\partial z }{\partial x} + 18y(z + x\dfrac{\partial z}{\partial x}) &= 0\\\\x^5 + z^5 \dfrac{\partial z }{\partial x} + 3y(z + x\dfrac{\partial z}{\partial x}) &= 0\\\\\dfrac{\partial z}{\partial x} &= - \dfrac{(x^5 + 3yz)}{z^5 + x} \end{aligned}[/tex]
Similarly, differentiate partially the function with respect to y treating x as a constant.
[tex]\begin{aligned} \dfrac{\partial}{\partial y} x^6 + y^6 + z^6 + 18xyz &= 0\\\\ 0 + 6y^5+ 6z^5 \dfrac{\partial z }{\partial y} + 18x(z + y\dfrac{\partial z}{\partial y}) &= 0\\\\y^5 + z^5 \dfrac{\partial z }{\partial y} + 3x(z + y\dfrac{\partial z}{\partial y}) &= 0\\\\\dfrac{\partial z}{\partial y} &= - \dfrac{(y^5 + 3xz)}{z^5 + y} \end{aligned}[/tex]
More about the implicit function link is given below.
https://brainly.com/question/6472622
What is the equation of the line that passes through the point (3,6) and has a slope of 4/3
Answer:
y = 4/3x+2
Step-by-step explanation:
We can use the slope intercept form of the equation
y = mx+b
Where m is the slope and b is the y intercept
y= 4/3 x +b
Substitute the point into the equation
6 = 4/3(3) +b
6 = 4 +b
Subtract 4 from each side
2 = b
y = 4/3x+2
Find the unknown side length, x. Write your answer in simplest radical form.
A. 3
B. 34
C. 6.
D. 41
Answer:
√41
Step-by-step explanation:
Considering the sides with lengths 48 and 52 units, we would use Pythagoras theorem to find the third side. Let that side be t
52² = 48² + t²
t² = 52² - 48²
= 2704 - 2304
= 400
t = √400
= 20
Considering the next triangle with sides t (20 units) and 12 units, again using the theorem
20² = 12² + y²
where y is the third side
400 = 144 + y²
y² = 400 - 144
= 256
y = √256
= 16 units
Considering the triangle with two sides given as 5 and 13 units, the third side (which is part of the 16 units calculated earlier)
13² = 5² + u²
where u is the 3rd side
169 = 25 + u²
u² = 169 - 25
u² = 144
u = √144
u = 12
The other part of the side of that triangle
= 16 - 12
= 4
Considering the smallest triangle whose sides are x, 5 and 4,
x² = 5² + 4²
= 25 + 16
= 41
x = √41
What is the equation for the plane illustrated below?
Answer:
Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].
Step-by-step explanation:
The general equation in rectangular form for a 3-dimension plane is represented by:
[tex]a\cdot x + b\cdot y + c\cdot z = d[/tex]
Where:
[tex]x[/tex], [tex]y[/tex], [tex]z[/tex] - Orthogonal inputs.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex], [tex]d[/tex] - Plane constants.
The plane presented in the figure contains the following three points: (2, 0, 0), (0, 2, 0), (0, 0, 3)
For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:
xy-plane (2, 0, 0) and (0, 2, 0)
[tex]y = m\cdot x + b[/tex]
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - x-Intercept, dimensionless.
If [tex]x_{1} = 2[/tex], [tex]y_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]y_{2} = 2[/tex], then:
Slope
[tex]m = \frac{2-0}{0-2}[/tex]
[tex]m = -1[/tex]
x-Intercept
[tex]b = y_{1} - m\cdot x_{1}[/tex]
[tex]b = 0 -(-1)\cdot (2)[/tex]
[tex]b = 2[/tex]
The equation of the line in the xy-plane is [tex]y = -x+2[/tex] or [tex]x + y = 2[/tex], which is equivalent to [tex]3\cdot x + 3\cdot y = 6[/tex].
yz-plane (0, 2, 0) and (0, 0, 3)
[tex]z = m\cdot y + b[/tex]
[tex]m = \frac{z_{2}-z_{1}}{y_{2}-y_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
If [tex]y_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]y_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:
Slope
[tex]m = \frac{3-0}{0-2}[/tex]
[tex]m = -\frac{3}{2}[/tex]
y-Intercept
[tex]b = z_{1} - m\cdot y_{1}[/tex]
[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]
[tex]b = 3[/tex]
The equation of the line in the yz-plane is [tex]z = -\frac{3}{2}\cdot y+3[/tex] or [tex]3\cdot y + 2\cdot z = 6[/tex].
xz-plane (2, 0, 0) and (0, 0, 3)
[tex]z = m\cdot x + b[/tex]
[tex]m = \frac{z_{2}-z_{1}}{x_{2}-x_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - z-Intercept, dimensionless.
If [tex]x_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:
Slope
[tex]m = \frac{3-0}{0-2}[/tex]
[tex]m = -\frac{3}{2}[/tex]
x-Intercept
[tex]b = z_{1} - m\cdot x_{1}[/tex]
[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]
[tex]b = 3[/tex]
The equation of the line in the xz-plane is [tex]z = -\frac{3}{2}\cdot x+3[/tex] or [tex]3\cdot x + 2\cdot z = 6[/tex]
After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:
[tex]a = 3[/tex], [tex]b = 3[/tex], [tex]c = 2[/tex], [tex]d = 6[/tex]
Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].
Answer:
It is A 3x+3y+2z=6
Step-by-step explanation:
The winery sold 81 cases of wine this week. If twice
as many red cases were sold than white, how many
white cases were sold this week?
A. 32 cases
B. 61 cases
C. 27 cases
D. 54 cases
Answer:
Option (C)
Step-by-step explanation:
Let the red cases sold = r
and the number of white cases sold = w
Total number of cases sold by the winery = 81
r + w = 81 -------(1)
If number of red cases sold is twice of white cases sold,
r = 2w ------- (2)
By substituting the value of r from equation (2) to equation (1),
2w + w = 81
3w = 81
w = 27 cases
From equation (1),
r + 27 = 81
r = 54 cases
Therefore, number of white cases sold are 27 cases
Option (C) is he answer.
Which input value produces the same output value for the two functions on the graph?
Answer:
x=3
Step-by-step explanation:
To solve this problem, we should check the x coordinate of the point where both graphs intersect. Based on both graphs, they intersect at the point (3,-1). So, the input value for which both graphs have the same value is x=3.
Answer:
its x=-2
Step-by-step explanation:
cause i got it wrong and it said the answer was x=-2
If ABCD is dilated by a factor of 2, the
coordinate of C'would be:
Answer:
(4, 4)
Step-by-step explanation:
All you really need to do is multiply C's original coordinates with the scale factor. So (2, 2), becomes (4, 4).
Answer:
( 4 , 4 )
Step-by-step explanation:
original C coordinates : ( 2 , 2 )
since the problem is telling us to dilate by the factor of 2 we multiply both 2's by 2.
( 2 ‧ 2 ) ( 2 ‧ 2 )
= ( 4 , 4 )
Solve by factoring or find square root. x^2-3x-4=0
Answer:
x = -1 and x = 4.
Step-by-step explanation:
x^2 - 3x - 4 = 0
(x - 4)(x + 1) = 0
x - 4 = 0
x = 4
x + 1 = 0
x = -1
Check your work...
(4)^2 - 3(4) - 4
= 16 - 12 - 4
= 4 - 4
= 0
(-1)^2 - 3(-1) - 4
= 1 + 3 - 4
= 4 - 4
= 0
So, x = -1 and x = 4.
Hope this helps!
Please answer this correctly without making mistakes
Answer:
I believe 45.50
Step-by-step explanation: The locksmith is 18.3 miles W from furniture, the hotel is 27.2 E from furniture store so 18.3+27.2=45.50
During a timed test, Alexander typed 742words in 14minutes. Assuming Alexander works at this rate for the next hour, which of the following best approximates the number of words he would type in that hour?
Answer:
3,180 words in the hourStep-by-step explanation:
First, you have to figure out how many words he types in one minute. Then, have to multiply by the number of minutes. So,
Number of words per minute:
742 = Total number of words in 14 min
14 = time given
742/14 = 53 words per minute
Number of Words in 1 hour:
53 = words per min
60 = number of minutes
53*60 = 3,180
3,180 words in one hour.Hope my answer helps,
Kavitha
Answer:
3180 words
Step-by-step explanation:
We can use a ratio to solve
742 words x words
--------------- = -----------------
14 minutes 60 minutes
Using cross products
742 * 60 = 14x
Divide each side by 14
742*60/14 = x
3180 words
Find the measure of each unknown angle
Answer:
1. 55 degrees, 2. 316 degrees
Step-by-step explanation:
When it shows interior angles on a triangle it adds up to 180 degrees
When it shows exterior angles on a triangle it adds up to 360 degrees
1. ? = 55 degrees
85 + 40 = 125
180 - 125 = 55
2. ? = 316 degrees
Inside of triangle:
14 + 30 = 44
180 - 44 = 136 degrees
Exterior of triangle:
360 - 14 = 346 degrees
360 - 30 = 330 degrees
360 - 44 = 316 degrees
Janet, an experienced shipping clerk, can fill a certain order in 14 hours. Jim, a new clerk, needs 15 hours to do the same job. Working together, how long will it take them to fill the order?
Answer:
7.24 hrs
Step-by-step explanation:
Janet can do the order in 14 hours.
In 1 hour, she can do 1/14 of the order.
Jim can do the order in 15 hours.
In 1 hour, he can do 1/15 of the order.
Let the total amount of time they take to do the job working together be x hours.
[tex]\frac{1}{14} x+\frac{1}{15}x =1[/tex]
[tex]\frac{29}{210} x=1[/tex]
[tex]\frac{210}{29}* \frac{29}{210} x=1*\frac{210}{29}[/tex]
[tex]x= 7.241379...[/tex]
¿Qué escala se utilizó en un mapa, donde la distancia en la vida real es 45 km y en el plano es 5cm?please ayuda
Answer:
La escala utilizada en el mapa es 1 : 900000.
Step-by-step explanation:
El enunciado describe claramente una escala de reducción. El factor de escala se define como sigue:
[tex]n = \frac{s_{plano}}{s_{real}}[/tex]
Donde:
[tex]n[/tex] - Factor de escala, adimensional.
[tex]s_{plano}[/tex] - Distancia en el plano, medida en centímetros.
[tex]s_{real}[/tex] - Distancia real, medida en centímetros.
Si [tex]s_{plano} = 5\,cm[/tex] y [tex]s_{real} = 4500000\,cm[/tex], entonces el factor de escala es:
[tex]n = \frac{5\,cm}{4500000\,cm}[/tex]
[tex]n = \frac{1}{900000}[/tex]
La escala utilizada en el mapa es 1 : 900000.
Graph y less than or equal to 3x
Answer:
See Image Below.
Step-by-step explanation:
The Shaded region is the area of numbers that this equation satisfies.
Answer:
Please see attached image
Step-by-step explanation:
In order to graph the inequality, start from plotting the boundary line defined by the equality;
y = 3 x
You just need two points to accomplish such. so let's use two simple values for x and find what the y-values are:
for x = 0 then y = 3 (0) = 0
for x = 1 then y = 3 (1) = 3
Then use the points (0, 0) and (1, 3) to plot the boundary line.
After this, grab any point on the plane either clearly above the boundary line, or clearly below it and check if the inequality satisfies. For example, you can pick the point (3, 0) which is on the x line, 3 units to the right of the origin, and clearly below the boundary line we just plot.
When you use it in the inequality, you get:
(0) [tex]\leq[/tex] 3 (3)
0 [tex]\leq[/tex] 9
which is a true statement, therefore, the points below the boundary lie are also solutions of the inequality.
Then the solution consists of all the points in the boundary line we just plotted (and indicated by drawing a solid line), plus all the points below the line, as depicted in the attached image.
A city has a population of 240,000 people. Suppose that each year the population grows by 7.75%. What will the population be after 7 years?
round your answer to the nearest whole number.
people
Answer:
[tex]\large\boxed{\sf \ \ \ 404,699 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
At the beginning the population is 240,000
After 1 year the population will be
240,000*(1+7.75%)=240,000*1.0775
After n years the population will be
[tex]240,000\cdot1.0775^n[/tex]
So after 7 years the population will be
[tex]240,000\cdot1.0775^7=404699.058...[/tex]
So rounded to the nearest whole number gives 404,699
Hope this helps
Please do either 40 or 39
Answer:
y = 1.8
Step-by-step explanation:
Question 39).
Let the operation which defines the relation between a and b is O.
Relation between a and b has been given as,
a O b = [tex]\frac{(a+b)}{(a-b)}[/tex]
Following the same operation, relation between 3 and y will be,
3 O y = [tex]\frac{3+y}{3-y}[/tex]
Since 3 O y = 4,
[tex]\frac{3+y}{3-y}=4[/tex]
3 + y = 12 - 4y
3 + y + 4y = 12 - 4y + 4y
3 + 5y = 12
3 + 5y - 3 = 12 - 3
5y = 9
[tex]\frac{5y}{5}=\frac{9}{5}[/tex]
y = 1.8
Therefore, y = 1.8 will be the answer.
9 less than twice a number is 13. What is the number?
Answer:
11
Step-by-step explanation:
Answer:
x = 11.
Step-by-step explanation:
9 less than twice a number is the same thing as twice a number minus 9. Let's say that the number is x.
2x - 9 = 13
2x = 22
x = 11
Hope this helps!
A certain forest covers an area of 2100 km². Suppose that each year this area decreases by 3.5%. What will the area be after 5 years
Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
[tex]\large\boxed{\sf \ \ \ 1757 \ km^2 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
I would recommend that you checked the answers I have already provided as this is the same method for all these questions, and maybe try to solve this one before you check the solution.
At the beginning the area is 2100
After one year the area will be
2100*(1-3.5%)=2100*0.965
After n years the area will be
[tex]2100\cdot0.965^n[/tex]
So after 5 years the area will be
[tex]2100\cdot0.965^5=1757.34027...[/tex]
So rounded to the nearest square kilometer is 1757
Hope this helps
Answer: 1757 km²
Step-by-step explanation:
Because 3.5% = 0.035, first do 1-.035 to get .965. Then do 2100*.965*.965*.965*.965*.965 to get 1757.34027.
The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism? PLEASE COMMENT, I Can't SEE ANSWERS CAUSE OF A GLITCH
Answer:
x + 1 - ( 4 / x³ + 3x² + 8 )
Step-by-step explanation:
If the volume of this rectangular prism ⇒ ( x⁴ + 4x³ + 3x² + 8x + 4 ), and the base area ⇒ ( x³ + 3x² + 8 ), we can determine the height through division of each. The general volume formula is the base area [tex]*[/tex] the height, but some figures have exceptions as they are " portions " of others. In this case the formula is the base area [tex]*[/tex] height, and hence we can solve for the height by dividing the volume by the base area.
Height = ( x⁴ + 4x³ + 3x² + 8x + 4 ) / ( x³ + 3x² + 8 ) = [tex]\frac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}[/tex] = [tex]x+\frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex] = [tex]x+1+\frac{-4}{x^3+3x^2+8}[/tex] = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex] - and this is our solution.
Answer:
[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
Step-by-step explanation:
[tex]volume=base \: area \times height[/tex]
[tex]height=\frac{volume}{base \: area}[/tex]
[tex]\mathrm{Solve \: by \: long \: division.}[/tex]
[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]
[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]
[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
A coin is tossed and an eight-sided die numbered 1 through 8 is rolled. Find the probability of tossing a tail and then rolling a number greater than 3. The probability of tossing a tail and then rolling a number greater than 3 is
Answer:
5/16
Step-by-step explanation:
P(tails) = 1/2
P(>3) = 5/8
P(tails AND >3) = 1/2 × 5/8 = 5/16
what is the ratio of the number of black keys to the total number of keys on the keyboard, if the same pattern of keys I continued 5 black keys 7 white keys
Answer:
5 : 7 i guess
Step-by-step explanation:
The range of f(x) = cos(x) is y ≤ 0
Answer:
Look at the image below↓
A subcommittee is randomly selected from a committee of eight men and seven women. What is the probability that all three people on the subcommittee are men
Answer:
The probability that all three people on the subcommittee are men
= 20%
Step-by-step explanation:
Number of members in the committee = 15
= 8 men + 7 women
The probability of selecting a man in the committee
= 8/15
= 53%
The probability of selecting three men from eight men
= 3/8
= 37.5%
The probability that all three people on the subcommittee are men
= probability of selecting a man multiplied by the probability of selecting three men from eight men
= 53% x 37.5%
= 19.875%
= 20% approx.
This is the same as:
The probability of selecting 3 men from the 15 member-committee
= 3/15
= 20%
Tensile strength tests were performed on two different grades of aluminum spars used in manufacturing the wing of a commercial transport aircraft. From past experience with the spar manufacturing process and the testing procedure, the standard deviations of tensile strengths are assumed to be known. The data obtained are as follows:
n_1 = 10
x_1 = 87.6
σ_1 = 1
n_2 = 12
x^2 = 74.5
σ_2 = 1.5.
Required:
If μ _1 and μ _2 denote the true mean tensile strengths for the two grades of spars. Construct a 90 percentage confidence interval on the difference in mean strength.
Answer:
(12.141, 14.059)
Step-by-step explanation:
Explanation is provided in the attached document.
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 240240 engines and the mean pressure was 7.57.5 pounds/square inch (psi). Assume the population standard deviation is 1.01.0. The engineer designed the valve such that it would produce a mean pressure of 7.67.6 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.10.1 will be used. Find the P-value of the test statistic. Round your answer to four decimal places.
Answer:
p-value = 0.1213 (to 4-decimal places)
Step-by-step explanation:
Given:
N = 240
mean = 7.5
s = 1.0
Solution
With N=240 and using the central limit theorem, distribution can be approximated as normal.
Let
Null hypothesis H0, mu = 7.6
Alternate hypothesis, mu not equal to 7.6 (two-tail test)
for
Alpha = 0.1 (two sided)
Z = sqrt(N)(mean – mu)/s = sqrt(240)(7.5-7.6)/1.0 = -1.54919
p-value
= P(|Z|>1.54919)
= 2P(Z>1.54919)
= 2(1-P(Z<1.54919)
=2(1-0.9393) (using normal distribution table)
=0.12134
Since alpha = 0.1 < p-value (0.1213), H0 that mean = 7.6 is not rejected.
Intelligence quotients (IQs) measured on the Stanford Revision of the Binet Simon Intelligence Scale are normally distributed with a mean of 100 and a standard deviation of 16. Determine the percentage of people who have an IQ between 115 and 140.
Answer:
the percentage of people who have an IQ between 115 and 140 is 16.79%
Step-by-step explanation:
From the information given:
We are to determine the percentage of people who have an IQ between 115 and 140.
i.e
P(115 < X < 140) = P( X ≤ 140) - P( X ≤ 115)
[tex]P(115 < X < 140) = P( \dfrac{X-100}{\sigma}\leq \dfrac{140-100}{16})-P( \dfrac{X-100}{\sigma}\leq \dfrac{115-100}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq \dfrac{140-100}{16})-P( Z\leq \dfrac{115-100}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq \dfrac{40}{16})-P( Z\leq \dfrac{15}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.9375)[/tex]
[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.938)[/tex]
From Z tables :
[tex]P(115 < X < 140) = 0.9938-0.8259[/tex]
[tex]P(115 < X < 140) = 0.1679[/tex]
Thus; we can conclude that the percentage of people who have an IQ between 115 and 140 is 16.79%
Using the normal distribution, it is found that 82.02% of people who have an IQ between 115 and 140.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.In this problem:
The mean is of [tex]\mu = 100[/tex].The standard deviation is of [tex]\sigma = 15[/tex].The proportion of people who have an IQ between 115 and 140 is the p-value of Z when X = 140 subtracted by the p-value of Z when X = 115, hence:
X = 140:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 100}{16}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a p-value of 0.9938.
X = 115:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{115 - 100}{16}[/tex]
[tex]Z = -0.94[/tex]
[tex]Z = -0.94[/tex] has a p-value of 0.1736.
0.9938 - 0.1736 = 0.8202.
0.8202 = 82.02% of people who have an IQ between 115 and 140.
More can be learned about the normal distribution at https://brainly.com/question/24663213
i need help emergrncy shots fire shots fire we neeed all back ups
Answer:
a = 9h + bn
Step-by-step explanation:
total = $9 an hour + (bonus x number of items repaired)