The normal approximation for the given binomial distribution with p = 0.10 and n = 40 has a mean of 4 and a standard deviation of 1.93.
The binomial probability distribution can be approximated by the normal distribution when certain conditions are met, such as a large sample size and a probability of success not too close to 0 or 1.
In this case, n = 40 and p = 0.10. To determine if the normal approximation is appropriate, we can check if both np and n(1-p) are greater than or equal to 10
np = 40 x 0.10 = 4
n(1-p) = 40 x 0.90 = 36
Both np and n(1-p) are greater than or equal to 10, so the normal approximation is appropriate.
The mean of the binomial distribution is given by μ = np = 4, and the standard deviation is given by σ = √(np(1-p)) = √(40 x 0.10 x 0.90) ≈ 1.93.
To find the mean and standard deviation of the normal approximation, we use the same mean and standard deviation values
μ = np = 4
σ = √(np(1-p)) ≈ 1.93
Learn more about binomial probability distribution here
brainly.com/question/30786502
#SPJ4
(2x+15)
Find the value of a.
to
Answer: 7.5
Step-by-step explanation: 2 x 7.5 = 15
How much money in commission does a real
estate agent who works on a 2.5% commission
rate earn from a $260,000 sale?
A. $6,500
C. $65.000
B. $10,400
D. $1,040,000
It seems like the answer could be $6,500, but I prefer to wait for a professional tbh☹.
Choose ALL answers that describe the quadrilateral LMNO if
ZL ZM≈ ZN≈ ZO.
O Parallelogram
Answer: Parallelogram
Step-by-step explanation: A parallelogram is a quadrilateral with opposite sides parallel. If ZL, ZM, ZN, and ZO are approximately equal, it implies that the opposite sides LM and NO are parallel, and the opposite sides LO and MN are also parallel.
It may not be a rectangle: While a parallelogram is a quadrilateral with opposite sides parallel, a rectangle is a special type of parallelogram with additional properties, such as all angles being right angles. The given information does not provide any information about the angles of the quadrilateral, so we cannot conclude that it is a rectangle.
It may not be a rhombus: A rhombus is a special type of parallelogram in which all sides are equal. The given information only states that the angles ZL, ZM, ZN, and ZO are approximately equal, but it does not provide any information about the lengths of the sides LM, LO, MN, or NO. Therefore, we cannot conclude that LMNO is a rhombus based solely on the given information.
PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer: A and D as for angle 24 deg, we are using the sin=opp/hyp and for angle 66 we are using cos=adj/hyp.
To find angle 66, you just subtract all 180 by the angles we know. 180-24-90.
Does anyone help me with this?
Answer:
20/8 or 20:8
Step-by-step explanation:
Ok, so we start off with a smaller square with one side being 8.
We then have to go from one side being 8 to one side being 20.
So, the ratio has to be a number larger than 1 to go from smaller to larger, so we can use the ratio of 20/8 (or 2.5).
Check:
2.5x8=20
please help would be appreciated
The solution of the system of equations in this problem is given as follows:
(4,0).
How to solve the system of equations?The equations that compose the system in this problem are given as follows:
y = -0.5x + 2.3x - 2y = 12.We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.
From the graph given by the image presented at the end of the answer, the solution to the system is given as follows:
(4,0).
More can be learned about a system of equations at brainly.com/question/30347294
#SPJ1
pls hlp thx ur great
Answer:
x = - [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
14 = [tex]\frac{8}{3}[/tex] (x + 6) ← multiply both sides by 3 to clear the fraction
42 = 8(x + 6) ← distribute parenthesis
42 = 8x + 48 ( subtract 48 from both sides )
- 6 = 8x ( divide both sides by 8 )
[tex]\frac{-6}{8}[/tex] = x , that is
x = - [tex]\frac{3}{4}[/tex]
a measure of relative fit for a simple regression line is called the r² or _ of _.
A measure of relative fit for a simple regression line is called the r² or coefficient of determination.
What is a regression line?A regression line, or line of best fit, is a straight line used to model the relationship between two variables in a data set. It is drawn through the data points to minimize the distance between the line and the points, representing the best fit. The line's equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept represents the value of y when x is equal to 0. The line is often used to predict the dependent variable based on the independent variable, and the accuracy of the predictions depends on how well the line fits the data.
The coefficient of determination, also known as r², is a statistical measure used to determine the relative fit of a simple regression line. This measure represents the proportion of variance in the dependent variable that can be predicted by the independent variable. The calculation involves squaring the correlation coefficient (r) between the two variables. The resulting value of r² ranges from 0 to 1, where 0 indicates that the independent variable has no explanatory power over the dependent variable, while 1 implies that the independent variable explains all the variability in the dependent variable.
To know more about regression line visit:
brainly.com/question/29753986
#SPJ1
In the following procedure, the parameters x and y are integers.
Which of the following is the most appropriate documentation to appear with the calculate procedure?
Displays the value of (x + y) / x. The value of the parameter x must not be 0.
The documentation provided with the procedure states that the procedure will display the value of (x + y) / x.
This means that the result of the calculation will be shown to the user, and it will be the value obtained by adding x and y, then dividing the result by x.
However, the documentation also includes a very important requirement for the parameter x: it must not be 0. This is because dividing by zero is not a valid mathematical operation, and will result in an error. Therefore, it is crucial to ensure that the value of x passed to the procedure is a non-zero integer.
To summarize, the "calculate" procedure takes two integer parameters, x and y, and displays the value of (x + y) / x.
It is important to note that the value of x must not be 0, as dividing by zero is not a valid mathematical operation.
To know more about integers here
https://brainly.com/question/15276410
#SPJ4
Ana has $15 in the bank. Her sister Benita has 1/3 as much money in the bank. How much money does Benita have in the bank?
Answer:5
Step-by-step explanation: you divide 15 by 3 which gives you 5
Find the surface area of the pyramid.
19 m
14 m
14 m
i need it asap
The surface area of the pyramid is 532m²
What is a pyramid?A pyramid is a 3D polyhedron with the base of a polygon along with three or more triangle-shaped faces that meet at a point above the base. It is made by connecting each vertex of the base to a common tip or apex giving it its typical shape.
The general formula for the lateral surface area of a regular pyramid is L.S.A.=1/2pl
where
p =represents the perimeter of the base and l= the slant height.Given that The pyramid is a rectangular,
Therefore the surface area is
L.S.A.=1/2(14*4) *19
Surface area = 28*19 = 532m²
Learn more about surface area of a pyramid on https://brainly.com/question/16720917
#SPJ1
Pamela has $50,000 in a savings account. The interest rate is 3% per year and is not
compounded. How much will she have in total in 1 year?
Answer:
$51,500 in her savings account.
Step-by-step explanation:
If Pamela has $50,000 in a savings account with an interest rate of 3% per year and the interest is not compounded, then in 1 year she will earn an interest of $50,000 * 0.03 = $1,500.
So, after 1 year, Pamela will have a total of $50,000 + $1,500 = $51,500 in her savings account.
The owner purchases 5 buckets, 10 brushes, 48 towels, and 1 case of air fresheners for the car wash. The total cost of the purchases is $144.08. Each bucket costs $2.89, each brush costs $7.91, and each towel costs $0.36. What is the cost, in dollars, of the case of air fresheners?
The cost of the case of air fresheners is $33.25.
What is the cost of the case of air fresheners?Let the cost of the case of air fresheners be represented by the variable a.
Then, the cost of 5 buckets is 5 times $2.89, or 5 x 2.89 = $14.45.
The cost of 10 brushes is 10 times $7.91, or 10 x 7.91 = $79.10.
The cost of 48 towels is 48 times $0.36, or 48 x 0.36 = $17.28.
The total cost of the purchases, including the case of air fresheners, is $144.08.
Therefore, we can write the equation:
14.45 + 79.10 + 17.28 + a = 144.08
Simplifying the left side of the equation, we get:
110.83 + a = 144.08
Subtracting 110.83 from both sides of the equation, we get:
a = 33.25
Therefore, the cost of the case of air fresheners is $33.25.
Read more about equations at
https://brainly.com/question/148035
#SPJ1
5. A path bounds a circular lawn at a park. If the inner edge of the path is 132 ft. Around, approximate the amount of
area of the lawn inside the circular path. Use T < 22
6. The area of a circle is 367 cm?. Find its circumference.
7. Find the ratio of the area of two circles with radii 3 cm and 4 cm.
8. If one circle has a diameter of 10 cm and a second circle has a diameter of 20 cm, what is the ratio of the area of
the larger circle to the area of the smaller circle?
9. Describe a rectangle whose perimeter is 132 ft. And whose area is less than 1 ft?. Is it possible to find a circle whose
circumference is 132 ft. And whose area is less than 1 ft?? If not, provide an example or write a sentence explaining
why no such circle exists.
10. If the diameter of a circle is double the diameter of a second circle, what is the ratio of area of the first circle to the
area of the second?
The circumference of a circle: C = 67.98 cm
Radius of the circular lawn, which is difference between outer radius of path and inner radius of path.
outer radius: [tex]r1 = (132 + 2T)/2 = (132 + 2(22))/2 = 88 ft[/tex]
inner radius: [tex]r2 = 132/2 = 66 ft[/tex]
radius of circular lawn is r = r1 - r2 = 22 ft
Now using formula for the area of a circle:
A = πr^2 = π(22^2) ≈ 1520.53 ft^2
To find the circumference of a circle with area 367 cm^2, we can use the formula for the area of a circle to find the radius:
[tex]A = \pi r^2 \\r^2 = A/\pi = 367/\pi[/tex]
r ≈ 10.80 cm
Then we can find the circumference using the formula for the circumference of a circle:
C = 2πr ≈ 2π(10.80) ≈ 67.98 cm
To know more about circumference, here
brainly.com/question/28757341
#SPJ4
Victoria wants to fill a container with sand as part of an art project. Which measurement should Victoria use to BEST determine how much sand she should buy?
Answer:
volume
Step-by-step explanation:
Victoria should use volume measurement to determine how much sand she should buy.
22 ft
30 ft
Find the area of each triangle
The Orchard Cafe has found that about 4% of the diners who make reservations don't show up. If 81 reservations have been made, how many diners can be expected to show up
The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made
To determine how many diners can be expected to show up at The Orchard Cafe, we can follow these steps:
1. Identify the percentage of diners who actually show up: Since 4% of diners with reservations don't show up, the percentage of diners who do show up is 100% - 4% = 96%.
2. Calculate the expected number of diners who show up: Multiply the total number of reservations (81) by the percentage of diners who show up (96%).
81 reservations x 0.96 (96% as a decimal) = 77.76
Since the number of diners must be a whole number, you can round the result to the nearest whole number.
In this case, 77.76 can be rounded down to 77.
Your answer: The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made.
To know more about "Whole numbere" refer here:
https://brainly.com/question/13242016#
#SPJ11
Find the equation of a straight line passing through (5, 7) and is (i) parallel to x axis
For any value of x, the corresponding value of y will always be 7, and the line will be a horizontal line passing through the point (5,7).
If a straight line is parallel to the x-axis, then it means that the line will have a constant y-value for all values of x. This means that the slope of the line will be zero, because there will be no change in y for any change in x.
To find the equation of a straight line passing through the point (5,7) that is parallel to the x-axis, we need to find the equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.
Since the slope of the line is zero, we can write the equation as:
y = 0x + b
where b is the y-intercept.
To find the value of b, we can use the point (5,7) that the line passes through. Substituting x = 5 and y = 7 in the equation, we get:
7 = 0(5) + b
Simplifying, we get:
b = 7
Therefore, the equation of the straight line passing through the point (5,7) that is parallel to the x-axis is:
y = 7
To learn more about equation click on,
https://brainly.com/question/23139211
#SPJ4
the base of a pyramid is a rectangle with a length of 7.5 cm and a width of 2 cm. what is the height if the volume is 50 cm^3
The solution to the given problem of volume comes out to be the pyramid is 10 cm tall.
What does volume actually mean?The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are the symbols for cubic measures.
Here,
The formula: gives the volume of a pyramid.
=> V = base_area * height * (1/3)
The area of the base (base_area) of a pyramid whose base is a rectangle with dimensions of 7.5 cm in length and 2 cm in width can be computed as follows:
base_area equals length * width,
=> 7.5 cm * 2 cm =15 cm².
Additionally, we are informed that the pyramid's (V) volume is 50 cm3.
=> (1/3) * 15 * height = 50
=> height = (3 * V)/base_area.
When V and base_area's values are entered, we obtain:
=> height = (15/15) / (3*50) = 10 cm
Consequently, the pyramid is 10 cm tall.
To know more about volume, visit:
brainly.com/question/13338592
#SPJ1
The box plots show a random sample of wait times for two more rides at the theme park. 4) Compare the wait times in the box plots. > The median wait time for Thrill Tower is 5 minutes shorter than the median wait time for River Rapids. The IQR for both rides is ? minutes. Wait Times for Rides Thrill Tower 6 8 River Rapids 12 10 Time (min) 14 16
The IQR for both runs is 8 minutes.
What is the interquartile range?If there are outliers or extreme values in the data set, we summarize the typical value using the median instead of the mean. When there are outliers in a data set, the variation is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles.
Based on the given box pairs, we can make the following comparisons:
The average wait time at Thrill Tower is about 5 minutes shorter than the average wait time at River Rapids. That's because the centerline of Thrill Tower is about 5 units below the centerline of River Rapids. The IQR (interquartile range) for both times is not directly in the box. However, we can estimate this by finding the distance between the first quartile (Q1) and the third quartile (Q3) of each run. From the box plot of Thrill Tower, we can see that Q1 is around 6 and Q3 is around 14. Therefore, the IQR for Thrill Tower is:
Thrill Tower IQR = Q3 - Q1 = 14 - 6 = 8 minutes
From the box plot for River Rapids, we can see that Q1 is about 8 and Q3 is about 16. Therefore, the IQR for River Rapids is:
River Rapids IQR = Q3 - Q1 = 16 - 8 = 8 minutes
Therefore, the IQR for both runs is 8 minutes.
Learn more about Interquartile range here
https://brainly.com/question/29204101
#SPJ1
Answer: HERE IS THE ANSWER BELOW :)
Which of the values in the set {1, 2, 3, 4} is a solution to the equation 3x + 3 = 15? (4 points) Group of answer choices 1 3 4 2
4 is the correct value from the set {1, 2, 3, 4} which is the solution to the equation 3x + 3 = 15.
What is a solution of an equation?A solution of an equation refers to a value or values that satisfy the given equation. It is the value or values that make the equation true when substituted for the variable(s) in the equation. Equations are mathematical expressions that contain an equals sign and can have one or more variables. A solution is typically represented as a number, but it can also be a set of numbers, a range of values, or an expression. Finding the solutions of an equation is an important part of solving mathematical problems and has many practical applications in fields such as engineering, physics, and finance.
Solution of the given equation 3x + 3 = 15 means when we put a value in x we should get the result as 15, that is left hand side of the equation should be equal to the right hand side of the equation.
Solving the equation we get,
3x + 3 - 3 = 15 - 3
3x = 12
x = 4
Therefore, the value 4 is a solution to the equation.
To know more about solution visit:
brainly.com/question/14603452
#SPJ1
the radius of a circle is 24 cm and an arc length on that same circle is 148.8 cm. what's the radian measure of th central angle which intercepts the arc
The radian measure of the central angle which intercepts the arc is 6.2 radians.
We can use the formula relating the arc length to the angle and radius of the circle:
arc length = radius x central angle in radians
Plugging in the given values, we get:
148.8 = 24 x central angle in radians
Solving for the central angle, we have:
central angle in radians = 148.8/24
central angle in radians = 6.2 radians
Therefore, the radian measure of the central angle which intercepts the arc is 6.2 radians.
Learn more about radian measure
https://brainly.com/question/7383164
#SPJ4
you want to determine what uniform color shirt is the most preferred among 7th grade students. You survey 6 random students in your art class. 4 choose red, so you conlude that red us the preferred color of shirt. is your conclusion valid. explain.
The conclusion that red is the preferred color of shirt among 7th grade students based on a survey of 6 random students in an art class is not necessarily valid due to the small sample size, sampling bias, and lack of generalizability.
How to determine if the conclusion is valid.The sample size of six pupils is tiny and may not be typical of the overall seventh-grade population. It's probable that the six students in the art class have different preferences or biases than the other seventh-grade students.
Also, the sample of six pupils is drawn at random from an art class rather than from the total 7th grade population. Students who are interested in art may have different preferences than students who are not. This can add bias into the sample.
Finally, the language of the survey question is critical. If the survey question specifically asks about the most chosen color of shirt among 7th grade kids in general, the conclusion that red is the most preferred color of shirt follows.
Learn more about sample size at https://brainly.com/question/30520316
#SPJ1
Find the perimeter and area of a regular octagon that has a radius of 10m.
Case A is 12 times heavy than Case B,Case B is 16 times heavy than case C. If case A is 8,640 g, what is the weight of case C
Let's the weight of Case C = "x" grams.
From the information:
Case A = 12 times heavier than Case B,
Therefore, the weight of Case B = 1/12 of Case A's weight:
Weight of Case B = (1/12) * Weight of Case A
Case B = 16 times heavier than Case C,
so, weight of Case C = 1/16 of Case B's weight:
Weight of Case C = (1/16) * Weight of Case B
The weight of Case A = 8,640g,
Let's substitute the value into the equations to find the weight of Case C:
Weight of Case B = (1/12) * 8,640 = 720g
Weight of Case C = (1/16) * 720 = 45g
Thus, the weight of Case C is 45 grams.
There are 30 students in Mr.McRoberts' Grade 8 class. One-third of the students are girls. Three-quarters of the boys play basketball. The number of boys in the class who play basketball is:
PLEASE! :(
Answer: 15.
Step-by-step explanation: If one-third of the students are girls, then two-thirds of the students are boys:
number of boys = (2/3) * 30 = 20
Three-quarters of the boys play basketball, so the number of boys in the class who play basketball is:
number of boys who play basketball = (3/4) * 20 = 15
Therefore, the number of boys in the class who play basketball is 15.
i need help pls i dont get it
Answer:
3/5 = 60% = 0.6
In the bottom row, 3/5 is the wrong fraction. 2/3 is the correct fraction.
p+p=60
p+p+s=90
s-p+k=90
p+s+k-k+s-k=x
what is x giving brianliste away
Answer:
p=30 s=30 k=90 x=0
Step-by-step explanation:
000000000000
Suppose that we are testing H0: µ = µ0 versus H1: µ > µ0. Calculate the P -value for the following observed values of the test statistic (round all answers to 4 decimal places.
(a)z0 = 2.35,
(b)z0 = 1.53,
(c)z0 = 2.00,
(d)z0 = 1.85,
(e)z0 = -0.15.
For a hypothesis testing, [tex]H_0 : µ = µ_0[/tex] ; [tex]H_1 : µ > µ_0.[/tex] the calculated P-value for test statistic value are following a) 0.9906 ; b) 0.9370 ; c) 0.9773; d) 0.9678 ; e) 0.4404.
We are testing the null hypothesis versus alternative hypothesis. Both are defined as [tex]H_0 : µ = µ_0[/tex]
[tex]H_1 : µ > µ_0.[/tex].
We have to calculate the P-value for the following observed values test statistic one by one.
a)z = 2.35
The P -value is calculated for as follows P ( z > Zo) = 1 - P( z≤ z0)
= 1 - P( z≤ 2.35)
Now, using the normal distribution table, the value of P( z≤ 2.35) is equals to 0.009387. So, P( z> 2.35) = 1 - 0.009387
= 0.990613
b) z₀ = 1.53
The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)
= 1 - P( z≤ 1.53)
Now, using the normal distribution table , the value of P( z≤ 1.53) is equals to 0.063008. So, P( z> 1.53) = 1 - 0.063008
=0.936992
c) z₀ = 2.00
The P-value is calculated for as follows, P ( z > z₀) = 1 - P( z≤ z₀)
= 1 - P( z≤ 2.00)
Now, using the normal distribution table , the value of P( z≤ 2.00) is equals to 0.02275. So, P( z> 2.00) = 1 - 0.02275
=0.97725
d) z₀ = 1.85
The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)
= 1 - P( z≤ 1.85)
Now, using the normal distribution table , the value of P( z≤ 1.85 ) is equals to 0.032157. So, P( z> 1.85) = 1 - 0.032157
=0.967843
e) z₀ = -0. 15
The P-value is calculated for as follows P ( z > -z₀) = P( z ≤ z₀)
= P( z≤ 0.15 )
Now, using the normal distribution table , the value of P( z≤ 0.15) is equals to 0.440382. So, P( z > - 0.15) = 0.44038. Hence the required P-value is 0.44038.
For more information about P-value, refer:
https://brainly.com/question/13786078
#SPJ4
Show: The diagonals bisect each other, and the diagonals are congruent.
From the attached picture, it is proven that the diagonals of rectangle MNOP are congruent.
Proof that the diagonals are congruentTo show that the diagonals of rectangle MNOP bisect each other, we need to show that they intersect at their midpoint. Let's label the diagonals as AC and BD, where AC is the diagonal that goes from vertex M to vertex O, and BD is the diagonal that goes from vertex N to vertex P.
First, let's find the midpoint of AC. The midpoint of a line segment is the point that is exactly halfway between the two endpoints. The endpoints of AC are M and O, so we can find the midpoint by averaging their x-coordinates and y-coordinates:
midpoint of AC = ((Mx + Ox)/2, (My + Oy)/2)
Similarly, we can find the midpoint of BD:
midpoint of BD = ((Nx + Px)/2, (Ny + Py)/2)
Now we need to show that these midpoints are the same point. That is, we need to show that:
((Mx + Ox)/2, (My + Oy)/2) = ((Nx + Px)/2, (Ny + Py)/2)
To do this, we can set the x-coordinates equal to each other and the y-coordinates equal to each other:
(Mx + Ox)/2 = (Nx + Px)/2
(My + Oy)/2 = (Ny + Py)/2
Now we can solve for the values of x and y. First, we'll solve for x:
Mx + Ox = Nx + Px
2Mx + 2Ox = 2Nx + 2Px
Mx + Ox - Nx - Px = 0
(Mx - Nx) + (Ox - Px) = 0
Similarly, we can solve for y:
My + Oy = Ny + Py
2My + 2Oy = 2Ny + 2Py
My + Oy - Ny - Py = 0
(My - Ny) + (Oy - Py) = 0
Now we can see that the x-coordinate and y-coordinate of the midpoint of AC are equal to the x-coordinate and y-coordinate of the midpoint of BD, respectively. Therefore, the diagonals of rectangle MNOP bisect each other.
To show that the diagonals are congruent, we can use the Pythagorean theorem. Let's label the length of AC as a and the length of BD as b. Then we have:
a^2 = OM^2 + ON^2 (by the Pythagorean theorem in triangle OMN)
b^2 = PN^2 + PO^2 (by the Pythagorean theorem in triangle PON)
But we know that OM = ON and PO = PN, since MNOP is a rectangle. Therefore, we can simplify these expressions:
a^2 = 2OM^2
b^2 = 2PO^2
Since OM = PO (they are opposite sides of a rectangle), we can substitute to get:
a^2 = 2OM^2 = 2PO^2 = b^2
Therefore, a = b, and the diagonals of rectangle MNOP are congruent.
Learn more about Diagonals here:
https://brainly.com/question/23008020
#SPJ1