Probability of answering exactly 4 questions correctly = 0.206
P (More than 2) = 0.475
How to solve for the probability1.
ind P(4): Probability of answering exactly 4 questions correctly.
P(X=4) = (10C4) * (0.25^4) * (0.75^6)
10C4 = 10! / (4! * (10-4)!) = 210
P(X=4) = 210 * (0.25^4) * (0.75^6)
= 0.206
2. P(More than 2):P(X=0) = (10C0) * (0.25^0) * (0.75^10) ≈ 0.056
P(X=1) = (10C1) * (0.25^1) * (0.75^9) ≈ 0.187
P(X=2) = (10C2) * (0.25^2) * (0.75^8) ≈ 0.282
Now, calculate P(X>2):
P(X>2)
= 1 - (P(X=0) + P(X=1) + P(X=2))
= 1 - (0.056 + 0.187 + 0.282)
= 1 - 0.525
= 0.475
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QUESTION SIX Solve the following problems: (a) Find the gradient, x and y intercepts of 3x + 4y + 12 = 0. Sketch the graph. (6 Marks) (b) Find the gradient, x and y intercepts of the line I, passing through the points P (-1,4) and Q (3,0). Sketch the graph. (6 Marks) (c) A line 1₂ is perpendicular to 4. Find its gradient. (2 Marks) (14 Marks)
The sketches of the graphs are added as an attachment and the gradient of the perpendicular line l₂ is 1
Finding the gradient, x and y interceptsGiven that
3x + 4y + 12 = 0
Set x = 0 to determine the y-intercept
4y + 12 = 0
So, we have
y-intercept = -3
Set y = 0 to determine the x-intercept
3x + 12 = 0
So, we have
x-intercept = -4
For the gradient, we make y the subject in 3x + 4y + 12 = 0.
y = -3/4x - 12/4
y = -3/4x - 3
So, the gradient is -3/4
The sketch of the graph is attached.
Finding the gradient, x and y interceptsHere, we have the points P (-1,4) and Q (3,0).
The gradient is
gradient = (0 - 4)/(3 + 1)
gradient = -1
From the point, we have
x-intercept = 3
For the y-intercept, we have
(0 - 4)/(3 + 1) = (y - 4)/(0 + 1)
(y - 4)/(0 + 1) = -1
y - 4 = -1
y-intercept = 3
So, the equation is
y = -x + 3
The sketch of the graph is attached.
Finding the gradient of l₂We understand that l₂ is perpendicular to l
The gradients of perpendicular lines are
Gradient 1 = -1/Gradient 2
So, we have
l₂ = -1/-1
Evaluate
l₂ = 1
Hence, the gradient of line l₂ is 1
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ANSWER PLEASE! It's multiple choice
Answers are: 13FT, 125FT, 313FT, AND 425 FT.
Answer:125
Step-by-step explanation:
the drawing (fountains) was 10 inches apart, but real life was 400. 400/10 = 40. this means that the real life distance is 40x the distance of the drawing.
therefore, multiply 3.125 by 40 as well. you get 125.
Answer: 125 ft
Step-by-step explanation:
Let x be the real remove between the two shows.
At that point, we are able set up the extent:
10 inches / 400 feet = 3.125 inches / x
To illuminate for x, able to cross-multiply and disentangle:
10 inches * x = 400 feet * 3.125 inches
10x = 1250
x = 125 feet
Please answer number 3
For 3 personal training session both gym cost same.
We have,
At Silver gym, membership is $25 per month and personal training sessions are $30 each.
At Fit Factor, membership is $65 per month, the and personal training sessions are $20 each.
let the number of personal session be x.
So, 25+ 30x = 65 + 20x
30x - 20x = 65 - 25
10x = 30
x= 3 sessions
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Study this table.
X
-3
-2
0
4
y
-2
0
4
12
Which best describes the function represented by the data in the table?
O linear with a common ratio of 2
Olinear with a common first difference of 2
O quadratic with a common ratio of 2
O quadratic with a common first difference of 2
The Function is linear with a common first difference of 2.
We have,
x y
-3 -2
-2 0
0 4
4 12
For the first set of points
m=(0-(-2))/(-2--3)
m = (0+2)/(-2+3)
m= 2/1 = 2
For the second set of points
m = (4-0)/(0-(-2))
m = 4/(0+2)
m = 4/2 = 2
For the third set of points
m = (12-4)/(4-0)
m = 8/4
m = 2
Thus, the function is linear with a common first difference of 2.
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Select the correct answer. What is the solution to 4|x − 3| + 1 = 1? A. x = 3 B. x = 3 or x = 4 C. x = 3 or x = 6 D. No solutions exist.
Answer:
a
Step-by-step explanation:
A
Select the correct answer.
Which system of linear inequalities is represented by this graphed solution?
OA y> -+2
V≤ 32-1
OB V<= +2
v2 32-1
Ocy> -2x + 2
vs-1
OD S-2 +2
v < 30-1
The two inequalities of the graph are:
y ≥ 3x - 1
y < -¹/₂x + 4
How to identify inequality graph?
The general form of the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
The first inequality with a solid line has a y-intercept of -1 and since it is shaded above the line, we will use ≥.
Two coordinates on the line are: (0, -1) and (1, 2)
The slope = (2 + 1)/(1 - 0) = 3
Thus, inequality is:
y ≥ 3x - 1
The second inequality with a dashed line has a y-intercept of 4 and since it is shaded below the line, we will use <.
Two coordinates on the line are: (4, 0) and (0, 2)
The slope = (2 - 0)/(0 - 4) = -1/2
Thus, inequality is:
y < -¹/₂x + 4
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What is the slope of the line that passes through the points (2,-4) and (5,2)
Answer:
2.
Step-by-step explanation:
To find the slope of the line that passes through the points (2,-4) and (5,2), we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (2,-4) and (x2, y2) = (5,2)
slope = (2 - (-4)) / (5 - 2)
slope = 6 / 3
slope = 2
Therefore, the slope of the line that passes through the points (2,-4) and (5,2) is 2.
Which set of ordered pairs gives the polygon shown?
(-4.2), (-4, -5), (1.5, -5), (1.5, 2)
(1.5, 2), (1.5, -4.5), (-4.5, -4), (2, -4)
(-4, -4.5), (-4.5, 1.5), (1.5, 2), (-4, 2)
(1.5, -4.5), (-4, -4.5), (-4, 2), (1.5, 2)
The points of the polygon are:
(1.5, 2)
(-4, 2)
(-4, -4.5)
(1.5, -4.5)
Option D is the correct answer.
We have,
From the coordinate plane,
There are 4 points that form the polygon,
The points are all in ordered pairs.
So,
(1.5, 2)
(-4, 2)
(-4, -4.5)
(1.5, -4.5)
Thus,
The points of the polygon are:
(1.5, 2)
(-4, 2)
(-4, -4.5)
(1.5, -4.5)
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Rewrite the logarithmic equation below as an equivalent exponential equation.
log3(N) = x
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_3(N)=x\implies 3^x=N[/tex]
A set of data items is normally distributed with a mean of 80 and a standard deviation of 9. Convert 71 to a z-score.
271 = 0
(Type an integer or a decimal.)
The z-score for 71 is -1.
Understanding Z-score calculationz-score is a measure of how many standard deviations an observation or data point is away from the mean of a distribution.
It is calculated by subtracting the mean from the observation and then dividing the result by the standard deviation: z = (x - μ) / σ
A positive z-score means that the data point is above the mean, while a negative z-score means that it is below the mean.
Applying the formula to solve our question
Here is a proven formula to use:
z = (x - μ) / σ
where:
x = the data item (x = 71)
μ = the mean of the distribution (μ = 80)
σ = the standard deviation of the distribution (σ = 9)
Substituting the values, we get:
z = (71 - 80) / 9
z = -1
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A children's clothing company sells hand-smocked dresses for girls. The length of one particular size of dress is designed to be 29 inches. The company regularly tests the lengths of the garments to ensure quality control, and if the mean length is found to be significantly longer or shorter than 29 inches, the machines must be adjusted. The most recent simple random sample of 22 dresses had a mean length of 31.53 inches with a standard deviation of 8.24 inches. Assume that the population distribution is approximately normal. Perform a hypothesis test on the accuracy of the machines at the 0.005 level of significance. Step 3 of 3: Draw a conclusion and interpret the decision. Answer Tables Keypad Keyboard Shortcuts We reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the O particular size of dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted. O We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.005 level of significance that the mean length of the particular size of dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted. O We reject the null hypothesis and conclude that there is sufficient evidence at a 0.005 level of significance that the mean length of the particular size of dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length O of the particular size of dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.
We will conduct a one-sample t-test to determine if the mean length of the particular size of dress is significantly different from 29 inches.
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We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.
What is the null hypothesis?
The null hypothesis is the assertion that there is no association between the two sets of data or variables being investigated in a scientific study. The term "null" refers to the idea that any empirically observed difference is entirely attributable to chance and that no underlying causal relationship exists.
Here, we have
Given: A children's clothing company sells hand-smocked dresses for girls. The length of one particular size of the dress is designed to be 29 inches. The most recent simple random sample of 22 dresses had a mean length of 31.53 inches with a standard deviation of 8.24 inches.
We will conduct a one-sample t-test to determine if the mean length of the particular size of the dress is significantly different from 29 inches.
In the null hypothesis, the mean length of the particular size of the dress is equal to 29 inches.
In the alternative hypothesis, the mean length of the particular size of the dress is significantly longer or shorter than 29 inches.
We will use a 0.005 level of significance, which corresponds to a critical value of ±2.807 for a two-tailed test with 21 degrees of freedom.
Our test statistic is: t = (31.53 - 29) / (8.24 / sqrt(22)) = 1.774
Since our test statistic (1.774) is not greater than the critical value (2.807) or less than the negative of the critical value (-2.807), we fail to reject the null hypothesis.
Hence, We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.
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A bottle of water has a diameter of 3 inches and a height of 8 inches, and a mass of 1250 g. What is the volume and density?
The volume of the bottle is 56.52 cubic inches, and the density is 22.12 g/in³.
What is the volume and density of the bootle water?The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 ).
Density is expressed mathematically as;
p = m / v
Where m is mass and v is volume.
Given that:
Diameter = 3 in
Radius r = diameter/2 = 3/2 = 1.5 in
Height h = 8 in
Mass m = 1250 g
Find the volume:
V = π × r² × h
V = 3.14 × (1.5 in )² × 8in
V = 56.52 in³
Find the density:
p = m / v
p = 1250g / 56.52 in³
p = 22.12 g/in³
Therefore, the density is 22.12 g/in³.
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Can someone help me with the 4 questions
math hw for tonight
help solve this problem! Thank you!
ap cal bc
The slope of the polar curve at θ = π/4 is 24. Therefore, option D is correct.
To find the slope of the polar curve r = 6cos(2θ) - 5 at θ = π/4, we need to find the derivative of r with respect to θ, and then substitute θ = π/4 into the resulting expression.
Using the chain rule of differentiation, we have:
dr/dθ = dr/d(cos(2θ)) * d(cos(2θ))/dθ
To find the first derivative, we can use the power rule of differentiation:
dr/d(cos(2θ)) = -12sin(2θ)
To find the second derivative, we can use the chain rule again:
d(cos(2θ))/dθ = -2sin(2θ)
Substituting these into the expression for dr/dθ, we get:
dr/dθ = -12sin(2θ) * (-2sin(2θ)) = 24sin^2(2θ)
Now, substituting θ = π/4, we get:
dr/dθ|θ=π/4 = 24sin^2(π/2) = 24
The slope of the polar curve at θ = π/4 is therefore 24.
None of the given options match this result.
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Nine to the second power +4 to the second power
Answer:
Step-by-step explanation:
9 * 9 = 81
4 * 4 = 16
81 + 16 = 97
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Is this right. Don’t know the difference between the stratified and systematic random. Pic below
The difference between the stratified and systematic random sampling is explained below.
Systematic random sampling is a method where every Kth person of the population is chosen to be part of the sample, whereas stratified random sampling is a method where the population is first divided into subgroups, and then drawing a simple random sample from each subgroup.
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8, 40, 200, ...
Find the 10th term.
Answer: 15,625,000
Step-by-step explanation: x5, 8, 40, 200, 1,000, 5,000, 25,000, 125,000, 625,000, 3,125,000, 15,625,000
Find the surface area of the prism
The surface area of the triangular prism is 70.2 yd²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as ;
SA = 2B +ph
where h is the height,
B is the base area and
p is the perimeter of the base
Base area = 1/2 bh( since the base Is a triangle)
Base area = 1/2 × 3 ×3 = 4.5yd²
The other side of the triangle is calculated as;
x= √ 3²+3²
x = √9+9
x = √18
x = 4.2
Therefore perimeter = 4.2 + 3+3 = 10.2yds
SA = 2× 4.5 + 10.2 × 6
SA = 9 + 61.2
SA = 70.2 yd²
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Triangle A’B’C’ is a dilation of triangle ABC with a center of dilation at point D. What is the scale factor of this dilation?
Work Shown:
(A'C')/(AC) = 12/5 = 2.4
or you could say
(B'C')/(BC) = 16.8/7 = 2.4
or
(A'B')/(AB) = 9.6/4 = 2.4
The sides of triangle A'B'C' are 2.4 times longer compared to the corresponding sides of triangle ABC.
Use mathematical induction to prove that the statement is true for all positive integers: 30 + 138 + 318...
The mathematical induction has been used to prove that the statement is true for all positive integers: 30 + 138 + 318.
What is mathematical induction?In mathematics, mathematical induction is a way of proving propositions. The method entails demonstrating that a statement is true for a base case, usually the smallest feasible value, and then demonstrating that if the statement is true for some value, it is likewise true for the next value.
The key to the proof is the inductive step. It is typically accomplished by assuming that the statement is true for some value and then utilizing that assumption to establish that the statement is true for the following value.
Check the attachment.
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For questions 18-19, describe the end behavior of the graph for each function.
18. f(x) = x³ +2x² - 5x+1
19. g(x) = -2x³-8x2 +18x+72
Answer:
18. The end behavior of the graph of f(x) = x³ + 2x² - 5x + 1 is as follows: as x approaches negative infinity, the function f(x) approaches negative infinity, and as x approaches positive infinity, the function f(x) approaches positive infinity. This is because the leading term of the polynomial is x³, which has a positive coefficient, so the graph of the function will have a "smile" shape, with the ends of the graph pointing upwards.
19. The end behavior of the graph of g(x) = -2x³ - 8x² + 18x + 72 is as follows: as x approaches negative infinity, the function g(x) approaches negative infinity, and as x approaches positive infinity, the function g(x) approaches negative infinity. This is because the leading term of the polynomial is -2x³, which has a negative coefficient, so the graph of the function will have a "frown" shape, with the ends of the graph pointing downwards.
Step-by-step explanation:
T/F True Logistic Regression is applied when the Dependent Variable is of Continuous nature.
It is used in various fields, such as healthcare, marketing, and social sciences.
False. Logistic regression is used when the dependent variable is binary or categorical (i.e., a nominal or ordinal variable). It is not appropriate for continuous dependent variables.
Logistic regression models the probability of an event occurring, where the event is represented by a binary variable (such as yes/no, success/failure, etc.). The output of the logistic regression model is the probability of the event occurring given the values of the independent variables. This probability can take any value between 0 and 1.
The logistic regression model assumes that the log odds of the event occurring (i.e., the logarithm of the probability of the event divided by the probability of its complement) can be modeled as a linear function of the independent variables. The coefficients of this linear function are estimated using maximum likelihood estimation.
Overall, logistic regression is a commonly used technique in statistics and data analysis for modeling the probability of a binary or categorical outcome. It is used in various fields, such as healthcare, marketing, and social sciences.
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Which equation represents a direct variation?
Oy - 4x = 8
Oy + 2 = 7x
Oy - 3x = 0
O y = 5x - 2
Answer:
The equation that represents a direct variation is y = 5x - 2.
In a direct variation, one variable is proportional to the other variable, which means that as one variable increases or decreases, the other variable also increases or decreases in direct proportion. The general form of an equation that represents direct variation is y = kx, where k is a constant of proportionality.
In this case, the equation y = 5x - 2 is in the form of y = kx, where k = 5. This means that as x increases or decreases, y will also increase or decrease proportionally, with a constant rate of change of 5. Therefore, this equation represents a direct variation.
The annual profits for a company are given in the following table, where x represents the number of years since 2012, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected profit (in thousands of dollars) for 2022, rounded to the nearest thousand dollars.
The linear regression equation is y = 22.6x + 52.33
The profit would reach 234 thousand dollars during the calendar year of 2020.
How to calculate the valueReplacing the means, the intercept a is given by:
108.8 = 22.6(2.5) + a.
a = 108.8 - 22.6(2.5)
a = 52.33
Therefore, the linear regression equation is y = 22.6x + 52.33
The profit would reach 234 thousand dollars during the calendar year of 2020.
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Answer:
Step-by-step explanation:
Please help asap please
The expansion and simplification of the expression, (3x - 2)(2x² + 5x - 1) is 6x³ + 11x² - 13x + 2.
How to simplify and expand an expression?In order to expand and simplify an expression, we need to multiply out the brackets and then simplify the resulting expression by collecting the like terms.
Therefore, let's expand and simplify the expression.
Hence,
(3x - 2)(2x² + 5x - 1)
Therefore, let's multiply
(3x - 2)(2x² + 5x - 1) = 6x³ + 15x² - 3x - 4x² - 10x + 2
6x³ + 15x² - 3x - 4x² - 10x + 2 = 6x³ + 15x² - 4x² - 3x - 10x + 2
6x³ + 15x² - 4x² - 3x - 10x + 2 = 6x³ + 11x² - 13x + 2
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Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each. How much total money would Ellie have to pay for her family if she were to buy 4 snacks for everybody to share? How much would Ellie have to pay if she bought x snacks for everybody to share?
Total cost with 4 snacks:
Total cost with x snacks:
Answer:
The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.
Step-by-step explanation:
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Ellie is going to see a movie and is taking her 2 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $5 each.
The amount of tickets is given as,
Ticket's amount = 3 x $13
Ticket's amount = $39
Then the amount spent on snacks is given as,
Snack's amount = 4 x $5
Snack's amount = $20
Then the total amount is given as,
Total amount = $39 + $20
Total amount = $59
The amount of money spent on tickets and snacks will be $39 and $20. And the total amount is $59.
Use the information given in the figure to find the length RU. If applicable, round your answer to the nearest whole number.
Answer:7
Step-by-step explanation:
use the Pythagoras theorem to find su (40^2-32^2) take the square root =24 use this to solve for ru. (25^2-24^2=49) square root of 49 is
Hurry up (time limit )
State the domain and range and tell if the graph is a function yes or no?
What’s the domain and range?
In this problem, we have that the graph in fact represents a function, as there are no vertically aligned points, that is, each input is mapped to a single output.
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Solve for x. Assume that lines which appear to be diameters are actual diameters.
Answer:
x = 9
Step-by-step explanation:
We Know
A circle is 360°
An angle is 85° & one is 130°
Find x
We Take
85° + 130° + 16x + 1 = 360°
216 + 16x = 360°
16x = 144°
x = 9
