The statement that is true about the triangle ABC with vertices A(-6, 6), B(4, 2), and C(-4, 0) is C. Since two of the sides have slopes that are negative reciprocals, it is a right triangle.
How to check if the triangle is right triangleRight triangles are triangles with have perpendicular relationships
The lines will be checked for perpendicularity by calculating the slopes, if any two slopes are negative reciprocals then they are perpendicular and the triangle is a right triangle'
the points A(-6, 6), B(4, 2), and C(-4, 0)
Using point A(-6, 6) and B(4, 2)
m = (y₂ - y₁) / (x₂ - x₁)
m = (4 - 6) / (2 - -6)
m = -1/2
Using point B(4, 2), and C(-4, 0)
m = (y₂ - y₁) / (x₂ - x₁)
m = (4 - -4) / (2 - 0)
m = 2
Comparing the slopes shows that slopes calculated are negative reciprocals
2 and -1/2Therefore the triangle is a right triangle
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Given the following probability distributions:
Distribution A Distribution B x p(x) x p(x)
0 .50 0 0.05
1 .20 1 0.10
2 .15 2 0.15
3 .10 3 0.20
4 .05 4 0.50
a. Compute the expected value for each distribution.
b. Compute the standard deviation for each distribution.
c. Compare the results of distributions A and B.
The expected value of distribution A is 1 and distribution B is 3. The standard deviation for both distributions is the same which is 1.225. In conclusion, distribution B is better than distribution A.
Events with countable or finite outcomes are counted in a discrete probability distribution. This includes the probability values for the discrete random variable. The expected value for this type of distribution is calculated by E(X)=μ=ΣxP(x). And the standard deviation is calculated by σ=√(E(X²)-(E(X))²).
a) Expected value for the distributions A and B is calculated as follows,
The expected value for distribution A,
[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.50)+(1\times0.20)+(2\times0.15)+(3\times0.10)+(4\times0.05)\\&=1\end{aligned}[/tex]
The expected value for distribution B,
[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.05)+(1\times0.10)+(2\times0.15)+(3\times0.20)+(4\times0.50)\\&=3\end{aligned}[/tex]
b) The standard deviation for the distributions A and B is calculated as follows,
First, find E(X²) for distribution A and B to substitute in the standard deviation formula.
The E(X²) for distribution A is,
[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.50)+(1^2\times0.20)+(2^2\times0.15)+(3^2\times0.10)+(4^2\times0.05)\\&=2.5\end{aligned}[/tex]
The E(X²) for distribution B is,
[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.05)+(1^2\times0.10)+(2^2\times0.15)+(3^2\times0.20)+(4^2\times0.50)\\&=10.5\end{aligned}[/tex]
Then, the standard deviation for distribution A is,
[tex]\begin{aligned}\sigma_A&=\sqrt{2.5-1^2}\\&=1.225\end{aligned}[/tex]
The standard deviation for distribution B is,
[tex]\begin{aligned}\sigma_B&=\sqrt{10.5-3^2}\\&=1.225\end{aligned}[/tex]
Distribution A and B have the same standard deviation.
c) The standard deviation values are the same for both distributions. But the expected value of distribution A is lesser than the expected value of distribution B. So distribution B looks better than distribution A.
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d • r = r • d what is the property
Answer:
Commutative Property of Multiplication
Step-by-step explanation:
Hope it helps!
Olaf has 11 more than triple the amount of customers as when he started selling newspapers. He now has 71
customers. Write an equation that can be used to solve for how many customers Olaf had originally, then solve
your equation to find the answer.
The equation representing the situation is written as
3x + 11 = 71the number of customers Olaf had originally is 80
How to write the equationFrom the given information the following is deduced
Olaf has 11 more than triple the amount of customers as when he started selling newspapers
let the amount be x
3x + 11 = ?
He now has 71 customers
3x + 11 = 71
solving the equation
3x = 71 - 11
3x = 60
x = 20
Olaf had 80 customers
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A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?In similar triangles, both the two triangles must satisfy the two properties. One is the side proportional, and the other is equal in angles. There are three criteria in similarity. They are AA similarity, SSS similarity, and SAS similarity. The below one satisfies the AA similarity.
The change in rate of length of shadow is 2.692 ft/sec.
Given,
Height of tall person =7 ft
Height of tall lamp post = 20 ft
Rate at which tall person walks = 5 ft/sec
Let,
Distance between tall person and lamp post be x ft
the length of shadow be y ft
From similar triangles,
[tex]\frac{x+y}{20}=\frac{y}{7}\\\\7(x+y)=20y\\\\7x+7y=20y\\\\13y=7x\\\\y=\frac{7x}{13}[/tex]
Differentiating on both sides with respect to time 't'
[tex]\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}[/tex]
here, [tex]\frac{dx}{dt}[/tex] is nothing but the change in distance between tall person and lamppost it means rate at which tall person walks=5 ft/sec
[tex]\frac{dy}{dt}=\frac{7}{13}*5\\\\\frac{dy}{dt}=\frac{35}{13}=2.692\ ft/sec[/tex]
Thus, the change in rate of length of shadow is 2.692 ft/sec.
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Ellis's backyard has a 6.25m by 6.25m patio. She would like to build a 1.5m wide extension around 3 sides of the patio. She will buy 0.25m b 0.25m tiles that come 25 to a package. How many packages does Ellis need to buy to build the extension?
Answer:
21
Step-by-step explanation:
The amount added to each of the 3 sides is a rectangle 6.25 m by 1.5 m.
Then there are two square corners added that each one is 1.5 m by 1.5 m.
Total added area = 3 × 6.25 m × 1.5 m + 2 × 1.5 m × 1.5 m
Total added area = 28.125 m² + 4.5 m²
Total added area = 32.625 m²
The area of each tile is:
0.25 m × 0.25 m = 0.0625 m²
A box of tiles has 25 tiles. The total area covered by a box of tiles is:
25 × 0.0625 m² = 1.5625 m²
The number of boxes need is:
32.625 m² / 1.5625 m² = 20.88
Since 20.88 boxes are needed, but she needs to buy full boxes, she needs 21 boxes of tiles.
Answer: 21
A certain type of mango that weighs over 425 grams is considered to be large in size. the weights for this type of mango, x grams, are normally distributed with a mean of 400 and a standard deviation of 25. find the probability that a randomly selected mango of this type will not be considered as large size. round your answer to four decimal places.
The probability that a randomly chosen mango of this type won't be deemed to be large in size is 26.43%.
Explain the term z-distribution/normal distribution?The statistics field is where z-distribution probability is most frequently employed. It is used to determine a person's height, weight, and pay. The graph produced by these measurements is symmetrical.For the stated question;
The formula for the z-score is;
z = (x - μ)/σ
x < 425 gram
mean μ = 400,
standard deviation σ = 40:
Thus,
z = (425 - 400)/40
z = 0.625
P(X < 425) = 1 - P(z = 0.625)
P(X < 425) = 1 - 0.7357
P(X < 425) = 0.2643
Thus, there is a 26.43% chance that a randomly chosen mango of this sort will not be regarded as being huge in size.
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Answer:0.8413
Step-by-step explanation:
0.8413
The mean is μ=400, and the standard deviation is σ=25.
Open Excel. Click on an empty cell. Type =NORMDIST(425,400,25,1) and press ENTER.
The probability, rounded to four decimal places, is P(X<425)≈0.8413.
4. Identify each of the following polygons:
Answer:
H
Step-by-step explanation:
given the slope m of a line and a point (x, y) on that line, how can you determine the coordinates of another point on the line?
To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.
When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
The equation of the line is written in the slope-intercept form, which is:
y = mx + b, where m represents the slope and b represents the y-intercept.
Finding the distance from the known endpoint to the midpoint and then applying the same transformation to the midpoint is the quickest way to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, so the new x-coordinate is 2-2 = 0.
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he fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) use the data to test the hypothesis that the proportion is not 0.04. use ????α
The proportion is not equal to 0.04.
The test statistic
Z = 1.149
What is the random sample?
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
Since the calculated value of Z = 1.149 is less than 1.96 at 5% (0.05) level of significance.
The null hypothesis is accepted
Hence the proportion is not equal to 0.04
Given data a random sample of 300 circuits is tested, revealing 17 defectives.
The proportion of success
P = 17 / 300 = 0.056
Null hypothesis:- H₀ = P ≠0.04
Alternative hypothesis:- H₁ = P =0.04
Q = 1-P = 1-0.04=0.96
Level of significance ∝ =0.05
The test statistic
[tex]z = \frac{p -P}{\sqrt{PQ/n} }[/tex]
now substitute all values, and we get
on calculation, Z = 1.149
Since the calculated value of Z = 1.149 is less than 1.96 at a 5% (0.05) level of significance.
The null hypothesis is accepted.
Hence the proportion is not equal to 0.04.
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A recipe for cheesecake requires 3 cups of sugar per
batch.
A. Write an equation that can be used to determine y,
the number of cups of sugar required to make
cheesecake, based on x, the number of batches.
B. Use your equation to determine how many cups of
sugar are required to make 4 batches of cheesecake.
Pls hurry!!
Answer:
y = x × 3, 12
Step-by-step explanation:
If a recipe for cheesecake requires 3 cups of sugar per batch, we can use this equation:
y = x × 3
Using this, we can determine how many cups are needed when we need to make 4 batches.
y = 4 × 3 = 12
You need 12 cups of sugar for 4 batches.
question content area top part 1 it is believed that gpa (grade point average, based on a four point scale) should have a positive linear relationship with act scores. attached below is the technology output for predicting gpa using act scores based on a data set of 8 randomly chosen students from a big-ten university. what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between gpa and act scores?
The p-value is greater than the significance level, so we do not reject the null hypothesis for the significance level is 0.01 (1%)
What is significance level?
"Significance" in statistics refers to something that is "not by chance" or "likely true." We can infer that when a statistician claims that a finding is "very significant," he or she is implying that it may very well be true. It does not imply that the finding is very significant, but it does imply that it is highly likely. The fixed likelihood of incorrectly eliminating the null hypothesis when it is, in fact, true is what is referred to as the level of significance. The probability of type I error is defined as the degree of significance, and the researcher sets it based on the results of the error. The statistical significance is measured by its level of significance. It specifies whether the null hypothesis is thought to be accepted or rejected.
The p-value for ACT is 0.0286
The significance level is 0.01 (1%)
Hence, the p-value is greater than the significance level, so we do not reject the null hypothesis. We conclude that there is insufficient evidence to conclude that there is any linear relationship at a 1% level of significance between GPA and ACT scores.
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what is the rule for multiplying two integers that have the same sign
If multiplying 2 negative integers then it's a positive
If multiplying 2 positive integers it's positive
Answer: I hope this is helpful
Step-by-step explanation:
The proceeding pattern is summarized in the following rule for multiplying integers. Rule for Multiplying Two Integers: TO MULTIPLY INTEGERS WITH THE SAME SIGN, multiply the absolute value of the factors. The product is positive.
what is a general pattern in data
Answer:
rhe general pattern in data is........
Step-by-step explanation:
.....
Iris's checking account pays simple interest at 5% per year. She has $185 in
Answer:
Step-by-step explanation:
Answer 3700
find two positive numbers that satisfy the given requirements. the sum of the first number squared and the second number is 51 and the product is a maximum. (first number) (second number)
The two positive numbers that satisfy the given requirements are √17 and 34
Given the sum of the first number squared and the second number
is 51.
Let's assume first number is x.
second number is y.
Square of first number is [tex]x^2[/tex].
sum of the first number squared and the second number = [tex]x^2 + y[/tex].
[tex]x^2 + y = 51[/tex]
subtract [tex]x^2[/tex] from both side of equal sign.
[tex]x^2 + y- x^2 = 51 - x^2[/tex]
[tex]y = 51 - x^2[/tex]
Product of both numbers p = x*y.
[tex]p = x*(51 - x^2)[/tex]
[tex]p = 51*x - x^3.[/tex]
Given the product is a maximum.
so derivative of p with respect to x will be = 0.
derivative of p with respect to x is [tex]51-3*x^2[/tex]
[tex]51-3*x^2 = 0[/tex]
[tex]3*x^2=51[/tex]
[tex]x^2 = 17[/tex]
x = √17.
put value of x in [tex]y = 51 - x^2[/tex]
[tex]y = 51 - (\sqrt17)^2[/tex] = 51 - 17 = 34
So the value of x and y is √17 and 34 respectively.
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amanda chicopee bought a new car and drove 8,000 miles in the first four months. at the same rate, how many miles will amanda drive in 3 years?
If Amanda stays on her current course, she will go 72,000 km in three years.
Given data,
In the first four months after purchasing a new car, Amanda Chicopee covered 8,000 kilometers. How many miles will Amanda log in three years if she continues on her path?
Here,
She drove 8000 km in 4 months.
⇒ In 1 month = 8000/4 = 2000 km
To find how many miles in 3 years,
⇒ In 36 months = 2000 * 36
= 72000 km
Hence, 72000 km will Amanda log in three years if she continues on her path.
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What is the value of x?
Enter your answer in the box.
Answer:
x=36
Step-by-step explanation:
how do the results compare to your hypothesis? explain why your hypothesis was/was not supported by the results?
Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.
A Gram-positive bacterium called S. epidermidis is a component of the flora of humans. Anaerobic bacteria are what it is. It promotes the growth of pathogens that are present in medical equipment. These may enter the bloodstream. Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling s. epidermidis.
Molds produce a class of antibiotics known as penicillium. Actinomycetes produce the antibody known as novobiocin, which has antibacterial characteristics. Gentamicin is one of the antibodies that can treat infections and aid in halting bacterial development.
Hence the answer is Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.
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a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south carolina average? use
The hypotheses for [tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)
Given:
Nationwide scores as n1=1000, [tex]x_{1}[/tex]` = 21.4 ,σ1 = 3
Carolina scores as n2=500, [tex]x_{2}[/tex]` = 21.2 ,σ2 = 3
So from here we can say
µ represents population mean.
[tex]u_{1}[/tex] represent population mean for nationwide scores.
[tex]u_{2}[/tex] represents population mean for Carolina scores.
[tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)
Given Question is incomplete, Complete Question here,
a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south Carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south Carolina average?
use α=0.01 and [tex]\µ_{1}[/tex] for the nationwide mean act score.
State the hypotheses and identify the claim.
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a piece of wire 10 m long is cut into two pieces. one piece is bent into an equilateral and the other is bent into a circle. how should the wire be cut so that the total area enclosed is (a) a maximum? (b) a minimum?
For maximum area the wire should be bent in the form of circle and for minimum area the wire should bent into equilateral triangle.
What is the area of any geometrical shape?
The area of a shape is the “space enclosed within the perimeter or within the boundary” of the given shape. We calculate the area for different shapes using math formulas.
Given that a piece of wire 10m long is cut into two pieces so now we have two wires with lengths of 5m and 5m.
One wire is bent into an equilateral so the perimeter of that triangle would be 3 m.
Perimeter = 3 m
3*side = 3 m
side = 1 m
Now the area of the equilateral triangle = [tex]A=\frac{\sqrt{3}}{4}\times (side)^2[/tex]
A = 0.4330 m² -----(I)
Now the circumference of the circle = 5 m
2π×r = 5
r = 5/2π
r = 0.7957 m.
Now the area of the circle = π×r²
= 3.14 × (0.7957)²
= 1.988 m² --------(II)
From (I) and (II), we can say that
Area of the equilateral triangle < Area of the circle
Hence, for maximum area the wire should be bent in the form of circle and for minimum area the wire should bent into equilateral triangle.
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describe a procedure that could be used to write an equation having the first 7 natural numbers as solutions.
the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
Now the simplest way to write an equation is to multiply all the factors.
The zeroes of the equation are 1,2,3,4,5,6,7.
The factors can be written as (x-1)* (x-2)*(x-3)*(x-4)*(x-5)*(x-6)*(x-7).
So the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]
Hence, the equation will be [tex]x^{7}-28x^{6}+322x^{5} -1960x^{4} +6769x^{3} -13132x^{2} +1306[/tex]
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Solve the system algebraically.
4x+2y=104x+2y=10
x=y+13x=y+13
The solution of the system of equation are;
⇒ x = 6
⇒ y = - 7
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equations are,
4x + 2y = 10
x = y + 13
Now,
Since, The system of equations are,
⇒ 4x + 2y = 10 ..(i)
⇒ x = y + 13
⇒ x - y = 13 ..(ii)
Multiply by 2 in equation (ii) and add with (i);
⇒ 2x - 2y + 4x + 2y = 26 + 10
⇒ 6x = 36
⇒ x = 6
And, x - y = 13
⇒ 6 - y = 13
⇒ 6 - 13 = y
⇒ y = - 7
Thus, The solution of the system of equation are;
⇒ x = 6
⇒ y = - 7
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5/3 x + 1/3 x = 40/3 + 8/3 x
Work in attachment
any of y'all willing to do this? me on gram quietstorm703
read my comments
What is your question dude???????
A professor wants to estimate how many hours per week her students study. A simple random sample of 65 students had a mean of 16 hours of studying per week. Construct a 98% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 2.4 hours per week. Round to two decimal places. Answer 2 Points Keypad Keyboard Shortcuts Lower Endpoint Upper Endpoint: Prev
98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)
mean x = 16
standard deviation σ = 2.4
sample size n = 65
z score for 98% = 2.576
Interval = x±z*s/
= 16±2.576*2.4/
= 16±2.576*0.39629
= 16±1.0208
Interval = (21.0208,18.9792)
Therefore 98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).
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use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.
The coefficient of determination is 0.588 and the percentage of the total variation is 58.8%.
The coefficient of determination (r^2) refers to a measurement used to explain how much variability of one variable can be caused by its relationship to another related variable. It is the fit of goodness and measures how well a statistical model fits the observed data and is a number between 0 and 1. When the value of linear correlation coefficient r is known, the coefficient of determination can be computed simply by squaring r.
Hence if r = 0.767, then the coefficient of determination = r^2 = 0.588
As percentage of the total variation is same as the coefficient of determination (given in percentage) and is given by the R² value = 58.8%. Hence, about 58.8% of variation is explained by the linear relationship between the two variables.
Note: The question is incomplete. The complete question probably is: Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. r = 0.767.
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Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players? a. 196 b. 151 c. 249 d. None of the answers is correct.
Option B, The center 95% of players had an average weight of 151 pounds.
Football players' weights have a mean of 200 pounds as well as a standard deviation of 25 pounds, which corresponds to a normal distribution.
So, let x represent a football player's weight.
X ≅ N(200, (25)²)
The minimal weight of the center 95% of the members is
P(X > 95) = P((95 - 200) ÷ 25) < (X - µ) ÷ σ)
P(X > 95) = P(-4.2 < z)
P(X > 95) = - P(z < -4.2)
P(X > 95) = 0.1512
The needed percentage is 0.1512 × 100 = 151.2 percent.
A probability distribution that is equal around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
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under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean?
When the population standard deviation is much greater than 5.
What is the standard deviation?
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Here, we have
The circumstance is a score that is 5 points above the mean considered a central value.
We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.
We concluded from the above statement that when the population standard deviation is much greater than 5.
Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.
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Nobody ANSERS MY QUESTONS pleas help me
Answer:
∠RPQ = 105
∠R = 45
Step-by-step explanation:
Question 1
By intersecting chord theorem ? = (175 + 35) / 2
? = (175 + 35) / 2
? = 210 / 2
? = 105
(See image below)
Question 2
By intersecting secant theorem ∠R = (140 - 50)/2
∠R = (140 - 50)/2
∠R = 90/2
∠R = 45
(See image below)
Intersecting chord theorem : Corresponding angle equals sum of corresponding arcs divided by two
Intersecting secant theorem : The inscribed angle equals major arc minus minor arc divided by two
At what point do the curves and intersect? find their angle of intersection correct to the nearest degree.
The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.
What are angles?When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.
The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.
When two rays are linked at their ends, they create an angle in geometry.
The sides or arms of the angle are what are known as these rays. Read on to learn about the various components of an angle.
Hence, The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.
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