The probability that your cat has both a kidney disorder and is diabetic is 15%. With a 40% chance of having a kidney disorder and a 50% chance of being diabetic, the combined probability is found by subtracting the probability of neither condition from the total probability of having either condition. Therefore, the probability of having both conditions is 15%.
To compute the probability that your cat has both a kidney disorder and is diabetic, we can use the concept of conditional probability.
Let's denote:
A = Event that the cat has a kidney disorder
B = Event that the cat is diabetic
We have:
P(A) = Probability of the cat having a kidney disorder = 0.40 (40%)
P(B) = Probability of the cat being diabetic = 0.50 (50%)
We are looking for the probability of the cat having both a kidney disorder and being diabetic, which can be represented as P(A ∩ B).
According to the veterinarian, there is a 75% probability that your cat has either a kidney disorder or is diabetic.
Mathematically, this can be represented as:
P(A ∪ B) = 0.75
To compute P(A ∩ B), we can use the formula:
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Substituting the given values, we have:
P(A ∩ B) = 0.40 + 0.50 - 0.75
P(A ∩ B) = 0.90 - 0.75
P(A ∩ B) = 0.15 (15%)
Therefore, the probability that your cat has both a kidney disorder and is diabetic is 0.15 or 15%.
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Which of the following assumptions is not true for multiple linear regression?
Group of answer choices
o The independent variables are not correlated.
o The residuals are normally distributed.
o The relationship between dependent and independent variables is linear.
o There will be a multi-collinearity effect.
The assumption which is not true for multiple linear regression is that there will be a multi-collinearity effect. What is multiple linear regression? Multiple linear regression is a regression method where the response variable is dependent on more than one independent variable. Multiple linear regression is an extension of linear regression, where one response variable is dependent on one independent variable. It helps to determine the nature of the relationship between dependent variables and independent variables in the form of linear equations. It is used to find out the relationship between variables and make predictions based on that relationship. Assumptions of multiple linear regression1. Linearity, It is assumed that the relationship between the independent variables and dependent variables is linear. This implies that as the value of the independent variable changes, the change in the dependent variable is constant.2. Independence, There should be independence among the observations. This implies that there should not be any relationship between the residuals of the observations.3. Homoscedasticity implies that the variance of residuals should remain constant across all levels of the independent variable.4. Multicollinearity, It is the condition where the independent variables are highly correlated with each other. If there is perfect collinearity, it will not be possible to obtain the estimates of regression coefficients.5. Normality, The residuals should follow a normal distribution with mean zero and constant variance. The residuals should be normally distributed and centered on zero. The assumptions that are true for multiple linear regression are: The independent variables are not correlated. The residuals are normally distributed. The relationship between dependent and independent variables is linear. The assumption which is not true for multiple linear regression is that there will be a multi-collinearity effect. Hence, the correct option is D) There will be a multi-collinearity effect.
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which properties are being used to solve the question
Answer:
Both commutative and associative
Find the nth Maclaurin polynomial for the function.
f(x) = (4x − 5)/(x + 1), n = 4
The nth Maclaurin polynomial for the function f(x) = -5 - x + 4x² - 5x³ + 4x⁴ + ...
The nth Maclaurin polynomial for the function f(x) = (4x − 5)/(x + 1), we need to expand the function as a power series centered at x = 0 (the Maclaurin series) and then truncate it to the desired degree.
First, let's find the Maclaurin series expansion of f(x):
f(x) = (4x − 5)/(x + 1)
To expand this as a power series, we'll use the concept of geometric series expansion. We'll start by expressing f(x) as a product of two functions:
f(x) = (4x − 5)×(x + 1)⁻¹
Now, let's find the power series expansion for each factor separately.
1.The power series expansion for (4x - 5) centered at x = 0 is given by:
(4x - 5) = -5 + 4x
2.The power series expansion for (x + 1)⁻¹ centered at x = 0 is given by the geometric series formula:
(x + 1)⁻¹ = 1 - x + x² - x³ + x⁴ - ...
Note that this expansion is valid when |x| < 1 since it's based on a geometric series.
Now, we'll multiply these two expansions together to get the expansion for f(x). We'll keep terms up to the fourth degree (n = 4).
f(x) = (4x - 5) × (x + 1)⁻¹ = (-5 + 4x) × (1 - x + x² - x³ + x⁴)
Expanding this expression:
f(x) = -5 + 4x - 5x + 4x² - 5x³ + 4x⁴ + ...
Simplifying the terms:
f(x) = -5 - x + 4x² - 5x³ + 4x⁴ + ...
This is the Maclaurin series expansion for f(x). The nth Maclaurin polynomial, we'll truncate the series at the fourth degree (n = 4):
f(x) ≈ -5 - x + 4x² - 5x³ + 4x⁴
Therefore, the fourth Maclaurin polynomial for f(x) is given by:
P₄(x) = -5 - x + 4x² - 5x³ + 4x⁴
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how do you solve 1/2(6)(h+1)=18
Multiply 6 by 1/2 to get 3
Ow you have :
3( h + 1) = 18
Distribute the 3:
3h + 3 = 18
Subtract 3 from both sides:
3h = 15
Divide both sides by 3:
H = 5
Factor the expression completely. 12X+18
Answer:
6(2x+3)
Step-by-step explanation:
There's really no way to explain this. Take the number that all of the numbers in the equation can be divisible by and then single it out and then yeah.
Hope this helped! :)
I need help with this , 7x-3y+4x-5y+8x-6y
Answer:
19x−14y
Steps:
7x-3y+4x-5y+8x-6y
=19x-3y-5y-6y
= 19x−14y
plz mark as brainliest
Answer:
19x-14y
Step-by-step explanation:
rearrange
7x+4x+8x-3y-5y-6y
solve the coefficient and add the variables
A swimming pool measures 25.8 meters by 11.9 meters. It is filled with water to a depth of 1.1 meters. The pool is emptied by a tube that emits 29.8 liters per second. Estimate the approximate time required to empty the pool
Answer:
11 Seconds
Step-by-step explanation:
Swimming pool volume:
25.8 × 11.9 × 1.1 = 337.722
Time to empty pool:
337.722 ÷ 29.8 = 11.3329530201 ≈ 11 seconds
2. Write a ratio expressing the slope of the line through each pair of points.
(-6, 1) and (-2, 0)
Answer:
Step-by-step explanation:
m = [tex]\frac{-1}{4}[/tex]
Find the value of x and y.
Answer:
Step-by-step explanation:
If the answer isn’t an integer express in simplest radical form
Answer:
[tex]x = \frac{20}{ \sqrt{3} } \\ y = \frac{40}{ \sqrt{3} } [/tex]
Step-by-step explanation:
[tex]for \: \: x \\ \tan(60) = \frac{20}{x} \\ \sqrt{3} = \frac{20}{x} \\ x = \frac{20}{ \sqrt{3} } \\ \\ for \: y \: \\ \sin(60) = \frac{20}{y} \\ \frac{ \sqrt{3} }{2} = \frac{20}{y} \\ \sqrt{3} \: y = 20 \times 2 \\ y = \frac{40}{ \sqrt{3} } [/tex]
I hope that is useful for you :)
Jericho has m paintings and n drawings. He sold his paintings for $x each and drawings for $y each. His earnings for one day are
represented by the expression given below.
x(m) + y(m- 12)
Which statement best describes the term (m - 12)?
A. It is the number of paintings sold, which was 12 more than the number of drawings sold.
B. It is the number of drawings sold, which was 12 more than the number of paintings sold.
C. It is the number of paintings sold, which was 12 less than the number of drawings sold.
D. It is the number of drawings sold, which was 12 less than the number of paintings sold.
Answer:
b
Step-by-step explanation:
Certain standardized math exams have a mean of 100 and a standard deviation of 60. Of a sample of 36 students who take this exam, what percent could you expect to score between 80 and 90?
16
15.85
13.5
12.5
Approximately 12.5% percentage of the students could be expected to score between 80 and 90.
To determine the percentage of students who could be expected to score between 80 and 90, we need to calculate the z-scores for these scores and use the standard normal distribution.
First, we need to calculate the z-scores for 80 and 90 using the formula:
z = (x - μ) / σ
where x is the individual score, μ is the mean, and σ is the standard deviation. Plugging in the values of μ = 100, σ = 60, and x = 80 or x = 90, we can calculate the z-scores.
For x = 80:
z = (80 - 100) / 60 = -0.3333
For x = 90:
z = (90 - 100) / 60 = -0.1667
Next, we need to find the area under the standard normal distribution curve between these two z-scores. This represents the percentage of students who scored between 80 and 90.
Using a standard normal distribution table or calculator, we can find that the area between -0.3333 and -0.1667 is approximately 0.1210 or 12.1%.
Therefore, approximately 12.5% of the students could be expected to score between 80 and 90.
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what is the equation of the line that has a slope of -3 and a y-intercept of -1
Answer:
y=4x+2
Step-by-step explanation:
Complete the two-way frequency table below, which shows the relationship between adults' gender and whether these adults buy a truck or a car for their first new vehicle. From a sample of 94 adults, the following data are collected:
Truck Car Total
Female 9 36
Male 18 31
Total 94
What is the probability (rounded to the nearest whole percent) that an adult will buy a car, given that he is a male? Are the events being male and buying a car independent? (1 point)
63%; they are dependent
46%; they are dependent
63%; they are independent
33%; they are independent
I will come back to this question when it has been further clarified.
(Honestly I just really need to delete this answer since I misread the question but it doesn't give me an option to delete it).
a rational expression is undefined whenever its denominator is zero.T/F
True. A rational expression is undefined whenever its denominator is zero. This is because division by zero is not defined.
In mathematics, a rational expression is defined as the quotient of two polynomials, where the denominator represents the divisor. When the denominator of a rational expression becomes zero, it results in division by zero, which is undefined. Division by zero is not a valid operation in mathematics, and it leads to an undefined value. Therefore, to determine if a rational expression is undefined, we need to check if its denominator evaluates to zero. If the denominator is zero, the rational expression is undefined. Also there is division by zero, or related concepts in mathematics.
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a whole number that is a factor of two or more numbers is called a
Answer: Common factor
common factor. a whole number that is a factor of two or more nonzero whole numbers
Step-by-step explanation:
[tex] \purple{ \tt{ \huge{ \: ✨Answer ✨ \: }}}[/tex]
[tex] \: \: \: \red{ \boxed{ \boxed{ \huge{ \tt{ \: common \: factor \: }}}}}[/tex]
a whole number that is a factor of two or more numbers is called a common factor.490 students and 10 teacher will ride the bus to go to the zoo if each bus can seat so passengers how many buses will be needed many zoo trip
Answer:
If you add teacher plus students which is 490+10=500
you get 500 people in total after that you divide 500 by 50 and you get 10 so you will need 10 busses in total hope this helped!
Step-by-step explanation:
A glass is formed by rotating the shaded region shown above about the y axis. The curve that forms the inside of the glass is the graph of y = x^4/2. Length units in the figure are cm.
(a) What is the volume of the glass? (That is, what is the volume of the solid formed when the shaded region is rotated about the y axis?)
To find the volume of the glass formed by rotating the shaded region about the y-axis, we can use the method of cylindrical shells.
The volume of a solid of revolution using cylindrical shells is given by the integral:
V = ∫[a,b] 2πx * f(x) * dx
In this case, the function representing the curve that forms the inside of the glass is y = x^4/2. We need to find the limits of integration, a and b, which correspond to the x-values where the shaded region begins and ends.
From the graph, it appears that the shaded region begins at x = -1 and ends at x = 1. So, the limits of integration are -1 to 1.
Now, we can calculate the volume of the glass using the integral formula:
V = ∫[-1,1] 2πx * [tex](x^4/2) * dx[/tex]
V = π * ∫[-1,1] [tex]x^5 dx[/tex]
Using the power rule of integration, we integrate x^5:
V = π * [x^6/6] from -1 to 1
V = π * [[tex](1^6/6) - (-1^6/6)][/tex]
V = π * [(1/6) - (1/6)]
V = π * 0
Therefore, the volume of the glass is 0 cubic units.
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what is the volume of the cylinder?
5 yd
4 yd
cubic yards.
Volume
Answer:
volume=1yd x 1yd = q cubic yard
12 pumpkins cost 24.60 how much will it cost for 8 pumpkins also
I can run 5 laps in 1 1/4 hours how many laps could I run in a day
Answer:
the second one is 20 i think
Step-by-step explanation:
School: Your future depends on me
Me: Nahhhhh, I'll spend my time on Brianly making s.tupid questions
Answer:
lol same facts though
Step-by-step explanation:
Answer:
Your future doesn't really depend on school to be honest, but school is one of the options to a great future. Even college and etc dropouts become successful.
HELPPPPPPPPP
What is the value of x in the figure at the right?
Answer:
Answers is D
Step-by-step explanation:
2x = 60° because they are vertically opposite angles.
x=60÷2=30°
which shows a difference of squares?
a.10 y squared minus 4 x squared
b.16 y squared minus x squared
c.8 x squared minus 40 x + 25
d.64 x squared minus 48 x + 9
The expression that shows a difference of squares is option B, i.e., 16y² − x². We can represent it as (4y - x)(4y + x).Therefore, the correct option is B.
Difference of Squares is a squared quantity that can be represented as the difference of the squares of two variables or numbers. In simple terms, when two squares are subtracted, a difference of squares is produced. The squares of the two quantities, x and y, are subtracted from each other in the Difference of Squares.Here, the expression that shows a difference of squares is option B, i.e., 16y² − x². We can represent it as (4y - x)(4y + x).Therefore, the correct option is B. In this expression, we have the square of two quantities subtracted, which results in the Difference of Squares.Checking the other options, we can say that option A (10y² − 4x²) cannot be considered a difference of squares because there is no squared quantity subtracted from it. Similarly, option C (8x² − 40x + 25) and option D (64x² − 48x + 9) do not show the Difference of Squares as they do not have two squared quantities subtracted from each other.
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Tell whether the angles are complementary or supplementary. Then find the value of X.
Answer:
Complementary
x= 60
Step-by-step explanation:
Answer:
The angles are complementary.
X = 60
Step-by-step explanation:
help me please asap subtract with renaming
Answer:
1. 1/4
2. 43/10 or 4 3/10 either are correct.
3. 67/12 or 5 7/12 either are correct.
Step-by-step explanation:
I hope this helped.
help please :) A, B , C , or D?
Answer:
the answer is 120 degree
Answer:
(A) 30 degree
Step-by-step explanation:
Just subtract 180 with 120 = 60
then add 60 and 90 = 150
after that 180 - 50 = 30
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You call 5 friends, tomorrow they call 5 each. Write an equation.
Answer:
5+5=10
Step-by-step explanation:
5+5=10
hope this helps. plz mark me as brainliest.
a business woman bought a personal computer for $108000.calculate her selling price on the personal computer if she wants to make profit of 25%
Answer:
$135,000
Step-by-step explanation:
108000*1.25
Which expression is equivalent to (-3)x+(3)(-12)?
Answer:
Step-by-step explanation:
(-3)x + (3)(-12)
= -3x -36
or -3(x + 12)
Answer:
Step-by-step explanation:
(-3)x + 3(-12) = (-3) (x + 12)
(-3) is both the two terms. So we can take (-3) as common
One customer purchases 8 bags of cat food and 2 bags of dog food. The total weight of the purchase is 44 pounds. Another customer purchases 5 bags of cat food and 2 bags of dog food. The total weight of the purchase is 35 pounds.
A. You write the following system of linear equations to represent this
situation. Is your answer correct?
8x + 2y = 44
5x + 2y = 35
B. Your answer for the next step is 13 79, x = which is incorrect. Explain
the error.
Answer:
answer is x=3 and y=10
Step-by-step explanation:
Forgot to isolate y and x and simplify