If you are told 20% of people prefer all three forms of recreation is 60 when 60% of all college professors enjoy tennis, 65% enjoy bridge.
Given that,
Assume that 60% of all college professors enjoy tennis, 65% enjoy bridge, 50% enjoy chess, and 45% enjoy any certain pair of recreational activities.
We have to find if you are told 20% of people prefer all three forms of recreation, should you be suspicious.
We know that,
Let the total professors be =100
n(tennis) = 60
n( bridege) = 65
n( chess)= 50
n( T U B) = 45, n(BU C) = 45, n(T UC)=45
n( T UBUC)= n(T) + n(B) + n(C) - n( T U B) - n( BU C) - n(TUC) + n(T∩B∩C)
100 = 60 + 65 + 50 - 45-45-45 +n(T∩B∩C)
n(T∩B∩C)=60
Therefore, If you are told 20% of people prefer all three forms of recreation is 60 when 60% of all college professors enjoy tennis, 65% enjoy bridge.
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how many ways are there to assign each of $6$ friends to either the chemistry class or the biology class if one of these six, manoj, refuses to be in a class without any of his friends?
There are 62 number of ways in which classes to these students can be assigned. It can be solved by using the fomula of combination.
What is the formula of combination?
Following is the fomula of combination:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Here, n is the total objects available and r is the number of object need to choose from n objects.
Let six friends are A, B, C, D, E, and manoj.
Consider all 6 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_6[/tex]
Consider 5 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_5[/tex]
Consider 4 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_4[/tex]
Consider 3 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_3[/tex]
Consider 2 friends are in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_2[/tex]
Consider 1 friend is in chemistry class. Hence, number of ways in which it can be is,
[tex]^6C_1[/tex]
Consider no friend is in chemistry class all are in biology class. Hence, number of ways in which it can be is,
[tex]^6C_0[/tex]
Hence, total number of ways in which classes can be assigned to 6 students is,
[tex]^6C_6+^6C_5+^6C_4+^6C_3+^6C_2+^6C_1+^6C_0=64[/tex]
Now, the number of ways in which mnoj is alon. There are two ways. Either he will be in the chemistry class or he will be in the physics class.
Hence, subtract 2 from 64 to get the answer.
[tex]64-2=62[/tex]
Hence, there are 62 number of ways in which classes to these students can be assigned.
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>) The Johnsons set aside money in their budget for food for their anniversary party. They spent $320 but had set aside 25% more than that. How much money did the Johnsons set aside in their budget for food for the party?
Answer:
$400
Step-by-step explanation:
y= 320×(1+0.25)=400
Find all solutions to the equation b² = 13
Answer: The correct answer is b = √13 or b = −√13
Step-by-step explanation:
When factoring squared variables or numbers, use the square root
b^2 = 13
Take the square root of both sides
√b^2 = √13
b = √13 or b = −√13
Put the steps in order that are used to solve the following systems of equations by substitution.
-7x - 2y
2y
= x= 2 (-4) +11 → x = 3
x
-
=
= - 13
11
= x - 2y = 11 → x = 2y + 11
=y=-4
= -7 (2y + 11) - 2y = -13
= (3,-4)
= -16y = 64
= -16y - 77 = -13
= -14y-77-2y = -13
The steps that are used to solve the above equation by substitution include the following:
1.) X = 11 + 2y
2.) -7 ( 2y + 11) -2y = -13
3.) -14y -77- 2y = -13
4.) -16y - 77 = -13
5.) -16y = 64
6.) y= -4
7.) X = 2(-4) + 11 --> X = 3
8.) (3, -4)
What is a substitution equation?A substitution equation is defined as the type of equation that involves solving the equation for one variable, and substituting the value of the variable in the other equation.
The given equation is as follows;
-7x -2y = -13
X - 2y = 11.
To solve for X the following is done;
X = 2y + 11
Substitute X = 2y + 11 into equation 1
-7 ( 2y + 11) -2y = -13
Multiple out to open the brackets;
= -14y -77- 2y = -13
= -16y - 77 = -13
= -16y = 64
= y= -4
Then substitute y = -4 into equation two as follows;
X = 2(-4) + 11
X = 3
Therefore, y = -4, while X = 3 that is ( 3,-4)
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the board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 4.00 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 42 randomly selected calls. the mean wait time was calculated to be 4.14 minutes. assuming the population standard deviation is 0.55 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 4.00 minutes with a 98% level of confidence?
Answer of the following questions for given mean and standard deviation along with sample size are:
a. Null hypothesis , H₀: μ = 4.00
Alternative hypothesis, H₁ : μ > 4.00
b. Value of test statistic is 1.647
c. Conclusion is no evidence to conclude mean wait time for customer is longer than 4.00 minutes.
As given in the question,
Wait time for customer is at most 4.00 minutes
a. Null hypothesis is given by
H₀: μ = 4.00
Mean time is not exceeding the requirement
Alternative hypothesis is given by:
H₁ : μ > 4.00
b. Value of test statistic is given by :
([tex]\bar{x}[/tex] - μ₀) ÷ ( s/√n )
Sample mean [tex]\bar{x}[/tex] = 4.14
Population mean μ₀ = 4.00
Standard deviation 's' = 0.55 minutes
Sample size 'n' = 42
Substitute the value in the formula we get,
(4.14 - 4.00) ÷ (0.55/ √42)
= 0.14 / (0.55/ 6.5)
=0.14/ 0.085
= 1.647
c. α = 1 - 98%
= 1 - 0.98
= 0.02
Decision value limit :
Reject H₀ ; if P value < α
Using table ,
P value = P(Z < 1.647)
= 0.04997
⇒P value = 0.04997
0.04997 > 0.02
Here P value > α
Fail to reject Null hypothesis .
Therefore, from the given standard deviation and mean conclusion is that there is no sufficient evidence to prove that mean wait time for customers is longer than 4.00.
The complete question is:
The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 4.00 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 42 randomly selected calls. the mean wait time was calculated to be 4.14 minutes. assuming the population standard deviation is 0.55 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 4.00 minutes with a 98% level of confidence?
1. State the null and alternative hypotheses for the test.
2. Compute the value of the test statistic.
3. Draw a conclusion and interpret the decision.
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you have nine different color paints. you want to paint five different pots such that no two pots have the same color. how many ways are there to paint the pots?
The number of ways to paint the pots can be found using permutations and is found to be 15120 ways.
What are permutations?
An arrangement of all or a portion of a collection of items, taking into account the arrangement's order, is referred to as a permutation.
Here, we know that there are 9 different paints to choose from, so we are required to find the number of ways we can paint 5 pots without repeating any color.
This can be given by [tex]9P_{5}[/tex] ways.
[tex]=\frac{9!}{(9-5)!} \\=\frac{9!}{4!} \\=15120\space\ ways[/tex].
Therefore, the number of ways to paint the pots is 15120 ways.
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in multiple regression analysis, the correlation among the independent variables is termed . select one: a. homoscedasticity b. linearity c. multicollinearity d. adjusted coefficient of determination
In multiple linear regression analysis, the correlation among independent variables is termed multicollinearity i.e. option C.
Definition:
a) Homoscedasticity: Homoscedasticity, also known as homogeneity of variances, is the presumption that variations in various groups being compared are equivalent or comparable.
b) Linearity: A mathematical relationship (function) that can be graphically represented as a straight line is said to be linear. Proportionality and linearity are closely linked concepts.
c) Multicollinearity: Multiple independent variables in a model that are correlating from a statistical concept known as multicollinearity.
d) Adjusted Coefficient of Determination: The number of variables in a data collection is taken into account when calculating the adjusted coefficient of determination (also known as adjusted R-squared). Additionally, it penalizes you for any points that deviate from the model.
Hence, the required choice is Option C.
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va 15 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 10 feet above the ground?
The foot be moving away from the wall when the top is 10 feet above the ground is 2.4077
How to solve word problems?
It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.
Aloud to yourself, read the issue.Make a Drawing.Ask yourself, "What am I looking for?"List the items that have been provided.Locate the key phrases, then Solve.Verify your work.The ladder against the wall is a right triangle:
x² + y² = 15²
Top slips down => dy/dt = -2 ft/s. When y = 10 ft. dx/dt = ?
1) Take the derivative with respect to time:
2x (dx/dt) + 2y (dy/dt) = 0
2) Substitute y = 10, x =sqrt(69) z =15
2(sqrt(69)) (dx/dt) + 2(10) (-2) = 0
dx/dt = 40/2(sqrt(69))
dx/dt = 20/(sqrt(69))
= 20/8.30
=2.4077
Hence, the foot be moving away from the wall when the top is 10 feet above the ground is 2.4077.
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Answer is below! Answer please!
Answer: 8 phones sold and 24 accessories
What is the value of the expression when a = 3 and b = 5?
3a+b−4
Responses
4
4
7
7
10
10
34
34
Answer: It's ten...please give me brainliest. I'm begging you.
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
a = 3; b = 5
3a + b − 4 =
= 3(3) + 5 - 4
= 9 + 5 - 4
= 14 - 4
= 10
how many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s? (2019 amc 10 b)
The number of sequence of 0s and 1s of length 19 are there that begin with a 0, end with a 0 are 65 .
In the question ,
After any particular 0, the next 0 in sequence must appear exactly 2 or 3 positions down.
In this case, we start at position 1 and end at position 19,
that is , we move a total of 18 positions down the line.
So , we must add the series of 2s and 3s to get 18.
There are several number of ways to do this:
Case 1: nine 2s - there is only 1 way to arrange them.
Case 2: two 3s and six 2s - there are ⁸C₂ ways = 28 ways
Case 3: four 3s and three 2s - there are ⁷C₄ ways = 35 ways
Case 4: six 3s - there is only 1 way to arrange them.
So , the number of sequences is = 1 + 28 + 35 + 1 = 65 .
Therefore , the total number of sequence is = 65 .
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how do I compare 6.098 and 6.908
6.908 is greater than 6.098 as the second digit from the left is greater.
What is rounding off of numbers?We round off numbers to make them easier to remember and it also keeps its value approximately to the place it has been rounded off.
To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.
Given, are two numbers 6.098 and 6.908.
Now, starting from left both the numbers have the same digit so we can't
differentiate.
The digit after the decimal place to the first number is 0 and on the second it is 9 so definitely, the second number is greater.
∴ 6.098 < 6.908.
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. Review the equation 0.10(m + 1000) = 3000 + 3000 Select the appropriate column to identify the reasoning that would justify each step in solving for m.
Answer:
Step-by-step explanation: 12
4(4m-3)-1(m-5)=-52
solve for M
Answer:
m = -3
Step-by-step explanation:
4(4m - 3) - 1(m - 5) = -52
Distribute both expressions (don't forget that the 1 is -1, so distribute -1.)
16m - 12 - m + 5 = -52
Add like terms
15m - 7 = -52
Add 7 on both sides
15m = -45
Divide by 15 on both sides
m = -3
it as been suggested that 4% of all cars on the freeway are going over 70 mph. if 4 cars are checked what is the probability that at lest 1 is going over 70 mph
It has been suggested that 4% of all cars on the freeway are going 70 mph. If 4 cars are examined, the probability that at least 1 is going 70 miles per hour is 0.151.
A probability is a numerical representation of the likelihood or possibility that a particular event will occur. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Here, it is said that 4% of all vehicles on the roadway are going more than 70 mph.
P(speed excess of 70 mph) = 0.04. Radar is used to determine the speeds of four random cars. Then, n = 4. Then, X = the number of cars going over 70 mph.
Then, the probability that at least one car is going over 70 mph
= P(x = 1, 2, 3, 4)
= 1 - P(x = 0)
= [tex]1 - 4_{C}_{0} (0.04)^{0} (1 - 0.04)^{4-0}[/tex]
= 1 - 0.849
= 0.151
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parker travels the country speaking to college students about the importance of staying in school. he analyzes sophomores in particular. what do college sophomores represent?
The college sophomores analysed by Parker represent demographics.
Demographics is defined as the statistics concerned with characteristics and population of any particular group. Inspecting the question, we see the Parker travels multiple countries focussing on sophomores.
Hence, sophomores are specific population being studied thus representing demographics. They will be represented as statistical data. There are multiple examples of demographics characteristics such as age, religion, gender, ethnicity, disability status, home ownership, income, education, psychiatric diagnosis and many others.
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2. Which equation has a graph perpendicular to the graph of 7x = 14y-8? (1 point)
Oy=-2x - 7
Oy=-=x+4
2
Oy= 2x+1
2
Oy = 2x +9
Answer:
Step-by-step explanation:
the 2nd one
Use point-slope form to write the equation of a line that passes through the point
(-1, 3) with slope-11/6
Answer:
y-3= -11/6(x+1)
Step-by-step explanation:
y-3 = -11/6(x-(-1)
y-3 = -11/6(x+1)
Right triangle... One leg of a right triangle is 4 centimeters longer than the other leg. If the area of the triangle is 6 square centimeters, then what are the lengths of the legs?
Answer:
2 cm and 6 cm
Step-by-step explanation:
x = first leg
y = second leg
y = 4 + x
xy/2 = 6
y = 4 + x
xy = 12
x(4+x) = 12
x²+4x - 12 = 0
(x+6)(x-2) = 0
x = -6 (impossible because a length can’t be negative)
x = 2 cm
y = 2 + 4 = 6 cm
Which expressions are equivalent to -5x - 15 + 25x - 30? Choose ALL that apply. −5(2 − 3+52 – 6) −5(2 – 5x + 9) −5(2+3 – 5x – 6) -5(6x - 9) -5(-4x+9) −5(2+3–52+6)
The correct expression that is equivalent to the algebraic expression -5x - 15 + 25x - 30 is -5(-4x + 9).
How to determine the equivalent expressionWe shall simplify the given algebraic expression by carrying out basic mathematics operations as follows;
Given: -5x - 15 + 25x - 30
we group like terms together
25x - 5x - 15 - 30
20x - 45
the number 5 is a common factor of 20x and 45, so we have that;
5 × 4x - 5 × 9
by factoring out 5
5(4x - 9)
also;
5(4x - 9) = -5(-4x + 9)
Therefore, -5(-4x + 9) is an equivalent expression to the algebraic expression -5x - 15 + 25x - 30
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write the equation for the parabola that has its x-intercepts at (-2, 0) and (4, 0) and its y-intercept at (0, 4).
The equation for the parabola is y = (5/3)(x + 2)(x - 1.2)
What is equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about mathematical equations.
How do we solve equations?Remove parentheses from each side of the equation and combine similar terms to make it simpler.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
y = A [x - (-2)] (x - 1.2)
y = A(x + 2)(x - 1.2)
At the y-intercept,
-4 = A(0 + 2)(0 - 1.2)
-4 = -2.4A
A = 4/2.4 = 5/3
y = (5/3)(x + 2)(x - 1.2)
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9. identify two different conditions under which the regression line should not be used to make predictions.
Extrapolation is the process of making predictions outside the range of numbers by using the regression line.
Explain the term regression line?The assessment of the line that depicts the actual, but unidentified, linear correlation is called a regression line. When the values of the explanatory variable is known, the regression line's equation is applied to predict (as well as estimate) the quantity of the response variable.The linear regression model is predicated on the following premises: Linearity: X and also the mean of Y have a straight line connection. Homoscedasticity: For every value of X, the variance of the residual is the same. Independent of one another: Observations are separate from one another.Extrapolation refers to using the regression line to produce predictions outside of the data's range.
Thus,despite the correlation maybe having a linear shape within the range being observed, this method can be risky because it's possible that it wouldn't hold true over a wider range.
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which technique is likely to discover a value that is 10x larger than the next highest value in a dataset of 500,000 records? group of answer choices basic statistical tests. visual inspection. advanced testing techniques. auditing a sample.
The correct option is (a). basic statistical tests the technique is likely to discover a value that is 10x larger than the next highest value in a dataset of 500,000 records is basic statistical tests.
Statistical assessments are utilized in speculation trying out. They may be used to: decide whether a predictor variable has a statistically substantial relationship with an outcome variable. estimate the distinction between or more groups.
Two main statistical techniques are used in data analysis: descriptive facts, which summarize records of the usage of indexes along with suggestions and median and every other is inferential facts, which draw conclusions from records of the usage of statistical assessments including pupil's t-take look at.
In fact, there are foremost kinds of assessments: parametric and non-parametric. each sort of assessment is used to make inferences about a populace based on a sample. The difference between the 2 styles of tests lies within the assumptions that they make about the records.
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Please find x and y! And explain!
Answer:
x = 10
y = 15
Step-by-step explanation:
Start with y.
The smaller triangle has a right angle and two congruent legs.
Since the legs are congruent, then the opposite angles are also congruent.
The measures of the 3 angles of the right triangle are:
3y, 3y, 90
The sum of the measures of the angles of a triangle is 180°.
3y + 3y + 90 = 180
6y + 90 = 180
6y = 90
y = 15
The larger triangle has 2 congruent sides. The opposite angles are congruent. Each of the congruent angles measures 2x + 3y. The angle above measures 50°.
2x + 3y + 2x + 3y + 50 = 180
4x + 6y + 50 = 180
4x + 6y = 130
We know from above that y = 15.
4x + 6(15) = 130
4x + 90 = 130
4x = 40
x = 10
h(x) =(√x + 1)(√x - 3)
A researcher developing a regression equation to predict income in thousands of dollars from age (A) and educational status (%) found a significant interaction between age and educational status (X). Educational status is a dummy variable with 0 = high school or less and 1 = some education beyond high school Given the equation = 14.2 + 0.5 1 + 1.7X2 + 0.1X3 + e, what is the predicted income for a 43-year- old who left school after the 10th grade? $35,700 $37.400 $34,000 $35,800
The predicted income for a 43-year- old who left school after the 10th grade is in option (A) i.e. $35,700.
Given that:
Educational status is a dummy variable with 0 = high school or less and 1 = some education beyond high school
Regression equation = 14.2 + 0.5 X1 + 1.7X2 + 0.1X3 + e
X1 => Age; X3→ (0 if high school or less and 1 if some education beyond high school)
X2 => (X2 * X3)→ (0 if high school or less and X1 if some education beyond high school)
Given: X1 = 43, X2 and X3 = 0
Putting these values in the below equation.
y = 14.2 + 0.5 X1 + 1.7X2 + 0.1X3 + e
y = 14.2 + (0.5 x 43) + 1.7 x 0 + .1 x 0 + e
y = 14.2 + (0.5 x 43) + 0 + 0 + e
y = 14.2 + 21.5 + e
y = 35.7 + e
The value of e can be neglected as it is a constant value.
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There are 16 squares and 4 circles. What is the simplest ratio of circles to total shapes?
Answer: 4:1
Step-by-step explanation:
We know that there are 16 squares in 4 circles, so the ratio is 16:4 and we can simplify this ratio by dividing by 4 which equal 4:1
If you can please give me a Brainliest, I only need 3 more to become an Ace, thank you!
a cylinder with open top with radius r and height h has surface area 8 cm2 . find the largest possible volume of such a cylinder.
If the surface area of the cylinder is 8cm , then the largest possible volume of such cylinder is (16/3)√(2/3π) cubic units .
In the question ,
it is given that ,
the cylinder is an open top ,
given that surface area = 8cm² ,
So , the surface area is = 2πrh + πr²,
8 = 2πrh + πr²
So , h = (8 - πr²)/2πr ,
the volume of the cylinder is (V) = πr²h ,
Substituting the value of h ,
we get ,
V = (8r - πr³)/2,
to find the largest volume , we differentiate it with respect to "r" and equate to 0 ,
we get ,
(8r - πr³)/2 = 0
On Simplifying we get ,
r = √(8/3π) ,
the volume is maximum when r = √(8/3π) ,
So , Volume is = ( 8(√8/3π) - π√(8/3π)³)/2
V = 4(√(8/3π)) - (4/3)(√(8/3π))
V = (8/3)√(8/3π)
V = (16/3)√(2/3π) cubic units .
Therefore , the maximum volume is (16/3)√(2/3π) cubic units .
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At the beginning of 1st grade, Steve is initially able to spell 10 words. He is planning to learn 3 new words each week. How many weeks will it take him to
learn to spell a minimum of 46 words?
Answer:
15 weeks.........
Step-by-step explanation:
3×15=45
can somone please help me with this i kmnow its alot but im begging you
Answer: The answers to the first page
Step-by-step explanation:
Question 1
Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.
6
−48
>x
Divide −48 by 6 to get −8.
−8>x
Swap sides so that all variable terms are on the left-hand side. This changes the sign direction.
x<−8
Question 2
−3x+8>11
Subtract 8 from both sides.
−3x>11−8
Subtract 8 from 11 to get 3.
−3x>3
Divide both sides by −3. Since −3 is negative, the inequality direction is changed.
x<
−3
3
Divide 3 by −3 to get −1.
x<−1
Question 3
15x+60>240
Subtract 60 from both sides.
15x>240−60
Subtract 60 from 240 to get 180.
15x>180
Divide both sides by 15. Since 15 is positive, the inequality direction remains the same.
x>
15
180
Divide 180 by 15 to get 12.
x>12
Question 4
3rd answer choice
Question 5
First, let's calculate how many miles he has left.
80 - 14 = 66
Now, to figure out how many miles a day in 6 days, divide.
66/6 = 11
Xavier should bike 11 miles on each of the 6 remaining days.