Answer:
(a) How many are there to select 2 pairs of gloves?
10 ways
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
130 ways
Step-by-step explanation:
We solve the above questions using Combination
Combination = C(n, r) = nCr
= n!/n! ×(n - r)!
(a) How many are there to select 2 pairs of gloves?
We have 5 pairs of gloves. Therefore, the number of ways to select 2 gloves =5C2
= 5!/2! × (5 - 2)!
= 5!/2! × 3!
= 5 × 4 × 3 × 2 × 1/(2 × 1) × (3 × 2 × 1)!
= 10 ways.
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
We are told to select 4 gloves out of the 10 gloves = 10C4
We have 5 pairs, we need to make sure that two out of the selected 4 make a pair = 5 × 2⁴
= 80
Hence,
10C4 - 5C4
= [10!/4! × (10 - 4)!] - 80
= 210 - 80
= 130 ways
5/1-6i = (simplified)
Answer:
5/37+30/37*i
Step-by-step explanation:
we multiply by 1+6i
so 5*(1+6i)/(1^1-36i^2)=(5+30i)/37=
5/37+30/37*i
Prove that if four numbers are chosen from the set {l, 2, 3, 4.5.6}, at least one pair of the selected numbers must add up to 7
Answer:
Step-by-step explanation:
GIven that:
The set is : {l, 2, 3, 4.5.6}
To Prove that:
If four numbers are to be chosen , at least one pair of the selected numbers must add up to 7
From the data set given, this set has three pairs of number which can add up to 7. These are:
{1, 6} i.e 1 + 6 = 7
{2,5} i.e 2+ 5 = 7
{3,4} i.e 3 + 4 = 7
So, if four number are chosen from the set that contains six numbers, then that the possibility for such to occur is either by selecting two pairs out of the three pairs or one pair and two numbers.
Thus, in both cases, at least one pair of the selected numbers must add up to 7.
I need help on how to do this!!!?
Let's say you had a cake that is cut into 5 equal slices. Then someone eats 2 of those slices. They ate 2/5 of the cake.
Now let's say you have another cake that you cut into 10 equal slices. If someone eats 4 of those ten, then they have eaten 4/10 = 2/5 of the cake.
Check out the diagram below to see a visual of how 4/10 and 2/5 are equivalent fractions.
Going from 2/5 to 4/10 has us multiply top and bottom by 2.
-----------
Similarly, 1/2 = 5/10 after multiplying top and bottom by 10
The original expression 2/5 + 1/2 turns into 4/10 + 5/10
Then you add the numerators to get 4+5 = 9, placing that over the common denominator of 10
Answer: 9/10Interpret the regression coefficients. Fill in the blanks below.
The [a. coefficient of determination b. correlation coefficient intercept
slope coefficient] is the estimated amount of a purchase if time spent viewing the online catalog were zero. The a. intercept b. coefficient of determination
c. slope coefficient d. correlation coefficient] is the estimate of amount that a purchase changes for one extra minute spent viewing the online catalog.
b. Compute the coefficient of determination and interpret its meaning. Fill in the blanks below.
The [a. proportion b. amount] of the total variation in purchases that can be explained by variation in the minutes spent viewing the? on-line catalog is equal to the coefficient of? determination, which is ____. (Round to three decimal places as needed)
State the conclusion. Fill in the blanks below. [a. Do not Reject b. Reject] the null hypothesis. There is [a. sufficient b. insufficient] evidence to support the claim that the overall model is significant.
The p-value is ____. (Round to three decimal places as needed.)
State the conclusion. Fill in the blanks below.
a.Do not Reject b. Reject c. the null hypothesis. There is a. sufficient b. insufficient
evidence to support the claim that the overall model is significant.
Determine the p-value.
The p-value is ____. (Round to three decimal places as needed.)
State the conclusion. Fill in the blanks below.
[a. Reject b. Do not Reject] the null hypothesis. There is [a. insufficient b. sufficient]
evidence to support the claim that the regression slope coefficient is not equal to zero.
Answer:
With the information given in the question, the blank spaces are filled thus:
Step-by-step explanation:
1. The intercept is the estimated amount of a purchase, if time spent viewing the online catalog was zero minutes.
2. The slope coefficient is the estimate of amount that a purchase charges/changes, for one extra minute spent viewing the online catalog.
3. The proportion of total variation in purchases that can be explained by variation in the minutes spent viewing an online catalog is equal to the coefficient of determination.
4. The p-value is the probability value
5. Reject the null hypothesis if there is sufficient evidence to support the claim that the regression slope coefficient is not equal to zero.
NOTE: In the case of number 5, the assumption is that;
Null Hypothesis: The regression slope coefficient = 0
Alternative Hypothesis: The regression slope coefficient ≠ 0
Other answers require numerical information and full data, in order to be computed or calculated.
Question 2
A square room of side length x is made 5 m longer (its width stays the same). What is the new area
of the room?
Answer:
To find the width, multiply the length that you have been given by 2, and subtract the result from the perimeter. You now have the total length for the remaining 2 sides. This number divided by 2 is the width.
Step-by-step explanation:
The area of any quadrilateral can be determined by multiplying the length of its base by its height. Since we know the shape here is square, we know that all sides are of equal length. From this we can work backwards by taking the square root of the area to find the length of one side. hope this helps you :)
Each gallon of gas costs $3.50. Sheridan spent $42.00 on gas. Which value of x represents the number of gallons of gas that Sheridan has purchased?
Answer:
12
Step-by-step explanation:
$42.00/($3.50 per gallon) = 12 gallons
Select the correct answer.
Given
D = {xIx is a whole number}
E = {xl x is a perfect square between 49 and 100}
F={xl x is an even number between 10 and 20}
The expression Du F means...
The expression DNF means
The expression Dn E means
The expression E N F means
The expression Dn (EU F) means
Answer:
Step-by-step explanation:
D = {x | x is a whole number}
D = {0, 1, 2, 3, 4,......}
E = {x | x is a perfect square between 49 and 100}
E = {64, 81}
F = {x | x is an even number between 10 and 20}
F = {12, 14, 16, 18}
D∪F = {x | x is whole number}
D∩F = {x | x is an even number between 10 and 20}
D∩E = {x | x is a perfect square between 49 and 100}
E∩F = {null set}
D∩(E∪F) = {12, 14, 16, 18, 64, 81}
A website reports that 70% of its users are from outside a certain country, and 60% of its users logon the website every day. Suppose that for its users from inside the country, that 80% of them log onevery day. What is the probability that a person is from the country given that he logs on the websiteevery day? Has the probability that he is from the country increased or decreased with the additionalinformation?
Answer:
The value is [tex]P (I | L ) = 0.63[/tex]
The probability has increased
Step-by-step explanation:
From the question we are told that
The percentage that are from outside the country is [tex]P(O) = 0.70[/tex]
The percentage that logs on everyday is [tex]P(L) = 0.60[/tex]
The percentage that logs on everyday that are from the inside the country is [tex]P(L | I) = 0.80[/tex]
Generally using Bayes' Rule the probability that a person is from the country given that he logs on the website every day is mathematically represented as
[tex]P (I | L ) = \frac{P(I)* P(L|I)}{ P(O) *P(L|O) + P(I) *P(L|I) }[/tex]
Where [tex]P(I)[/tex] is the percentage that are from inside that country which is mathematically represented as
[tex]P(I) = 1 - P(O)[/tex]
[tex]P(I) = 1 - 0.70[/tex]
[tex]P(I) = 0.30[/tex]
And [tex]P(L| O)[/tex] is percentage that logs on everyday that are from the outside the country which is evaluated as
[tex]P(L| O) = 1- P(L| I)[/tex]
[tex]P(L| O) = 1- 0.80[/tex]
[tex]P(L| O) = 0.20[/tex]
[tex]P (I | L ) = \frac{ 0.3* 0.80 }{ 0.7 *0.20 + 0.3 * 0.8 }[/tex]
[tex]P (I | L ) = 0.63[/tex]
Given that the percentage that are from inside that country is [tex]P(I) = 0.30[/tex]
and that the probability that a person is from the country given that he logs on the website every day is [tex]P (I | L ) = 0.63[/tex]
We see that the additional information increased the probability
A function f, defined on the set of positive integers, has f(1) = 2 and f(2) = 3. Also f(f(f(n))) = n + 2 if n is even and f(f(f(n))) = n + 4 if n is odd. What is f(777)?
pls answer, I'm really confused
Answer:
f(777) = 390
Step-by-step explanation:
f(1) = 2 . . . . given
f(2) = f(f(1)) = 3 . . . . given
f(3) = f(f(f(1))) = 1+4 = 5
f(5) = f(f(3)) = f(f(f(2))) = 2+2 = 4
f(4) = f(f(5)) = f(f(f(3))) = 3+4 = 7
f(7) = f(f(4)) = f(f(f(5))) = 5+4 = 9
Then the sequence of sequential function values is ...
2, 3, 5, 4, 7, 9, 6, 11, 13, ... (pattern repeats in groups of 3)
__
Each odd number of the form 4n+1 is the function value f(4n-1) = 4n+1.
Similarly, the next function value is f(4n+1) = (4n+1+3)/2.
Since 777 is 4(194) +1, we have ...
f(777) = (777+3)/2
f(777) = 390
The price of gas started out at 100¢/gallon on the 1st of the month. Every day since then, it has gone up 2¢/gallon. My car takes 10 gallons of gas. (As you might have guessed, these numbers are all fictional.) Let d equal the date (so the 1st of the month is 1, and so on). Let g equal the price of a gallon of gas, in cents. Let c equal the total price required to ll up my car, in cents.
a. Write a function g (d) that gives the price of gas on any given day of the month. ______________
b. Write a function c (g) that tells how much money it takes to ll up my car, as a function of the price of a gallon of gas. ______________
c. Write a composite function c (g (d)) that gives the cost of filling up my car on any given day of the month.
d. How much money does it take to ll up my car on the 11th of the month? First, translate this question into function notation then solve it for a number.
e. On what day does it cost 1,040¢ (otherwise known as $10.40) to ll up my car? First, translate this question into function notation then solve it for a number.
Answer:
Explained below.
Step-by-step explanation:
At the start of every month the price of gas started out at 100¢/gallon.
Then every day since, it has gone up 2¢/gallon.
The variables are denoted as follows:
d = the date
g = price of a gallon of gas
c = total price required to fill up my car, in cents.
(a)
The function that gives the price of gas on any given day of the month is:
g (d) = 100 + 2(d - 1)
The (d - 1) represent the number of times the price has gone up by 2¢/gallon.
(b)
The function that tells how much money it takes to fill up my car, as a function of the price of a gallon of gas is:
c (g) = 10 × g
Since the car takes 10 gallons of gas.
(c)
The composite function that gives the cost of filling up my car on any given day of the month is:
c (g (d)) = 10 × g (d)
= 10 [100 + 2(d - 1)]
c (g (d)) = 1000 + 20 (d - 1)
(d)
On the 11th day the price of gas has increased by 2¢/gallon for the past 10 days.
Compute the total price it takes to fill up my car on the 11th of the month as follows:
c (g (d)) = 1000 + 20 (d - 1)
c (g (11)) = 1000 + 20 (11 - 1)
= 1000 + (20 × 20)
= 1000 + 400
= 1400¢
Thus, the it takes to fill up my car on the 11th of the month is 1400¢.
(e)
The total price to fill the car on the nth day is 1040¢.
Compute the value of n as follows:
c (g (d)) = 1000 + 20 (d - 1)
1040 = 1000 + 20 (n - 1)
1040 - 1000 = 20 (n - 1)
40 = 20 (n - 1)
(n - 1) = 2
n = 3
Thus, the day on which it cost 1,040¢ to fill up the car is the 3rd day.
Which choice is the solution to the inequality below?
x/10>7
O A. X>7
O B. x> 1.43
O c. X>70
D. x < 70
Answer: C. x>70
Step-by-step explanation:
x/10>7
x/10 × 10>7 × 10
x>70
Hope this helps!! :)
Enter the correct value so that each expression is a perfect square trinomial
Answer:
12x
Step-by-step explanation:
This is b/2^2, so basically you take the square root of 36 and multiply that value by 2.
so [tex]\sqrt{36}[/tex] = 6(2)=12
Hope this makes sense!
Step-by-step explanation:
First, let's look at some examples of what a perfect square trinomial looks like. [tex]x^2 + 16x + 64[/tex]
This trinomial is made from:
[tex](x+8)^2[/tex]
So for your second question (x^2 + ___x + 36), we need to work backwards, starting with the last number of the trinomial, 36. Think of two identical numbers that would make 36 if they got multiplied together. Or: √36. Either way, we get 6. So we can put this as a squared binomial.
[tex](x+6)^2[/tex]
Then, we could solve the binomial to get our middle number. (Use FOIL: Multiply the First terms, then Outer terms, then Inner terms, and Last terms)
[tex](x+6)(x+6)[/tex]
[tex]x^2+6x+6x+36\\x^2+12x+36[/tex]
As you can see, our middle number is 12x, and that is what goes into the blank.
Answer: 12x
i will mark brainliest !!!! Which method of solving quadratic equations do you prefer: factoring, completing the square, or quadratic formula? Why? Your response should be 3-5 sentences long and show that you’ve thought about the topic/question at hand. Please be aware we are looking for YOUR PERSONAL OPINION and there is not a single “correct answer.”
I prefer solving quadratic equations with the quadratic formula. The formula is great for solving any equations like ones that factoring can’t. It is also easy to memorize and type in and check with a calculator.
I always prefer quadratic formula as compared to factoring or completing the square to solve a quadratic equation.
What is a quadratic equation?"A quadratic equation is an algebraic equation of the second degree in 'x'. The quadratic equation in its standard form is ax² + bx + c = 0, where 'a' and 'b' are the coefficients, 'x' is the variable, and 'c' is the constant term."
In order to solve a quadratic equation, I always prefer quadratic formula as compared to the other methods.
In many cases, a quadratic equation can not be converted into a square or into factors.
Therefore, quadratic formula is the only method to solve all type of quadratic equation.
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What is the radius of a circle with a diameter of 9 meters? Enter as a decimal number.
Answer:
4.5 m
Step-by-step explanation:
The diameter is twice the radius
d = 2r
Divide each side by 2
d/2 = r
9/2 = r
4.5 = r
Answer:
4.5 meters
Step-by-step explanation:
radius is half of the diameter
Which digit in 2,385,679 has a value that is greater than 10 times the value of the first digit to its right?
A-8
B-5
C-7
D-2
Answer:
Hey there!
8 is the correct answer.
It is 16 times greater than the digit to it's right.
Let me know if this helps :)
One consequence of the popularity of the internet is that it is thoughout to reduce television watching. Suppose that a random sample of 55 individuals who consider themselves to be avid Internet users results in a mean time of 2.10 hours watching television on a weekday.
Required:
Determine the likelihood of obtaining a sample mean of 2.10 hours or less from a population whose mean is presumed to be 2.45 hours.
Complete Question
One consequence of the popularity of the internet is that it is throughout to reduce television watching. Suppose that a random sample of 55 individuals who consider themselves to be avid Internet users results in a mean time of 2.10 hours watching television on a weekday. The standard deviation is [tex]\sigma = 1.93[/tex]
Required:
Determine the likelihood of obtaining a sample mean of 2.10 hours or less from a population whose mean is presumed to be 2.45 hours.
Answer:
The likelihood is [tex]P(X \le 2.10 ) = 0.08931[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 55[/tex]
The population mean is [tex]\mu = 2.45 \ hours[/tex]
The random mean considered [tex]\= x = 2.10 \ hours[/tex]
Generally the standard error of mean is mathematically represented as
[tex]\sigma _{\= x } = \frac{\sigma }{ \sqrt{n} }[/tex]
=> [tex]\sigma _{\= x } = \frac{1.93 }{ \sqrt{55} }[/tex]
=> [tex]\sigma _{\= x } = 0.2602[/tex]
The likelihood of obtaining a sample mean of 2.10 hours or less from a population whose mean is presumed to be 2.45 hours is mathematically represented as
[tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 1 - P( \frac{X - \mu }{\sigma_{\= x }} > \frac{ 2.10 - 2.45}{ 0.2602} )[/tex]
Generally [tex]\frac{X - \mu }{\sigma_{\= x }} = Z(The \ standardized \ value \ of \ X )[/tex]
[tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 1 - P( Z > -1.345 )[/tex]
From the z-table the value of
[tex]P( Z > -1.345 ) = 0.91069[/tex]
So
[tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 1 - 0.91069[/tex]
[tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 0.08931[/tex]
[tex]P(X \le 2.10 ) = 0.08931[/tex]
Steven travel for 10 hours at a constant rate of 53 miles per hour Stephanie traveled the same distance at a constant rate of 48 miles per hour how long did it take Stephanie to travel the same distance as Steven write your plan to solve in the correct order.
Answer:
11.04hrs
Step-by-step explanation:
Since Steven traveled 530 miles (number of hrs times mph) we would just divide 530 and 48 which is 11.04 hrs
can someone please help??
Answer:
look it up on brainly then you'll get it
Step-by-step explanation:
yes you really will
A particle is moving on the x-axis. Its position is given by x = 2t^2 - 12t + 4 for times t ≥ 0
Answer:
a) - 10 m/s
b) 10 m/s
c) - 10 m/s²
Step-by-step explanation:
Given, a particle moving on the x-axis. Its position is:
x = 2t^2 - 12t + 4, t ≥ 0Let's assume unit of x is m.
For t= 0,
x = 0 - 0 + 4 = 4 mFor t = 1,
x = 2*1^2 - 12*1 + 4 = 2 - 12 + 4 = - 6 ma) Velocity at time t=1
Velocity = displacement/time = (-6- 4)/1 = - 10 m/s as it moves to the left
b) Speed at time t = 1
Speed = distance/time = (4 + |6|)/1 = 10 m/s
c) Acceleration at t = 1
Acceleration is rate of change of velocity.
It took 1 sec to change velocity from 0 to - 10 m/s
So acceleration is:
-10 m/s / 1 s = -10 m/s²SUPER HARD QUESTION (I POSTED THE DIAGRAM) In the diagram of.....
Answer:
A
Step-by-step explanation:
Since m∠JOK is 1/5th of the measure of the full circle (we know this because 72° is 1/5th of 360° and 360° is the measure of the whole circle), we know that the measure of minor arc JK will be 1/5th of the circumference of the circle. C = 2πr and we know that r = 5 so the circumference is 10π. 1/5th of that is 2π.
zach invested $50 and was able to triple his money in two years. Kayla also began with in investments, and was able to cube her money in two years. Who had more money after two years? Explain
Please help:
A holiday punch recipe calls for 1,500 mL of fruit punch, 375 mL of pineapple juice, and 1 L of ginger ale. How many liters (L) of punch will this recipe yield if doubled?
Answer:
5.75 L
Step-by-step explanation:
2(1500mL + 375mL + 1L)
=2(1875mL + 1L)
=2(1.875L + 1L)
=2(2.875)
=5.75
The recipe will yield 5.75 liters (L) of punch when doubled.
To find the total volume of punch that the recipe will yield if doubled, we need to add the amounts of each ingredient and then multiply by 2.
Original recipe:
Fruit punch: 1,500 mL
Pineapple juice: 375 mL
Ginger ale: 1,000 mL (since 1 L = 1,000 mL)
Total volume of punch in the original recipe:
= 1,500 mL + 375 mL + 1,000 mL
= 2,875 mL
Now, if we double the recipe, we need to multiply the total volume by 2:
Total volume of punch when doubled = 2×2,875 mL
= 5,750 mL
To convert this to liters (L), we divide by 1,000 since 1 liter is equal to 1,000 mL:
Total volume of punch when doubled = 5,750 mL / 1,000
= 5.75 L
Hence, the recipe will yield 5.75 liters (L) of punch when doubled.
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in the state of Texas, about 3/100 of the population lives in the city Fort Wroth. the population of Huston, Texas, is about 3 times the population of Fort Worth, Texas. What fraction of the population of Texas lives in Huston?
Answer:
population of Fort Worth, Texas. =9/100(x)
Step-by-step explanation:
in the state of Texas, about 3/100 of the population lives in the city Fort Wroth.
Let the population of the state of texas = X
Fort wroth population= 3/100(x)
the population of Huston, Texas, is about 3 times the population of Fort Worth, Texas. = 3*(3/100(x))
the population of Huston, Texas, is about 3 times the population of Fort Worth, Texas. =9/100(x)
The fraction of the population of Texas that lives in Huston is 9/100x.
Let the population of Texas be represented by x.
Since the state of Texas is about 3/100 of the population lives in the city Fort Wroth and the population of Huston, Texas, is about 3 times the population of Fort Worth, Texas, then the fraction of the population of Texas lives in Huston will be:
= 3/100 × 3 × x
= 9/100 × x
The fraction of the population of Texas that lives in Huston is 9/100x.
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Which of the following is the solution to 4/5 = 20/(x-5)?
Answer:
x=30
Step-by-step explanation:
[tex]\frac{4}{5}=\frac{20}{x-5} \\\\4(x-5)=20*5\\\\4x-20=20(5)\\\\4x=20(5)+20(1)\\\\4x=20(5+1)\\\\4x=20(6)\\\\x=\frac{20(6)}{4} \\\\x=5*6\\\\x=30[/tex]
[tex] \frac{4}{5} = \frac{20}{(x - 5)} [/tex]
By Cross-multiplication
[tex] \implies4 \times (x - 5) = 20 \times 5[/tex]
[tex] \implies4x - 20 = 100[/tex]
[tex] \implies4x = 100 + 20[/tex]
[tex] \implies4x = 120[/tex]
[tex] \implies \: x = \cancel \frac{120}{4} [/tex]
[tex] \implies \: x = 30[/tex]
Simplify the expression 2(-2x+4-5-3)
Answer:2 (-2x + 4 - 5 - 3)
2(-2x -4)
-4x - 8
Solve for j - 1/3 = j/4 - 10/3
The value of j is equal to -4
What are like and unlike terms in an expression?In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.
Given here: j - 1/3 = j/4 - 10/3
j-j/4 = -10/3+1/3
j = -3/0.75
j=-4
Hence, The value of j is equal to -4
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Which of the following is equivalent to -21(6 - 71)?
a (0 – 21(6-71)
b (0 + 206 - 71)
c (-2 + 1)(6 – 71)
d (6-21) – (71-21)
Answer:
a
Step-by-step explanation:
-21(-65)
= - 86
A
(0-21(6-71)
(-21-65)=-86
Bob and Laquisha have volunteered to serve on the Junior Prom Committee. The names of twenty volunteers,
including Bob and Laquisha, are put into a bowl. If two names are randomly drawn from the bowl without
replacement, what is the probability that Bob's name will be drawn first and Laquisha's name will be drawn
second?
Answer:
1/380
Step-by-step explanation:
Probability of Bob's name drawn first is:
1/20 as there are 20 people with equal chanceAnd probability of Laquisha's name drawn second is:
1/19 as there are 19 people left with equal chanceProbability of the two events happening is:
1/20*1/19 = 1/380 product of individual probabilitiesAnswer:
Hey there!
1/19 (1/20)=1/380, so the probability is 1/380
Let me know if this helps :)
What is the sum of the measure of the inner angle of a 13 sided polygon? A. 2340° B. 1300° C. 2700° D. 1980°
Hi there! :)
Answer:
D. 1980°
Find the sum of the measure of a 13-sided polygon using the formula:
Sum = 180(n-2), where n = number of sides
Therefore:
S = 180(13 - 2)
S = 180(11)
S = 1980°
How long will it take you to drive 135 miles at a speed of 45 miles per hour?