Does the equation 3x-6y=0 represent a direct variation? *

Answer:

0.3711 = 37.11% probability that 5 or more of the 100 people will get the flu

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they will develop the flu after getting the shot, or they will not. The probability of a person developing the flu after getting the shot is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that a person will develop the flu after getting a flu shot is 0.04.

This means that [tex]p = 0.04[/tex]

Random sample of 100 people:

This means that [tex]n = 100[/tex]

What is the probability that 5 or more of the 100 people will get the flu?

This is:

[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]

In which

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{100,0}.(0.04)^{0}.(0.96)^{100} = 0.0169[/tex]

[tex]P(X = 1) = C_{100,1}.(0.04)^{1}.(0.96)^{99} = 0.0703[/tex]

[tex]P(X = 2) = C_{100,2}.(0.04)^{2}.(0.96)^{98} = 0.1450[/tex]

[tex]P(X = 3) = C_{100,3}.(0.04)^{3}.(0.96)^{97} = 0.1973[/tex]

[tex]P(X = 4) = C_{100,4}.(0.04)^{4}.(0.96)^{96} = 0.1994[/tex]

Then

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0169 + 0.0703 + 0.1450 + 0.1973 + 0.1994 = 0.6289[/tex]

[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.6289 = 0.3711[/tex]

0.3711 = 37.11% probability that 5 or more of the 100 people will get the flu

Answer:

a) [tex]P(Adult)=\frac{73}{249}=0.2932=29.32%[/tex]

b) [tex]P(Chocolate)=\frac{91}{249}=0.3655=36.55%[/tex]

c) [tex]P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%[/tex]

d) [tex]P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%[/tex]

e) [tex]P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%[/tex]

f) [tex]P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%[/tex]

Step-by-step explanation:

a)

In order to solve part a of the problem, we need to find the number of adults in the survey and divide them into the number of people in the survey by using the following formula>

[tex]P=\frac{desired}{possible}[/tex]

In this case we have a total of 17+43+13 adults which gives us 73 adults and a total of 249 people surveyed so we get:

[tex]P(Adults)=\frac{73}{249}=0.2932=29.32%[/tex]

b)

The same principle works for part b

there are: 40+34+17=91 people who likes chocolate ice cream the best so the probability is:

[tex]P(Chocolate)=\frac{91}{249}=0.3655=36.55%[/tex]

c)

when it comes to the or statement, we can use the following formula:

P(A or B) = P(A) + P(B) - P( A and B)

In this case:

[tex]P(Adult)=\frac{73}{249}[/tex]

[tex]P(Vanilla)=\frac{10+10+43}{249}=\frac{63}{249}[/tex]

[tex]P(AdultandVanilla)=\frac{43}{249}[/tex]

so:

[tex]P(AdultorVanilla)=\frac{73}{249}+\frac{63}{249}-\frac{43}{249}[/tex]

[tex]P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%[/tex]

d)

Is a child and likes vanilla the best.

In the table we can see that 10 children like vanilla so the probability is:

[tex]P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%[/tex]

e)

Likes strawberry the best, GIVEN that the person is a child.

In this case we can make use of the following formula:

[tex]P(B/A)=\frac{P(AandB)}{P(A)}[/tex]

so we can get the desired probabilities. First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:

[tex]P(childrenandstrawberry)=\frac{44}{249}[/tex]

Then, we know there are 40+10+44=94 children, so the probability for the person being a child is:

[tex]P(Child)=\frac{94}{249}[/tex]

Therefore:

[tex]P(Strawberry/Child)=\frac{\frac{44}{249}}{\frac{94}{249}}[/tex]

[tex]P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%[/tex]

f)

The same works for the probability of the person being a child given that the person likes strawberry the best.

First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:

[tex]P(childrenandstrawberry)=\frac{44}{249}[/tex]

Then, we know there are 44+38+13 persons like strawberry, so the probability for the person liking strawberry is:

[tex]P(Child)=\frac{95}{249}[/tex]

Therefore:

[tex]P(Child/Strawberry)=\frac{\frac{44}{249}}{\frac{95}{249}}[/tex]

[tex]P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%[/tex]

Answer:

227.5

Step-by-step explanation:

basically for a triangle prism you would do is

(1÷2) since it's a triangle and multiple all 3 angels

ex: 1/2 × 5 × 7 × 13

Answer:

227.5 cubic yards

Step-by-step explanation:

Formula for area of triangular prism is:

1/2 • length x height x width

Use formula with the given dimensions:

1/2 • 7 • 5 • 13 = 227.5

Answer:

The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.

Step-by-step explanation:

The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was $13,252. Test if the mean cost has increased.

At the null hypothesis, we test if the mean cost is still the same, that is:

[tex]H_0: \mu = 13252[/tex]

At the alternative hypothesis, we test if the mean cost has increased, that is:

[tex]H_1: \mu > 13252[/tex]

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

13252 is tested at the null hypothesis:

This means that [tex]\mu = 13252[/tex]

The following year, a random sample of 20 two-year institutions had a mean of $15,560 and a standard deviation of $3500.

This means that [tex]n = 20, X = 15560, s = 3500[/tex]

Value of the test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{15560 - 13252}{\frac{3500}{\sqrt{20}}}[/tex]

[tex]t = 2.95[/tex]

P-value of the test and decision:

The p-value of the test is found using a t-score calculator, with a right-tailed test, with 20-1 = 19 degrees of freedom and t = 2.95. Thus, the p-value of the test is 0.0041.

The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.

Answer:

41 feet

Step-by-step explanation:

12 +12 + [tex]\sqrt{144+144}[/tex]

Answer:

Perfilar. Comienza por delimitar la forma y dimensión del macizo. ...

Cavar y abonar. ...

Enmarcar y rastrillar. ...

Distribuir y plantar.

Step-by-step explanation:

Answer:

24 .30ms is the answer I think so if the answer is correct plz mark me as brainliest.

The papaya's speed just before it hits the water will be 24.24 m/s.

The rate at which objects moves is called speed. It is given by

[tex]s = \frac{d}{t}[/tex]

An object held above the ground has a potential energy related to the height at which it is held,

PE = mgh

If you drop the object, its potential energy will become the kinetic energy of motion:

KE = ½ mv²

½ mv² = mgh

v  = √(2gh)

v =  √(2*9.8*30)

v =  24.24 m/s

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Answer:

3/2 x^5 y

Step-by-step explanation:

3x^5y^3

----------------

2y^2

Simplify the y terms

y^3 / y^2 = y^(3-2) = y

3/2 x^5 y

Answer:

[tex] \frac{3}{2} x {}^{5} y {}^{} [/tex]

Step-by-step explanation:

it's all in the image

Answer:

Price per bottle is 1.5 or $1.50

Step-by-step explanation:

To get price per unit, you just divide the amount of money spent by the items purchased. 9/6 = 1.5

Given:

Two coins are tossed.

To find:

1. P(H on first coin)?

2. P(H on second coin)?

3. List the paired outcomes for tossing two coins.

4. How many ways are there for two coins to land?

5. What is P(HH)?

Solution:

If a a coin is tossed, then we have to possible outcomes, i.e., heads (H) and tails (T).

It is given that two coins are tossed.

1. The probability of getting a heads on first coin is:

[tex]P(H \text{ on first coin})=\dfrac{1}{2}[/tex]

2. The probability of getting a heads on second coin is:

[tex]P(H \text{ on second coin})=\dfrac{1}{2}[/tex]

3. If two coins are tossed, then the total possible outcomes are:

[tex]\{HH,HT,TH,TT\}[/tex]

4. The number of ways for two coins to land is 4.

5. The probability of the heads on both tosses is:

[tex]P(HH)=\dfrac{1}{4}[/tex]

Therefore, the required solution are:

1. [tex]P(H \text{ on first coin})=\dfrac{1}{2}[/tex]

2. [tex]P(H \text{ on second coin})=\dfrac{1}{2}[/tex]

3. List of possible outcomes is [tex]\{HH,HT,TH,TT\}[/tex].

4. Number of possible outcomes is 4.

5. [tex]P(HH)=\dfrac{1}{4}[/tex]

Answer:

[tex] \large{ \tt{❃ \: S \: O \: L \: U \: T \: I \: O \: N : }}[/tex]

[tex] \large{ \tt{⇢m \: \angle \: GHI= m \: \angle \: GHQ + m \: \angle \: QHI}}[/tex]

[tex] \large{ \tt{➝14x + 6 = 3x - 3 + 130 \degree}}[/tex]

[tex] \large{ \tt{➝14x + 6 = 3x + 127}}[/tex]

[tex] \large{ \tt{➝ \: 14x - 3x = 127 - 6}}[/tex]

[tex] \large{ \tt{➝ \: 11x = 121}}[/tex]

[tex] \large{ \tt{➝ \: x = \frac{121}{11} }}[/tex]

[tex] \large{ \tt{➝ \: x = 11}}[/tex]

[tex] \large{ \tt{✣ \: REPLACING \: VALUE}} : [/tex]

[tex] \large{ \tt{✺ \: m \: \angle \: GHI = 14x + 6 = 14 \times 11 + 6 = \boxed{ \tt{160 \degree}}}}[/tex]

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

35.1

Step-by-step explanation:

45×78/100 that's 100% correct

Answer:

multiplication by -1 will reflect over the x-axis

multiplication by a positive number will "scale" or "stretch" the function

Step-by-step explanation:

Answer:

Domain: [-2,1)

Range: [0,4]

Step-by-step explanation:

The required domain and range of the function graphed are -2 ≤ x < 1 and 0 ≤ y ≤ 4.

Given that,
To determine the domain and range of the function graphed below, in interval notation.

Range, it is the set of the values that come out to an outcome for a certain mathematical operations.

Here,
The projected line of the curve on the horizontal axis is from greater and equal to -2 to less than 1,
Domain = -2 ≤ x < 1
The projected line of the curve on  the vertical axis is from greater or equal to 0 to less than or equal to 4,
Range = 0 ≤ y ≤ 4.

Thus, the required domain and range of the function graphed are -2 ≤ x < 1 and 0 ≤ y ≤ 4.

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Answer:

√3 x^5y

First, let's do √3

√3=1.7

1.7 • x^5 • y

if you want

1.7 • X^4• x• y.

There are tons of equivalent's!

Answer:

15

Hope this helped ^^

2[30          5[45

 3[15           3[9

  5[5             3[3

     [1               [1

    30=2*3*5*1

     45=5*3*3*1    HCF= 3*1=3

hope its helps you

keep smiling be happy stay safe

Answer:

3x-3

Step-by-step explanation:

3x has a variable attach, because no other numbers have a variable attached leave it alone.

2+(-5) are like terms so combine these two. 2+(-5)=-3

now put back in the equation

3x-3

Answer:

d. The sample mean used to build this interval was 170 pounds.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

In this question:

Bounds 160 and 180, so the sample mean used was (160+180)/2 = 170, and thus the correct answer is given by option d.

Answer:

7/13

Step-by-step explanation:

Half the deck is red so there are 26 reds.

There are 4 kings but we already counted two of these in the 26.

So there are 26+2 red or king cards total.

The probability of selecting a king or red is 28/52.

This can be reduced by dividing top and bottom by 4: 7/13.

Answer:

No it is not

Step-by-step explanation:

The median is 84200

The mean is 85300

Low income is 65100

High income is 103400

From this information, we can see a skewed data. The mean would not be a good estimate value. Rather the center (median) would be more appropriate.

When we calculate the middle value for this data

65100+103400 = 168500/2 = 84250

84250 is closer to the median score of 84200. The median is best in the presence of outliers.

Answer:

10^3000

Step-by-step explanation:

1000¹⁰⁰⁰

= (10³)¹⁰⁰⁰

= 10^(3×1000)

= 10³⁰⁰⁰ or 10^3000

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

This is a related rates problem from calculus using implicit differentiation. The main equation is Pythagorean's Theorem. Basically, what we are looking for is [tex]\frac{dx}{dt}[/tex] when y = 6 and [tex]\frac{dy}{dt}=-2[/tex].

The equation for Pythagorean's Theorem is

[tex]x^2+y^2=c^2[/tex] where x and y are the legs and c is the hypotenuse. The length of the hypotenuse is 10, so when we find the derivative of this function with respect to time, and using implicit differentiation, we get:

[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex] and divide everything by 2 to simplify:

[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex]. Looking at that equation, it looks like we need a value for x, y, [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex].

Since we are looking for [tex]\frac{dx}{dt}[/tex], that can be our only unknown and everything else has to have a value. So what do we know?

If we construct a right triangle with 10 as the hypotenuse and use 6 for y, we can solve for x (which is the only unknown we have, actually). Using Pythagorean's Theorem to solve for x:

[tex]x^2+6^2=10^2[/tex] and

[tex]x^2+36=100[/tex] and

[tex]x^2=64[/tex] so

x = 8.

NOW we can fill in the derivative and solve for [tex]\frac{dx}{dt}[/tex].

Remember the derivative is

[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex] so

[tex]8\frac{dx}{dt}+6(-2)=0[/tex] and

[tex]8\frac{dx}{dt}-12=0[/tex] and

[tex]8\frac{dx}{dt}=12[/tex] so

[tex]\frac{dx}{dt}=\frac{12}{8}=\frac{6}{4}=\frac{3}{2}=1.5 m/sec[/tex]

Answer:

Below

Step-by-step explanation:

It is 5 1/4 PERCENT not just 5 1/4.

5 1/4 % = 5.25%

= 5.25/100

= 0.0525.

Answer:

Both the numbers are 8.

Step-by-step explanation:

Let the two numbers are p and 64/p.

The sum is given by

[tex]S = p +\frac{64}{p}\\\\\frac{dS}{dp}= 1 - \frac{64}{p^2}\\\\\frac{dS}{dp}=0\\\\\frac{64}{p^2}=1\\\\p= \pm 8[/tex]

So, the sum is minimum for p = 8 0r - 8, so the two numbers 8.

Answer:

sorry i cannot help you

9514 1404 393

Answer:

  (b)  x -3 ≥ 0

Step-by-step explanation:

The square root function will return non-negative values, so the inequality √(x-3) ≥ 0 gives no new information. What is required is that the argument of the square root function be non-negative:

  x -3 ≥ 0

The first sum is a geometric series:

[tex]1+\dfrac15+\dfrac1{5^2}+\dfrac1{5^3}+\cdots+\dfrac1{5^n}+\cdots=\displaystyle\sum_{n=0}^\infty\frac1{5^n}[/tex]

Recall that for |x| < 1, we have

[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]

Here we have |x| = |1/5| = 1/5 < 1, so the first sum converges to 1/(1 - 1/5) = 5/4.

The second sum is exponential:

[tex]1+5+\dfrac{5^2}{2!}+\dfrac{5^3}{3!}+\cdots+\dfrac{5^n}{n!}+\cdots=\displaystyle\sum_{n=0}^\infty \frac{5^n}{n!}[/tex]

Recall that

[tex]\exp(x)=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}[/tex]

which converges everywhere, so the second sum converges to exp(5) or e⁵.