The least expensive
buttons cost
$0.28 each. Yellow bought all of
the buttons she could for $1.40 and
wore them proudly.

(a) After t years, the height is 18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

So

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

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The probability that an individual attended the course given he passed

is 37.5%.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

We know the probability of A given B is P(A/B) = P(A∩B)/P(B).

Let, The number of students be 100.

Given, Thirty percent of the people who took the exam had attended the university's GRE review course which is  30 and hence 70 people did not attend the review course.

60% of those who attended the review passed the exam,

= (60/100)×30.

= 18 people.

20% who passed the exam did not attend the review course.

= (20/100)×70.

= 14.

So, The no. of people who passed is (18 + 14)/100 = 32/100 = 0.32.

The probability that a student passed and taken the course is (18/30)×(14/70) = 0.12.

Therefore, Given that he passed, the likelihood that someone took the course is = (0.12/0.32) = 0.375 Or 37.5%.

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The SSS congruence theorem is used to prove that triangles MAH and THA are congruent to each other. See proof below.

"SSS" stands for side-side-side congruence theorem, which says that given the criteria that two triangles both have three corresponding sides that are equal or congruent to each other, both triangles are congruent.

The proof below shows how we can apply the SSS to prove that triangles MAH and THA are congruent to each other.

Statement                                 Reason                                            

1. MA ≅ TH                               1. Given

2. MH ≅ AT                              2. Given

3. AH ≅ HA                              3. Reflexive property of congruence

4. ΔMAH ≅ ΔTHA                   4. SSS congruence theorem

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The given statement is a reasonable probability model because it fulfills the 4 conditions of binomial distribution.

The conditions for binomial distribution are;

1: The number of observations n must be fixed.

2: Each observation must be independent.

3: Each observation must represent one of two outcomes ("success" or "failure").

4: The probability of "success" p must be the same for each outcome.

Now, we are given the statement;

Joey buys a Virginia lottery ticket every week. x is the number of times in a year that he wins a prize.

From that statement, we can tell that the number of observations is fixed at 52 weeks since a year is made up of 52 weeks.

Secondly, we can say that there could be success by winning a price or failure by not winning the price.

Each weekly observation is independent.

The probability is the same for each outcome.

Thus, we conclude that since it fulfills all the four conditions then it is a binomial model.

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The percentage error in this situation will be 33%.

It's important to note that Percent error is a way to describe error, expressed as a percentage of the actual amount.

Since Frosty the Snowman thought he could last in a greenhouse for 2 hours before melting but it only took him 1 1/2 hours to melt. The percentage error in this situation will be:

= (2 - 1 1/2) / 1 1/2 × 100

= 1/2 ÷ 1 1/2 × 100

= 1/3 × 100

= 33.33%

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No. The proof is wrong.

Here we are asked to prove all Natural numbers are either even or odd.

Natural numbers start from 1 to infinity.

Hence to prove by mathematical induction, we need to take the base case to be n = 1.

here, 1 = 2X0 + 1, therefore 1 is odd

Then we need to assume that for any integer m < n, m is either even or odd.

Now n > 1

Therefore,

n -1 > 0

Hence n - 1 will be a natural number.

Hence by our earlier assumption where any number smaller than is either even or odd

n - 1 has to be either even or odd.

case 1

here n - 1 is odd

if n - 1 is odd then

n-1  + 1 is a sum of two odd numbers, hence n is even

Case 2- If n - 1 is even

then, n-1  +  1 is a sum of an even and n odd number hence n is odd

Therefore n will either be even or odd.

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Answer:

48 ≤ m ≤ 73

Step-by-step explanation:

Evie has 42, Max has x.

Total candy = x + 42

90 ≤ x+42 ≤ 115

48 ≤ m ≤ 73

Max can have 48 or more, but no more than 73

The probability of selecting the following marbles in order: red - blue - blue - blue will be 3 / 40.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

From the diagram Illustrated, it should be noted that that there are 2 blue balls and 3 red balls. The total number of balls will be 5.

The probability of selecting the following marbles in order: red - blue - blue - blue will be:

= 3/5 × 2/4 × 1/4 × 0/3

= 6 / 80

= 3 / 40

The probability is 3 / 40.

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Frequency is the number of occurrences of a repeating event.

The frequency of an occurrence or a value is the number of times it happens. A frequency table is a list of objects with the frequency of each item shown in the table.

The information that is gathered is called data. The quantity of occurrences of an event or value is referred to as its frequency. A frequency table is a table that lists items and displays how frequently each item happens.

The number of times a specific data value occurs is the frequency of that data. We use f to symbolise the frequency of a data value.

As an illustration, the grade A is said to occur frequently if five students received an A in science.

Here we have the events:

shopping time between occurrences frequency

18 to 22: 20, 18 2

23 to 27: 27, 24, 26, 24, 24 5

28 to 32 29, 31 2

33 to 37 37, 34, 35, 33, 36, 32 6

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The first blank as required to be filled in the task content should be filled with; two.

The second blank as required to be filled in the task content should be filled with; 134.1 in³.

According to the information given; the diameter of the beachball is; 8 inches. Therefore, it's radius is half that; 4 inches.

On this note, the volume of the beachball which is spherical in shape given by the formula;

Volume of a sphere = (4/3)πr³ where;

Radius, r = 4;

Therefore, volume of beachball is;

4/3 π (4)³ = 256π / 3.

Also, the volume of the cone which is given by the formula;

Volume of a cone = (1/3) π r² h

where; Radius, r = 4 and Height, h = 8.

Therefore, volume of the cone is;

(1/3) π (4²) × 8 = 128π / 3.

On this note, by dividing the volume of beachball by that of cone; we have that;

( 256π / 3 ) / ( 128π / 3 ) = 2.

On this note, the cone will fit into the beachball about 2 times.

Also, the volume of the cone given that; π = 22 / 7 can be evaluated as;

( 128 × 22 ) / ( 7 × 3 )

= 134.1 in³.

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Step-by-step explanation:

(-3x⁴)(-4x²)

as multiplication is commutative (that means the sequence of the factors is irrelevant), we get

-3×-4×x⁴×x²

we can combine everything of the same type (constants or variable names).

-3×-4 = 12

remember, -×- = +

x⁴×x² = x⁶

remember, when multiplying terms with the same base variable, we can simply add the exponents.

why ? because an exponent is a short way of saying that the base variable has to be multiplied by itself that many times.

e.g.

a³ = a×a×a

a⁷ = a×a×a×a×a×a×a

a³×a⁷ = a×a×a × a×a×a×a×a×a×a = a¹⁰

that's why.

so, the complete simplified expression is

12x⁶

Answer:

1656

Step-by-step explanation:

Answer: 1656

Step-by-step explanation:

just trust me, that's the answer! I did the same question.

The rate at which the energy pass through an area of 1.0 m² at 2.0 km is equal to 1.97 × 10⁹ J/s.

At a constant power, the intensity of a wave is inversely proportional to the distance from the source. Mathematically, the intensity of a wave with respect to the distance from a source can be modeled (represented) by this mathematical expression;

I ∝ 1/r²

Where:

Next, we would re-write the mathematical expression and then determine the intensity of a wave from source as follows;

I₁/I₂ = r₂²/r₁²

I₁ = I₂(r₂²/r₁²)

Note: We know that its intensity when it passed a point from the source is 2.0 km.

Substituting the given parameters into the formula, we have;

I₁ = 2.8 × 10⁶ × (53²/2²)

I₁ = 1.97 × 10⁹ J/m²s.

Now, we can calculate the rate of the energy by using this formula;

Power = intensity × area

Power = 1.97 × 10⁹ × 1.0

Power = 1.97 × 10⁹ J/s.

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Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map f: X --> X such that f(x) = x- 1 is an example of continuous map is one to one and honto but is not a homemorphism .

A function f: A --> B is said to be bijective or bijection if it satisfies both injective (one-to-one function) and surjective (over-function) properties. Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map

f : X--> X such that f(x) = x- 1 ; x∈X (domain)

Now, we show that it is bijective, so

One to One : let x₁ and x₂ belongs to X such that f(x₁) = f(x₂) we have to show x₁= x₂

f(x₁) = f(x₂) => x₁ - 1 = x₂ - 1

=> x₁ = x₂ -1 + 1

=> x₁ = x₂

So, f(x) is one to one.

Onto : let y be a element of X ( co-domain) We can show that there exists x∈A such that f(x)=y. Choose x= f⁻¹(y) and so f(f⁻¹(y))=y. So for all y∈B, there exists an x∈A such that f(x)=y. Therefore, it is onto. Thus, f(x) is one to one and onto and continus( due to polynomial nature) i.e it is a continuous bijection from X to itself, but it is not a

homeomorphism, since the image of N is not open.

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The number of hours that each student work on the project is 2 hours.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, the equation the quantity x plus 28 end quantity over 5 equals 3 times x models the workload of a class project, where x is the number of hours each student must contribute.

This will be:

(x + 28) /5 = 3x

Cross multiply

x + 28 = 15x

Collect like terms

15x - x = 28

14x = 28

Divide

x = 28 / 14

x = 2

The number of hours is 2 hours.

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Answer: that answer is right ^

Step-by-step explanation:

Answer: -6

Step-by-step explanation: Since 9 is being subtracted from 3, we know that it will be a negative number. So, 9-3 = 6, and a greater number subtracted from a smaller number is a negative number. So, that results in this being -6. I hoped this helped.

[tex]3-9[/tex]

[tex]3+(-9)[/tex]

[tex]=\fbox{-6}[/tex]

[tex]3+(-9)[/tex] on a number line:

Answer:

Below

Step-by-step explanation:

The solution set is the point(s) where the two plotted graphs intersect:

Answer:

15.1

Step-by-step explanation:

Step-by-step explanation:

I don't know if this is valid but

We can think of this problem like

(6^7-6^6+6^5)/31 = x

Where x is a whole number so 6^7-6^6+6^5 is divisible by 31

Multiply each side with 31 :

6^7-6^6+6^5 = 31x

We can turn 6^7 into 6^5 x 6^2

We can also turn 6^6 into 6^5 x 6

So the equation turns into this :

(6^5 x 6^2) - (6^5 x 6) + (6^5 x 1) = 31x

We can factor out the 6^5 out of the left side of the equation, which turns into :

(6^5) x (6^2 - 6 + 1) = 31x

Which is also :

(6^5) x (31) = 31x

Divide each side with 31

6^5 = x

X is obviously a whole number

The relationship between 'h' and 't' when r=20 and rate = 1 rad/min is [tex]h=20sin(t)[/tex] and when r=30 and rate = 2 rad/min is [tex]h=30sin(2t)[/tex]

Given,

The Ferris wheel is rotating at constant angular speed.

"h" represents Alex's height above the center of the Ferris wheel (in feet)

"t" represents the number of minutes since the ride started.

a)

Here, the conditions are

the radius if ferris wheel is, r = 20 feet

and the ferris wheel is rotating at the ratei.e. angular speed, [tex]\omega = 1 rad/min[/tex]

Here, 'h' represents the height of Alex's measured in the y-direction.

As per the given conditions the relationship between 'h' and 't' can be determined by the equation,

[tex]y= rsin\theta[/tex]

Where, [tex]\theta =\omega t[/tex]

here y=h,

then,[tex]h=rsin(\omega t)\\\\h=20sin(t)...i[/tex]

b)

Now, the given conditions are

radius of ferris wheel is ,r = 30 feet

ferris wheel is rotating at ratei.e angular speed , [tex]\omega = 2 rad/min[/tex]

Now, the relationship between h and t becomes ,

[tex]h=30sin(2t)....ii[/tex]

Thus, the graph plots for eq. i and eq.ii are shown in the figure.

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The slope of the linear relationship will be 2.

The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

A linear relationship is given in the table.

Now,

Let two point on the table are (- 1, - 3) and (2, 3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - (-3)) / (2 - (-1))

m = 6 / 3

m = 2

Thus, The slope of the linear relationship = 2.

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Answer: $0.75

Step-by-step explanation:

-We know that the line must also contain the point (0,0), as 0 pounds of potatoes would cost $0. Thus we can find the slope of the line and write an equation:

slope = Δy/Δx = (3-0)/(4-0) = 3/4

y = (3/4)x

(The y-int (aka b) is 0 since the line passes through (0,0))

Plugging in 1 yields $0.75

Answer:

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

Proportional relationship equation:

Given point (4, 3).

Use its coordinates to find the value of k:

This is representing the price of 1 pound of potatoes.

Answer:

Step-by-step explanation:

The 95% confidence interval for this situation is (0.95, 9.71).

What is the Standard deviation?

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

The formula for Confidence Interval for Population Mean When Population Standard deviation is known

[tex]\bar{x} \pm Z_{a/2} * \frac{\sigma}{\sqrt{n} }[/tex]

α for 95% confidence level = (100-95)/100 =0.05

[tex]Z_{\alpha/2}[/tex] = 0.05/2=0.025

[tex]Z_{\alpha/2}[/tex] = Z0.025 = 1.96

σ = 20

95% Confidence Interval for Population Mean When Population Standard deviation is known

[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]

a.

n=70 ; [tex]\overline{x}=27[/tex]

[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]

27 ± 1.96 × (20/√70)

= 27 + 1.96 x 2.3905

= 27 + 4.6853 = (22.31.31.69)

(22.31, 31.69)

b.

n=150 ; [tex]\overline{x}=115[/tex]

[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]

= 115 + 1.96 x

= 115 +1.96 x 1.633 = 115 + 3.2007 = (111.8, 118.2)

(111.8, 118.2)

c.

n=80 ,  [tex]\overline{x}=18[/tex]

[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]

= 18 + 1.96 x 2.2361 = 18 + 4.3827 = (13.62.22.38) V8018+

(13.62, 22.38)

d.

n=80,  [tex]\overline{x}=5.33[/tex]

[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]

= 5.33 1.96 x 2.2361 = 5.33 4.3827 = (0.95, 9.71)

(0.95, 9.71)

e.

No. Since Sample sizes are large [tex](n\small \geq30)[/tex] and randomly selected from the target population, the condition guarantees that the sampling distribution of [tex]\overline{x}[/tex] is approximately normal.

Hence, the 95% confidence interval for this situation is (0.95, 9.71).

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Answer:

2 2/7 - 4 5/7      

= -2 3/7

Step-by-step explanation:

Answer:

f slopes was  [tex]\frac{3}{2}[/tex]  ,the y intercepts was -3

g slopes was [tex]-\frac{1}{3}[/tex],the y intercepts was -2

Step-by-step explanation:

g slopes :

functions g has point (0,-2) and (3,-3)

the slopes =[tex]\frac{-2-(-3) }{0-3} =-\frac{1}{3}[/tex]

The conclusion of the hypothesis test is 0.342112

What is meant by hypothesis?

In statistics, hypothesis means an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

Here we have given that the factors that contribute to a person's wellbeing, That is Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status.

And we need to find the null and alternative hypothesis and the conclusion of the hypothesis test.

As per the given table of data we have to calculated the p value in order to find the null and alternative hypothesis,

For that we gathered the value of the following,

Number of samples = 9

Then the mean value of data = 83.63

And the standard deviation of the data = 80.475

Then the p - value is calculated as,

p-value ≈ 0.342112

This decision is made at significance level α = 0.05.

Therefore, the result is not statistically significant: there is not enough evidence to reject the null hypothesis.

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The t critical value and confidence interval must be determined.

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics.

The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

The percentage of related CIs over the long run that include the parameter's actual value is represented by the confidence level.

For instance, 95% of all intervals calculated at the 95% confidence level should include the parameter's actual value.

The sample size, sample variability, and confidence level are all variables that have an impact on the width of the CI.

Assuming all other factors remain constant, a larger sample results in a narrower confidence interval, while a sample with more variability results in a wider confidence interval.

According to our question-

At a confidence level of 90%, we have α = 1 - 0.90 = 0.1

α/2 = 0.1/2 = 0.05.

Degree of freedom = 4-1 = 3

When we look this up in the t critical value table,

t critical = 2.353

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