Which sentence below represents the number of test questions in the problem below?

A test is worth 80 points. Multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points. If the test has 25 questions, how many multiple choice questions are there?

A. The number of multiple-choice questions plus the number of short-answer questions is 25.
B. The number of multiple-choice questions times the number of short-answer questions is 25.
C. The number of multiple-choice questions minus the number of short-answer questions is 80.
D. The number of multiple-choice questions plus the number of short-answer questions is 80.

Answer:Yuan received $50 last year

Step-by-step explanation:

Yuan receives money from his relatives every year on his birthday.

Let x represent the amount of money that Yuan received last year on his birthday.

This year, Yuan received a total of $56. The amount that he received this year is 12% more than he received last year. This means that

the increment on the amount that he received last year is would be

12/100×x = 0.12x. Therefore,

x + 0.12x = 56

1.12x = 56

x = 56/1.12 = $50

Answer:

There are a total of  [tex] { 6 \choose 3} = 20 [/tex] functions.

Step-by-step explanation:

In order to define an injective monotone function from [3] to [6] we need to select 3 different values fromm {1,2,3,4,5,6} and assign the smallest one of them to 1, asign the intermediate value to 2 and the largest value to 3. That way the function is monotone and it satisfies what the problem asks.

The total way of selecting injective monotone functions is, therefore, the total amount of ways to pick 3 elements from a set of 6. That number is the combinatorial number of 6 with 3, in other words

[tex] {6 \choose 3} = \frac{6!}{3!(6-3)!} = \frac{720}{6*6} = \frac{720}{36} = 20 [/tex]  

Using the values in the table you can easily use the provided x-values to plug into any equation to get a corresponding f(x) value. When applying this to the 4 functions, we see that only the second answer choice will give the exact same outputs when the inputs are plugged in from the table.

[tex]4x^2+3x-6[/tex]

[tex]x=-2\\f(-2)=4(-2)^2+3(-2)-6\\f(-2)=4[/tex]

[tex]x=0\\f(0)=4(0)^2+3(0)-6\\f(0)=-6[/tex]

[tex]x=4\\f(4)=4(4)^2+3(4)-6\\f(4)=70[/tex]

Answer:

[tex]P(\mu -1< \bar X <\mu +1)=0.6826[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the Shear strength of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(\mu,10)[/tex]  

Where [tex]\mu[/tex] and [tex]\sigma=10[/tex]

And let [tex]\bar X[/tex] represent the sample mean, the distribution for the sample mean is given by:

[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]

On this case  [tex]\bar X \sim N(\mu,\frac{10}{\sqrt{100}})[/tex]

We are interested on this probability

[tex]P(\mu -1<\bar X<\mu +1)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

If we apply this formula to our probability we got this:

[tex]P(\mu -1<\bar X<\mu +1)=P(\frac{\mu- 1-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{\mu +1-\mu}{\frac{\sigma}{\sqrt{n}}})[/tex]

[tex]=P(\frac{\mu -1-\mu}{\frac{10}{\sqrt{100}}}<Z<\frac{\mu +1-\mu}{\frac{10}{\sqrt{100}}})=P(-1<Z<1)[/tex]

And we can find this probability on this way:

[tex]P(-1<Z<1)=P(Z<1)-P(Z<-1)[/tex]

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

[tex]P(-1<Z<1)=P(Z<1)-P(Z<-1)=0.8413-0.1587=0.6826[/tex]

The probability that the sample mean will be within 1 psi of the true population mean is approximately 68.2%, according to the properties of a normal distribution and the central limit theorem.

This is a problem of standard deviation and probability in relation to the sample mean. This type of problem can be solved by knowing the properties of a normal distribution.

The central limit theorem states that if we have a large enough sample, the distribution of the sample mean will approximate a normal distribution regardless of the distribution of the population.

For this scenario, where the true population mean is unknown, the standard deviation of the sampling distribution (also known as the standard error) can be calculated as the original standard deviation (10 psi) divided by the square root of the sample size (100 test welds in this case), hence 10 ÷ √100 = 1 psi.

Then, to find the probability that the sample mean is within 1 psi of the true population mean, we can refer to the Z-table (a standard normal distribution table) to find the corresponding probability for z = ±1 (because the z-score for ±1 standard error from the mean is ±1). This value is approximately 68.2%

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Answer:

Step-by-step explanation:

The standard form equation of a circle with radius r is expressed as

( x − h )^2 + ( y − k )^2 =r ^2 ,

where r represents the radius

h and k are the coordinates of the center of the circle C( h , k )

To determine the coordinates at the center of the circle, the midpoint formula would be used. It is expressed as

[(x1 + x2)/2 , (y1 + y2)/2]

Midpoint of the circle =

(6 - 4)/2 , (2 + 7)/2 = (1, 4.5)

h coordinate of the center = 1

k coordinate of the center = 4.5

r^2 = (x - h)^2 + (2 - k)^2

r^2 = (6 - 1)^2 + (2 - 4.5)^2

r^2 = 5^2 + (- 2.5)^2 = 25 + 6.25

r^2 = 31.25

Substituting r^2 = 31.25, h = 1 and k = 4.5 into (x − h )^2 + ( y − k )^2 = r^2, the standard equation of the circle becomes

(x − 1 )^2 + ( y − 4.5 )^2 = 31.25

Final answer:

The standard form of the equation is (x - 1)² + (y - 4.5)² = 31.25.

Explanation:

The student is asking for the standard form equation of a circle given the endpoints of a diameter. To find the center of the circle, we average the x-coordinates and the y-coordinates of the endpoints, resulting in the center coordinates (1, 4.5).

The radius can be calculated using the distance formula between the center and one of the endpoints, which gives us √((6-1)²+(2-4.5)²) = √(5²+2.5²) = √(25+6.25) = √31.25.

The radius in its simple form is √31.25.

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Substituting the values we have, the equation becomes (x - 1)² + (y - 4.5)² = (√31.25)², which simplifies to

(x - 1)² + (y - 4.5)² = 31.25.

Answer:

There were 440 Standard version of songs downloaded in Web music store.

Step-by-step explanation:

Given,

Total number of songs downloaded = 1310

Total size of the downloaded songs = 4752 MB

Size of standard version of song = 2.1 MB

Size of high quality version of song = 4.4 MB

Solution,

Let the number of standard version  of song be 'x'.

And also let the number of high quality version of song be 'y'.

Now, total number of songs is the sum of total number of standard version  of song and total number of high quality version of song.

On framing the above sentence in equation form, we get;

[tex]x+y=1310\ \ \ \ \ equation\ 1[/tex]

Now, Total size of the downloaded songs is the sum of total number of standard version of song multiplied with size of standard version  of song and total number of high quality version of song multiplied with size of high quality version of song.

On framing the above sentence in equation form, we get;

[tex]2.1x+4.4y=4752[/tex]

Multiplying with 10 on both side, we get;

[tex]10(2.1x+4.4y)=4752\times10\\\\21x+44y=47520\ \ \ \ equation\ 2[/tex]

Now multiplying equation 1 by 21, we get;

[tex]21(x+y)=1310\times21`\\\\21x+21y=27510\ \ \ \ equation\ 3[/tex]

Now subtract equation 3 from equation 2, we get;

[tex](21x+44y)-(21x+21y)=47520-27510\\\\21x+44y-21x-21y=20010\\\\23y=20010\\\\y=\frac{20010}{23}\\\\y=870[/tex]

On substituting the value of y in equation 1, we get the value of x;

[tex]x+y=1310\\\\x+870=1310\\\\x=1310-870=440[/tex]

Hence There were 440 Standard version of songs downloaded in Web music store.

Answer:

0.64

Step-by-step explanation:

Given: Craig has a box of chocolate with 5 rows in it.

           Each row has 20 chocolate.

           Craig and his friends eat 64 chocolate.

As given, we understand that there is box of chocolate with 5 rows and each row have 20 chocolate, therefore we can find total number of chocolate.

Total number of chocolate=[tex]5\ rows \times 20\ chocolates = 100\ chocolates[/tex]

∴ Total number of chocolates in box= 100.

Now, we know craig and his friends eat 64 chocolate.

∴ To find decimal of number chocolate eaten out of 100 chocolate, we need to  put numbers in fraction first then convert it in decimal.

Number of chocolate ate by craig and his friends is [tex]\frac{64}{100} = 0.64[/tex]

∴ Craig and his friends eat 0.64 chocolates.

Answer:

cos(3x) --> cos³(x) - 3sin²(x)cos(x)

Step-by-step explanation:

The text in pink are the trig identities I used to convert cos(2x) and sin(2x) into their other equivalent forms.

This question is pretty much asking if you know how to use your trig identities if i understand it correctly.

Final answer:

To rewrite cos 3x using only sin x and cos x, we can use the trigonometric identity: cos 3x = 4(cos x)^3 - 3(cos x). This identity allows us to express cos 3x in terms of cos x. However, if we want to rewrite it using only sin x and cos x, we can use the Pythagorean identity: (cos x)^2 = 1 - (sin x)^2.

Explanation:

To rewrite cos 3x using only sin x and cos x, we can use the trigonometric identity: cos 3x = 4(cos x)^3 - 3(cos x). This identity allows us to express cos 3x in terms of cos x. However, if we want to rewrite it using only sin x and cos x, we can use the Pythagorean identity: (cos x)^2 = 1 - (sin x)^2. So, we can substitute this identity into the previous equation to get: cos 3x = 4(1 - (sin x)^2)^3 - 3(1 - (sin x)^2).

Answer: 0.036756909

Step-by-step explanation:

Formula for Binomial probability distribution.

[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]

, where x= number of success

n= total trials

p=probability of getting success in each trial.

According to the given information , we have

n= 10 , p= 0.30  and x= 6

Then, the required probability will be :

[tex]P(x=6)=^{10}C_6(0.3)^6(1-0.3)^{10-6}\\\\= \dfrac{10!}{6!(10-6)!}\times(0.3)^6(0.7)^4\\\\=\dfrac{10\times9\times8\times7\times6!}{6!4!}(0.3)^6(0.7)^4\\\\=(210)(0.000729)(0.2401)=0.036756909[/tex]

Hence, the required provability = 0.036756909

The probability of 6 successes given that a single success has a probability of 0.30 is given by the binomial distribution and P ( A ) = 0.03675 or 3.675 %

Given data ,

To find the probability of exactly 6 successes in 10 trials, with a probability of success (p) equal to 0.30, we can use the binomial probability formula:

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ

P(X = k) is the probability of getting exactly k successes,

n is the total number of trials,

k is the number of desired successes,

p is the probability of success for a single trial,

In this case, n = 10, k = 6, and p = 0.30. The binomial coefficient C(n, k) is calculated as:

P(n, k) = n! / (k! * (n - k)!)

Substituting the values into the formula, we have:

P(X = 6) = C(10, 6) x (0.30)⁶ * (1 - 0.30)⁽¹⁰⁻⁶⁾

Calculating the binomial coefficient:

C(10, 6) = 10! / (6! x (10 - 6)!)

= 10! / (6! x 4!)

= (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)

= 210

Substituting the values into the formula:

P(X = 6) = 210 x (0.30)⁶ (0.70)⁴

P ( X = 6 ) = P ( A ) = 210 ( 0.000729 ) ( 0.2401 )

P ( A ) = 0.036756909

Therefore, the probability of getting exactly 6 successes in 10 trials, with a probability of success of 0.30, is approximately 0.03675 or 3.675 %

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Answer:

[tex]\frac{y}{x+y}[/tex]

Step-by-step explanation:

The required answer is the rate at  which Machine A  works when the two machines are combined.

Note: the rate of doing work is express as

[tex]rate=\frac{1}{time taken} \\[/tex]

Hence we can conclude that Machine A working rate is

[tex]machine A=\frac{1}{x} \\[/tex] and machine B working rate is

[tex]machine B=\frac{1}{y} \\[/tex]

When the two machine works together, the effective working rate is

[tex]\frac{1}{x}+\frac{1}{y}\\\frac{xy}{x+y}\\[/tex]

The fraction of the work that Machine B will not have complete because of Machine A help is the total work done by machine A

Hence the fraction of work done by A is expressed as

[tex]\frac{1}{x}*combine working rate[/tex]

[tex]\frac{1}{x}*\frac{xy}{x+y}\\\frac{y}{x+y} \\[/tex]

Hence the fraction of the work that Machine B will not have complete because of Machine A help is the total work done by machine A is [tex]\frac{y}{x+y} \\[/tex]

Answer:

The ratio of the incumbent”s votes in the total number of votes = 7:8

Step-by-step explanation:

Given:

Number of students who cast vote for the incumbent = 7,000

Number of students who cast vote for the opponent = 900

Number of protest votes = 100

To find ratio of the incumbent”s votes in the total number of votes.

Solution:

Total number of votes cast = [tex]7000+900+100=8000[/tex]

Number of votes for incumbent = [tex]7000[/tex]

Ratio of incumbent”s votes in the total number of votes can be calculated as:

⇒ [tex]\frac{\textrm{The incumbent's votes}}{\textrm{Total number of votes}}[/tex]

⇒ [tex]\frac{7000}{8000}[/tex]

Simplifying to simplest fraction by dividing numerator and denominator by 1000.

⇒ [tex]\frac{7000\div1000}{8000\div1000}[/tex]

⇒ [tex]\frac{7}{8}[/tex]

Thus, ratio of the incumbent”s votes in the total number of votes = 7:8

Answer:

d) Y - 6 = x²; f) Y = 2x² + 5 - 3x²  

Step-by-step explanation:

Functions in which the exponent of x is not equal to one are nonlinear.

Functions in which the exponent of x is equal to one are linear.

Answer:

Step-by-step explanation:

The probability that you can turn your current $15,000 into $50,000. This means that the probability of success is 0.35. In terms of percentage, it is 0.35×100 = 35%

You have a 0.65 probability that fierce competition will drive you to ruin, losing all your money. This means that the probability of failure is 0.65. In terms if percentage, it is 0.65×100 = 65%

Looking at the percentage, entering the market will be too risky so I won't enter market since the chance of failing is very high compared to that of succeeding

Answer: the measure of angle A is 12 degrees

Step-by-step explanation:

Let x represent the measure of angle A.

Let y represent the measure of angle B.

Let z represent the measure of angle C.

In triangle ABC, the measure of angle B is 60 more than A. This means that

y = x + 60

The measure of angle C is eight times the measure of A. This means that

z = 8x

Also, the sum of the angles in a triangle is 180 degrees. Therefore

x + y + z = 180 - - - - - - - - - 1

Substituting y = x + 60 and z = 8x into equation 1, it becomes

x + x + 60 + 8x = 180

10x + 60 = 180

10x = 180 - 60 = 120

x = 120/10 = 12

Answer:

Step-by-step explanation:

measure of A=x

∠C=8x

∠B=x+60

in a triangle sum of angles=180°

x+8x+x+60=180

10x=120

x=12

m∠A=12°

Answer: the amount of money invested at the 5% rate is $15000

Step-by-step explanation:

Let x represent the amount of money invested at the rate of 5%.

Let y represent the amount of money invested at the rate of 8%.

Mrs. Mary Moolah invested $20,000 in two different types of bonds. This means that

x + y = 20000

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time

Considering the investment at the rate of 5%,

P = x

R = 5

T = 1

I = (x × 5 × 1)/100 = 0.05x

Considering the investment at the rate of 8%,

P = y

R = 8

T = 1

I = (y × 8 × 1)/100 = 0.08y

If Mrs. Moolah's combined profit from both investments was $1,150, it means that

0.05x + 0.08y = 1150 - - - - - -1

Substituting x = 20000 - y into equation 1, it becomes

0.05(20000 - y) + 0.08y = 1150

1000 - 0.05y + 0.08y = 1150

- 0.05y + 0.08y = 1150 - 1000

0.03y = 150

y = 150/0.03 = 5000

Substituting y = 5000 into x = 20000 - y, it becomes

x = 20000 - 5000

x = 15000

Answer:

Currency= $291 and check= $581.25.

Step-by-step explanation:

Given: Cash received= $75

          Total deposit= $872.25

Lets assume currency deposited be dollar "x"

∴  As given check deposited will be "2x"  

Now, calculating amount of currency deposited.

We know that, [tex]currency\ deposit + check\ deposit= \$872.25[/tex]

∴ [tex]x+2x= \$872.25[/tex]

⇒[tex]3x=\$872.25[/tex]

Cross multiplying

∴[tex]x= \$290.75 \approx \$291 \textrm{ as Kenneth John have not deposited any coins}[/tex]

∴  Amount of currency deposited is $291.

Next, computing to get amount deposited through check.

As we know check deposited is double of currency.

Check deposited= [tex]2\times \$291= \$ 582[/tex]

∵ No coins were deposited and there is total deposit is $872.25.

∴ We will consider amount deposited through check is $581.25.

Kenneth John deposited $290.75 in currency and $581.50 in checks.

To determine the amounts of currency and checks deposited by Kenneth John, we will define the variables for clarity. Let C represent the amount in currency deposited and CH represent the amount in checks deposited.

Given:

The total deposit after adding checks and currency is $872.25.

The checks deposited totaled twice the currency deposited (CH = 2C).

We can set up the following equation based on the given information:

[tex]C + CH = 872.25[/tex]

Since CH = 2C, we substitute CH:

[tex]C + 2C = 872.25[/tex]

This simplifies to:

[tex]3C = 872.25[/tex]

Solving for C, we divide both sides of the equation by 3:

[tex]C = \[\frac{872.25}{3} = 290.75[/tex]

Kenneth deposited $290.75 in currency.

Then, we calculate the amount in checks:

[tex]CH = 2 \times 290.75 = 581.50[/tex]

Blaire has 20 tomato plants altogether.

Step-by-step explanation:

Given,

Tomatoes plants ready to pick = 18

This represents 90% of total tomato plants.

Let,

x be the original number of tomato plants.

90% of x = 18

[tex]\frac{90}{100}*x=18[/tex]

[tex]0.9x=18[/tex]

Dividing both sides by 0.9

[tex]\frac{0.9x}{0.9}=\frac{18}{0.9}[/tex]

[tex]x=20[/tex]

Blaire has 20 tomato plants altogether.

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Answer: her interest in 3 years is $45

Step-by-step explanation:

For simple interest, the principal is not compounded. The interest is only on the original capital. The formula for simple interest is expressed as

I = PRT/100

Where

I represents the interest on the principal

P represents the initial amount

R represents the interest rate.

T represents the time in years.

From the information given

P = $300

R = 5%

T = 3 years

I = 300×5×3)/100

I = 4500/100 = 45

Answer:

The Amount draw from the account after 10 years is $109,555 .

Step-by-step explanation:

Given as :

The principal deposited in account = p = $50,000

The rate of interest = 8% semiannually

The time period for the amount will be in account = t = 10 years

Let The Amount draw from the account after 10 years = $A

Now, From Compound Interest method

Amount = principal × [tex](1+\dfrac{\texrm rate}{2\times 100})^{\textrm 2\times time}[/tex]

A = p × [tex](1+\dfrac{\texrm r}{2\times 100})^{\textrm 2\times t}[/tex]

Or, A = $50,000 × [tex](1+\dfrac{\texrm 8}{2\times 100})^{\textrm 2\times 10}[/tex]

Or, A = $50,000 × [tex](1.04)^{20}[/tex]

Or, A = $50,000 × 2.1911

Or, A = $109,555

So, The Amount draw from the account after 10 years = A = $109,555

Hence,The Amount draw from the account after 10 years is $109,555 . Answer

Answer:

the answer is 1:12

Step-by-step explanation:

hope it helps!

Answer: Our required probability is 0.7241.

Step-by-step explanation:

Since we have given that

Probability that new product have been successes P(S) = 60%

Probability that new product have not been successes P(F) = 40%

Probability that their successful products were predicted to be successes = P(A|S)=70%

Probability that their failed products were predicted to be successes =P(A|F) = 40%

So, Probability that this new camera phone will be successful if its success has been predicted is given by

[tex]P(S|A)=\dfrac{P(S).P(A|S)}{P(S).P(A|S)+P(F).P(A|F)}\\\\P(S|A)=\dfrac{0.7\times 0.6}{0.7\times 0.6+0.4\times 0.4}\\\\P(S|A)=0.7241[/tex]

Hence, our required probability is 0.7241.

Answer:

Goal amount of $10,000

Deadline of next year

Step-by-step explanation:

Tyrone can make his financial goal ‘specific’ by deciding on a target amount for his emergency fund. He can make it 'timely' by assigning a deadline by which to save that amount.

To make Tyrone's financial goal specific, he could give himself a target amount to save for the emergency fund. This could be a fixed sum, like $1000, or a figure based on monthly expenses, like saving for 6 months' worth of living expenses. This clarity can help him to plan and track his progress.

To make his goal timely, he could give himself a deadline by which he wants to achieve this goal. For example, he might aim to save his specified amount within a year or two. The timetable can provide added motivation to adhere to a budget and save consistently.

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Answer: [tex]24\ liters[/tex]

Step-by-step explanation:

Let be "x" the amount of gasoline in liters that the car's tank had at the beginning of the trip.

 1. In the first part of the trip the amount of gasoline the car used can be expressed as:

 [tex]\frac{2}{3}x[/tex]

2. After the first part of the trip, the remaining was:

[tex]x-\frac{2}{3}x=\frac{1}{3}x[/tex]  

3. In the second part of the trip the car used [tex]\frac{1}{2}[/tex] of the remaining. This is:

[tex](\frac{1}{3}x)(\frac{1}{2})=\frac{1}{6}x[/tex]

4. The total amount ot gasoline used in this trip was 20 liters.

5. Then, with this information, you can write the following equation:

[tex]\frac{2}{3}x+\frac{1}{6}x=20[/tex]

6. Finally, you must solve for "x" in order to find its value. This is:

[tex]\frac{2}{3}x+\frac{1}{6}x=20\\\\\frac{5}{6}x=20\\\\5x=120\\\\x=24[/tex]

Final answer:

The experimental probability of a string of lights being defective is calculated by dividing the number of defective strings found during the inspection by the total number of strings inspected, leading to a probability of 6/25.

Explanation:

The experimental probability that a string of lights is defective is determined by dividing the number of defective strings of lights by the total number of strings inspected. This probability can be calculated as follows:

Number of defective strings = 6

Total number of strings inspected = 25

Experimental Probability = Number of defective strings / Total number of strings

So, the experimental probability of finding a defective string of lights is 6/25.

Answer:

The length of each side is 17 in, 24 in, 24 in.

Step-by-step explanation:

Given,

Perimeter of the triangle = [tex]25\ in[/tex]

Length of 1st side = [tex]2w+1[/tex]

Length of 2nd side = [tex]3w[/tex]

Length of 3rd side = [tex]3w[/tex]

The perimeter of a triangle is equal to the sum of the length of all the three sides of the triangle.

Perimeter of the triangle = Length of 1st side + Length of 2nd side + Length of 3rd side

Now substituting the given values, we get;

[tex]2w+1+3w+3w=25\\\\8w+1=25\\\\8w=25-1\\\\8w=24\\\\w=\frac{24}{8}=3[/tex]

Now we have the value of w so we can calculate the length of each side.

Length of 1st side = [tex]2w+1=2\times8+1=16+1=17\ in[/tex]

Length of 2nd side = [tex]3w=3\times8=24\ in[/tex]

Length of 3rd side = [tex]3w=3\times8=24\ in[/tex]

Thus the length of each side is 17 in, 24 in, 24 in.

Answer:

See explanation below

Step-by-step explanation:

Data given and notation  

First we need to find the sample mean and deviation from the data with the following formulas:

[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

[tex]\bar X[/tex] represent the sample mean  

[tex]s[/tex] represent the sample standard deviation

[tex]n[/tex] sample size  

[tex]\mu_o [/tex] represent the value that we want to test  

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We have three possible options for the null and the alternative hypothesis:

Case Bilateral  

Null hypothesis:[tex]\mu = \mu_o[/tex]  

Alternative hypothesis:[tex]\mu \neq \mu_o[/tex]

Case Right tailed

Null hypothesis:[tex]\mu \leq \mu_o[/tex]  

Alternative hypothesis:[tex]\mu > \mu_o[/tex]

Case Left tailed

Null hypothesis:[tex]\mu \geq \mu_o[/tex]  

Alternative hypothesis:[tex]\mu < \mu_o[/tex]

We assume that w don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) and the value obtained is assumed as [tex]t_o[/tex]

Calculate the P-value  

First we need to find the degrees of freedom:

[tex] df=n-1[/tex]

Case two tailed

Since is a two-sided tailed test the p value would be:  

[tex]p_v =2*P(t_{df}>|t_o|)[/tex]  

Case Right tailed

Since is a one-side right tailed test the p value would be:  

[tex]p_v =P(t_{df}>t_o)[/tex]  

Case Left tailed

Since is a one-side left tailed test the p value would be:  

[tex]p_v =P(t_{df}<t_o)[/tex]  

Conclusion  

The rule of decision is this one:

[tex]p_v >\alpha[/tex] We fail to reject the null hypothesis at the significance level [tex]\alpha[/tex] assumed

[tex]p_v <\alpha[/tex] We reject the null hypothesis at the significance level [tex]\alpha[/tex] assumed

Denzel took 1/40 of his earnings to the park but did not spend it on rides or popcorn.

Let's break down the information provided step by step to find the fraction of Denzel's earnings that he took to the park but did not spend on rides or popcorn.

Denzel put 1/2 of his earnings into savings. This means he kept 1/2 as his spending money for the amusement park.

Denzel spent 1/5 of the remaining amount on popcorn. This means he spent 1/5 * 1/2 = 1/10 of his earnings on popcorn.

Denzel also spent 3/4 of the remaining amount on rides. This means he spent 3/4 * 1/2 = 3/8 of his earnings on rides.

To find the fraction of his earnings that he took to the park but did not spend on rides or popcorn, we need to subtract the fractions spent on rides and popcorn from the fraction he took to the park.

Fraction taken to the park but not spent on rides or popcorn = 1/2 - (1/10 + 3/8)

To subtract fractions, we need a common denominator. The least common multiple of 10 and 8 is 40.

Converting the fractions to have a common denominator:

1/2 - (1/10 + 3/8) = 20/40 - (4/40 + 15/40) = 20/40 - 19/40 = 1/40

Therefore, Denzel took 1/40 of his earnings to the park but did not spend it on rides or popcorn.

Question: Denzel earned money after school. He put 1/2 of this month's earnings into savings. He took the rest to spend at the amusement park. He spent 1/5 of this amount on popcorn and 3/4 of it on rides. What fraction of his earnings did he take to the park but not spend on rides or popcorn?

Answer: Our required probability is [tex]\dfrac{1}{36}[/tex]

Step-by-step explanation:

Since we have given that

Total number of outcomes in single die = 6

So, total number of outcomes if three different die = [tex]6^3=216[/tex]

Number of favourable outcome i.e. exactly roll the same number = (1,1,1), (2,2,2) (3,3,3) (4,4,4) (5,5,5), (6,6,6) = 6

So, Probability of getting exactly roll the same number is given by

[tex]\dfrac{\text{number of favourable outcome}}{\text{Number of total outcomes}}\\\\=\dfrac{6}{216}\\\\=\dfrac{1}{36}[/tex]

Hence, our required probability is [tex]\dfrac{1}{36}[/tex]

Answer:

Correct answer: False

Step-by-step explanation:

coeff c= 3/2 = 1,5        coeff c₁ = 18/8 = 2,25

c ≠ c₁

God is with you!!!

Answer: False

Step-by-step explanation: When we are asked to determine whether two ratios form a proportion, what we are really being asked to do is to determine whether the ratios are equal because if the ratios are equal, then we know they form a proportion.

So in this problem, we need to determine whether 3/2 = 18/8. The easiest way to determine whether 3/2 = 18/8 is to use cross products. If the cross products are equal, then the ratios are equal.

The cross products for these two ratios are 3 x 8 and 2 x 18.

Since 3 x 8 is 24 and 2 x 18 is 36, we can easily see that 24 ≠ 36 so the cross products are not equal which means that the ratios are not equal and since the ratios are not equal, we know that they do not form a proportion.

So the answer is false. 3/2 and 18/8 do not form a proportion.