Please help me on this question:

A circle has diameter 9 cm

A square has side length 5 cm

Use Pythagoras' theorem to show that

the square will fit inside the circle without

touching the edge of the circle.

9 cm

5 cm

Step-by-step explanation:

the easy straight forward method is to simply sum up the 5 terms.

you know that this symbol just means "sum", right ?

and that the index variable is "running" from 1 to 5.

so, you have to sum up

3×1 + 3×2 + 3×3 + 3×4 + 3×5 = 3 + 6 + 9 + 12 + 15 = 45

now, if you want it done via a summary formula to add the first n terms of an arithmetic sequence, like in this case

a1 = 3

an = an-1 + 3 = a1×n = 3n

then

the sum of the first n terms in an arithmetic sequence is (n/2)⋅(a₁+aₙ).

it simply means : first plus last term added up n/2 times.

why ?

because a1 + an = a2 + an-1 = a3 + an-2 = ...

we get n/2 times such part sums.

so, in our case, n = 5, and we get

(3 + 3×5)×5/2 = (3 + 15)×5/2 = 18×5/2 = 9×5 = 45

Answer:

∑ (i = 1 to 5) (3·i)

= 3·∑ (i = 1 to 5) (i)

= 3·(1 + 2 + 3 + 4 + 5)

= 3·15

= 45

You would expect 4.5 diodes to fail. The standard deviation of the number that are expected to fail is 2.089.

The number of diodes failing, E(X), can be calculated by multiplying the population, n, with the probability, p.

n = 150

p = 0.03

E(X) = n × p

E(X) = 150(0.03)

E(X) = 4.5

Standard deviation, denoted by σ, is defined as the measure that indicates the average distance of observations from the mean of the data set.

σ = √(n x p x (1 - p))

σ = √(150 x 0.03 x (1 - 0.03))

σ = √150 x 0.03 x 0.97

σ = √4.365

σ = 2.089

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Probability that x greater than or equal to 5 is 0.6 i.e., Probability that x ≥ 5 = 0.6

The probability distribution for a random variable x is given in the table.

x                |  -10       -5       0       5      10    15     20

probability | 0.20   0.15   0.05   0.1  0.25  0.1   0.15

If a random variable x has values x₁, x₂, .. ,xₙ with their corresponding probabilities given for each of them P(xₐ), then probability that x ≥ xₐ, for some a = 1, 2, .. , n is,

        P(x ≥ xₐ) = P(xₐ) + P(xₐ₊₁) +...+P(xₙ).

Here we need to find the probability that the random variable x is greater than equal to 5. So we need to add up the probabilities corresponding to the random variables x  ≥ 5.

So here, probability that x ≥ 5 is

P(x ≥ 5) = P(5) +P(10) + P(15) + P(20)

            = 0.1 + 0.25 + 0.1 + 0.15

            = 0.6

Hence Probability that x ≥ 5 is 0.6.

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Answer: m < -1

Step-by-step explanation:

Step 1: 6 + 5m < 1.              Step 2:  5m/5 < -5/5         m = -1

           -6.           -6                              

Answer: m < −1

Step-by-step explanation:

1. Rearange: 5m+6<1

2. 5 + 6−6 < 1−6

3. 5m < -5

4. 5m/5 < -5/5

5. Cancel terms that are in both the numerator and denominator then divide the numbers.

6. answer: m < -1

(b-2)x = 8

In the given equation, b is a constant. If the equation

has no solution, what is the value of b ?

Step 1

identify

b is a constant, so (b-2) is a constant too.

If the equation has no solution, it is, there is not a value of x to satisfy (b-2)x=8

Step 2

solve for x

This value becomes indeterminate when the denominator takes the value of zero,it is

so , the value of b=2 makes the equation has no solution.

Answer

A) 2

The prοbability οf getting the desired οutcοme is 1/9 οr apprοximately 0.1111 (rοunded tο fοur decimal places)

In mathematics, prοbability is a measure οf the likelihοοd οr chance οf an event οccurring, expressed as a number between 0 and 1, where 0 represents an impοssible event and 1 represents a certain event. It is a fundamental cοncept in statistics and is used tο mοdel and analyze a wide range οf real-wοrld phenοmena.

The prοbability οf getting a 1 οn a single die is 1/6, and the prοbability οf getting anything but a 3 οr 4 οn a single die is 4/6 (since there are 6 pοssible οutcοmes and 3 οf them result in a 3 οr a 4).

Tο find the prοbability οf getting the desired οutcοme when rοlling twο dice, we can use the multiplicatiοn rule οf prοbability, which states that the prοbability οf twο independent events οccurring tοgether is the prοduct οf their individual prοbabilities.

Sο the prοbability οf getting a 1 οn οne die and anything but a 3 οr 4 οn the οther die is:

(1/6) x (4/6) = 4/36 = 1/9

Since there are 36 pοssible οutcοmes when rοlling twο dice, the prοbability οf getting the desired οutcοme is 1/9 οr apprοximately 0.1111 (rοunded tο fοur decimal places).

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The equation of the linear function represented in the table in slope intercept form is y = 7x -2

A linear function can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the table follows a linear pattern.

Hence, using (0, -2)(1, 5) we can find the slope and the y-intercept of the linear function.

Therefore,

m = 5 - (-2) / 1 - 0

m = 5 + 2 / 1

m = 7

Therefore, let's find the y-intercept using (0, - 2).

y = mx + b

-2  = 7(0) + b

hence,

b = -2

Therefore, the slope intercept form of the table is y = 7x - 2

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Estimate intercepts of the graph of the functions

1.  [tex]y=\frac{1}{3} x+1[/tex]

=>At x axis

x = 0

y= 0+ 1

y = 1

=>At y axis

y= 0

1/3x = -1

x= -3

The x intercepts:( -3, 0)

The y intercepts : (0,1)

2. [tex]y= x^{2} -3x-4[/tex]

=> At x axis

x=0

y= - 4

=> At y axis

y= 0

[tex]x^{2} -3x-4= 0[/tex]

(x-4)(x+1) = 0

x= 4,-1

The x intercepts: (4,0) ( -1, 0)

The y intercepts : (0,-4)

3. y= -2 |x-5|

=> At x axis

x=0

y= -2(5)

y= -10

=> At y axis

y= 0

-2|x-5|=0

Divide both sides by -2

|x - 5|= 0

x-  5 = 0

x = 5

The x intercepts: (5,0)

The y intercepts : (0,-10)

4. [tex]y= -4x^{3} -13x^{2} -10x[/tex]

=> At x axis

x= 0

y = 0

=>At y axis

y=0

[tex]0=-4x^{3} -13x^{2} -10x \\\\4x^{3} +13x^{2} +10x =0[/tex]

By factorization ,

x( 4x+5 )( x+2)= 0

x= 0, -2, -5/4

The x intercepts: (0,0) (-2,0) ,(-5/4,0)

The y intercepts: (0,0)  

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By taking the difference between the y-intercepts, we conclude that the distance between the lines is 3 units.

A general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two linear equations are parallel if and only if both lines have the same slope and different y-intercepts.

And the distance is given by the difference between the y-intercepts.

Here the lines are:

y = -3*x + 1

y = -3*x + 4

The difference between the y-intercepts gives:

4 - 1 = 3

That is the distance between the lines.

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Hope this will be helpful.

The length of the building should be measured in meters, as that is the most appropriate unit.

The most suitable unit to measure the length of the building will be measuring the length of the building in meters.

Therefore, the length of the building should be measured in meters, as that is the most appropriate unit.

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The length of the arc intercepted by a central angle of

6 radians is 60.34 cm.

An arc is any smooth curve joining two points.

Given is an circle of radius 10 cm intercepted by a central angle of

6 radians.

We can calculate the length of the arc using the formula -

L[arc] = (Ф/360°) x 2πr

Ф = 6 radians = 343.78 degrees

L[arc] = (343.78/360) x 2π x 10

L[arc] = 0.96 x 2π x 10

L[arc] = 60.34 cm

Therefore, the length of the arc intercepted by a central angle of

6 radians is 60.34 cm.

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The total profit made by the company over the course of its first 24 years of operation is $10,016,640

Given,

The annual profit made by a company in first year = $111,000

The increase in profit per year = 24% = $26640

We have to find the total profit made by the company over the course of its first 24 years of operation

Lets take this as an arithmetic progression.

First term, a = 111,000

Common difference, d = 26640

nth term = 24

Sum of nth term,

Sₙ = n/2 [2a + (n - 1) d]

S₂₄ = 24/2 [2 × 111,000 + (24 -1) 26640]

S₂₄ = 12 [222,000 + 23 × 26640]

S₂₄ = 12 [222,000 + 612,720]

S₂₄ = 12 × 834,720

S₂₄ = 10,016,640

That is,

The total profit made by the company over the course of its first 24 years of operation is $10,016,640

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Answer:

y=1/2x+2

Step-by-step explanation:

y=mx+b

m = slope = rise/run

b = y-intercept

Look at the graph, and find the slope.

m= slope = rise/run = 1/2

b = y-intercept = 2

Therefore, the correct answer is option y=1/2x+2

The given statement is an example of the law of detachment.

Given that,
Premises:
If I'm a student, then I go to school. If I go to school, then I learn.
Conclusion:
If I'm a student, then I learn.

This is an example of the Law of which is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Following the statement given in the premises gives a certain conclusion which shows the detachment behavior.

Thus, the given statement is an example of the law of detachment.

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Answer: M + 7

Step-by-step explanation:

Well, it doesn’t show the variable’s number correct?

So, since we don’t have the number, we are going to multiply -1 by -7, getting 7 from this. Now, change it to addition. You should have m + 7.

I hope this helps!

Answer:

250

Step-by-step explanation:

4^4+400÷(4+6^2)−2^4

256 + (400 ÷(4+36) ) -16  

256 + (400÷40) -16

256+ (400 (1/40) ) -16

256 + (400/40) -16

256 + (2 · 6) -16

256 + 10 =16

250

Two decimals are 0.34, 0.83, and 0.83 and Holland could have used it to make a sum of 2.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.

We get x + x = 2x by using x to signify our missing values and the assumption that there are two missing values. We obtain the equation 2x + 0.34 since it is the product of these integers and 0.34; after setting it equal to 2, 2x + 0.34 equals 2.

First, take 0.34 off both sides to get 2x = 1.66. To get x = 0.83, divide both sides by 2 now.

Therefore, the decimals are 0.34, 0.83, and 0.83.

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The journal entry will be prepared thus:

Date General Journal Debit Credit

2-Aug

Cash $540

Unearned Service Revenue  $378

Sales Revenue  $162

2-Aug

Cost of goods sold $105

Inventory  $105

3-Aug

Accounts receivable $550

Sales revenue  $550

3-Aug

Cost of goods sold $450

Inventory  $450

6-Aug

Sales return (550/5) $110

Accounts receivable  $110

6-Aug

Inventory $90

Cost of goods sold (450/5)  $90

10-Aug

Unearned service revenue $126

Service Revenue  $126

(378/3 = 126 each)  

20-Aug

Cash $350

Sales revenue  $350

20-Aug

Cost of goods sold $121

Inventory  $121

22-Aug

Cash $440

Accounts receivable $440

A journal entry is the act of recording any transaction, whether one that is economic or not.

An accounting diary that displays the debit and credit balances of a corporation lists transactions. Multiple recordings, each of which is either a debit or a credit, may be included in the journal entry.

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Aug.2 Sold a bundle of spa services with a merchandise basket. When sold separately, the spa service part of the bundle sells for $420 and the merchandise basket normally sells for $180. Together, the bundle was sold to Val Amy for cash at a selling price of $540 (total). Val booked a spa treatment for August 10, and she took the basket of goods with her. The goods had cost NGS $105.

Aug.3 Sold 5 identical items of merchandise to Cosmetics R Us on account at a selling price of $550 (total); terms n/30. The goods cost NGS $450.

Aug.6 Cosmetics R Us returned one of the five items purchased on August 3. The item could still be sold by NGS in the future and credit was given to the customer.

Aug.10 Val Amy used one of the three spa treatments she had purchased as part of the bundle sold to her on August 2.

Aug.20 Sold two at-home spa kits to Meghan Witzel for $350 cash. The goods cost NGS $121.

Aug.22 Cosmetics R Us paid its remaining account balance in full.

Prepare all journal entries

The number of engineering students for 750 college students will be 176 students

Number of engineering students: 19

The number of total students for 19 engineering students = 81 students

Percentage: A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Percentage of engineering students in relation to the total students = Number of engineering students/ Total students*100

= 19/81*100

= 23.45%

So, for 750 students the number of engineering students will be

= 23.45% of 750

= 23.45/100*750

= 175.87 or 176 students

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Answer:

B

Step-by-step explanation:

Kusa=10x0.75=7.5

Chaman=12x0.6=7.2

7.5>7.2

so kusa rode further than chaman.

Answer:

b

Step-by-step explanation:

Answer:

d. It is the same distance from zero as the number she tells you.

Step-by-step explanation:

Case 1: Let Shanika thought a positive rational

number

Let the number that Shanika thought be c.

Then, the distance of it from zero = lc - Ol = c.

But, the number she told = -c

The distance of -c from zero = 10--(-c)| = c

Case 2: Let Shanika thought a negative rational number

Let the number that Shanika thought be -c (c>0).

Then, the distance of it from zero = 10--(-c)| = c.

But, the number she told = c

The distance of -c from zero = Ic-01 = c

In both cases, the number she thought is the same distance from zero as the number she tells us.

Answer:

–87.75

Step-by-step explanation:

Write the equation:

200 ÷ 5 • 32 + 12 – 101 = ?

PEMDAS

200 ÷ (5 • 32) + 12 – 101 = ?

(200 ÷ 160) + 12 – 101 = ?

(1.25 + 12) – 101 = ?

(13.25 – 101) = ?

–87.75 = ?

–87.75

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The conditions necessary for binomial distribution is option C that is I and III only "There is a series of N trials." and "The outcomes are mutually exclusive."

In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.

If the following circumstances hold true, the binomial distribution describes the behavior of a count variable X: 1: There will always be n observations. 2: Every observation stands alone. Three: Each observation corresponds to one of two results ("success" or "failure").

Option C, which consists solely of I and III, meets the requirements for the binomial distribution. "The results are mutually exclusive" and "There is a series of N trials."

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The null hypothesis is that the reaction time for students in the regular population averages 200 milliseconds.

The alternate hypothesis is that the reaction time for students in not the regular population averages 200 milliseconds.

In statistical hypothesis testing, null and alternate hypotheses are utilized. The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

With the aid of a statistical test, researchers weigh the evidence in favor of and against the null and alternative hypotheses, which are two opposing claims:

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Answer: y = -90, 90

Step-by-step explanation:

     To solve this, we will isolate the variable.

 Given:

10 = |[tex]\frac{y}{9}[/tex]|

 Absolute value:

10 = [tex]\frac{y}{9}[/tex]     &     -10 = [tex]\frac{y}{9}[/tex]

 Multiply both sides of both equations by 9:

90 = y    &     -90 = y

 Answer:

y = -90, 90

Hong has 16 one-dollar bills. he wants to give each of his 6 children the same number of bills. Then  Hong will give 12 bills to his 6 children and  4 bills Hong have remained

Hong has 16 one-dollar bills.

he wants to give each of his 6 children the same number of bills.

how many bills can he give each child?

how many bills will Hong have remaining?

since Hong has 16 one dollar bills and he wants 6 children the same number of bills

then he give 6 children two bills to each  

then the total number of bills he give to 6 children is 12

and he has 16 bills and 12 bills give to his children

the remaining bills left = 16 bills - 12 bills = 4 bills

Hence , Hong will give 12 bills to his 6 children and  4 bills Hong have remained

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Answer:

y=3x-4

Step-by-step explanation: