The radius of a circular clock is 10.5 inches.Which measurement is the closet to the measurement of the circumference of the clock in inches.


A.33

B.132

C.66

D.346

To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

Answer:

The width of the prisim is equal to 2.23 feet.

Step-by-step explanation:

let l is length and b is width.

Length, l = 4b

The volume of the prism is 160 ft³.

The height of the prism is 8 ft.

The formula for the volume of a prism is given by :

\(V=lbh\\\\160=4b\times b\times 8\\\\160=32b^2\\\\b^2=\dfrac{160}{32}\\\\b=\sqrt5\\\\b=2.23\ ft\)

So, the width of the prisim is equal to 2.23 feet.

Answer:

a = 1.4 and d = 6.9

Step-by-step explanation:

To get the value of d and a, we will use the SOH CAH TOA identity

For the first tringle;

Opposite = d ((opposite angle 60 degrees)

Adjacent = 4

Tan theta = opp/adj

Tan 60 = d/4

d  = 4tan60

d = 4(1.732)

d = 6.9

For the second triangle;

Opposite = a

Hypotenuse = 2

Since sin theta = opp/hyp

Sin45 = a/2

a = 2sin45

a = 2(0.7071)

a = 1.4

Hence a = 1.4 and d = 6.9

On solving the provided question. the vector of then only possible answer is - IAI=4 and IBI=3

A vector is an object having magnitude and direction in geometry. A vector is represented as a line with an arrow pointing in the direction of the magnitude and the length of the vector. Consequently, vectors have starting and ending points and are shown as arrows. There are ten different types of vectors in mathematics: the equal vector, the co-initial vector, the co-planar vector, the zero vector, the unit vector, the position vector, and the like and unlike vectors.

When the angle between the two vectors is 90°, the cross product of the two vectors will have its maximum magnitude. Then

IAXBI= IABI= 12

IA+BI= 7

then only possible answer is - IAI=4 and IBI=3

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Answer:

I think the answer you're looking for is 86400

Step-by-step explanation:

Answer:

-17/5

Step-by-step explanation:

Multiply ten to everything to get

6x-1= x+2-20

Simplify to 5x= -17

Solve to get x = -17/5

A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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The cumulative downtime per year of an SLA percentage of 99.95 is 4 hours, 21 minutes, 58 seconds.

The  SLA Downtime refers to the time duration that a machine or service is unavailable.

The SLA Uptime is the amount of time a machine or service is available.

The cumulative downtime per year of an SLA percentage of 99.95 will give the following:

An SLA percentage of 99,95 gives 43 seconds daily downtime.

In a year, cumulative downtime = 43 seconds  * 365 = 15695 seconds

Converting to hours and minutes give a downtime of 4 hours, 21 minutes, 58 seconds.

In conclusion, downtime refers to unavailability of a given machine or service.

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Answer:

A = 8

Step-by-step explanation:

Answer:

a=8

Step-by-step explanation:

-2a=8a-8(2a-6)

distribute the 8

-2a=8a-16a+48

Add all the variables that have a "a" on the right

-2a=-8a+48

+8a   +8a

6a=48

divide 6 on both sides to isolate a

a=8

HOPE THIS HELPS!

The linear function h can be expressed as h(x) = -4x + 7. So, h(1) is equal to 3.

To find the linear function h, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

Given that h(4) = -9 and h(-4) = 23, we can use these points to determine the slope of the line.

First, we find the slope (m) using the formula:

m = (change in y) / (change in x) = (h(-4) - h(4)) / (-4 - 4) = (23 - (-9)) / (-8) = 32 / -8 = -4

Now that we have the slope, we can find the y-intercept (b) using one of the given points. Let's use h(4) = -9:

-9 = -4(4) + b

-9 = -16 + b

b = -9 + 16

b = 7

Therefore, the linear function h is h(x) = -4x + 7.

To find h(1), we substitute x = 1 into the equation:

h(1) = -4(1) + 7

h(1) = -4 + 7

h(1) = 3

So, h(1) = 3.

Therefore, the linear function h is h(x) = -4x + 7, and h(1) = 3.

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To find the z-score for the amount spent yesterday by a customer which made a purchase of $32.25, we first need to calculate the standard deviation of the sampling distribution of the means.

We can use the formula:
Standard Deviation = standard deviation of population / square root of sample size
Since we don't know the sample size, we will assume that it is large enough (more than 30) and use the central limit theorem to estimate the standard deviation of the sampling distribution of the means.
The standard deviation of the sampling distribution of the means is:
Standard Deviation = 2.50 / sqrt(n)
Assuming n is large enough, we can estimate the standard deviation to be approximately:
Standard Deviation ≈ 2.50 / sqrt(30) ≈ 0.456
Now we can calculate the z-score using the formula:
z-score = (x - μ) / σ
Where:
x = $32.25 (amount spent by the customer)
μ = $28.50 (mean amount spent by a typical customer)
σ = 0.456 (estimated standard deviation of the sampling distribution of the means)
z-score = (32.25 - 28.50) / 0.456 ≈ 8.24
Therefore, the z-score for the amount spent yesterday by a customer which made a purchase of $32.25 is approximately 8.24. This suggests that the amount spent by this customer is quite unusual, as it is more than 8 standard deviations above the mean.

To calculate the z-score for a customer's purchase of $32.25 at a convenience store chain, where the mean amount spent by a typical customer is $28.50 and the standard deviation is $2.50, you can follow these steps:
1. Determine the mean (μ) and the standard deviation (σ). In this case, μ = $28.50 and σ = $2.50.
2. Identify the individual data point (x) for which you want to calculate the z-score. Here, x = $32.25.
3. Use the z-score formula: z = (x - μ) / σ.
4. Plug in the values: z = ($32.25 - $28.50) / $2.50 = $3.75 / $2.50 = 1.5.
So, the z-score for the amount spent yesterday by the customer who made a purchase of $32.25 is 1.5.

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The integer has 6 positive divisors and the smallest non-negative integer with the given factorization is 12.

We can use the fact that the number of divisors of an integer is equal to the product of one more than the exponent of each prime factor in its prime factorization.

In this case, the prime factorization of our integer is p^2*q, so the exponent of p is 2 and the exponent of q is 1. Therefore, the number of positive divisors is (2+1)*(1+1) = 3*2 = 6. So the integer has 6 positive divisors.

For the second question, we're asked to find the smallest nonnegative integer with the given factorization. Since p and q are unique primes, the smallest possible values for them are 2 and 3 (in some order). If we let p = 2 and q = 3, then the factorization becomes 2^2 * 3 = 12.

So the smallest non-negative integer with the given factorization is 12.

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Answer:

2.8625

This is 916 divided by 320

Answer:

Full Answer - 2.8625

Rounded - About 3

Nearest Tenth - 2.9

Nearest Hundredth - 2.86

Step by Step:

Shown Below  

Hope this Helps

In Maya Angelou's poem "Caged Bird," the caged bird represents the confinement and oppression of African Americans during the time of segregation and racism. One unique aspect of the caged bird in this poem is that it is able to sing despite its confinement, representing the resilience and spirit of African Americans who were able to find joy and hope in difficult circumstances.

The caged bird is unable to fly or fully express itself, symbolizing the limited opportunities and freedoms that were afforded to African Americans during this time. The poem compares the caged bird to a free bird, which is able to fly and sing freely, representing the freedom and opportunities that were available to white Americans.

One unique aspect of the caged bird in this poem is that it is able to sing despite its confinement, representing the resilience and spirit of African Americans who were able to find joy and hope in difficult circumstances. The caged bird's song is also described as a "caged bird's song," suggesting that the bird's song is a metaphor for the struggles and experiences of African Americans. Through the poem, Angelou conveys the themes of freedom, confinement, and the human spirit.

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Answer: I think it's D

Step-by-step explanation:

Answer:

6mph

Step-by-step explanation:

180/4.5=40

180 × (1+15%)=207

207/4.5=46

46-40=6

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

\( \textbf{Let's see if the sequence is Arithmetic or Geometric :} \)

\( \textsf{If the difference between successive terms is } \) \( \textsf{equal then, the terms are in AP} \)

\( \textsf{Since the common difference is same, } \) \( \textsf{we can infer that it's an Arithmetic progression} \) \( \textsf{with common difference of } \sf \dfrac{1}{3} \)

Answer:

Arithmetic with common difference of \(\sf \frac{1}{3}\)

Step-by-step explanation:

\(\textsf{Given sequence}=4, \dfrac{13}{3}, \dfrac{14}{3}, 5, \dfrac{16}{3},...\)

If a sequence is arithmetic, the difference between consecutive terms is the same (this is called the common difference).

If a sequence is geometric, the ratio between consecutive terms is the same (this is called the common ratio).

\(\sf 4\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad\dfrac{13}{3}\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad \dfrac{14}{3}\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad 5\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad \dfrac{16}{3}\)

As the difference between consecutive terms is \(\sf \frac{1}{3}\) then the sequence is arithmetic with common difference of \(\sf \frac{1}{3}\)

General form of an arithmetic sequence: \(\sf a_n=a+(n-1)d\)

where:

Given:

So the formula for the nth term of this sequence is:

\(\implies \sf a_n=4+(n-1)\dfrac{1}{3}\)

\(\implies \sf a_n=\dfrac{1}{3}n+\dfrac{11}{3}\)

Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.

The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.

Congruence :

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.

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Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

These two equations are perpendicular it's pretty tough to figure it out with the only the equations like last time but if you graph it's more easier because it's visual.

So the equations solved for y is...

\(y=-\frac{2}{3} x+\frac{1}{3}\)

\(y=\frac{3}{2}x-\frac{1}{2}\)

Answer:

Step-by-step explanation:

1/2*(x-8)+3x=x/2-4+3x=3.5x-4

Hope this helps!

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius is given as,

r = 36 / 2

r = 18 inches

The area of the circle is given as,

A = π x (18)²

A = 3.14 x 324

A = 1,017.36 square inches

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

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The complete question is given below.

A circle is cut from a square piece of cloth, as shown:

A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.

How many square inches of cloth is cut from the square?

(π = 3.14)

1,017.36 in2

1,489.24 in2

1,182.96 in2

1,276.00 in2

Answer:

1] x=4.21

2] 52.5

3] 3.82

4] 38.73

5] 32.005

6] 31.21

Step-by-step explanation:

The system of inequalities to represent the maximum amount of flooring needed and the maximum amount of money Samuel wants to spend is x + y <= 2000 and 4.50x + 8.25y <= 10000.

Let x be the number of square feet of carpet and y be the number of square feet of hardwood.

The most amount of flooring area he can cover is 2000 square feet. So the first inequality represents the maximum amount of flooring area that Samuel can cover:

x + y <= 2000

The carpet is $4. 50 per square foot and the hardwood is $8. 25 per square foot and Samuel has a budget of $10,000. So the second inequality represents the maximum amount of money that Samuel wants to spend:

4.50x + 8.25y <= 10000

So the system of inequalities is:

x + y <= 2000

4.50x + 8.25y <= 10000

This system represents the possible combinations of carpet and hardwood that Samuel can use while staying within his budget and the maximum amount of flooring area he can cover.

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Answer:

1935

Step-by-step explanation:

Trust Me

Universal introduction (i) is used to deduce any universally quantified formula. It has the inference rule A  xA, where A is a well-formed formula and x is a variable that may or may not be free in A. Universal introduction can only be used to deduce universally quantified formulas.

Universal introduction (∀i) is used to deduce any universally quantified formula. Universal introduction (∀i) has the following inference rule: A ∴ ∀xA. where A is a well-formed formula, and x is a variable that may or may not be free in A. ∀xA is the universal quantification of A with respect to x.

The variable x is a universally quantified variable, meaning it ranges over all values or items in the universe of discourse. This is the most fundamental inference principle in predicate logic. According to the inference rule, any universally quantified formula can be inferred using universal introduction. It follows that the answer to the question, "Can universal introduction (∀i) be used to deduce any type of formula other than a universally quantified formula?" is no, because universal introduction can only be used to deduce universally quantified formulas.

The universal introduction inference rule can be used in a variety of ways, but it is generally used to prove that a universally quantified formula is true. A statement that is true for all values of a variable x in the universe of discourse can be represented as ∀xA. Universal introduction is used to deduce such statements. In conclusion, ∀i can only be used to derive universally quantified formulas and not any other kind of formula.

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Answer:

Step-by-step explanation:

n - the first number

n+1 - the number consecutive to x

n + n+1 = 115

      -1       -1

  2n = 114

  ÷2      ÷2

   n = 57

n+1 = 57 + 1 = 58

Check:  57 + 58 = 115

The R9,000 loan offer can be analyzed as follows;

A loan is a financial agreement that is made between a lender and a borrower, such that the borrower accepts a certain amount of money provided by the lender, which is to be paid back after a specified period of time, with an interest.

The total amount which has to be paid as repayment for the loan can be obtained by finding the product of the monthly installment and the total number of months to repay the loan:

Total amount Theo pays = R318.92 × 48 = R15308.16

The reasons banks and other financial institutions offer loans to people that did not apply for loans includes;

Theo's investment options can be analyzed as follows;

Option 1: Investment with simple interest calculation

Interest earned = R9,000 × 8% × 4 years = R2,880

The total value of the investment after 4 years = R9,000 + R2,880 = R11,880

Option 2: Investment with compound interest calculation

The total value of the investment after 4 years = R9,000 × (1 + 7%)⁴ = R11,797.16409

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The answer is B. because (4-10) equals -6 and (4-4) equals 0. -6 times 0 is 0.

The measure of acute angle are  22.5 degree and  67.5 degree

Acute angles are those angle which is less than 90 degree.

According to the question,

Given that One acute angle in triangle is 3 times the measure of the other in Right angled triangle

Let "x" be the one acute angle

Then, the other acute angle will be = 3x

As we know , the sum of three angles in triangle is 180°

Therefore, x + 3x + 90 = 180

=> 4x = 180 - 90

=> 4x = 90

=> x = 90 / 4

=> x = 22.5°

Hence , the measure of each acute angle is 22.5 and  67.5 degree

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