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The remainder when a 90-digit number 9999 is divided by 89 is 0, as the result of applying the divisibility rule of 89, which involves reversing the digits of the number and subtracting the smaller from the larger.

To find the remainder when a 90-digit number 9999 is divided by 89, we can use the divisibility rule of 89. The rule states that for any integer n, the number obtained by reversing the digits of n and subtracting the smaller from the larger is divisible by 89.

In this case, we reverse the digits of 9999 to get 9999 again, and subtract the smaller from the larger to get 0. Since 0 is divisible by any number, including 89, the remainder when 9999 is divided by 89 is 0.

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Complete Question

We have a total of 420 students. 2 times 3 times the number of girls is equal to 2 times the number of boys how many girls and how many boys

Answer:

The number of boys = x = 315 boys

The number of girls = y = 105 girls

Step-by-step explanation:

Let

The number of boys = x

The number of girls = y

We have 420 students

2 times 3 times the number of girls is equal to 2 times the number of boys

x + y = 420..... Equation 1

2 × 3y = 2x

6y => 2x

x => 6y/2 = 3y

We substitute 3y for x in Equation 1

3y + y = 420

4y = 420

y =>420/4

y => 105

Solving for x

x = 3y

x = 3 × 105

x = 315

Therefore,

The number of boys = x = 315 boys

The number of girls = y = 105 girls

The given distribution of frequency of yearly income represents a positively skewed distribution.

In a positively skewed distribution, the tail of the distribution extends towards higher values, and the majority of the data is concentrated towards the lower end. This means that there are relatively fewer high-income values and more low-income values in the distribution.

Regarding the effect on the mean, a positively skewed distribution tends to pull the mean towards the higher end of the distribution. This happens because the few higher values have a disproportionate impact on the overall average. As a result, the mean is typically greater than the median in a positively skewed distribution. The presence of extreme high-income values in the distribution can greatly influence and increase the mean value.

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Answer:

the answer would be a % because of the divisibility rule

The parametrization for C inducing a counterclockwise orientation and starting at (8, 0) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π, the parametrization for C inducing a clockwise orientation and starting at (0, 8) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π and parametrization for C if it is now centered at the point (2, 4) is C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π

The circle C of radius 8, centered at the origin, parametrization for C inducing a counterclockwise orientation and starting at (8, 0). c(t) :0 ≤ t ≤ 2π,

a) equation of the circle is x² + y² = 64.

starting point it (80) and orientation Counterclockwise.

c(t) (8cos, 8sin) 0 ≤ t ≤ 2π

b) Starting point is (0,8) and orientation is clockwise

c(t) (8cos, 8sin) 0 ≤ t ≤ 2π

c) equation of circle is (x-4)²+ (4-2)² - 64

For counterclockwise orientation

C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π

Therefore, the parametrization for C inducing a counterclockwise orientation and starting at (8, 0) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π, the parametrization for C inducing a clockwise orientation and starting at (0, 8) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π and parametrization for C if it is now centered at the point (2, 4) is C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π

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If the function f(3) has a value of 6, then the value of f⁻¹(6) is 3

From the question, the definition of the function is given as

f(x)

Such that

The value of f(3) is 6

This is represented as

f(3) = 6

Also, the function can be represented as

y = f(x)

In f(3) = 6, we have

x = 3 and y = 6

When the inverse function is calculated, we have

f⁻¹(y) = x

This means that

f⁻¹(6) = 3

Express as an inverse function

f⁻¹(6) = 3

Hence, the inverse function f⁻¹(6) has a value of 3

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Lee Jenkins worked the following hours as a manager for a local Pizza Hut 5 4/1​, 9 4/3​, 7 4/3​ and 8 4/3​.

Now, the above-mentioned hours are not in the proper form that we are required to calculate. Therefore, we need to change them into the proper format .In order to add these hours, we must first convert the hours and minutes to the same format.

We'll need to convert each fraction to a common denominator of 3x3=9.  5 4/1​ in the mixed format is 5 + 4/1,
which is equal to 9. 9 4/3 in the mixed format is 9 + 4/3,
which is equal to 10 1/3.7 4/3​ in the mixed format is 7 + 4/3,

which is equal to 8 1/3.8 4/3​ in the mixed format is 8 + 4/3,
which is equal to 9 1/3.Now that we've converted the times,

we can add them together to get a total of 36 1/3 hours.

Therefore, Lee worked for 36 1/3 hours. the total number of hours Lee worked as a manager for the local Pizza Hut is 36 1/3 hours.

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Answer:

y + 5 = x

Step-by-step explanation:

y= 15 * 3x

Subtract 15 on both sides

y - 15 = 3x

Divide 3 on both sides

y + 5 = x

(I hope this helps and sorry if i'm wrong)

Answer:

The last one (2/3 and 8/12)

Step-by-step explanation:

When you reduce 8/12, you would get 2/3. If you multiply 2/3, you would get 8/12. Therefore, this ratio is proportional.

Have a good day :)

Answer:

1. Always translate the question stem, set up equations (limit the number of variables) and breakdown the question stem of possible

2. Never overlook the constraints the question provides.

Now the question stem tells us that on the

1st day Joe earned = x

2nd day = 2x

3rd day = 4x

4th day = 8x

Question stem: Did Joe earn less than $35 on the 4th day -----> 8x < 35 ----> x < 4.375

Since x is an integer, the question becomes 'Is x <= 4

Statement 1 : Joe earned more than $120 in total for the first five days he worked in December.

x + 2x + 4x + 8x + 16x > 120

31x > 120 ---> x > 3.9....

This gives us both a YES and a NO since x can be 4 or any integer greater than 4

Statement 2: Joe earned less than $148 on the 6th day he worked in December

32x < 148 ----> x < 4.625

Since x is an integer, x <=4. Sufficient.

hope this helps

-lvr

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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The landform region is the Atlantic Coastal Plain.

The Atlantic Coastal Plain is a significant landform region that spans along the eastern coast of the United States, extending from Florida in the south to Massachusetts in the north.

It is characterized by relatively flat or gently sloping terrain and is primarily composed of sedimentary deposits, including sand, silt, and clay.

The formation of the Atlantic Coastal Plain can be attributed to processes such as erosion, deposition, and sea-level changes over millions of years. It is a result of sedimentary materials being deposited by rivers and streams, as well as the gradual retreat of the ocean over time.

This region is known for its diverse landscapes, which can include barrier islands, marshes, estuaries, and coastal forests. It is an important area for agriculture, as the fertile soils and favorable climate support various crops.

Additionally, the Atlantic Coastal Plain is home to numerous cities and metropolitan areas, including Miami, Washington D.C., and New York City. It also features several prominent geographic features such as the Chesapeake Bay, Delaware Bay, and Cape Cod.

Overall, the Atlantic Coastal Plain is a significant landform region with a distinct geological history and unique ecological characteristics, playing a vital role in the geography and development of the eastern United States.

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Answer:

-15

Step-by-step explanation:

Answer: w = -15

Step-by-step explanation:

-9 = 6 + w

Solve to isolate W.

-9 = 6 + w

-6    -6  

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

-15 = w

Based on the info provided, that should be right!

The feature NOT associated with the function h(x) is that the domain of h(x) is [0.).

The function h(x) is defined as (x - 5)² - log₁ x + 6.

Let's analyze each given option to determine which one is NOT a key feature of h(x).

Option 1 states that the domain of h(x) is [0, ∞).

However, the function h(x) contains a logarithm term, which is only defined for positive values of x.

Therefore, the domain of h(x) is actually (0, ∞).

This option is not a key feature of h(x).

Option 2 states that the x-intercept of h(x) is (5, 0).

To find the x-intercept, we set h(x) = 0 and solve for x. In this case, we have (x - 5)² - log₁ x + 6 = 0.

However, since the logarithm term is always positive, it can never equal zero.

Therefore, the function h(x) does not have an x-intercept at (5, 0).

This option is a key feature of h(x).

Option 3 states that the y-intercept of h(x) is (0, 25).

To find the y-intercept, we set x = 0 and evaluate h(x). Plugging in x = 0, we get (0 - 5)² - log₁ 0 + 6.

However, the logarithm of 0 is undefined, so the y-intercept of h(x) is not (0, 25).

This option is not a key feature of h(x).

Option 4 states that the end behavior of h(x) is as x approaches infinity, h(x) approaches infinity.

This is true because as x becomes larger, the square term (x - 5)² dominates, causing h(x) to approach positive infinity.

This option is a key feature of h(x).

In conclusion, the key feature of h(x) that is NOT mentioned in the given options is that the domain of h(x) is (0, ∞).

Therefore, the correct answer is:

O The domain of h(x) is (0, ∞).

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Answer:

$6.18

Step-by-step explanation:

43.28÷7 units = 6.18 per 1 unit

We obtain that the conditional probability that X₁ = 1, given that E1 X₁ = k for (k = 1, ..., n) is equal to (n - 1)C(k - 1) / nCk k / n.

Given that the random variables X₁, ..., Xn form n Bernoulli trials with parameter p. We need to determine the conditional probability that X₁ = 1, given that

E1 X₁ = k for (k = 1, ..., n).

Let us compute the probability of

E1 X₁ = k = P(X₁ + X₂ + ... + Xn = k).

Since X₁, X₂, ..., Xn are independent, therefore, we can compute the probability by using the Binomial distribution.

P(X₁ + X₂ + ... + Xn = k) = nCk pk (1 - p) n-k.

Now, let us consider the conditional probability of

P(X₁ = 1 | E1 X₁ = k) using Bayes' theorem.

The Bayes' theorem states that,

P(A | B) = P(B | A) P(A) / P(B).

Therefore, the probability can be computed as,

P(X₁ = 1 | E1 X₁ = k) = P(E1 X₁ = k | X₁ = 1) P(X₁ = 1) / P(E1 X₁ = k) … equation (1)

We have, P(E1 X₁ = k | X₁ = 1) = P(X₂ + ... + Xn = k - 1),
since if X₁ = 1, then E1 X₁ = k

if and only if the sum of the remaining (n - 1) variables is k - 1.

Hence, by using the Binomial distribution, we can write,

P(E1 X₁ = k | X₁ = 1) = (n - 1)C(k - 1) p(k-1) (1-p) (n-k).

Also, we have P(X₁ = 1) = p and P(E1 X₁ = k) = nCk pk (1-p)n-k.

Substituting the above values in equation (1), we get,

P(X₁ = 1 | E1 X₁ = k)

= (n-1)C(k-1) p(k-1) (1-p)(n-k) p / nCk pk (1-p)n-k.

= (n-1)C(k-1) / nCk k / n.

The above formula gives the conditional probability that X₁ = 1, given that E1 X₁ = k for (k = 1, ..., n).  

Therefore, we obtain that the conditional probability that X₁ = 1, given that E1 X₁ = k for (k = 1, ..., n) is equal to (n - 1)C(k - 1) / nCk k / n.

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Answer:

A

Step-by-step explanation:

For a number to be written in scientific notation, you need to have it in the form:

a x 10^n

Where a is between 1 and 10(not including 10), and n is an integer. We can notice that in option A, 0.1(a) is not between one and ten, so it is not in scientific notation.

Answer:

181 mi^2

Step-by-step explanation:

Dimensions of large rectangle, on the left, are 6 mi by 8 m; area is 48 m^2;

Dimensions of small rectangle, in the middle of the diagram, are 4 mi by 5 mi, or 20 mi^2; area is 20 mi^2.

Dimensions of circle:  r = 12 mi; area of quarter circle is (1/4)(3.14)(12 mi)^2, or 113 mi^2.

Total area is 113 mi^2 + 20 mi^2 + 48 mi^2, or 181 mi^2

Answer:

Step-by-step explanation:

So first off. lets take chunks of this shape. We have a 6x8 rectangle, a 4x5 rectangle, and a 1/4 circle with a radius of 12.

The area of a rectnagle is just length x width.

So lets plug in our values for our two ractnagles, and see what we get:

6*8

=

48

So our first rectangle has a area of 48

Next we have:

4*5

=

20

So our second rectangle has an area of 20.

Add these otgether you get 68.

Finally we have our 1/4 circle. To solve this, find the area of the full circle and divide by 4.

We already know the radius, which is 12, and the formula for area of a circle is:

a=πr^2

Plug in 12:

a=π12^2

=

a=π144

dividing by four for the 1/4circle:

a=π36

So this means your answer is either:

68 +36π

Or:

181.097(solving pi*36)

Either of these work, if the problem allows pi, then use the first one, If not, use the bottom one.

Hope this helps!

As a result, the sequence's first five terms are:a1 = 768 ,a2 = 192 ,a3 = 48,a4 = 12 and a5 = 3.

A list of numbers or other mathematical objects arranged in a specific order is referred to as a sequence in mathematics. Terms are the individual numbers that make up a sequence; the order in which they appear can be significant. Sequences might have an infinite number of terms or a finite number of terms (having an unlimited number of terms). Moreover, they can be defined in several ways, such as by the use of a formula or a recursive definition. Many branches of mathematics, such as number theory, analysis, and algebra, as well as other disciplines including physics, computer science, and engineering, all use sequences.

given

For the specified sequence, the appropriate explicit formula is:

n 1: a = 768 * (0.25)(n-1)

We can simplify the formula and enter n = 1, 2, 3, 4, and 5 to obtain the first five terms:

\(a1 = 768 * (0.25)^(1-1) = 768 * 1 = 768\)

\(a2 = 768 * (0.25) (0.25)^(2-1) = 768 * 0.25 = 192\)

\(a3 = 768 * (0.25) (0.25)^(3-1) = 768 * 0.0625 = 48\)

\(a4 = 768 * (0.25) (0.25)^(4-1) = 768 * 0.015625 = 12 \\a5 = 768 * (0.25)^(5-1) = 768 * 0.00390625 = 3\)

As a result, the sequence's first five terms are:a1 = 768 ,a2 = 192 ,a3 = 48,a4 = 12 and a5 = 3.

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The solution set of the given equation is x = 8.39 or x = -12.39

\( \frac{1}{4} {{(x + 2} )}^{2} = 27\)

cross product

\( {1} {{(x + 2}^{} )}^{2} = 27 \times 4\)

(x + 2²) = 108

find the square root of both sides

\( \sqrt{ ({x + 2)}^{2} } = ± \sqrt{108}\)

x + 2 = ± 10.39

So,

x = 10.39 - 2 or x = -10.39 - 2

x = 8.39 or x = -12.39

Therefore, the equation has a solution set of x = 8.39 or x = -12.39

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Answer:

5.81$

Step-by-step explanation:

Conditions for the parallel lines are as follow :

a. Lines should not intersect each other.

b. Slope of the given lines should be equal.

c. Parallel lines represent equations has no solution.

As given in the questions ,

Conditions for the parallel lines are given by :

a. If the two given lines are parallel to each other then they should not intersect each other.

Distance between the lines remains same.

b. Slope of the two parallel lines should be equal.

y = m₁ x + c

y = m₂ x + c

Here slope represented by m.

⇒m₁ = m₂

c. If two given equation has no solution then the given lines are parallel lines.

2x = 4x + 5

x = 2x + 3

Here m₁ = m₂ = 2

Therefore, the condition of the parallel lines are:

a. Lines should not intersect each other.

b. Slope of the given lines should be equal.

c. Parallel lines represent equations has no solution.

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Step-by-step explanation:

So to start

Perpendicular lines are lines that form 90 degree angles when they meet.

Parallel lines will never touch, no matter how far they go.

So

Top left

A vertical line and a horizontal line

This would be perpendicular

Lines that intersect to form right angles

As mentioned above this would be perpendicular

Two nonvertical lines that have a product of -1 for their slopes.

Parallel lines always have the same slope, so this goes for parallel.

Equations that can be written in slope intercept form

This would be both as all lines can be written in this form

Non vertical lines that have the same slope and different y-intercepts

As they have the same slope this would make it parallel

You can determine the relationship between two lines by comparing their slopes and y-intercepts.

This is both as this is a way to compare all lines

Lines in the same plane never intersect

This would be parallel

Slopes are opposite reciprocals

This is perpendicular as the slopes of perpendicular lines are reciprocals

Vertical lines that have different x-intercepts

This would be parallel

Sorry this is a lot

Hope this helped though :)

The compound from the table provided is Salt, which is CaCl2. We can determine the number of atoms in the formula by analyzing the chemical formula of the compound.Salt's formula is CaCl2, and it has one calcium atom and two chlorine atoms in its formula. Each ion is present in the compound as a whole

. Calcium chloride's formula contains one calcium atom and two chlorine atoms; the number of atoms is known simply by looking at the subscript attached to the element's symbol in the formula.

In the formula CaCl2, the number 2 indicates that there are two chlorine atoms and one calcium atom in the compound, in other words, the formula means there is one calcium atom combined with two chlorine atoms in the compound.

The formula of a compound is used to determine the number of atoms present in the compound.

The number of atoms of each element in a compound can be found by examining the subscript attached to the element's symbol in the chemical formula.

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Answer:

36:18= 16:9

2 eggs for every guest

We will repeat the exact same procedure. Something may have gone wrong.                                                                                                    

The special theory of relativity by German-born scientist Albert Einstein contains the equation \(E=mc^{2}\), which conveys the idea that mass and energy are one and the same physical substance and may be transformed into one another. The kinetic energy (E) of a body is equal to its increased relativistic mass (m) multiplied by the square root of the speed of light.

Because the mass and the speed of light are both constants, we are unable to test a new variable. Since our findings don't match the accepted formula, we cannot share them.

The result obtained is wrong we cannot apply it to another experiment. The only way we can find the correct result is by repeating the experiment. Because something may have gone wrong on the first attempt.

Therefore, the correct answer is

d) Repeat the exact same procedure.  

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The correct question is: Suppose you conduct one experiment and find that the \(E=mc^{3}\), rather than the historically accepted formula, \(E=mc^{2}\). What should you do next?

a.Test a new variable

b.Share your findings

c.Apply your results to a new experiment

d.Repeat the exact same procedure                                                                                                                                                                                                                                                                                                                                                                                      

The solution to the given expression after evaluating would be \(21\). ←Here

Hope this helps!

The value of the 10% trimmed mean is approximately 1.3027. To calculate the 10% trimmed mean, we need to trim off the lowest and highest 10% of the data and then find the mean of the remaining values.

First, let's sort the data in ascending order:

0.2, 0.21, 0.26, 0.3, 0.33, 0.41, 0.54, 0.57, 1.41, 1.7, 1.84, 2.2, 2.26, 3.06, 3.24

Next, we calculate the number of values to trim from each end:

10% of 15 (total number of values) = 0.1 * 15 = 1.5

Since we can't remove half a value, we round up to the nearest whole number, which is 2.

Now, we remove the two lowest and two highest values:

0.26, 0.3, 0.33, 0.41, 0.54, 0.57, 1.41, 1.7, 1.84, 2.2, 2.26

Finally, we calculate the mean of the remaining values:

(0.26 + 0.3 + 0.33 + 0.41 + 0.54 + 0.57 + 1.41 + 1.7 + 1.84 + 2.2 + 2.26) / 11 = 14.33 / 11 ≈ 1.3027

Rounding to four decimal places, the value of the 10% trimmed mean is approximately 1.3027.

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Answer:  $42,236.97

Work Shown:

A = P*(1+r/n)^(n*t)

A = 25000*(1+0.06/1)^(1*9)

A = 42236.9739750673

A = 42236.97