there are 12 people in an office with 4 different phone lines. if all the lines begin to ring at once, how many groups of 4 people can answer these lines?

Answer:

The length of the segment is 8 units.

We can use the formula for the volume of a cone to calculate the height of the cone:

V = (1/3)πr^2h

320 = (1/3)π(8^2)h

h = 320/(1/3)(π)(64)

h = 8 units

Answer:

Let's assume that the original size of the trial-size bottle of dishwashing soap is "x" ounces.

According to the problem, the new size of the bottle is 10% less than the original size, which means that the new size is 90% of the original size. So we can set up an equation as follows:

0.90x = 4.5

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.90:

x = 4.5 ÷ 0.90

x = 5

Therefore, the original size of the trial-size bottle of dishwashing soap is 5 ounces.

Answer:

Step-by-step explanation:

To solve the expression 2 × 3/4 ab, we can first simplify the fraction by multiplying the numerator (3) by the whole number (2) to get:

2 × 3/4 = 6/4 = 3/2

So the expression becomes:

3/2 ab

This means that we take the value of 3/2 and multiply it by the product of a and b. For example, if a = 4 and b = 5, then:

3/2 ab = 3/2 × 4 × 5 = 30

Therefore, the solution to the expression 2 × 3/4 ab is 3/2 ab or 1.5ab, which means we take the value of 3/2 and multiply it by a and b.

Answer:

Ashok's salary increases by 4%, which means his new salary will be:

New salary = Old salary + (4% of old salary)

New salary = 2500 + (4/100) * 2500

New salary = 2500 + 100

New salary = 2600

In addition to the increase, Ashok also gets an extra ₹75 per week, so his new salary will be:

New salary = Old salary + Increase + Extra amount

New salary = 2500 + 100 + 75

New salary = ₹ 2675 per week

Therefore, Ashok's new salary next week will be ₹ 2,675 per week.

Micah received 1/2 of Savi's share and Juan got the balance.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

total amount = $280=x

savi= 4*juan= 11

micah= 1/2 savi= 1/2*280/100= 1.4

juan got balance= 267.6

Hence, Micah received 1/2 of Savi's share and Juan got the balance.

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Approximately 7.30% of the bearings produced will not be acceptable.

We know that the mean value of the diameters of the ball bearings produced after the change in setting is 0.499 inches and the standard deviation is 0.002 inches. We need to find the percentage of bearings produced that will not be acceptable, i.e., the diameter of the bearing will be outside the range of (0.500 - 0.004) inches to (0.500 + 0.004) inches.

Let X be the diameter of a ball bearing produced after the change in setting. Then, X is normally distributed with mean µ = 0.499 inches and standard deviation σ = 0.002 inches.

We need to find P(X < 0.496 or X > 0.504), which is the probability that the diameter of a ball bearing will be outside the acceptable range.

Using the standard normal distribution, we can find the z-scores corresponding to the lower and upper limits of the acceptable range:

z1 = (0.496 - 0.499) / 0.002 = -1.5

z2 = (0.504 - 0.499) / 0.002 = 2.5

Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:

P(Z < -1.5) = 0.0668

P(Z > 2.5) = 0.0062

Therefore, the probability that a ball bearing produced after the change in setting will not be acceptable is:

P(X < 0.496 or X > 0.504) = P(Z < -1.5 or Z > 2.5) = P(Z < -1.5) + P(Z > 2.5) = 0.0668 + 0.0062 = 0.0730

So, the percentage of the bearings produced that will not be acceptable is:

0.0730 x 100% = 7.30%

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Answer:

20÷100×4.75=0.95

4.75-0.95=$3.8

Answer:

i got 4.55$

Step-by-step explanation:

i just converted the percentage (20%) and then subtracted that number (0.2) from the original price (4.75$)

Answer:

5.40

Step-by-step explanation:

let X represent the price of a 18 minute phone call

X=18 ×1.80

6

= 5.40

Answer:

18

Step-by-step explanation:

The probability that a randomly selected cap had a strength greater than 11 inch-pounds is approximately 0.2033 or 20.33% (rounded to two decimal places).

We know that cap strength, C, follows a normal distribution with mean μ = 10 inch-pounds and standard deviation σ = 1.2 inch-pounds. Therefore, we can standardize the variable C using the z-score formula:

z = (x - μ) / σ

where x is the value of cap strength we are interested in. In this case, we want to find the probability that a randomly selected cap had a strength greater than 11 inch-pounds, so x = 11. Plugging in the values for μ and σ, we get:

z = (11 - 10) / 1.2 = 0.83

Next, we need to find the probability that a standard normal random variable Z is greater than 0.83. This can be looked up in a standard normal distribution table or calculated using software. Using a standard normal distribution table, we find that the probability of Z being greater than 0.83 is approximately 0.2033.

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The price per foot of the 2-yard rope is $6.36.

To find the price per foot of the 2-yard rope, we need to first convert the length to feet. Since there are 3 feet in a yard, a 2-yard rope is equal to 6 feet.

Next, we divide the total cost of the rope ($22.86) by the length of the rope in feet (6 feet) to get the price per foot:

$22.86 ÷ 6 = $3.81 per yard

To convert this to the price per foot, we divide $3.81 by 3 (since there are 3 feet in a yard):

$3.81 ÷ 3 = $1.27 per foot

Therefore, the price per foot of the 2-yard rope is $1.27 x 5 = $6.36.

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The test statistic: X² = 42.620, Critical values: X²=38.932.

What are critical values?

A critical value is one that can be used to compare the test statistic to determine if the null hypothesis can be rejected or not.

Here, we have

Given: In one town, monthly incomes for men with college degrees are found to have a standard deviation of $650. A random sample of 22 men without college degrees resulted in incomes with a standard deviation of $926.

s = 926, n = 22

The null and alternative hypotheses:

H₀ : σ = 650; H₁ : σ > 650

Test statistic:

X² = (n-1)s²/σ²

X² = (22-1)926²/650²

x = 42.62

Critical values:

X² = X²a(n-1)

X² = X²(0.01)(21)

X² = 38.932.

Hence, the test statistic: X² = 42.620, Critical values: X²=38.932.

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Answer:

In the equation y = 210(1.082)^e, the y-intercept is the value of y when e = 0. When e = 0, the exponent (1.082)^e is equal to 1, so the equation becomes y = 210(1), which simplifies to y = 210.

Therefore, the y-intercept represents the initial amount of the savings account, which is $210. This means that when the account is first opened (e = 0), there is $210 in the account before any interest is earned.

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Answer:

it's b or 4.03

Step-by-step explanation:

your welcome

For the following data, the slope of the linear relationship is option D.

A line's direction and steepness are measured by the line's slope. by solving the slope of the line we can determine whether the lines are perpendicular, parallel, or none at all.

from the given data the first two coordinate points are:

(2,5) and (1,2)

The representation of the slope is given by the variable m.

The slope formula is :

m = (y2 - y1) / (x2 - x1)

by substituting the values in the equation

m = (2 .0- 5.0) / (1.0 - 2.0)

m = -3 / -1

m = 3

Therefore, the slope of the linear relationship is m = 3.

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Answer:

It's not "wrong", per se, it just didn't quite include the info that your teacher wanted! I personally would have said "Rotate 180 degrees about F", so I think that may be it.

Let me know if this helped by hitting the thanks button/marking brainliest! If not, please comment and I'll get back to you ASAP.

Question: It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

The probability that 2 students do not have the same birthday when 3 students are chosen is given as 0.992.Probability of two students not having the same birthday = 0.992

We need to find the probability that 2 students have the same birthday when 3 students are chosen.

Let's represent the probability that two students have the same birthday by p.

Since the number of possible outcomes when 3 students are chosen from 365 days in a year is 365^3.

Now, we can use the complement rule to find p.

Probability of 2 students having the same birthday

p = 1 - Probability of 2 students not having the same birthday p = 1 - 0.992p = 0.008

Thus, the probability that the 2 students have the same birthday is 0.008.

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We found for the line passing through (-1, 0) and (0, -1.5), we can see that the correct inequality is option A is -2y + 2x ≥ 7x + y + 5.

An inequality is a mathematical statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

Inequalities can involve variables or constants, and can be expressed in one variable or multiple variables. The solution to an inequality is the set of values that satisfy the inequality.

For example, the inequality 2x + 3 > 7 is true for values of x that are greater than 2, since if we substitute x = 2, we get 2(2) + 3 = 7, which is not greater than 7. On the other hand, if we substitute x = 3, we get 2(3) + 3 = 9, which is greater than 7, so the inequality is true for x > 2.

Inequalities have many applications in mathematics and other fields, such as economics, physics, and engineering. They are used to represent constraints in optimization problems, to model relationships between variables, and to describe ranges of possible values for a quantity or variable.

To determine the correct inequality, we need to find the equation of the line that passes through the points (-1, 0) and (0, -1.5).

The slope of the line can be calculated as follows:

m = (y2 - y1) / (x2 - x1)

m = (-1.5 - 0) / (0 - (-1))

m = -1.5

The y-intercept of the line can be found by substituting one of the points and the slope into the point-slope form of a line:

y - y1 = m(x - x1)

y - 0 = -1.5(x - (-1))

y + 1.5 = -1.5x - 1.5

y = -1.5x - 3

Now we can rewrite the inequality in the form y <= mx + b, where m is the slope and b is the y-intercept.

-2y + 2x >= 7x + y + 5 can be simplified to:

-3y >= 5x + 5

Dividing both sides by -3, we get:

y <= (-5/3)x - 5/3

Comparing this to the equation we found for the line passing through (-1, 0) and (0, -1.5), we can see that the correct inequality is option A:

-2y + 2x ≥ 7x + y + 5

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2t

Question:

If the coconut from the shorter tree takes time t to reach the ground, how long (in terms of t) will it take the other coconut to reach the ground?

Solution:

We know that the time taken by the coconut to reach the ground is given by the formula:

t = √(2h/g)

Where,
t = time taken to reach the ground
h = height of the tree
g = acceleration due to gravity

If the height of the coconut from the shorter tree is h, then the time taken by it to reach the ground is t.

Now, the coconut from the taller tree has a height of 2h. Therefore, its time taken to reach the ground can be calculated as follows:

t_1 = √(2(2h)/g)
t_1 = √(4h/g)
t_1 = 2√(h/g)

Therefore, the time taken by the coconut from the taller tree to reach the ground is 2 times the time taken by the coconut from the shorter tree to reach the ground.

Hence, the answer is, the time taken by the other coconut to reach the ground is 2t.

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To perform the opposite translation, we add the opposite of the translation vector to the image point A': the coordinates of point A are (16, 5).

what is a vector?

In mathematics, a vector is an object that represents a quantity having both magnitude (or length) and direction. Vectors can be represented geometrically as arrows, where the length of the arrow represents the magnitude of the vector and the direction of the arrow represents the direction of the vector.

To find the coordinates of point A, we need to perform the opposite translation of moving along the vector 〈−6, 0〉 from the image point A'(10, 5). This is because a translation is a rigid motion that preserves the distance between points, so the distance between A and A' is the same as the distance between their respective translations.

To perform the opposite translation, we add the opposite of the translation vector to the image point A':

A = A' - 〈-6, 0〉 = (10, 5) - (-6, 0) = (16, 5)

Therefore, the coordinates of point A are (16, 5).

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The values for the variables x and y in the parallelogram are equal to 10 and 17 respectively.

The parallelogram OPSR have two pairs of parallel sides hence OP = RS and PS = OR.

We shall evaluate for variables x and y as follows:

2x - 1 = x + 9

2x - x = 9 + 1 {collect like terms}

x = 10

y = x + 7

y = 10 + 7 {substituting 10 for x}

y = 17

Therefore, the values for the variable x and y in the parallelogram are equal to 10 and 17 respectively.

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Answer:

8 pints=4 quarts,16 cups is 8pints

Step-by-step explanation:

It is multiplication, if you write it down then think about how the numbers connect its easier to understand.

Answer:

Step-by-step explanation:

First, we need to determine the cost of making one necklace.

The total cost of supplies is $46 + $30 = $76.

If she makes one necklace, that cost is divided by one, so the cost of making one necklace is $76.

To find the selling price, we need to add a markup of 75%.

Markup = 75% x Cost = 0.75 x $76 = $57

The selling price will be the cost plus the markup:

Selling price = Cost + Markup = $76 + $57 = $133.

Therefore, Layla should charge $133 for each necklace.

The answer is d) 133.04, although it should be rounded to the nearest cent, so the final answer would be $133.

The expression to represent how much Mason's mom spent for "g" games online is 12g + 7

An expression is a combination of numbers, variables, and operators that represent a mathematical phrase or statement. Expressions can be used to represent mathematical operations and relationships, and they can be simplified or evaluated using mathematical rules and techniques.

Let's say that Mason's mom bought "g" games online.

Each game costs $12, and there is an additional $7 shipping fee per order.

Therefore, the total amount spent on g games can be represented by the expression:

12g + 7

Here, 12g represents the cost of the games, and 7 represents the shipping fee.

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The given question is incomplete, the complete question is:

Mason's mom bought g games online. The games cost $12 each plus a $7 shipping fee. Write an expression to represent how much Mason's mom spent for the games

Answer:

Step-by-step explanation:

When answering questions on Brainly, it is important to be factually accurate, professional, and friendly. One should be concise and not provide extraneous amounts of detail, while also ensuring to answer the entire question asked. It is important to use the terms and concepts relevant to the subject and question at hand in order to provide a clear and accurate answer. Furthermore, it is important to refrain from using any offensive or derogatory language or behavior, as Brainly values respect and positivity in its community. Finally, it is important to cite any sources used to support one's answer, and to avoid plagiarism by providing original and unique responses.

Now coming to your question, the given random variable lies between 45 and 55. Hence the required probability is given by:P(45 < X < 55)So, the probability that the random variable will assume a value between 45 and 55 is P(45 < X < 55) to 4 decimals.

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Answer:

\

Step-by-step explanation:

Given expression: 3x+9

Take 3 outside from the expression, we get,

= 3(x+3), which is called the equivalent expresion

Definition of a rectangle. Opposite sides of a parallelogram are congruent. Reflexive Property of congruent , SSS, option D.

Every component of the set is connected to itself, according to the reflexive feature of sets. The reflexive property of congruence is known when the relation specified on a set is congruence, and the reflexive property of equality is known when the relation defined on a set of numbers is equality. When this occurs, the relation can be referred to as a reflexive relation or as a reflexive property being satisfied on that set.

Any geometric figure compared to itself is congruent to itself so this is why:

AC ≅ CA

∠B ≅ ∠B

Since we have a parallelogram, therefore we can say:

BC ≅ DA

BA ≅ Dc

CA ≅ AC

Both triangles ABC and CDA satisfy the side to side to side congruence, since their 3 sides are congruent.

So, It's D.

Notice that the angle measure information is not included in the data above that's why we cannot say it is SAS congruence.

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Complete question:

Given: ABCD is a rectangle.

Prove: ΔABC is congruent to ΔCDA ABDC is a rectangle.

ABCD is a parallelogram. AB is congruent to DC and BC is congruent to DA AC is congruent to AC ΔABC is congruent to ΔCDA Given Definition of a rectangle. Opposite sides of a parallelogram are congruent. _____________________ _____________________

A. Symmetric Property of congruent; SAS

B. Reflexive Property of congruent to; SAS

C. Symmetric Property of congruent; SSS

D. Reflexive Property of congruent; SSS

The gathering of statistical data is the main emphasis of quantitative research methodologies. set of potential solutions data from statistics on how people view social life independent elements dependent factors

              Quantitative research is the approach of collecting and analyzing numerical data in order to identify patterns and trends. Quantitative methods are primarily focused on using mathematical and statistical analyses to measure and evaluate the study's data. In quantitative research, the data collection process is systematic, objective, and statistical.

                Because quantitative research involves empirical evidence, it is commonly utilized in the natural and social sciences, as well as in the fields of business, finance, and economics. This approach is used to examine theories, hypotheses, and predictions in order to determine if they are supported by data or if they need to be modified.

                   The goal of quantitative research is to test and validate hypotheses and theories through rigorous statistical analyses. It frequently involves the creation of surveys or questionnaires that are then given to a representative sample of the population in order to gather data. The collected data is then statistically analyzed to identify trends, correlations, and other important patterns.

                 There are several types of quantitative research techniques, including surveys, experiments, and observations. Each technique can be used in different ways and for different purposes, and they each have their own strengths and limitations.

       Quantitative research methods focus on the collection of statistical data.

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To calculate the monthly periodic interest rate from an annual percentage rate (APR), we need to divide the APR by 12 (the number of months in a year). We can use the following formula:

Monthly periodic interest rate = APR / 12

In this case, the APR is 16.75%, so we can plug it into the formula and simplify:

Monthly periodic interest rate = 16.75% / 12

Monthly periodic interest rate = 1.395833...%

Rounding to the nearest hundredth of a percent, we get:

Monthly periodic interest rate = 1.40%

Therefore, the monthly periodic interest rate for the primary credit card holder is 1.40%.

a) There are three values of x, namely -3, -2, and -1, for which g(x) = 0.

b) The absolute minimum value of g on the interval -7 ≤ x ≤ 9 is 20, and the absolute maximum value of g is 90

a. To check if there is a value of x for -3 ≤ x ≤ 2 such that g(x) = 0, we can plug in each value in the interval and see if any of them make g(x) equal to 0:

g(-3) = -3² + 5(-3) + 6 = 0

g(-2) = -2² + 5(-2) + 6 = 0

g(-1) = -1² + 5(-1) + 6 = 0

g(0) = 0² + 5(0) + 6 = 6

g(1) = 1² + 5(1) + 6 = 12

g(2) = 2² + 5(2) + 6 = 20

So, we can see that there are three values of x, namely -3, -2, and -1, for which g(x) = 0.

b. To find the absolute minimum and maximum values of g on the interval -7 ≤ x ≤ 9, we can first find the critical points of g by taking its derivative:

g'(x) = -2x + 5

Setting g'(x) = 0, we get:

-2x + 5 = 0

-2x = -5

x = 5/2

So, the only critical point of g is x = 5/2.

We can now check the values of g at the endpoints of the interval and the critical point:

g(-7) = -7² + 5(-7) + 6 = 20

g(9) = 9² + 5(9) + 6 = 90

g(5/2) = (5/2)² + 5(5/2) + 6 = 43.25

Therefore, the absolute minimum value of g on the interval -7 ≤ x ≤ 9 is 20, which occurs at x = -7, and the absolute maximum value of g is 90, which occurs at x = 9.

We can justify this by noting that g is a quadratic function with a negative leading coefficient, which means that it opens downward and has a maximum value at its vertex (which occurs at x = 5/2). Since the vertex is within the given interval, and the function is decreasing on the left and increasing on the right of the vertex, the maximum and minimum values of g must occur at the endpoints of the interval.

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