whats the hcf of 108 and 308​

Answer:

138

Step-by-step explanation:

Answer:

C. 138

Step-by-step explanation:

Substitute the values for their given variables:

6(5)² - 5(4) + 8 ⇒ 150 - 20 + 8 ⇒ 138

Answer:

b + s = 14

5b + 10s = 80

Step-by-step explanation:

Answer:

b + s = 14

$5b + $10s = $80

Step-by-step explanation:

the sum of boogie board and surfboard rented is 14

boogie board rented + surfboard rented = 14

b + s = 14  equation 1

total income derived from renting the two types of boards is $80

total income derived = total income derived from renting boogie boards + total income derived from renting surfboards

total income derived from renting boogie boards = cost of renting one boogie board x number of boogie boards rented

= $5 x b = 5b

total income derived from renting surfboards = cost of renting one surfboard x number of surfboards rented

= $10 x s = 10s

80 = 5b + 10s   equation 2

In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.

In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.

Here,

To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.

For example:

f(0) = 4(0) - 6 = -6

f(1) = 4(1) - 6 = -2

f(2) = 4(2) - 6 = 2

f(-1) = 4(-1) - 6 = -10

f(3a) = 4(3a) - 6 = 12a - 6

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Answer:

6cm

Step-by-step explanation:

Given data

Width= 4.6cm

Length= 9cm

Volume= 82.8cm^3

The expression for the volume is given as

V= lwh/3

82.8= 9*4.6*h/3

cross multiply

82.8*3= 9*4.6*h

248.4= 41.4h

h= 248.4/41.4

h= 6cm

Step-by-step explanation:

the answer is 9 i hope it helps

The value of the function when x = 2 is 9

Functions are used to represent equations and graphs

The function is given as:

f(x) = 2x^2  - 3x + 7

When x =2, we have:

f(2) = 2(2)^2  - 3(2) + 7

Evaluate the exponent

f(2) = 2(4)  - 3(2) + 7

Evaluate the product

f(2) = 8  - 6 + 7

Evaluate the expression

f(2) = 9

Hence, the value of the function when x = 2 is 9

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The average number in line: 0.5 persons. Average number of persons in the system: 1 person. Average time spent in line: 2.5 minutes. Increased arrival rate will result in more people in the waiting line.

The average number in line can be calculated using the formula for the average number of customers in the system, Ls = λWs, where λ is the arrival rate and Ws is the average time a customer spends in the system. In this case, the arrival rate is 10 persons per hour and the time per player is 5 minutes. Converting the arrival rate to arrivals per minute, we have λ = 10/60 = 1/6 arrivals per minute. Plugging these values into the formula, we get Ls = (1/6) * 5 = 5/6 = 0.833, which can be approximated to 0.5 persons.

The average number of persons expected to be in the system includes both those in the line and those being served. Since the system follows a First-Come-First-Serve (FCFS) discipline, the number of people in line will be equal to the number of people in the system. Therefore, the average number of persons in the system is also 0.5 persons.

The average amount of time a person spends in line can be calculated using Little's Law, which states that the average number of customers in a stable system is equal to the arrival rate multiplied by the average time a customer spends in the system. In this case, the average number of customers in the system is 0.5 persons and the arrival rate is 10 persons per hour. Converting the arrival rate to arrivals per minute, we have λ = 10/60 = 1/6 arrivals per minute.

Plugging these values into the formula, we get 0.5 = (1/6) * Ws. Solving for Ws, we find Ws = 3 minutes. Since the average time spent in the system includes both waiting time and service time, and the service time is 5 minutes per player, the average time spent in line is Ws - service time = 3 - 5 = -2 minutes. However, a negative waiting time is not meaningful in this context. Therefore, we can approximate the average time spent in line to 2.5 minutes.

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The positive even integers whose sum of reciprocals is 7/24 are 6 and 8.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Let the two consecutive even integers be 2x and 2x+2 then there sum of reciprocal will be 7/24 that is now solving for positive value of x by finding roots of quadratic equation :

\(\begin{aligned}\frac{1}{2x}+\frac{1}{2x+2}&=\frac{7}{24}\\\frac{1}{x}+\frac{1}{x+1}&=\frac{7}{12}\\\frac{2x+1}{x^2+x}&=\frac{7}{12}\\24x+12&=7x^2+7x\\7x^2-17x+12x&=0\\x&=3, \frac{-4}{7} \end{aligned}\)

Consider only positive value of x that is 3

Therefore, The positive even integers whose sum of reciprocals is 7/24 are 6 and 8.

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Answer:

Step-by-step explanation:

BA = Number of hits / Times at bat

BA = 280 / 300

BA = 0.933

No one past or present, has ever had that kind of batting average.

Ty Cobb has a lifetime average of 0.366

Ted Williams was the last play to average 0.406 in a season. (Over 400). He did it in 1941.

Answer:

y=8

x=3

Step-by-step explanation:

Answer:

A width of 3 and a length of 9

Step-by-step explanation:

To solve this problem, we're going to have to create an equation. So, let's call the width w. The length of the rectangle is three times the width, so the length will be 3w. The total area is 27, and the length times the width must equal the area, so this gives us the following equation:

w(3w) = 27

Let's simplify and start solving.

3w² = 27

3w²/3 = 27/3

w² = 9

√w² = √9

w = 3

Remember, we defined w as the width. So, the width of the rectangle is 3. The length is 3w, or three times the width, so the length must be 9. And these are our dimensions: 3 × 9.

1. 45 out of the 105 tiles to be vowels.

2. 10 out of the 20 cards to have flowers on them.

1. The expected number of vowels among the 105 tiles, we can multiply the proportion of vowels by the total number of tiles:

Expected number of vowels

= Proportion of vowels x Total number of tiles

= (3/7) x 105

= (3/7) x 105

= 45

Therefore, you would expect 45 out of the 105 tiles to be vowels.

2. Now, to find the expected number of cards with flowers among the 20 cards, we can multiply the proportion of cards with flowers by the total number of cards:

Expected number of cards with flowers

= Proportion of cards with flowers x Total number of cards

= (2/4) x 20

= 10

Therefore, you would expect 10 out of the 20 cards to have flowers on them.

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a) The (9,009, 10,585) range represents the 99% confidence interval for the mean number of steps taken on an average workday for all New York City employees who wear activity trackers. No, we are unable to determine the likelihood of specific values using the confidence interval. Only inferences about the population mean can be drawn from it.

A 99% confidence interval for the mean needs to be calculated.

Since the population standard deviation is unknown, we must infer it from the sample standard deviation in order to get the critical number using a t-students distribution.

Sample Mean(M) = 9,797

Sample Standard Deviation(s) = 2,313.

Sample Size(N) = 61

When σ is unknown, an estimation of σM is made by dividing s by the square root of N:

S = s/√n

S = 2313/√61

S = 2313/7.8102

S = 296.1512

These sample size's degrees of freedom are:

df = n - 1

df = 61 - 1

df = 60

With 61 degrees of freedom and a 99% confidence interval, the t-value is 2.66.

The Margin of Error calculated as:

MOE = t × S

MOE = 2.66 × 296.1512

MOE = 787.7622

The confidence interval's lower and upper bounds are as follows:

Lower Bound = M - MOE

Lower Bound = 9797 - 787.7622

Lower Bound = 9,009.2378

Lower Bound = 9,009(approx)

Upper Bound = M + MOE

Upper Bound = 9797 + 787.7622

Upper Bound = 10,584.7622

Upper Bound = 10,585(approx)

We have a 95% confidence interval between 9,009 and 10,585 steps as the mean number of steps taken on a normal workday for all New York City employees using activity trackers.

b) The value of 8,500 steps is outside the confidence interval, which indicates that it is a high figure for the average number of steps taken by all New Yorkers using activity trackers.

The confidence interval cannot be used to calculate the likelihood of specific values.

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The complete question is:

Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.

a. Construct and interpret a 99 percent confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.

b. A wellness director at a company in New York City wants to investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on a typical workday. Is it appropriate to use the confidence interval found in part (a) to conduct the investigation.

Answer: First, we need to find the coordinates of points P and Q. Since both P and Q lie on the line 3x + 4y + 15 = 0 and are equidistant from the origin, we can set up two equations:

3x + 4y + 15 = 0 (equation of the line)

x^2 + y^2 = 5^2 (equation of the circle with radius 5)

Solving these two equations simultaneously, we get:

x = -3, -12/5

y = -4, 3/5

Since P and Q lie on the same line, we can find the midpoint of PQ as:

(((-3) + (-12/5))/2, ((-4) + (3/5))/2) = (-33/10, -37/10)

Let O be the origin. Then the length of PO is the distance between O and P, which is:

sqrt((-3 - 0)^2 + (-4 - 0)^2) = 5

Similarly, the length of QO is also 5. Thus, we have a right triangle POQ with hypotenuse of length 5 and legs of length 5. Therefore, the area of triangle POQ is:

(1/2) * base * height

= (1/2) * 5 * 5

= 12.5 square units.

Step-by-step explanation:

The area of triangle POQ is approximately 17.32 square units.

We will apply  the formula for the distance between a point and a line to find their coordinates.

The formula for the distance between a point (x0, y0) and a line Ax + By + C = 0 is:

d = |Ax0 + By0 + C| / √t(A^2 + B^2)

Here we have, A = 3, B = 4, and C = 15.

5 = |3x0 + 4y0 + 15| / sqrt(3^2 + 4^2)

Solving for |3x0 + 4y0 + 15|, we get:

|3x0 + 4y0 + 15| = 5 * sqrt(3^2 + 4^2) = 25

This gives us two equations, solving these equations simultaneously, we get two points:

3x0 + 4y0 + 15 = 25

3x0 + 4y0 + 15 = -25

P = (-5, 0)

Q = (5, 0)

PO = √((-5 - 0)^2 + (0 - 0)^2) = 5

QO = √((5 - 0)^2 + (0 - 0)^2) = 5

PQ = √((5 - (-5))^2 + (0 - 0)^2) = 10

Using Heron's formula to find the area of triangle POQ:

s = (5 + 5 + 10) / 2 = 10

Area = √ (s(s-5)(s-5)(s-10)) = √(300)

=17.32

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circumference = 2 x pi x r

r = 65 cm

so C ≈ 2 x 3,14 x 65 ≈ 408,20

Answer: C=408.41 centimeters

Step-by-step explanation:

2 times pi times 65

130 pi

Approximately 408.41

The correct way to measure the zone of inhibition is to place a known amount of an antimicrobial agent on a solid medium.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The zone of inhibition is then measured as the area surrounding the antimicrobial agent where microbial growth has been inhibited. This area is typically measured in millimeters. To accurately measure the zone of inhibition, it is important to ensure that the size of the inoculum and the amount of antimicrobial agent used remain constant. Additionally, it is important to consider the type of organism being studied, as different organisms can have different levels of susceptibility to the antimicrobial agent. Finally, the medium used should be appropriate for the organism being studied, as different media can produce different results.

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Answer:

Step-by-step explanation:

the answer its f (-5) i tink

Answer: 68

Step-by-step explanation: do 75+37 which equals 112 then subtract 180 by 112 which equals 68

hope this helps

Answer:

A

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , then

x + 37° + 75° = 180° , that is

x + 112° = 180° ( subtract 112° from both sides )

x = 68°

37.40 is  large a sample should you take in confidence interval.

What does confidence interval mean?

For the 95% confident interval of population mean , the margin of error (ME)

       ME = Z 1 - 0.05/2 5/√n

           2 = 1.96 * 6.24/√n

          n = ( 1.94 * 6.24/2)²

           n = 37.40

the required sample size (n) is 38 .

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Answer:

Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches.

, √4=√2²=2inches

2√3,=2×√3=2×1.735=3.5inches

√6=√2×√3=1.4×1.7=2.4inches

In order

2 inches,2.4inches and 3.5 inches.

Answer:

Step-by-step explanation:

Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches.

, √4=√2²=2inches

2√3,=2×√3=2×1.735=3.5inches

√6=√2×√3=1.4×1.7=2.4inches

In order

2 inches,2.4inches and 3.5 inches.

Answer:

bfcfbdgbcbcvgb

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

0.5=0.42 then the answer is 0.5

Using sampling concepts, it is found that the 33,043 infants represent the sample.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

In this problem, all infants represent the population, while 33,043 infants represent the sample.

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Answer:

-2

Step-by-step explanation:

y^3=-8.

y=cube root of -8 = -2

The p-value for testing H0 (null hypothesis) versus Ha (alternative hypothesis) is 0.0038. We need to determine whether H0 would be rejected at different significance levels: α = 0.10, α = 0.05, α = 0.01, and α = 0.001.

To make the decision, we compare the p-value with the chosen significance level. If the p-value is less than or equal to the significance level, we reject H0. Otherwise, we fail to reject H0.

At α = 0.10: Since the p-value (0.0038) is less than 0.10, we reject H0.

At α = 0.05: Since the p-value (0.0038) is less than 0.05, we reject H0.

At α = 0.01: Since the p-value (0.0038) is greater than 0.01, we fail to reject H0.

At α = 0.001: Since the p-value (0.0038) is greater than 0.001, we fail to reject H0.

In summary:

H0 would be rejected at α = 0.10 and α = 0.05.

H0 would not be rejected at α = 0.01 and α = 0.001.

Please note that the decision to reject or fail to reject the null hypothesis depends on the chosen significance level, and different levels of significance can lead to different conclusions.

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The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

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Answer:

I get 24...... ....... .......

The three possible side lengths of the third side are;

5, 6, and 7.

Polygon, which has three sides and three vertices, is called a triangle.

The sum of all the angles of the triangle is 180°.

Given:

A triangle has two side lengths of 4.75 centimeters and 8.5 centimeters.

To find the three possible side lengths of the third side:

The minimum possible value of the third side of triangle = max(s1, s2) – min(s1, s2) + 1

The minimum possible value = 8.5 - 4.75 + 1 = 4.75

The maximum possible side length = max(s1, s2) + min(s1, s2) - 1

The maximum possible side length = 8.5 + 4.75 - 1 = 12.25

Therefore, 4.75 < S3 < 12.25.

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The P-value is the probability of observing a test statistic as extreme as the one calculated from the sample data if the null hypothesis is accurate. This is a two-tailed test since the null hypothesis is "pregnant women do not have the ability to predict the gender of their baby."The p-value is 0.327.

Given probability value and form the conclusion:Study addressed the issue of whether pregnant women can correctly predict the gender of their baby and among 104 pregnant women, 57 correctly predicted the gender of their baby. If pregnant women have no such ability, there is a 0.327 probability of getting such sample results by chance. The P-value is the probability of observing a test statistic as extreme as the one calculated from the sample data if the null hypothesis is accurate.

This is a two-tailed test since the null hypothesis is "pregnant women do not have the ability to predict the gender of their baby."The p-value is 0.327. Since the p-value is higher than the standard significance level of 0.05, there isn't enough proof to dismiss the null hypothesis. Thus, there isn't enough evidence to indicate that pregnant women have the ability to predict the gender of their baby. To conclude, the result of the study doesn't provide any significant evidence to support the claim that pregnant women can correctly predict the gender of their baby.

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