least common denominator of 2/5 and 3/10

Answer:

3.125

Step-by-step explanation: np

Answer:

3.125

Step-by-step explanation:

3 is the full number so it goes before the decimal

1/8=0.125

3 1/8=3.125

Answer:

Each hamburger patty weighs 1/4 pounds.

Answer:

Ummmm.... Whats your qustion???? Im confused...

Step-by-step explanation:

Answer:

11/61

Step-by-step explanation:

sin K = opp/hyp

sin K = 11/61

Answer: 11/61

Answer:

SinK=11/61

Step-by-step explanation:

The function sin can be found by looking for the side opposite of the angle over the hypotenuse.

Answer:

8.35

Step-by-step explanation:

To get absolute value, just make it the opposite

Answer: |-8.35| = 8.35

Step-by-step explanation: |-8.35| = 8.35

The required length of the other piece of the board is  12.3 meters.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

To find out the length of the other piece we need to subtract the length of one piece from the original length of the board,
So,
Length of the other piece = 19.5 - 7.2 meters
                                        = 12.3 meters

Thus, the required length of the other piece of the board is  12.3 meters.

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Example of dependent events and independent events and their probabilities are as given below.

1. a. Two independent events that I know the probability of are:

Rolling a fair die and getting a 4 (probability of 1/6)

Flipping a fair coin and getting heads (probability of 1/2)

b. I know these events are independent because the outcome of one event does not affect the outcome of the other event. The outcome of rolling a die does not affect the outcome of flipping a coin, and vice versa.

c. The probability of both events occurring is (1/6) × (1/2) = 1/12

2a. Two dependent events:

i. Drawing a red card from a deck of cards and then drawing another card (without replacement)

ii. Drawing a red ace and then drawing another red card (without replacement)

b. I know these events are dependent because the outcome of the first event affects the outcome of the second event. The probability of the second event depends on the outcome of the first event.

c. These dependent events might require a different method for calculating the probability of both events occurring, such as conditional probability.

The probability of both events occurring would be P(A and B) = P(A) × P(B|A)

where P(A) is the probability of the first event and P(B|A) is the probability of the second event given that the first event has occurred.

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Answer:

Using the slope-intercept form, the slope is −2 .

Step-by-step explanation:

Step-by-step explanation:

solution

Equation of line,

y=-2x-2

2x+y=2 - - - - - - -1

Now,

slope of line,

m= -x coefficient/ y coefficient

= -2/1

= -2

Slope of required line which is perpendicular to the line

m.m = -1

-2.m = -1

m = -1/-2

m =1/2

Answer:

c

Step-by-step explanation:

The best graphical representation for the data on the number of hours 14-year-olds slept each night, gathered from a random sample of 130 athletic programs in the state, would be a histogram or a line plot.

A histogram is a graphical representation that uses bars to display the frequency or proportion of data in different intervals or bins. It is commonly used to visualize the distribution of a dataset and identify patterns, trends, or outliers.

To create a histogram, you first divide the range of the data into equal intervals or bins, and then count the number of observations that fall within each bin. The bins are usually represented on the x-axis, while the frequency or proportion of observations in each bin is represented on the y-axis.

A line plot, also known as a dot plot, is a simple graphical representation of a dataset that displays the individual data points as dots or small marks along a number line.

To create a line plot, you first choose a number line that covers the range of the data. Then, you plot each data point as a dot or a mark above its corresponding value on the number line. If there are multiple data points with the same value, you can stack the dots vertically to show their frequency.

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Answer:

Line Plot :)

Step-by-step explanation:

Answer:

  Patty, Karla, Cathy

Step-by-step explanation:

The scoring percentage of goals attempted can be computed by dividing goals made by those attempted, then multiplying the result by 100%.

__

Cathy's rate is ...

  27/54 × 100% = 50%

Karla's rate is ...

  18/45 × 100% = 40%

Patty's rate is ...

  given as 34%

__

By least to greatest scoring rate, the athletes are ...

  Patty (34%), Karla (40%), Cathy (50%)

It can be written as 13/35.

how do we rewrite a fraction.

Divide the numerator by the denominator

Write down the whole number result

Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.

A number that will divide evenly into both the numerator and denominator so it can be reduced, or

The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number

4/5-3/7

⇒4×7-3×5/ 35     ( 5 and 7 have no common divisor).

⇒ 28- 15/35

⇒13/35

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In the given figure, a line is given with two arrows over the letters U and V depicting the points. Such a line can be represnted as UV or VU with a double headed arrow above it.

Hence, option A and B are corrrect.

Answer:

 \(\dfrac{x^2+8x+8}{2x+4}\\\\\)

Step-by-step explanation:

Simplify:

        \(\dfrac{3x + 4}{x +2}+\dfrac{x^2+2x}{2x+ 4}\)

Multiply the denominator and the numerator of the first term by 2,

                        \(=\dfrac{2*(3x +4)}{2*(x+ 2)}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{2*3x+2*8}{2*x +2*2}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{6x+8}{2x+4}+\dfrac{x^2+2x}{2x+4}\)

                       \(\sf = \dfrac{6x+8+x^2+2x}{2x+4}\\\\\text{\bf Combine like terms,}\\\\=\dfrac{x^2+8x+8}{2x+4}\\\\\)

Answer: $12,000

Step-by-step explanation:

The Income statement shows the Net Profit or Loss for a company in a given period. That Net income is calculated by subtracting expenses from the revenue for the period:

= Revenue - Expenses

= 15,000 - 3,000

= $12,000

Answer:

34 and 17 feet.

Step-by-step explanation:

We have that the volume is given by:

V = x * x * y = (x ^ 2) * y

The surface area of the tank would be: x ^ 2 + x * y + x * y + x * y + x * y

SA = x ^ 2 + 4 * x * y

we know that the volume is 19652, replacing it would remain:

 19652 = (x ^ 2) * y, we solve for y:

y = 19652 / (x ^ 2)

replacing in SA we are left with:

SA = x ^ 2 + 4 * x * 19652 / (x ^ 2)

SA = x ^ 2 + 70608 / x

we derive and equal 0:

SA´ (x) = 2 * x - 70608 / (x ^ 2) = 0

2 * x = 70608 / (x ^ 2)

x ^ 3 = 39304

x = 34

for and would be:

y = 19652 / (34 ^ 2) = 17

dimensions are 34 and 17 feet.

The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)  

and the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

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Therefore, the annual simple interest rate charged by the pawnbroker is 5%

To determine simple interest, divide the balance by the cost of borrowing, the amount of time left, and other factors. Principal plus interest plus hours is the straightforward return strategy in marketing. The simplest approach to calculate interest is to use this method. The most popular method of calculating revenue is as a percent of the principal amount.

Here,

To find the annual simple interest rate, we need to use the formula:

Simple interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate, and Time is the time period in years.

In this case, the Principal is $270, and the amount paid back is $276.75, which means the interest paid is:

Interest = Amount paid back - Principal = $276.75 - $270 = $6.75

The time period is 5/360 years, since there are 360 days in a year and Elisa had the loan for 5 days.

Plugging these values into the formula, we get:

$6.75 = $270 x Rate x 5/360

Solving for Rate, we get:

Rate = $6.75 / ($270 x 5/360) = 0.05 or 5%

Therefore, the annual simple interest rate charged by the pawnbroker is 5%

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

The relative change from 6546 and 4392 is 49.04

Step-by-step explanation:

The expressions are simplified to;

1. 72n² + 63n

2. 18t - 18t²

3. -18b² - 18b

4. -56r - 21r²

5. -6m + 9m²

Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These operations are;

From the information given, we have;

1. -9n (-8n -7)

expand the bracket

72n² + 63n

2. -2t(-9 + 9t)

expand the bracket

18t - 18t²

3. -3b(6b + 6)

expand the bracket

-18b² - 18b

4. -7r(8 + 3r)

expand the bracket

-56r - 21r²

5. 3m(-2 + 3m)

expand the bracket

-6m + 9m²

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Answer:

r>5

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

7x=-13-8

7x=--21

x=-21/7

x=-3

points or brainleist please

Answer:

\(x=-3\)

Step-by-step explanation:

\(7x+8=-13\)

\(\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\)

\(7x+8-8=-13-8\)

\(\mathrm{Simplify}\)

\(7x=-21\)

\(\mathrm{Divide\:both\:sides\:by\:}7\)

\(\frac{7x}{7}=\frac{-21}{7}\)

\(x=-3\)

Hope it helps

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Pls mark me as brainliest

Answer:

0.967 = 96.7% probability the rock sample actually contains raritanium

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive reading

Event B: Contains raritanium

Probability of a positive reading:

98% of 13%(positive when there is raritanium).

0.5% of 100-13 = 87%(false positive, positive when there is no raritanium). So

\(P(A) = 0.98*0.13 + 0.005*0.87 = 0.13175\)

Positive when there is raritanium:

98% of 13%

\(P(A) = 0.98*0.13 = 0.1274\)

What is the probability the rock sample actually contains raritanium?

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1274}{0.13175} = 0.967\)

0.967 = 96.7% probability the rock sample actually contains raritanium

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line?

1)Yes as the probability of six having the correct shape is not unusual

2)NO. as the probability of six having the correct shape is unusual

3)Yes as the probability of six having the correct shape is unusual

4) No. as the probability of six having the correct shape is not unusual

Solution:

If exactly 6 of the 10 have the right shape, it means that the probability of success for the sample is

6/10 = 0.6

Expressing the probability in terms if percentage, it becomes

0.6 × 100 = 60%

Over time, the company has found that 89.4% of all their rugby balls have the correct shape. It means that the probability of success for the population is 89.4%

Comparing both probabilities, the probability of only 6 having the right shape is unusual. Therefore, the correct option is

3)Yes as the probability of six having the correct shape is unusual

Answer: is C

Step-by-step explanation:

Answer: 120 yds

Step-by-step explanation:

48+30+24+18+120 yds

A normal distribution has a mean of 50 and a standard deviation of 3 , the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241  option a) 0.025.

In probability theory, normal distribution is also known as Gaussian distribution. It is a probability distribution that is symmetrical, bell-shaped, and a continuous probability distribution. It's also a part of continuous probability distribution that describes real-valued random variables whose probability density function is affected by two parameters: the mean μ and the variance σ².

Let us consider the problem. Suppose a normal distribution has a mean of 50 and a standard deviation of 3. Firstly, we need to standardize the random variable X that is to convert it to the standard normal distribution. We use the following formula for this Z = (X - μ) / σwhere X is the random variable and μ is the mean, σ is the standard deviation of the population.

So in this case, we can write this as Z = (44 - 50) / 3 = -2

We have now obtained the standard score or standard deviation for the random variable X.

Now we need to calculate the probability P(X ≤ 44) = P(Z ≤ -2).

The probability of Z being less than -2 is denoted by the area under the standard normal curve to the left of Z = -2.

Using the standard normal table we look for the probability that corresponds to -2 and the closest we find is 0.0228.

This probability represents the area under the standard normal distribution to the left of Z = -2.

To calculate the area to the left of Z = -2, we add the area to the left of the next integer, which is -3, which we find from the standard normal table as 0.0013, 0.0228 + 0.0013 = 0.0241.

Therefore, the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241 or 0.025 (rounded to three decimal places)Therefore, the answer is option A. 0.025.

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