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The value of the expression when simplified is equal to √5. The correct option is D.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given radical expression can be simplified as shown below,

5√20 - 3√45

Write the under root values in the factored form,

= 5√(4×5) - 3√(9×5)

Simply the function that can be simplified,

= 5(√4 × √5) - 3(√9 × √5)

= 5(2√5) - 3(3√5)

= 10√5 - 9√5

Take √5 as the common term from the two of the given terms,

= (10 - 9) √5

= 1 √5

= √5

Hence, the value of the expression when simplified is equal to √5.

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Answer:

Step-by-step explain

∛12↔3³≈4x↑

Answer: 1/3, 1, 127/100, 1.4

Hope this helps

Confidence intervals are used to estimate the range of values in which a true population parameter is likely to lie.

One example where confidence interval must be used for statistical inference is when we want to estimate the mean or proportion of a population based on a sample.

For instance, if we want to estimate the average weight of adult females in a city, we can take a random sample of 100 women and calculate the sample mean and standard deviation.

We can then construct a 95% confidence interval for the population mean weight using the sample data and statistical formulas.

This interval provides us with a range of plausible values for the population mean weight with a 95% level of confidence. Hypothesis testing is used to determine whether a given hypothesis about a population parameter is supported by the sample data or not.

One example where hypothesis testing must be used for statistical inference is when we want to compare two population means or proportions based on their sample estimates.

For instance, if we want to test whether there is a significant difference in the mean salary between male and female employees in a company, we can take a random sample of 50 male and 50 female employees and calculate their sample means and standard deviations.

We can then use a t-test or z-test to test the null hypothesis that the population means are equal versus the alternative hypothesis that they are not equal.

If the p-value of the test statistic is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference between the two population means at that level of significance.

P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true.

It measures the strength of evidence against the null hypothesis and is used to make a decision about whether to reject or fail to reject the null hypothesis.

A smaller p-value indicates stronger evidence against the null hypothesis and supports the alternative hypothesis.

Typically, a significance level of 0.05 or less is used to determine whether the p-value is statistically significant or not.

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Answer:

-7

Step-by-step explanation:

The area of the shaded region is 27.53 cm².

Here, we ahve,

from the given information, we get,

It is given that,

radius of the semicircle = the width of the rectangle =  8cm

diameter of the semicircle = the length of the rectangle = 16 cm

The area of the semicircle is calculated as,

area = πr²/2

       = π8²/2

       = 100.48 cm²

The area of the rectangle is calculated as,

area = l * w

        = 16 * 8

        = 128 cm²

The area of the shaded region is calculated as,

area of the shaded region is:

= The area of the rectangle - The area of the semicircle

=128 cm² -  100.48 cm²

= 27.53 cm²

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complete question:

a rectangle is placed around a semicircle as shown below. the width of the rectangle is 8cm . find the area of the shaded region.

attached:

Answer:

Hi! Your answer is: -h-6

Step-by-step explanation:

~Write in standard form~

On solving the provided question, we can say that -  equation in slope-intercept form of the line that pae through the point (4, 7) and is parallel to the line represented by y = 2x - 5 is \(2x -y -1 = 0\)

A number that specifies a line's direction and slope is known as the slope or slope of a line in mathematics. A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x).

The provided equation is -

y = 2x - 5

since these are parallel to each other,

slope, m= 2

now the equation is -

\((y-y1) = m(x-x1)\\(y - 7) = 2(x - 4)\\y - 7 = 2x - 8\\2x -y -1 = 0\\\)

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Answer:

x=-64/11

Step-by-step explanation:

3x-14x-42=22

-11x-42=22

-11x-42+42=22+42

-11x=64

Answer:

\( - 5 \frac{9}{11} \)

Step-by-step explanation:

\(3x - 7(2x + 6) = 22 \\ \\ 3x - 14x - 42 = 22 \\ \\ - 11x = 22 + 42 \\ \\ - 11x = 64 \\ \\ x = \frac{64}{ - 11} \\ \\ x = - 5 \frac{9}{11} \)

Answer:

a)0.976

b)0.00926

c)0.2402

d)0.35

Step-by-step explanation:

Let \(X_i\) be an item passed by inspector i

Let Y be the event that there is a fault in an item

The probability that an item has a flaw is 0.1 i.e. P(Y)=0.1

If a flaw is present ,it will be detected by the first inspector with probability 0.92 i.e.\(P(\bar{X_1}|Y)=0.92\)

So, \(P(X_1|Y)=1-0.92=0.08\)

If a flaw is present ,it will be detected by the second inspector with probability 0.7 i.e.\(P(\bar{X_2}|Y)=0.7\)

So,\(P(X_2|Y)=1-0.7=0.3\)

If an item does not have a flaw, it will be passed by the first inspector with probability 0.95 i.e. \(P(X_1|\bar{Y}) = 0.95\)

So, \(P(\bar{X_1}|\bar{Y}) = 1-0.95=0.05\)

If an item does not have a flaw, it will be passed by the second inspector with probability 0.8 i.e. \(P(X_2|\bar{Y}) = 0.8\)

So, \(P(\bar{X_2}|\bar{Y}) = 1-0.8=0.2\)

a)P(found by atleast one inspector | It has flaw )=1-P(found by none inspector | It has flow )

P(found by atleast one inspector | It has flaw )=\(1-P(X_1|Y) P(X_2|Y)\)

P(found by atleast one inspector | It has flaw )=\(1-0.08 \times 0.3\)

P(found by atleast one inspector | It has flaw )=0.976

Hence the probability that it will be found by at least one of the two inspectors if it has flaw is 0.976

b)\(P(Y|X_1)=\frac{P(X_1|Y) P(Y)}{P(X_1|Y) P(Y)+P(X_1|\bar{Y}) P(\bar{Y})}\)

\(P(Y|X_1)=\frac{0.08 \times 0.1}{0.08 \times 0.1+0.95 \times 0.9}=0.00926\)

C)P( two inspectors draw different conclusions on the same item)=\(P(X_1 \cap \bar{X_2} \cap Y)+P(\bar{X_1} \cap X_2 \cap Y)+P(X_1 \cap \bar{X_2} \cap \bar{Y})+P(\bar{X_1} \cap X_2 \cap \bar{Y})\)

P( two inspectors draw different conclusions on the same item)=0.2402

D)

\(P(Y|(X_1 \cap X_2))=\frac{P(Y \cap X_1 \cap X_2)}{P(X_1 \cap X_2)}\\P(Y|(X_1 \cap X_2))=\frac{P(Y \cap X_1 \cap X_2)}{P(X_1 \cap X_2 \cap Y)+P(X_1 \cap X_2 \cap \bar{Y})}\\P(Y|(X_1 \cap X_2))=0.35\)

To find the value of the daily salary (X) such that 25% of the daily salaries are greater than X, we need to find the corresponding z-score using the standard normal distribution.

First, we convert the given percentage to a z-score. Since we want the upper 25% (greater than X), the corresponding z-score is the value that leaves 25% in the lower tail. Using a standard normal distribution table or a calculator, the z-score corresponding to 25% is approximately 0.674.

Next, we use the formula for z-score conversion: z = (X - μ) / σ, where μ is the mean and σ is the standard deviation. Plugging in the given values, we have 0.674 = (X - 70) / 10.

Solving for X, we get X = 0.674 * 10 + 70 = 6.74 + 70 = 76.74.

Rounding to one decimal place, the value of the daily salary X is approximately 76.7 JD. Therefore, option 3, 76.7 JD, is the correct answer.

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Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is \(12-0=12\).

\(\bold{12}\)

The question is asking for the probability of the chain failing under the given load. The strength of the links is independent of each other. We can use Bernoulli's trial to solve this problem.

Let's define the probability of any one link not failing under the given load as `p = 1 - q`. Here, q is the probability that any one link will fail under the given load.

The probability that all n links will not fail under the load can be calculated as `P(success) = p^n`. Here, we multiply the probability of success of one link by the probability of success of another link and so on until the nth link.

The probability of the chain failing is the complement of the probability that all the links will not fail. Hence, `P(failure) = 1 - P(success) = 1 - p^n`.

Therefore, the probability of the chain failing under the given load is `1 - p^n` or `1 - (1 - q)^n`.

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Answer:

Have a Nice Best Day : )

Step-by-step explanation:

Given

Divide by the following:

(a) 3x² + 2x + 1

Quotient = 2x, remainder = -3x + 5

(b) x³ - 3x + 2

Quotient  = 6, remainder  = 4x² + 22x - 7

(c) 6x² + x - 2

Quotient  = x, remainder = 3x² + x + 5

Answer:

add up variables and divide by 2

Answer:

work is shown and pictured

The probability that you need to pick 7 students to find 2 students using Chrome is approximately 65%.

To calculate this, we can use the formula P = (n!/r!(n-r)!) * p^r * q^(n-r), where n = 7 (number of students to pick), r = 2 (number of Chrome users to find), p = 0.49 (probability of Chrome user), and q = 0.51 (probability of non-Chrome user). By plugging the numbers into the equation, the probability of finding 2 Chrome users is 0.649.

In other words, if you randomly pick 7 students from the group, there is a 65% chance that you will find 2 students using Chrome.

This is because 49% of the group use Chrome, so if you pick 7 students randomly, the probability of picking 2 Chrome users is high.

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The runner's average speed in kilometers per hour is 24.257 km.

The total distance covered by the runner is 1 mile. The relation between kilometers and miles is given as 1 km = 0.62 mi. Converting 1 mile to km by using the given relation, we get-

Distance = 1 mile

 = 1 mile × [1 km/0.62 mile]

= 1.6129 km

The time taken to complete a 1-mile run is 3 minutes and 59.37 seconds. The relation between hours and minutes is given below.

1 hour = 60 minutes ……(1)

Converting 3 minutes to hours using equation (1), we get-

3 minutes = 3 minutes × [1 hour/60 minutes]

= 0.05 hours

The relation between hours and seconds is given below.

1 hour = 3600 second …….(2)

Converting 59.37 seconds to hours using equation (2), we get-

59.37 seconds = 59.37 seconds × [1 hour/3600 seconds]

= 0.016492 hours

Total time to cover 1 mile = (0.05 + 0.016491) hours = 0.066492 hours

The average speed of the runner is calculated by the following relation-

Average Speed = Distance (km)/time (hours)

= 1.6129 km/0.066492 hours

= 24.257 km/hour

Therefore, the average speed in kilometers per hour is 24.257km.

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Answer:

After solving the given equation, the value obtained for n will be equal to n < -0.6.

What is an equation?

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the equation given in the question,

7.2 > 0.9(n + 8.6)

Solve the equation for n,

7.2 > 0.9n + 7.74

7.2 - 7.74 > 0.9n

-0.54/0.9 > n

-0.6 > n or,

n < -0.6

After the logarithmic expression, "log(2x - 4) - log(x + 2) = 1", the value of x is -3.

In order to find the simplify the logarithmic expression, and find the value of "x", we use the "logarithmic-property", that : "log(a) - log(b) = log(a/b)",

The equation can be written as :

⇒ log[(2x - 4)/(x + 2)] = 1,

By using definition of logarithm, we can rewrite this equation as:

⇒ (2x - 4)/(x + 2) = 10

Simplifying this equation,

We get;

⇒ 2x - 4 = 10x + 20;

⇒ -24 = 8x

⇒ x = -3

Therefore, the required value of x is -3.

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\(-2(-1+2w)\)

distribute

\(2-4w\)

put in standard form

\(-4w+2\)

The coordinates of point A are given as follows:

A(19, 23).

The coordinates of point A are obtained applying the proportions in the context of this problem.

The segment AB is represented as follows:

AB = B - A.

Hence the segment 5AB is given as follows:

5AB = 5(B - A) = 5B - 5A.

Then the x-coordinate of A is obtained as follows:

5(16) - 5A = -15

5A = 95

A = 19.

The y-coordinate of A is obtained as follows:

5(30) - 5A = 35

5A = 115

A = 23.

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The equation of the line that passes through (4,2) and is parallel to the line shown is 3x + y = -10

An equation is an expression that shows the relationship between two or more numbers and variables.

The slope intercept form of a line is:

y = mx + b

where m is the slope and b is the y intercept

Two lines are said to be parallel if they have the same slope.

The line shown passes through point (0, 1) and (-1, -2). Hence:

Slope = (-2 - 1) / (-1 - 0) = 3

The line parallel will also have a slope of 3. It then passes through (4, 2). Hence:

y - y₁ = m(x - x₁)

y - 2 = 3(x - 4)

y = -3x - 10

3x + y = -10

The equation of the line is 3x + y = -10

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Answer:

Explanation below.

Step-by-step explanation:

1. a. \(\sqrt{x} =12\)

  b. \(\sqrt{x} ^{2}=12^{2}\)

  c. x=144

2. a. \(\sqrt{x^{2} } =\sqrt{196}\)

   b. x= 14

3.  

\(\sqrt{x} -4 +4= 8+4\\\sqrt{x} =12\\x= 3.46410161514 \\or \\2\sqrt{3}\)

4.

\(2(x^{2} +3)=398\\x^{2} +3= 199\\x^{2} =196\\x=14\)

Answer:

Hello!

1st problem: x = 144

2nd problem: x = 14

3rd problem: x = 144

4th problem: x = 14

Answer:

2 3/4

Step-by-step explanation:

this is the answer

The equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100. Option C is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Amount of ammonia in the solution 16%  x 22 gallons  =  3.52 gallons

The proportion of ammonia remains the same as the water evaporates, but the total composition of the solution is decreased by the amount of water that evaporates.

Quantity of ammonia = 3.52 gallons

Quantity of water after evaporation = 22 - n

Composition of ammonia after evaporation of water, 24% = 24/100

Now the percentage of ammonia after evaporates
Quantity of ammonia / Remaining water = 24%
3.52 / (22 - n) = 24 / 100

Thus, the equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100.

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Answer:

Question A)

\(=\sqrt{6}x\)

Question B)

\(=3a\sqrt{a}\)

Question C)

\(=5\sqrt{2}b^2\)

Step-by-step explanation:

A)

We are given:

\(\sqrt{6x^2}\, \text{ where } x\geq 0\)

We can rewrite the expression:

\(=\sqrt{6}\cdot \sqrt{x^2}\)

The square root and square will cancel each other out. Thus:

\(=\sqrt{6}x\)

B)

We are given:

\(\sqrt{9a^3}\)

Rewrite:

\(=\sqrt{9}\cdot \sqrt{a^3}\)

Note that the square root of 9 is simply 3. We can also factor the second part:

\(=3\cdot \sqrt{a^2\cdot a}\)

Rewriting:

\(=3\cdot\sqrt{a^2}\cdot\sqrt{a}\)

Simplify:

\(=3a\sqrt{a}\)

C)

We are given:

\(\sqrt{50b^4}\)

Rewrite. Note that 50 = 25(2):

\(=\sqrt{25}\cdot \sqrt{2}\cdot \sqrt{b^4}\)

Simplify. We can rewrite the factor as:

\(=5\cdot \sqrt{2}\cdot \sqrt{(b^2)^2}\)

The square and square root will cancel out. Thus:

\(=5\sqrt{2}b^2\)