Write the rationalized expression of:
Sqrt(9)/(sqrt(3)+sqrt(x))

Answer: x=16

Step-by-step explanation:

The two angles in the picture is equal to each other.

So the 6x + 4 = 100 degree

6x = 96

x= 16

The probability of both events occurring is 1/20.

What are examples and probability?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

                                   The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

Events X and Y are independent.

The probability of X occurring is 1/4

The probability of Y occurring is 1/5

Since both events are independent, then we have

P(X and Y ) = P(X) * P(Y)

                  = 1/4 * 1/5

                 = 1/20

 P( X and Y ) = 1/20

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Answer:

Step-by-step explanation:

Graph crosses the x-axis at x = 0 and has zeros at {-5, -5}.Step-by-step explanation: Note that f(x) factors as follows:  f(x) = 4x^5 (x^2 + 10x + 25) …

(a) The standard deviation is 2.582

(b) No, because the standard deviations of these two distributions are not too different from one another.

a) In this question we have been given

The given information is:

First Digit      1     2    3    4    5    6      7     8      9

Probability   1/9 1/9 1/9 1/9 1/9  1/9   1/9  1/9  1/9

Now we find the standard deviation.

The mean for given data is:

μ = ∑xP(X = x)

μ = (1*1/9) +(2*1/9)+(3*1/9)+(4*1/9)+(5*1/9)+(6*1/9)+(7*1/9)+(8*1/9)+(9*1/9)

μ = 5

The standard deviation is:

σ² = ∑(x - μ)²P(X)

σ² = (1 - 5)² *1/9 +(2 - 5)²*1/9+(3 - 5)²*1/9+(4 - 5)²*1/9 + (5 - 5)²*1/9+(6 - 5)²*1/9+(7-5)²*1/9+(8-5)²*1/9)+(9-5)²*1/9

σ² = 2.582

(b) The uniform distribution's standard deviation is 2.582, while Benford's law's standard deviation is 2.46

Using the standard deviation to detect fraud is not a good idea because the two distributions have about the same standard deviation

Therefore, (a) The standard deviation is 2.582

(b) using standard deviations would not be a good way to detect fraud.

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The complete question is:

Benford’s law and fraud

(a) Using the graph from Exercise 21, calculate the standard deviation σY. This gives us an idea of how much variation we’d expect in the employee’s expense records if he assumed that first digits from 1 to 9 were equally likely.

(b) The standard deviation of the first digits of randomly selected expense amounts that follow Benford’s law is . Would using standard deviations be a good way to detect fraud? Explain your answer.

Representing data sets using frequency distributions and using graphs of frequency distributions can have several benefits. Here are some of the benefits of representing data sets using frequency distributions:

a) Organizing the data into afrequency  distribution can make patterns within the data more evident. By organizing the data into classes or bins and counting the number of observations within each class, you can see how the data is distributed and identify patterns or trends that may not be immediately apparent when looking at the raw data.

b) Organizing the data into a frequency distribution makes it possible to graph quantitative data. Many types of graphs, such as bar graphs and histograms, are based on frequency distributions and can be used to visualize the distribution of data.

c) It is easier to determine the minimum and maximum values of a data set when it has been arranged into a frequency distribution. By organizing the data into classes, you can easily see the range of values within each class and determine the overall range of the data set.

Here are some of the benefits of using graphs of frequency distributions:

a) It can be easier to determine the class boundaries by looking at a graph of the frequency distribution. When you create a graph of a frequency distribution, the class boundaries are often marked along the x-axis, which makes it easy to see where one class ends and the next begins.

b) Graphing a frequency distribution makes it possible to determine the relative frequencies of each of the classes. By looking at the heights of the bars on a bar graph or the heights of the columns on a histogram, you can see how each class compares to the others and determine the overall shape of the distribution.

c) It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution. Graphs are a visual representation of data, and they can help you see patterns or trends that may not be immediately apparent when looking at the data in tabular form.

d) Graphing frequency distributions makes it possible to find the total number of observations. By adding up the frequencies of all the classes, you can determine the total number of observations in the data set.

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If we test the null hypothesis at the 5% level of significance, then the decision is (c)reject null hypothesis and conclude the means are different .

In the question ,

it is given that ,

the results of a mathematics placement exam for two different campuses of college ,

we have to test the hypothesis that the mean score on campus 1 is higher than on campus 2 .

sample size (n₁) is = 330

the sample size (n₂) is = 310

the sample mean (μ₁) = 33

the sample mean (μ₂) = 31

the standard deviation , σ₁ = 8

the standard deviation , σ₂ = 7

the test statistic test z can be calculated using the formula ,

z = (μ₁ - μ₂)/√(σ₁²/n₁ + σ₂²/n₂)

Substituting the values of the sample size , sample mean and standard deviation ,

we get ,

z = (33 - 31)/√(8²/330 + 7²/310)

Simplifying further ,

we get ,

Z = 3.37

the test is for the null hypothesis at the 5% level of significance .

that means ,

Z₀.₉₅ = 1.645 ;

So , the p value = P(Z > 3.37)

= 1 - P(Z < 3.37)

= 1 - 0.9996

= 0.0004

since the p-value is (0.0004) < the level of significance (0.05) .

we can reject the null hypothesis .

There is significant evidence to conclude that the mean score on campus 1 is higher than campus 2 .

Therefore , the correct option is (c) .

The given question is incomplete the complete question is

The results of a mathematics placement exam at two different campuses of mercy college follow: ( the table is given below)

The college wants to test the hypothesis that the mean score on campus 1 is higher than on campus 2. if we test the null hypothesis at the 5% level of significance, what is the decision ?

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Step-by-step explanation:

the volume of a pyramid is

base area × inner height / 3

we have the base area : 7×7 = 49 in²

so, we need to get the inner height h.

fit this we need to get the outer height l.

the surface area is

base area (49 in²) + 4×side triangle area = 185 in².

one of these 4 side triangle area is

baseline (7 in) × l / 2

so, we have a surface area

49 + 4×7×l/2 = 185

49 + 2×7×l = 185

49 + 14×l = 185

14×l = 136

l = 136/14 = 68/7 = 9.714285714... in

h we get now via Pythagoras

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle), a and b being the legs.

l² = h² + 3.5²

94.36734694... = h² + 12.25

h² = 94.36734694... - 12.25 = 82.11734694...

h = 9.061862222... in

so, the volume of the pyramid is

49 × 9.061862222... / 3 = 148.0104163... in³ ≈

≈ 148.01 in³

Dorothea needs 2.4 kilograms of filo pastry to make on pan of baklava.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b.

Given that,

The quantity needed of filo pastry to make one pan of baklava = 400 grams

To find the quantity of pastry to make 6 pans of baklava

Use ratio property,

1 pan of baklava needed = 400 grams

6 pans of baklava needed = 400 x 6 = 2400 grams

Since, 1000 gram = 1 kilogram

2400 gram = 2.4 kilograms

Hence, Dorothea needs 2.4 kilograms of filo pastry.

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For the  given case, in the residual plot, the x range is for the age  and  the y  range must be the  square foot

A residual plot appears the difference between the observed response and the fitted response values. The ideal remaining plot, called the null residual plot, appears as a random scatter of focuses shaping a roughly constant width band around the identity line. It is vital to check the fit of the model and presumptions – steady change, normality, and freedom of the errors, utilizing the residual plot, alongside normal, sequence, and lag plot.We  are given the information  that  there is a relationship between age and square foot range (sqft) of living space, so for  the  residual plot the y range must be for the  square foot and the  x range must the age

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The cost for 111 books is obtained as $3.5.

In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.

The given problem can be solved using unitary method as follows,

The cost for 666 books = $21

Then, cost for 1 book = 21/666

Thus, the cost of 111 books = 21/666 × 111

                                            = 21/6

                                            = 3.5

Hence, the cost for 111 comic book is given as $3.5.

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Answer: 0.0015813253

Step-by-step explanation:

is you ment to say 14,280 divided by 21 then it would be 632.380952381

Answer:  D) 2.95 units

Step-by-step explanation:
I just took this

The probability that all adjacent points differ in color is given as follows:

1/10. (second option).

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the total outcomes, we have an arrangement of 6 elements, due to the six points, with 3 and 3 repetitions, as 3 are green and 3 are red, hence the number of total outcomes is calculated as follows:

[tex]T = A_6^{3,3} = \frac{6!}{3!3!} = 20[/tex]

For the desired outcomes, there are two, given as follows:

This means that the probability that all adjacent points differ in color is calculated as follows:

p = 2/20 = 1/10.

Hence the second option is the correct option.

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Answer: 19

Step-by-step explanation:

4x in this equation is equal to 4(4), which equal sixteen, adding the three will then get you 19

Answer: 19

Step-by-step explanation:

Insert 4 into the x in the equation.

3+ 4 × 4

Multiply.

4 × 4 = 16

Add.

3 + 16= 19

Hope this helps!

Answer:

1. infinite

2. no

3. one

4.no

Step-by-step explanation:

Area of rectangle is length x breadth.

Area = (x + 7)(x + 5)

= (x² + 5x + 7x + 35)

= (x² + 12x + 35)

Answer:

[tex]\dfrac{(y+2)^2}{4} -\dfrac{(x-4)^2}{9}=1[/tex]

Step-by-step explanation:

Given equation:

[tex]-4x^2 + 9y^2 + 32x + 36y - 64 = 0[/tex]

Collect like terms:

[tex]\implies 9y^2 + 36y -4x^2+ 32x - 64 = 0[/tex]

Move the constant to the right side of the equation:

[tex]\implies 9y^2 + 36y -4x^2+ 32x =64[/tex]

Factor out 9 from the terms in y, and 4 from the terms in x:

[tex]\implies 9(y^2 + 4y) -4(x^2-8x)=64[/tex]

Add the square of half the coefficient of the term in y and x inside the parentheses on the LHS, and the distributed values on the RHS:

[tex]\implies 9\left(y^2 + 4y+\left(\dfrac{4}{2}\right)^2 \right) -4\left(x^2-8x+\left(\dfrac{-8}{2}\right)^2 \right)=64+9\left(\dfrac{4}{2}\right)^2 \right+4\left(\dfrac{-8}{2}\right)^2 \right[/tex]

Simplify:

[tex]\implies 9(y^2 + 4y+4) -4(x^2-8x+16)=64+36-64[/tex]

[tex]\implies 9(y^2 + 4y+4) -4(x^2-8x+16)=36[/tex]

Factor the perfect trinomials:

[tex]\implies 9(y+2)^2 -4(x-4)^2=36[/tex]

Divide both sides by 36:

[tex]\implies \dfrac{9(y+2)^2}{36} -\dfrac{4(x-4)^2}{36}=\dfrac{36}{36}[/tex]

Simplify:

[tex]\implies \dfrac{\diagup\!\!\!\!9(y+2)^2}{\diagup\!\!\!\! 9\cdot 4} -\dfrac{\diagup\!\!\!\!4(x-4)^2}{9 \cdot \diagup\!\!\!\!4}=1[/tex]

[tex]\implies \dfrac{(y+2)^2}{4} -\dfrac{(x-4)^2}{9}=1[/tex]

Therefore, the function is a hyperbola with:

Answer:

I'm sure the answer is 125

Step-by-step explanation:

Hope it helps ; )

by using log notation, the value of x =㏒₃500 or x = 5.657

Log notation is a mathematical expression used to represent any exponential relationship in its inverse form.

we use log notation to solve an equation in where an unknown variable is in index form. By applying logarithm laws, we write an exponential equation in the inverse form and finally we get the unknown values.

in the above equation 3ˣ = 500

using log notation, we get ㏒₃500 = x

                                    x= 5.657

hence, the solution is x = 5.657

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1. There are 80 Nickels, 120 dimes, and 300 quarters in the piggy bank.

2. The coins worth is $91

How many types of coins are there?

There are 4 types of coins. They are Quarter, Nickel, dime, and Penny.

1 Quarter = 25 cent

1 dime = 10 cents

1 Nickel = 5 cents

1 penny = 1 cent

Assume that, the number of Nickel coins is x.

Given that, 2 nickles there are 3 dimes.

1 nickle there are 3/2 dimes.

x nickles there are 3x/2 dimes.

Also given that,

2 dimes there are 5 quarters.

1 dimes there are 5/2 quarters.

3x/2 dimes there are (5/2) × (3x/2) quarters = 15x/4.

There is 500 coins in the piggy.

Therefore, x + (3x/2) + (15x/4) = 500

(4x + 6x + 15x) /4 = 500

25x/ 4 = 500

x = 80.

The number of dimes is (3 × 80)/2 = 120

The number of quarters is (15 × 80)/4 = 300.

The total cost of 80 nickles, 120  dimes, and 300 quarters is

= [(80 ×  5) + (120 × 10) + (300 × 25)] cents

= 400 + 1200 + 7500 cents

= 9100 cents

= $(9100/100)

= $ 91

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The equivalent fractions for 2/3 is (3×2)/(3×3) = 6/9 and for  5/12 is (4×5)/(4×12) = 20/48.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

The equivalent fraction for 2/3 is (3×2)/(3×3) = 6/9.

The equivalent fraction for 5/12 is (4×5)/(4×12) = 20/48.

We have to multiply the same number to both the numerator and denominator to get equivalent fractions.

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Answer:

Below

Step-by-step explanation:

( Your question asks for m^2 discharge......I think you need m^3 discharge per minute)

Find the volume of a cylinder that is 8 meters long with radius of 8cm ( .08 m)

area = pi r^2 = pi (.08)^2 = .0201 m^2

    area * 8 m   = volume PER SECOND

        volume PER SECOND  *  60 = volume per minute

                 .0201   * 8 * 60 = 9.65 m^3 / min  discharge

The probability that a five-digit integer chosen at random is divisible by 5 is 13.1 %.

Given :

what is the probability that a five-digit integer chosen at random is divisible by 5 .

Probability :

Probability is a branch of mathematics that deals with the occurrence of a random event.

Probability = 9^3 * 8 * 2 / 9 * 10^4

= 729 * 8 * 2 / 9 * 10000

= 5832 * 2 / 9 * 10000

= 11809 / 90000

= 0.131

converting into percentage :

= 0.131 * 100 %

= 13.1 %

Therefore The probability that a five-digit integer chosen at random is divisible by 5  is 13.1 %

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Answer:

Step-by-step explanation:

BRO what FACTOR????????????????????????///////////////////////

The slope-intercept form of the equation 8x = 4y + 16 will be y = 2x -4.

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The equation given is 8x = 4y + 16.

We must solve for y as follows;

8x = 4y + 16

4y = 8x -16

By dividing through by 4; we have;

y = 2x -16

Hence the equation for both lines will be y = x +3 and   y  = x+13

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average rate of change from 4 to 9 minutes is 2.25 min . division of the y-value change by the x-value change.

It represents the average change in the function's per-unit value during that time period. On the function's graph, it is generated from the slope of the line connecting the interval's ends.

the difference between the y- and x-values is divided. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity.

Given that

the change in y value occurred in 9 minutes and the change in x value occurred in 4 minutes, the average rate of change was 9 minutes by 4 minutes, or2.25 minutes.

9 min / 4 min

= 2.25 min

average rate of change from 4 to 9 minutes is 2.25 min . division of the y-value change by the x-value change.

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