10.
A
group of friends went to lunch. The bill,/before)
sales tax and tip, was $37.50. A sales tax of 8%
was added. The group then tipped 18% on the
amount after the sales tax was added.
What was
the amount, in dollars, of the sales tax?
What was the total amount the group paid,
including tax and tip?

The probability that a student passes both the tests is 0.5896.

The conditional probability deals with dependent events. In order to evaluate it, Bayes' theorem is applied which can be written as P(B|A) = P(A ∩ B)/P(A), where B|A denotes the event of occurring B when A has already happened and A ∩ B denotes the occurring of both events simultaneously.

The given problem can be solved as follows,

Suppose A be the event a student passes French 101 and B be the event that he passes French 102.

Then, as per the question the probabilities are given as,

P(A) = 0.67,

And, P(B|A) = 0.88.

Suppose, A ∩ B be the event a student passes both tests.

Apply Bayes' theorem to obtain,

P(B|A) = P(A ∩ B)/P(A)

Substitute the corresponding values in the above expression.

0.88 = P(A ∩ B)/0.67

=> P(A ∩ B) = 0.88 × 0.67

=>  P(A ∩ B) = 0.5896

Hence, the probability that a student selected at random will pass both French 101 and French 102 is 0.5896.

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The percentage of occupancy for the month of December is 86.5%.

What is percentage?

Percentage is a fundamental concept in mathematics that describes a portion or proportion of a whole number. It is expressed as a fraction or ratio of two numbers and is typically represented with a percent symbol (%). This concept is frequently used in business, finance, and other fields to compare and analyze data. For example, a company might use a percentage to track the success of a marketing campaign or to compare the amount of sales between two different stores. Percentage can also be used to calculate discounts, taxes, and other types of fees.

Given: Community Hospital December, 20XX

PCU Inpatient Service Days Bed Count Percentage of Occupancy

⇒ Med/Surg 1876, 70 = (1,876 x 100)/ (70 x 31)

= 187,600/ 2,170 = 86.45 = 86.5%

⇒ ICU 300, 10 (300 x 100)/ (10 x 31)

= 30,000/ 310 = 96.77 = 96.8%

⇒ CCU 240, 8 (240 x 100)/ (8 x 31)

= 24,000/ 248 = 96.77 = 96.8%

⇒ Rehabilitation 300, 12 (300 x 100)/ (12 x 31)

= 30,000/372 = 80.6%

⇒ Burn 75, 5 (75 x 100)/ (5 x 31)

= 7,500/ 155 = 48.38 = 48.4%

⇒ Psychiatry 200, 15 (200 x 100)/(15 x 31)

= 20,000/465 = 43.0%

⇒ Pediatric 870, 30 (870 x 100)/ (30 x 31)

= 87,000/ 930 = 93.5%

⇒ Total for patient care 3861, 150 (3,861 x 100)/ (150 x 31)

= 386,100/ 4,650 = 83.0%

⇒ Nursery 280, 10 (280 x 100)/ (910 x 31)

= 28,000/ 310 = 90.3%

For example, Med/Surg has 1,876 inpatient service days and 70 beds in the month of December (31 days). The percentage of occupancy is therefore the inpatient service days multiplied by 100 and divided by the product of the number of beds (70) and the number of days (31) to get 86.5%

⇒ (1,876 x 100)/ (70 x 31)

= 187,600/ 2,170 = 86.45 = 86.5%

Hence, the percentage is 86.5%.

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Answer:

6.825 ounces

Step-by-step explanation:

9.75 x 0.3 = 2.925

9.75 - 2.925 = 6.825

Answer:

—4—

_x+1_/4x+3

-(4x+4)

———–––

-1

#4x+3/x+1=4-1/x+1

The values of a2 and a3 that satisfy the sequence [tex]a_{n+1}[/tex] = [tex]\sqrt{a_{n} ^{2} + 3 }[/tex] are [tex]\sqrt{7}[/tex] and [tex]\sqrt{10}[/tex]

What is a sequence?

A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. If a1, a2, a3, a4 etc. denote the terms of a sequence, then 1,2,3,4 denotes the position of the term.

the rule of the sequence is  [tex]a_{n+1}[/tex] = [tex]\sqrt{a_{n} ^{2} + 3 }[/tex] when  n = 1

[tex]a_{2}[/tex]  = [tex]\sqrt{a_{1} ^{2} + 3 }[/tex] but [tex]a_{1}[/tex] = 2

[tex]a_{2}[/tex] =  [tex]\sqrt{(2) ^{2} + 3 }[/tex]

[tex]a_{2}[/tex] = [tex]\sqrt{7}[/tex]

when n = 2

[tex]a_{3}[/tex] =  [tex]\sqrt{a_{2} ^{2} + 3 }[/tex]

[tex]a_{3}[/tex]  =  [tex]\sqrt{a_{2} ^{2} + 3 }[/tex] but [tex]a_{2}[/tex]  = [tex]\sqrt{7}[/tex]

[tex]a_{3}[/tex]  =  [tex]\sqrt{(\sqrt{7}) ^{2} + 3 }[/tex]

[tex]a_{3}[/tex] = [tex]\sqrt{7 + 3}[/tex]

[tex]a_{3}[/tex] = [tex]\sqrt{10}[/tex]

In conclusion [tex]a_{2}[/tex] and [tex]a_{3}[/tex] are [tex]\sqrt{7}[/tex] and [tex]\sqrt{10}[/tex] respectively.

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According to the given consumer price index, President Hoover's 1931 salary is equivalent to what amount in 2005 is $962,250

Consumer price index:

In math, the concept of consumer price index (CPI) is significant in the analysis of inflation.

The general form of CPI of current years is computed as

=> (GDP of current period / GDP of base period) x 100.

Given,

In 1931, President Herbert Hoover was paid a salary of $75,000. Government statistics show a consumer price index of 15.2 for 1931 and 195 for 2005.

Here we need to find the President Hoover's 1931 salary is equivalent to what amount in 2005.

Here we have the values of

=> CPI = 15.2 in 1931,

=> salary 75000;

=> CPI = 195 in 2005,

Then the salary is calculated as,

=> 75000 x (195/15.2)

=> 75000 x 12.83

=> 962250

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Value of AB = 9 units by using property of equality according to given equation.

What is  a line?

In pure mathematics, a line is associate infinitely long object with no dimension, depth, or curvature. Thus, lines ar one-dimensional objects, although they'll exist in 2, three, or higher dimension areas. The word line might also see a line section in existence, that has 2 points to denote its ends.

Main body:

Question 12

According to question,

AB +BC = 12

BC= 3

therefore,

AB + 3 = 12

AB = 9   -------( by using property of equality)

Hence value of AB = 9 units.

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Answer:

Step-by-step explanation:

First factor the left expression to get

Then cancel out .[tex]\frac{(x+3)(x+2)}{(x+4)(x+2)}*\frac{x+4}{2x}\\ \\\frac{(x+3)}{2x}[/tex]

The x+2 cancel's as well as the x+4's.

To find the height of the column of water in the Fountain Hills fountain, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of elevation to the top of the fountain, the distance from the surveyor to the base of the fountain, and the height of the column of water to form a right triangle.

We can then use the tangent function to find the height of the column of water as follows:

tan(29.7°) = opposite/adjacent

opposite = tan(29.7°) * adjacent

opposite = tan(29.7°) * 980 feet

opposite = 0.56 * 980 feet

opposite = 548.8 feet

Therefore, the height of the column of water in the Fountain Hills fountain is approximately 549 feet. To the nearest 10 feet, this is 550 feet.

The number whose product of 5 and the difference between a number and 7 is 75 is, 22.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The given statement is The product of 5 and the difference

between a number and 7 is 75.

Let, The unknown number be 'n'.

∴ 5(n - 7) = 75.

Now, 5 will move from the numerator to the denominator.

n - 7 = 75/5.

n - 7 = 15.

Now, we'll move the constant to the other side such that the variable and the constants are on different sides for our further calculation.

n = 15 + 7.

n = 22.

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[tex]AC \cong BC \implies \angle A \cong \angle B \\ \\ \therefore m\angle A=m\angle B \implies 3x+18=7x-58 \\ \\ \implies 18=4x-58 \\ \\ 76=4x \\ \\ \boxed{x=19} \\ \\ m\angle A=3(19)+18 \implies \boxed{m\angle A=75^{\circ}} \\ \\ m\angle A=m\angle B \implies \boxed{m\angle B=75^{\circ}} \\ \\ m\angle C=180^{\circ}-m\angle A-m\angle B \implies \boxed{m\angle C=30^{\circ}}[/tex]

You forgot the question

point A' is the contracted point of A. The coordinate of point A is (-4,4) and coordinate of point A' is (-2,4) as per the given question and available figure.

The extension or contraction of image or figure based on a scale factor is called dilation. In this way, an image is transformed from one position to another.

Scale factor is defined as the ratio of original image and transformed image.

As stated in the question, the polygon ABCDE is contracted and moved to a shape A'B'C'D'E'. The coordinate of point A is (-4,4) and point A' is (-2,4) as shown in figure. Angle A is equal to angle A' that means the shape of polygon was not changed.

hence, A'B'C'D'E' is the reflected image of ABCDE

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Transformation involves changing the form of a function. The transformations are:

vertical translation 1 unit up .

horizontal translation 5 units left.

The functions are given as:

f(x) = 8x

g(x) = [tex]8^{x+5}[/tex] + 1

Start by translating the function 5 units left.

The rule of this translation is:

f'(x) = f(x+5)

So, we have:

f'(x) = 8(x+5)

Next, translate the function 1 unit up

The rule of this translation is:

f"(x) = f'(x) + 1

∴ f"(x) = 8(x+5) + 1

Rewrite as:

g(x) = 8(x+5) + 1

Hence, the transformations are: vertical translation 1 unit up  and horizontal translation 5 units left

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Transformation involves changing the form of a function. The transformations are:

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

The functions are given as:

f(x) = 8x

g(x) =  + 1

Start by translating the function 5 units left.

The rule of this translation is:

f'(x) = f(x+5)

So, we have:

f'(x) = 8(x+5)

Next, translate the function 1 unit up

The rule of this translation is:

f"(x) = f'(x) + 1

∴ f"(x) = 8(x+5) + 1

Rewrite as:

g(x) = 8(x+5) + 1

Hence, the transformations are: vertical translation 1 unit up  and horizontal translation 5 units left

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The inequality that shows how long the temperature in Austin will remain colder than that in San Antonio is 33.5 + 2.5t < 37.5 + 1.5t and the time is less than 4 hours

From the question, we have the following parameters that can be used in our computation:

Austin

Initial temperature = 33.5 degrees Fahrenheit

Rate of increment = 2.5 degrees Fahrenheit

San Antonio

Initial temperature = 37.5 degrees Fahrenheit

Rate of increment = 1.5 degrees Fahrenheit

The above parameters mean that

Current temperature = Initial temperature + Rate of increment x Number of hours

Austin: A(t) = 33.5 + 2.5t

an Antonio: B(t) = 37.5 + 1.5t

When Austin is colder than San Antonio, we have

Substitute the known values in the above equation, so, we have the following representation

33.5 + 2.5t < 37.5 + 1.5t

Divide both sides by 1

t < 4

Hence, the interval is less than 4 hours

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Answer:

(8, 0) and (0, 4)

Step-by-step explanation:

x-intercepts occur when y = 0, so just find the row in the table when y is 0, and then put the coordinates from that row into a ordered pair:

(8, 0)

y-intercepts occur when x = 0, so just find the row in the table when x is 0, and then put the coordinates from that row into a ordered pair:

(0, 4)

domain of (f.g)(x) is {x l x ≠ 13} i.e option (c) where f(x) = x+7 and g(x) = 1/(x-13)

Domain of a function is defined as all those values of x that can be substituted in function for which function is defined.

Given: f(x) = x+7

g(x) = 1/(x-13)

First we need to find (f.g)(x) i.e multiplication of  f(x) and g(x)

(f.g)(x) = (x+7) ×1/(x-13) = [tex]\frac{x+7}{x-13}[/tex]

Domain of function is values of x over which function is defined

For (f.g)(x) it is defined at all values of x except when x-13=0 as at this point denominator will be zero and function will become infinite that is not defined.

So,  x - 13 ≠ 0

Adding 13 on both sides, we get

x ≠ 13

So domain of  (f.g)(x) is x∈R - {13} i.e {x | x≠ 13}

Hence, option (c) is correct answer.

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Answer: A. 37.5%

Step-by-step explanation:

Technically, you can't even solve this, because you don't know how many athletes got exactly a 3.0 GPA.

Ignoring this major oversight, let's just say that no one received a 3.0 GPA. In that case, there would be 40 - 25 = 15 athletes who received a sub-3.0 GPA.

Therefore, the percentage of student athletes who received a sub-3.0 GPA is 15/40 = 3/8 = 37.5%.

Answer:

x= -7

Step-by-step explanation:

the 2 x values are the same so it is an undefined slope so we set this equation x=-7

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A minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.

What is the standard deviation?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The given data is:

{8, 12, 27, 32, 45, 57, 61, 73, 82, 94}

Now find the mean of the given data would be

Mean = sum of all points/n

         = 491/10

         = 49.1

Standard deviation(s) = [tex]\sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]

Standard deviation(s) = 29.31988

Considering one standard deviation from the mean, the lower and upper limits are given by the following

[49.1-29.31988, 49.1+29.31988}

=[19.78012, 78.41988]

We can see that only 6 {27,32,45,57,61,73} out of the 10 points, which is 60%, confine to the interval of one standard deviation from the mean.

Hence, a minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.

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Answer:

Option 2

Step-by-step explanation:

[tex]\begin{bmatrix} 3+6 & 9+0 \\ 5-8 & -2+4 \end{bmatrix}=\begin{bmatrix} 9 & 9 \\ -3 & 2 \end{bmatrix}[/tex]

Answer:

  (b)

Step-by-step explanation:

You want the sum of the given matrices.

The sum of two matrices is the matrix of the sums of corresponding terms.

Here, we observe that we can choose the correct answer by finding the bottom right term. The sum of bottom right terms is  -2+4 = 2. The only answer choice with that value at bottom right is the second answer choice.

__

Additional comment

You need to know how to work the problem, but you don't actually need to work the whole problem in order to make the correct answer choice. (This is often the case with multiple choice questions, so it pays to look before you leap.)

The linear functions for this problem are graphed on the image given at the end of the answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

Hence the functions in this problem are graphed as follows:

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221643611 ways of 6 numbers can be​ chosen

An arrangement of objects where the order in which the objects are selected does not matter.

Given,

A certain lottery requires players to select 6 different​ numbers in any​ order, from 1 to 53 inclusive.

We need to find different sets of 6 numbers can be​ chosen

Total=53

Numbers=6

The first number can be any of the 53 numbers

The second number can be any of the 53 numbers

The third number can be any of the 53 numbers

The fourth number can be any of the 53 numbers

And so on

Hence, number of selections is:

53×53×53×53×53×53

53⁶

221643611 ways

Hence, 221643611 ways of 6 numbers can be​ chosen

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Expressing the probability as a decimal rounded to 4 decimal places the value of p ( z < 0.74 ) is 0.7704.

Given :

for a standard normal distribution, find: p(z < 0.74) express the probability as a decimal rounded to 4 decimal places.

Standard normal distribution :

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.

Probability :

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

From z - score table :

the test statistic follows the standard normal distribution N(0,1).

the probability p = 0.7704

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Hence, the least square estimator is obtained when you substitute [tex]y_i[/tex] with [tex]Y_i[/tex] is

[tex]\beta _1=\frac{\sum_{i=1}^{n}x_iY_i}{\sum_{i=1}^{n}x_i^2}[/tex]

What is the line of regression?

A regression line indicates a linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis.

Here given that,

Suppose an investigator has data on the amount of shelf space [tex]x[/tex] devoted to display of a particular product and sales revenue [tex]y[/tex] for that product.

The investigator may wish to fit a model for which the true regression line passes through [tex](0, 0)[/tex]. The appropriate model is [tex]Y=\beta x+E[/tex]

Assume that[tex](x_1, y_1), . . ., (x_n, y_n)[/tex] are observed pairs generated from this model, and derive the least squares estimator of [tex]b_1[/tex].

Here, our motive is to minimize the function

[tex]f(b_1)=[/tex][tex]\sum_{i=1}^{n}(y_i-b_1x_i)^2[/tex]

Now,

[tex]f`(b_1)=0\\\\f`(b_1)=2\sum{i=1}^{n}(y_i-b_1x_i).(-x_i)\\\\[/tex]

So, the least square estimate [tex]b_1[/tex] is

[tex]\sum_{i=1}^{n}x_iy_i=b_1\sum_{i=1}^{n}x_i^2[/tex]

Hence, the least square estimator is obtained when you substitute [tex]y_i[/tex] with [tex]Y_i[/tex] is

[tex]\beta _1=\frac{\sum_{i=1}^{n}x_iY_i}{\sum_{i=1}^{n}x_i^2}[/tex].

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Answer: Chloe is 12 years old

y + 2.5

y = 9.5

9.5 + 2.5 = 12

The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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Step-by-step explanation:

greater than 6=0 cause no number on a dice is greater than six

an even number=1/2

less than 4=1/2