Rewrite the following equation in logarithmic form.
e^a=95/73

Answer:

A = 2

B = 12

C = 5

D = 13

Surface = B * A

Surface = 12 * 2

Surface = 24 mm²

CREDITS:

Answer:

Step-by-step explanation:

The required graph of the given function d(x)=−1/2x−3 has been shown.

Given that, to plot the graph of the linear function,  d(x)=−1/2x−3.

What is the graph?

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,

The graph of the liner function d(x)=−1/2x−3 can be plot by putting the values of the x in the equation which gives the value of y by calculating such an ordered pair we can plot the curve of the liner equation on the graph. i.e.

At x = 0

d(0) = -1/2 * (0) - 3

d(0) = -3

So, the ordered pair will be (0, -3).

Now, put x = 2

d(2) = -1/2 * 2 - 3

d(2) = -1 - 3

d(2) = - 4

So the ordered pair will be (2, -4)

joining these two points will show the graph of the given equation d(x)=−1/2x−3.

Thus, the required graph of the given function d(x)=−1/2x−3 has been shown.

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The expected value for the number of subjects who are vaccinated and are diseased is  56.7

Since we are given the information that a new vaccination is being used in a laboratory experiment to investigate whether it is effective. there are 273 subjects in the study.  We can calculate this by taking the total number of subjects who are vaccinated (119) and multiplying it by the proportion of subjects who are diseased

(47/273).  119 x (47/273) = 56.7

which is  the expected value for the number of subjects who are vaccinated and are diseased

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Answer: -20, -19, -18, |-18|, |-22|, |30|

Step-by-step explanation:

A number with vertical lines on either side means the absolute value of that expression, i.e. how far it is from 0. An absolute value can be 0 or positive but never negative.

|-18| = 18

|-22| = 22

|30| = 30

Positive numbers are bigger, greater, or higher than zero. They are on the opposite side of zero from the negative numbers. Negative numbers get smaller the farther they are from zero. You can think of positive and negative numbers as being opposites because they are on opposite sides of the number line.

I hope this helps :)

$100 much better off per month would the firm be if it adopted preventive maintenance.

Given that,

We have to find how much more profitable would the company be each month if it implemented preventive maintenance.

We know that,

Number of Breakdowns are 0, 1, 2, 3, 4

The problems for the breakdowns are 0.50, 0.25, 0.10, 0.10, 0.05

Cost of a breakdown is $2,000

A monthly preventive maintenance programme costs $2,000

Expected probability of breakdown:

E(x) = Σ(X × p(x))

= (0×0.5) + (1×0.25) + (2×0.10) + (3×0.10) + (4×0.05)

= 0.95

E(x) ×cost of breakdown = (0.95 × 2000) = $1900

So, Difference between breakdown and preventive maintenance

1900 - 2000 = - $100

Therefore, $100 much better off per month would the firm be if it adopted preventive maintenance.

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-25x+800=0

-25x =-800

25x=800

x=32

Answer:

x = 32

Step-by-step explanation:

0=-25x+800

To solve for x, add 25x to each side

0+25x=-25x+800+25x

25x = 800

Divide each side by 25

25x/25 = 800/25

x = 32

a) Number of bit string = 220

b)  Number of bit string = 299

c)  Number of bit string = 4017

d)  Number of bit string = 924

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

Given:

a) n= 12, r= 3

[tex]^{12}C_3[/tex] = 12! / 3! 9 !

      = 12 x 11 x 10 x 9! / 3 x 2 x 9!

      = 220

b)  n= 12, r ≤ 3

[tex]^{12}C_3[/tex] = 12! / 3! 9 !

      = 12 x 11 x 10 x 9! / 3 x 2 x 9!

      = 220

[tex]^{12}C_2[/tex] = 12! / 2! 10 !

      = 12 x 11 x 10! / 2 x 10!

      = 66

[tex]^{12}C_1[/tex] = 12! / 1! 11!

      = 12

[tex]^{12}C_0[/tex] = 12! / 0! 12 !

      = 12 x 11 x 10 x 9! / 3 x 2 x 9!

      = 1

So, total number of bit strings = 220 +66 + 12 +1 =299

c)  n= 12, r ≥ 3

[tex]^{12}C_3[/tex] = 12! / 3! 9 !

      = 12 x 11 x 10 x 9! / 3 x 2 x 9!

      = 220

[tex]^{12}C_4[/tex] = 495

[tex]^{12}C_5[/tex] = 792

[tex]^{12}C_6[/tex] = 924

[tex]^{12}C_7[/tex] = 792

[tex]^{12}C_8[/tex] = 495

[tex]^{12}C_9[/tex] = 220

[tex]^{12}C_{10[/tex] = 66

[tex]^{12}C_{12[/tex] = 12

[tex]^{12}C_{12[/tex] = 1

So, total String= 4017

d)  n= 12 and r= 6

[tex]^{12}C_6[/tex] = 12!/ 6! 6!

       = 12 x 11 x 10 x 9 x 8 x 7 x 6! / 6! 6!

       = 924

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The required choice for transformation is Option 1.

What is transformation?

When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects."

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift.

g(x) = (x - 4)^3 + 5  and f(x) = x^3

Then we get, g(x) is shifted 4 units to the right and 5 units up

Hence, the required answer for transformation is Option 1.

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Answer:

-----------------------------

If original function is f(x), translated function is g(x) and

Then:

Looking at the given functions we see that:

This is reflected in the answer choice A.

Answer: -10

Step-by-step explanation:

y2-y1

---------

x2-x1

Answer:a=6,25

Step-by-step explanation:

i did the test yesterday

The solution of the equation 34(2a − 6) + 12 = 25(3a + 20) + a will be negative 86.5.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

34(2a − 6) + 12 = 25(3a + 20) + a

Simplify the equation, then the value of the variable 'a' is given as,

34(2a − 6) + 12 = 25(3a + 20) + a

68a − 204 + 12 = 75a + 500 + a

68a − 192 = 76a + 500

Simplify the equation further, then the value of the variable 'a' is given as,

76a − 68a = − 192 − 500

8a = − 692

a = − 692 / 8

a = −86.5

The solution of the equation 34(2a − 6) + 12 = 25(3a + 20) + a will be negative 86.5.

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Answer: $10

Step-by-step explanation:

Sue has $10 more than Paul which means she has $20. Who is speaking has $16 more than Sue ($16 more than $20) which means they has $36.

Adding all of their money, $10, $20, and $36, equals $66

16% of a number is 73.6 by multiplying it by 5%, which is 23, and 1%, which equals 4.6.

Given that,

We have to calculate 16% of a number by multiplying it by 5%, which is 23, and 1%, which equals 4.6.

We know that,

Let the number be x

5% of a number = 5/100x

Now we are given that 5 percent of a number is 23

So,

5/100x=23

x=23×100/5

x=460

So, the number is 460

Now we are supposed to find the 16% of the number

=16/100×460

=73.6

Therefore, 16% of a number is 73.6 by multiplying it by 5%, which is 23, and 1%, which equals 4.6.

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The perpendicular distance of point 7 and point 2 from y-axis is 7 and 2, respectively.

The perpendicular distance of any point from the y-axis is the x-coordinate of the point. In the case of point 7 and point 2, their respective x-coordinates are 7 and 2. Therefore, the perpendicular distance of point 7 and point 2 from the y-axis can be calculated by using the formula d = |x|, where d is the perpendicular distance and x is the x-coordinate of the point.

By substituting the x-coordinates for point 7 and point 2, we get the perpendicular distance of point 7 from y-axis is d1 = |7| = 7 and the perpendicular distance of point 2 from y-axis is d2 = |2| = 2.

Therefore, the perpendicular distance of point 7 and point 2 from y-axis is 7 and 2, respectively.

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Answer:

62 + 6x + 10y

Step-by-step explanation:

1. add the x's together

3x+3x = 6x

2. add the constants together

66-6-6+4+4 = 62

3. add the y's together

5y + 5y = 10y

Answer:

Each bag of lemons cost: $3.81

Step-by-step explanation:

We know

He pays a total of $24.36.

He pays a total of $5.31 for the cheese.

He buys 5 bags of lemons that each cost the same amount.

Let's x represent the lemon

Our equation is

24.36 = 5x + 5.31

19.05 = 5x

x = $3.81

So, each bag of lemons cost $3.81

The correct statement regarding whether Maple Street and Elm Street are parallel lines is given as follows:

Yes, because angles 1 and 2 are supplementary.

Parallel lines are two lines that do not intersect, or technically, intersect only at infinity.

In this problem, we have that angles 1 and 2 are supplementary angles, hence:

m<1 + m<2 = 180º

As the sum of the measures of supplementary angles is of 180º.

Then these two angles are classified as consecutive interior angles, meaning that Maple Street and Elm Street are parallel lines cut by the transversal River Drive.

Thus the second option is the correct option.

The situation is represented by the image shown at the end of the answer.

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Answer: {4,3,0,-4}

Step-by-step explanation:

The range is the set of all the values of y

Range {4,3,0,-4}

Answer:

Step-by-step explanation:

its ab

Her total salary for the month would be $8300.

We have a women with $3,200 as a base salary each month. She gets 8.5% of everything she sells. If she sold $60,000 worth of items this month.

Assume her total salary to be y = $(3200 + x). Then, we can write -

y = $(3200 + {8.5/100} x 60000}

y = $(3200 + 5100)

y = $8300

Therefore, her total salary for the month would be $8300.

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There were 682 children's and 332 adults were admitted when the entrance charge to an park is $4 for adults and $1.50 for children.

Given that,

The entrance charge to an amusement park is $4 for adults and $1.50 for children. 351 persons visited the park on one particular day, and 1014 dollars in entrance fees were collected.

We have to find how many people and kids were allowed inside.

We know that,

We get equations as,

1.5x+4y=351 ----->equation(1)

The other equation is

x+y=1014 ----->equation(2)

Take the equation(2)

x+y=1014

y=1014-x

Substitute y=1014-x in equation(1)

1.5x+4y=351

1.5x+4(1014-x)=351

1.5x+2056-4x=351

1.5x-4x=351-2056

-2.5x=-1705

2.5x=1705

x=1705/2.5

x=682

Substitute x=682 in equation(2)

y=1014-x

y=1014-682

y=332

Therefore, There were 682 children's and 332 adults were admitted when the entrance charge to an amusement park is $4 for adults and $1.50 for children.

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Using PEDMAS to evaluate the expressions given, the values are -14 and 10.5 respectively

Evaluating an expression is the process of simplifying an expression by performing the necessary mathematical operations to determine its value. It involves substituting a given value for each variable and then carrying out the indicated operations.

In the question given, we have two expression which we can evaluate.

A) -2 + 12 - 2³ ÷ 2⁰ * 3

Applying the rules of PEDMAS;

We will have -2 + 12 - 8 ÷ 1 * 3 = -14

The value of the expression is -14

B) 1/2 + √25 - 8 ÷ 2 + 3²

Applying the rules of PEDMAS again;

1/2 + 5 - 8 ÷ 2 + 9 = 10.5

The value of the expression is 10.5

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The total number of methods to select the five-person committee and guarantee that there aren't any members with the same major is= 4004ways.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our question-

From the two students with same major we also use the combination Formula in knowing the number of ways any of the two students can be chosen. To choose one from these two students, we use the combination Formula 2C1.

the two students with same major aren't on the committee becomes:

14C5 * 2C1

2002 * 2

4004ways.

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Answer:

8−72+12−8

Step-by-step explanation:

The rectangular prism that has the dimensions of 3 inches by 4.75 inches by 20.5 inches, has a total surface area, found by adding the surface areas of the six faces of 346.25 in²

The surface area of a solid three dimensional object is the area of the boundary surface of the object and its surroundings.

The dimensions of the rectangular prism in the question can be defined as follows;

Let the length of the rectangular prism = 3 inches

Let the width of the prism = 4.75 inches

Let the height of the prism = 20.5 inches

The surface area, A, of a rectangular prism can be found using the formula

A = 2 × Length × Width + 2 × Length × Height + 2 × Height × Width

Therefore, the surface area of the rectangular prism in the question is found as follows;

Area, A = 2 × 3 × 4.75 + 2 × 3 × 20.5 + 2 × 20.5 × 4.75 = 346.25

The total surface area of the rectangular prism is; 346.25 in²

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The age of Michelle is 30 years old (option A).

The mathematical operation that would be used to determine the required value is multiplication. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is ×.

The first step is to determine Fiona's age.

Fiona's age = Madeline's age x 2

Fiona's age = 5 x 2 = 10

The second step is to determine Michelle's age.

Michelle's age = Fiona's age x 3

Michelle's age = 10 x 3

Michelle's age = 30

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The maximum value of x in the figure given is of:

x = 33º.

The maximum value of x is obtained when the segment traced represents a bisection of the angle at the vertex of the quadrilateral.

A bisection is defined as a segment that splits an angle measure into two equal measures.

The angle measures for this problem are given as follows, from the image:

Then the maximum value of x is obtained when these two measures are equal, as follows:

2x + 5 = 71

2x = 71 - 5

2x = 66

x = 66/2

x = 33º.

(the bisection concepts means that the larger angle, which would be of 2 x 71 = 142º, would be split into two angles with an equal measure of 71º).

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In a probability histogram, there is a correspondence between area and probability. Hence, option D is the right answer.

An histogram shows the variation in a variable over time. There are a certain number of samples in each category: this is called the frequency distribution. The number of children born according to their birth gender, such as males or females.

Probability histogram

A probability histogram is a histogram with probabilities on the y-axis and all the possible values on the x-axis. They represent chance. The area above a class interval represents the chance of that class interval.

A probability distribution shows the probabilities related to all possible outcomes of an event.

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The complete question is-

Fill in the blank.

In a probability histogram, there is a correspondence between--------------

A. volume and probability

B. area and volume

C. variation and area

D. area and probability

The integer the represent a flight overbooked by 4 passengers is y = x + 4

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given,

A flight overbooked by 4 passengers.

Let, x = Initial capacity of the flight to have passengers

and, y = Total capacity after adding all the passengers

so, the equation is

y = x + 4

Therefore, the integer the represent a flight overbooked by 4 passengers is y = x + 4.

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The correct answer is (a) 10-15, 15-20. This is an example of a Discontinuous class.

In the context of statistical data and classification, a class is a group of observations or data points that share certain characteristics. Classes can be either continuous or discontinuous, depending on whether the values or categories they represent are continuous or not.

A discontinuous class is a set of values or categories that are not continuous, meaning there are gaps or breaks between them. In this case, the classes 10-15 and 15-20 are discontinuous because there is a gap between them at 15. In contrast, the classes 5-9 and 10-14 are continuous because there are no gaps between them, and 0-5 and 10-15 are also continuous because the lower bound of the second class is equal to the upper bound of the first class.

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