Two students attempted to solve the literal equation[tex]a=1\fra/2(b+c)[/tex]

for c. Who solves it correctly? How do you know?

ANSWER.  B = 18,  A = B + 23 = 18+23 = 41.

Step-by-step explanation:

Yes (3,0) is the solution of the given equation.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given Data

Equation

3x - 2y-9=0

X + 8y-3 = 0

Solution(3, 0)

Finding the values of x,

x + 8y - 3=0

x = 3 + 8y...(1)

Substituting x in the equation

3x - 2y = 9

3(3+ 8y) -2y = 9

9 + 24y - 2y = 9

22y = 0

y = 0

Substituting the value in (1)

x = 3 + 8(0)

x = 3

Yes (3,0) is the solution of the given equation.

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Using probability we can calculate that the company must charge $697 for an expected return of 400 .

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

The probability that a 30 year old female lives throughout the year

= 0.99967

Death benefit = $900,000

Expected amount the company would pay = probability that a person dies × insurance amount.

Expected amount = (1 - 0.99967) × 900000 = $297

Now Company wants a profit of $400

Cost charged by company =$( 297 + 400 ) = $ 697

Therefore using probability we can calculate that the company must charge $697 for an expected return of $400 .

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Answer:

180=x+42

collect like terms

x=180-42

x=138

So if i have a bag of rice of 3.5 pounds, that means that it weighs:

since

that means that you will have enough rice for the recipe

Answer:

c>11

Step-by-step explanation:

you +12 on both sides then u now have 11 rather than -1 which leaves u with c>11

The principal amount is $693.33.

Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount.

The formula is

Simple Interest = P x R x T/100

Given:

Interest = 78

Rate= 7.5%

Time= 1 and half year = 1.5 year

Now, Simple Interest= P x R x T / 100

                             78 = P x 7.5 x 1.5 / 100

                             7800= P x 11.25

                             P = 7800/11.25

                              P = 693.33

Hence, the principal amount is $693.33.

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The most appropriate choice for average will be given by-

Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.

What is  average?

In a data set, there are many numbers. Average is the single number which acts as a representative of all the numbers in the data set.

Average is calculated by sum of all observations divided by total number of observations.

Here,

Let the score of Shureka Washburn in her last test be x

Score of Shurek Washburn on first test = 86

Score of Shurek Washburn on second test = 84

Score of Shurek Washburn on third test = 83

Score of Shurek Washburn on fourth test = 49

Total sum of all her scores = 86 +  84 + 83 + 49 + x

                                           =  302 + x

Average = [tex]\frac{302 + x }{5}[/tex]

By the problem,

                          [tex]\frac{302 + x}{5} \geq 76[/tex]

                          [tex]302 + x \geq 76[/tex] [tex]\times 5[/tex]

                          [tex]302 + x \geq 380[/tex]

                          [tex]x \geq 380 - 302[/tex]

                          [tex]x \geq 78[/tex]

Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.

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°

the two triangles have a bisetor that makes the adjacent side equal, so based on this 25 = 5x- 10

25+ 10 = 5x

meaning your x = 7

but on the equation 5x-10 =0

we get that x = 10/5

x >2

so the range would be 2

Yes, the triangle is a right-angle triangle.

Right angle triangle is a triangle in which one of the angles as 90 degree.

For the triangle to be right angle triangle

perpendicular² + base² = hypotenuse²

The three sides of a triangle are 6, 8 and 10

So,

6² + 8² = 10²

36 + 64 = 100

100 = 100

Therefore the triangle is a right-angle triangle.

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The volume of a right cone is one-third of the product of the area of the base B and the

Since the area of the base and the height is already given, substitute the values in to the equation and then simplify.

We may also find the exact value by substituting the given values into the equation below.

where V is the volume, r is the radius, and h is the height.

To obtain the exact value of the height, we use the Pythagorean theorem.

where a and b are the legs of the formed right triangle while c is its hypothenuse.

From the figure, the slant height is the hypothenuse while the radius, 9 ft, serve as one of the legs. Thus, the other leg, which is the height of the cone can be solved as follows.

Therefore, the height of the cone is as stated above.

Substitute the obtained height and the radius into the second formula that was stated.

Simplify the right side of the equation. Evaluate the exponential expression.

Multiply the numerator and then divide it by 3.

Note that the value that we obtain at first, 1415,603, is slightly different from the one that we obtained, which is 1419.36, since there are values that we already rounded off before substituting the values in the equation.

Therefore, to be more exact, it is best to indicate that the volume of the given cone is approximately 1419.36 ft³.

Based on the number of dice rolled, the probability of getting the sum of 6, and 4 and 6 or 4 can be found to be:

Probability of getting sum of 6:

(1 and 5) (2 and 4) (3 and 3) (4 and 2) ( 5 and 1)

= 5 / (6 x 6)

= 5 / 36

The number of sums of 4 are:

= (1 and 3), (2 and 2), (3 and 1)

= 3 / (6 x 6)

= 1 / 12

The probability of getting sums of 6 and 4 are:

= (5 + 3) / (6 x 6)

= 8 / 36

= 2 / 9

These events are mutually exclusive because they cannot roll a sum of 6 or 4.

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The standard deviation of the discrete distribution of the number of defects in a day is of 0.75 defects.

From the distribution at the end of the answer, the mean is:

E(X) = 0.1667 x 4 + 0.3333 x 5 + 0.5 x 6 = 5.3333.

Hence the standard deviation is of:

S(X) = sqrt(0.1667 x (4-5.3333)² + 0.3333 x (5 - 5.3333)² + 0.5 x (6 - 5.3333)²) = 0.75 defects.

The distribution is missing, and is given as follows:

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The perimeter of the semicircle with different r values is:

So, the formula for the perimeter of the semicircle:

Now, insert values as follows:

(A) (When r = 2)

(B) (When r = 4)

(C) (When r = 12)

Therefore, the perimeter of the semicircle with different r values is:

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The correct question is given below:

2 mm. em. 4 em 12 Manam. Find the perimeter of the semicircle. Use 3.14 for it when needed.

the prime factors of a positive integer are the prime numbers that divide that integer exactly.

The number of different ways that the three positions can be filled is 504 ways.

From the information, there are 9 candidates for three positions at a restaraunt. Based on the data, one position is for a cook, the second position is for a food server and the third position is for a cashier.

Therefore, the number of ways will be:

= 9P3

= 9! / (9 - 3)!

= 9! / 6!

= 9 × 8 × 7

= 504

The number of ways is 504 ways.

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Answer:

first evening = 27 calls

second evening = 42 calls

third evening = 21 calls

Step-by-step explanation:

Total of 90 calls

f = first evening

s = second evening

t = third evening

f=t+6

s = 2t

t=t

f+s+t=90

t+6 + 2t + t

(2t+t+t)+6 = 90

4t+6 = 90

4t=84

t=21

=21+6

= 27

s = 2t

 = 42

t = t

= 21

A is defined as a subset of the sample space, that is, the universal set

a. A∩B = { E3, E9}

b. A∪B = {E,  E1, E2, E3,E7, E9}

c. Yes, the union of A and B is collectively exhaustible

Sets are defined as in mathematical and logical collection of elements or objects, numbers or functions.

The members of a set are listed in enclosed braces.

The elements and objects of a set are well-defined and fixed.

Given the sets as;

S= [E1, E2, E3, E4, E5, E6, E7, E8, E9, E10]

A = [E1, E3, E6, E9]

A is defined as a subset of the sample space, S

a. It is important to note that the intersection of two sets involves the elements or objects that are common between them.

Given that;

A = [E1, E3, E7, E9]

B = [E2. E3, E, E9]

A∩B = { E3, E9}

b. Note that the union of sets involves the collection of the elements of both sets without repetition.

A∪B = {E,  E1, E2, E3,E7, E9}

c. The union of the sets A and B are together exhaustive as it contains all the elements in both sets.

Hence, A is defined as a subset of the universal set.

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Answer:

The small box price is 6.5 and The large box price is 16.5

Step-by-step explanation:

I did the question with a simultaneous equation

let's say the price of the small box = x and the price of the large box = y

Then, I just subtract downward;

18x+25y=529.50

- 18x+10y=282.00

_____________

0+15y=247.50

15y=247.50

— ————

15 15

I just canceled 15 by 15:

Then, y=247.50÷15=16.5

so I just find the value of Y which is 16.5, then I insert it into the second equation:

18x+10y=282

18x+10(16.5)=282

18x+165=282

18x=282-165

18x=117

— —

18 18

Cancel 18 by 18

finally x=6.5

Insert x and y into both equations, it works

Answer:Note that at least means greater than or equal to (≥) . It was stated that you must be at least 48 inches tall to ride the roller coaster. Hence, the inequality is h≥48 h ≥ 48

Step-by-step explanation: poopity poop UWU UWU UWU oodfijdisfioahgioahiodfhipodioajhierfia           MUSIC MUSIC MUSIC MUSIC MUSIC MUSIC HACKER HACKER HAKER HACKER HACKER OMG UWU UWU UWU YOUR 13 LOL YOUR FATHERLESS GT DELETED TRASH KID

To solve this problem, we will use the conditional probability definition: Given events A,B such that P(B)>0 we have that

Where P(A|B) means the probability of A given B occurred. This also leads to the following

Now, let us define two events. Let M1 be the event that we select a male first and let F2 be the event that we select a female second. We want to calculate the following probabilty

Using the definition of conditional probability, this is the same as

Now, we will calculate P(M1). At the beginning, when we have not picked anyone yet, we have 37 people (21 Female and 16 Male). So the probability of picking a male first is simply

Now, we will calculate the second probability. Since we already picked one male, we have now 36 people (21 female and 15 male). Then the probability of picking a female is

So,

The features of the graphs are

Function 1

The equation of the function is given as

f(x) = 3(x - 4)^2 + 3

A quadratic equation can be represented as

f(x) = a(x - h)^2 + k

Where, the vertex is

Vertex = (h, k)

And the axis of symmetry is

x = h

By comparing the equations, we have

Vertex = (4, 3)

Axis of symmetry: x = 4

See attachment 1 for the graph of the function

Function 2

The equation of the function is given as

f(x) = 5x^2 + 4x - 1

Differentiate the function

f'(x) = 10x + 4

Set to 0

10x + 4 = 0

This gives

x = -0.4

Substitute x = -0.4 in f(x) = 5x^2 + 4x - 1

f(-0.4) = 5(-0.4)^2 + 4(-0.4) - 1

Evaluate

f(-0.4) = -1.8

This means that

Vertex = (-0.4, -1.8)

Axis of symmetry: x = -0.4

See attachment 2 for the graph of the function

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Using proportions, the costs for the boats are given as follows:

Factory A:

Factory B:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using the standard operations such as addition, subtraction, multiplication and division with the unit rates to find the equivalent amounts.

Considering the costs per hour and the number of hours needed, the cost of a small boat at Factory A is given by:

15 x 1  + 11 x 0.5 + 12 x 0.2 = $22.9.

For example, 15 x 1 is because it requires one hour of cutting, and each hour of cutting pays of $15.

The cost of a medium boat at Factory A is given by:

15 x 1.6  + 11 x 1 + 12 x 0.2 = $37.4.

The cost of a large boat at Factory A is given by:

15 x 2.5 + 11 x 2 + 12 x 1.4 = $76.3.

The cost of a small boat at Factory B is given by:

13 x 1  + 11 x 0.5 + 10 x 0.2 = $20.5.

The cost of a medium boat at Factory B is given by:

13 x 1.6  + 11 x 1 + 10 x 0.2 = $33.8.

The cost of a large boat at Factory B is given by:

13 x 2.5 + 11 x 2 + 10 x 1.4 = $68.5.

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The system of equations for the given conditions in question includes equation: 3.40 = 0.05x + 0.1y + 0.25z, and 2x = z. and we have 2 nickels, 23 dimes, and 4 quarters.  

What is system of equations?

A system of equations is a collection of some equations with one or more numbers of variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the intersections of all of these equations.

Let the quantities of nickels, dimes, and quarters are x, y, and z respectively.

We know that, 1 nickel = $0.05, 1 dime = $0.1, and 1 quarter = $0.25

So, the values of nickels, dimes, and quarters would be value of one times total quantity.

Nickels = 0.05x, dimes = 0.1y, and quarters = 0.25z

As given in the question, the total value is 3.40

So, we get equation:

3.40 = 0.05x + 0.1y + 0.25z

Also it is given that there are twice as many nickels than quarters.

2x = z

Combining above two equations

3.40 = 0.05x + 0.1y + 0.25(2x)

3.40 = 0.05x + 0.1y + 0.5x

3.40 = 0.55x + 0.1y

Lets put 2 in place of x, we get y

(3.40 - 1.1)0.1 = y

y = 23.

Now, putting values of x, y in equation to get value of z

3.40 = 0.05(2) + 0.1(23) + 0.25z

3.40 = 0.1 + 2.3 + 0.25z

(3.40 - 2.4)/0.25 = z

z = 4

Therefore, we have 2 nickels, 23 dimes, and 4 quarters.  

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E = 38.33 the margin of error at a 98% confidence level by standard deviation mean.

What does standard deviation mean ?

Given that,

bar x = 36

s = 9

n = 12

Degrees of freedom = df = n - 1 =12 - 1 = 11

At 98% confidence level the t is ,

∝ = 1 - 98% = 1 - 0.98  ⇒ 0.02

∝/2 = 0.02/2 = 0.01

t∝/2 df = t0.01 ,11 = 1.231

Margin of error = E = t∝/2, df * ( s/n/sqrtn)

                             E = 1.231 * ( 9 /0.01/sqrt12)

                              E = 38.33

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The coordinates of the vertices of the image triangle A'B'C' after a rotation 90° counterclockwise about the origin are: A' (10, 5), B' (-4, -8), C'(0, 2)

A rotation simply refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, rotating a point 90° about the origin in a counterclockwise (anticlockwise) would produce a point that has the coordinates (-y, x).

By applying a rotation of 90° counterclockwise to triangle ABC, the coordinates of the vertices of the image triangle A'B'C' include the following:

(x, y)                    →            (-y, x)

Point A = (5, -10)   →  Point A' = (-(-10), 5) = (10, 5)

Point B = (-8, 4)   →    Point B' = (-4, -8)

Point C = (2, 0)   →     Point C' = (0, 2)

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