Complete the missing terms in the arithmetic sequence shown here: 2, ____, 7, ____, 12?

Answer:232 miles

Step-by-step explanation:

knowing that they travel 145 miles every 5 gallons I’d we divided 145 by 5 we get how many miles they would travel with 1 gallon which is 29 after that we are trying to find how many miles can we run with 8 gallons so we do 29 times 8 to get our answer of 232

Length of floor = 5 m and breadth of floor = 4 m

Area of floor = length x breadth

= 5 m x 4 m = 20 m.sq

Now, Side of square carpet = 3 m

Area of square carpet = side x side = 3 x 3 = 9 m.sq

Area of floor that is not carpeted = 20 m – 9 m = 11 m.sq

We know that the area of a rectangle is the width multiplied by its length, basically

But here, we have the area, which is a polynomial, same for the length, then, to find out the width we must do a division of polynomial, I'll call the unknown polynomial as P, we have

So now we got to solve

There is a lot of ways to solve it, first, I'll factor 3 in the denominator

As well the numerator

Then we can already simplify 3, and get an easier expression

Now I'll factor using the grouping method, I want the numerator to be something like (x+1)*(another polynomial), doing that we can "cut" the (x+1).

One way to do it is to expand it in some simple sums, look at 3x³, we want a 3x² to match with him, but look that 9x² is 3x²+6x², let's write that way

It doesn't seem to help us at all, but look that now we can factor 3x², then

Look, we have our first (x+1) in the numerator. Let's use the same idea but now for the term 6x², we want a 6x to match with him, we have 12x, so let's write it as 6x + 6x.

Similar to what we did before, factor 6x, and again

Now we have one more (x+1).

Now the easiest one, factor 6

As we can see we have (x+1) multiplied by something in all terms in the numerator, then we can factor (x+1) now

Now we can cancel (x+1), and our final expression will be

Therefore, the width is

Answer:

Yes, it is a positive correlation. It is a positive correlation because as the amount of calories goes up, the amount of fat goes up.

The relative intensity of the sound is 2.14 * 10 greater than the minimum threshold

The loudness equation is given as

L = 10log(R)

Where

R represents the relative intensity of the sound

From the question, we have the value of R to be

R = 138

Next, we substitute 138 for R in the loudness equation L = 10log(R)

So, we have

L = 10log(138)

Evaluate the logarithmic expression

L = 10* 2.14

Rewrite as

L = 2.14 * 10

Hence, the number of times is 2.14 * 10 times

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Given that the length of one of the sides of the triangle is the radius, the length of the other leg of the triangle is also 6 units.

Therefore, this is an instance of a 45-45-90 triangle. The value of x can now be solve by

Given that the side length of the 45-45-90 triangle is 6 units, the length of the hypotenuse x is

the percentage do holidays account for will be 50.7%

What are mathematics operations?

A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.

• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.

Given:

school accounts for holidays for a calendar year = 180 days or 49%

Now, the remaining days will be holidays that is :

365 - 180 = 185 days

Therefore, the percentage do holidays account for will be :

185/365 = 50.7%

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(a) Approximate the population standard deviation (?) with the sample standard deviation (s).

Approximate the standard normal distribution with the Student's t distribution.

(b) The lower bound is 40.35 and the upper bound is 41.65.

(a) Approximate the population standard deviation (?) with the sample standard deviation (s).

Approximate the standard normal distribution with the Student's t distribution.

(b) The degree of freedom =n-1=60-1=59

Given a=0.1, t(0.05, df=59) =1.67 (from student t table)

So the lower bound is

xbar -t*s/vn = 41 -1.67*3/sqrt(60) =40.35

So the upper bound is

xbar +t*s/vn = 41 +1.67*3/sqrt(60) =41.65

The standard deviation is a statistical metric that determines how much a bunch of values deviate from the mean. Simply said, standard deviation quantifies the distance between integers in a data collection. The square root of the variance is used to construct this measure.

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The midpoint, that is the middle point of any given line segment can be calculated if the endpoints have been made available.

The endpoints for the line segment is,

(7, 5) and (-3, -5) for points X and Y respectively.

The middle point can be found at this position;

(x1 + x2) / 2 and (y1 + y2) / 2

The points are shown as

(7, 5) = (x1, y1)

(-3, -5) = x2, y2)

Therefore we now have,

Midpoint = (7 + [-3])/2 and (5 + [-5])/2

Midpoint = (7-3)/2 and (0)/2

Midpoint = 4/2 and 0/2

Midpoint = (2, 0)

1. The number of students that the art academy has per teacher is 16.

2. The number of students that the art academy has per tutor is 9.

3. With 108 students, the art academy requires 12 tutors, given the student-to-tutor ratio of 9:1.

In this situation, we can use the mathematical operation of division to state the ratio of students to either teachers or tutors.

The parts of the division operation include the dividend, the divisor, and the quotient, which is the result of applying the divisor to the dividend.

The number of teachers for 80 students = 5

1. The number of students per teacher = 16 students (80/5)

The number of tutors for 36 students = 4

2. The number of students per tutor = 9 students (36/4)

3. If the students are 108, the number of tutors = 12 tutors (108/9)

Thus, after determining the quotients, we can relate the number of students to teachers and tutors using ratios.

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An arts academy requires there to be 5 teachers for every 80 students and 4 tutors for every 36 students.

A circuit in electronics is a complete circular channel via which electricity flows. A current source, conductors, and a load make up a straightforward circuit. In a broad sense, the word "circuit" can refer to any permanent path through which electricity, data, or a signal can pass.

Plucking crops as they move from field to field. Throughout California, Panchito and his family travelled to collect strawberries, cotton, grapes, and lettuce. a visitor who intends to settle permanently in a nation. From Mexico, Panchito and his family immigrated.

Young migrant labourer Panchito and his family make their living by working the seasonal agricultural harvesting circuit. The appearance of cardboard boxes, which contain all of the family's belongings, marks each move on the circuit. Panchito has the chance to go to school as the circuit takes the family to Fresno.

The members of Francisco's family gather various crops in each town they reside in as they migrate throughout the central coast of California.

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Answer:

5 batches

Step-by-step explanation:

60÷ 12=5 batches

The expression which is equivalent to the given expression as in the task content is; 4.5⁶.

It follows from the task content that the expression which is equivalent to the given expression is to be determined.

Since the given expression is;

(4.5)-⁵ • (4.5)¹¹

Hence, it follows from the product of exponents law of indices that we have;

(4.5)^(-5 + 11)

= (4.5)⁶

Therefore, the expression which is equivalent is; 4.5⁶.

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The probability of rolling a total of 7 on the two dice is 8/63

Probability:

In Mathematics, Probability is a branch that deals with the occurrence of possible outcomes in a random event or experiment. It is also defined as the ratio of the number of favorable outcomes and the total number of outcomes.

The probability of an event is denoted by P(E). And the probability of all the events in the sample space will equal to 1.  

Probability P(E) = No of favorable outcomes /Total No of outcomes  

Here we have,

The probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die, are in the ratio 1: 2: 3: 4: 5: 6  

Let x, 2x, 3x, 4x, 5x, and 6x are the probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die [ since they are in ratio 1: 2: 3: 4: 5: 6 ]  

As we know the total events in a probability = 1

=> x + 2x + 3x + 4x + 5x + 6x = 1  

=> 21 x = 1

=> x = 1/21  

From the above calculations,

The probabilities of rolling 1, 2, 3, 4, 5, and 6 are  [tex]\frac{1}{21} , \frac{2}{21}, \frac{3}{21}, \frac{4}{21}, \frac{5}{21}, \frac{6}{21}[/tex] respectively.  

The possible combinations of two dies that can give a total of 7 are

(1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1)

Therefore, the probability of rolling a total of 7 on the two dice

=  the sum of the probabilities of rolling each combination

=  [tex]\frac{1}{21} . \frac{6}{21} + \frac{2}{21} .\frac{5}{21} + \frac{3}{21} . \frac{4}{21} + \frac{4}{21} . \frac{3}{21} + \frac{5}{21} .\frac{2}{21} + \frac{6}{21} .\frac{1}{21}[/tex]  

=  [tex]\frac{6}{441} + \frac{10}{441} + \frac{12}{441} + \frac{12}{441} + \frac{10}{441} + \frac{6}{441}[/tex]  

=  [tex]\frac{56}{441}[/tex]

=  [tex]\frac{8}{63}[/tex]

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The complete question is

For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die are in the ratio 1:2:3:4:5:6. What is the probability of rolling a total of 7 on the two dice

The pairs of points that on the linear equations are:

a) (1, 7) and (0, 10).

b)  (1, 7/3) and (0, 2)

First, we need to find the slope of the equation of the line that passes through the points (-2, 6) and (1, -3).

Remember that if a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know that the line passes through the points (-2, 6) and (1, -3), then the slope is:

a = (-3 - 6)/(1 + 2) = -9/3 = -3

a) A parallel equation will have the same slope, so it will be of the form:

y = -3*x + b

To find the value of b w euse the fact that this line should pass through the point (2, 4), so:

4 = -3*2 + b

4 = -6 + b

4 + 6 = b = 10

The linear equation is:

y = -3*x + 10

To find two points we can evaluate in x = 1 and x = 0, we will get:

y = -3*1 + 10 = 7

y = -3*0 + 10 = 10

So we have the pair of points (1, 7) and (0, 10).

b) A perpendicular equation will have a slope equal to the inverse of the opposite, so we will have a line like:

y = (1/3)*x + c

To find the value of c we use the fact that this line passes through (3, 3), them:

3 = (1/3)*3 + c

3 = 1 + c

3 - 1 = c

2 = c

This line is:

y = (1/3)*x + 2

Again we evaluate in 0 and 1 to get the two points:

y = (1/3)*1 + 2 = 1/3 + 6/3 = 7/3

y = (1/3)*0 + 2 = 2

So we have the pair of points (1, 7/3) and (0, 2)

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V(4) of the photocopier is $6,210

The value of t when V (t) = 5780 is 4.5 years

The original price of the photocopier is $9,650

What does V(4)?

V(4) means that the requirement in this case is to determine value of the photocopier after 4 years since t means the number of years since the photocopier was initially acquired, in other words, in order to determine the value of the photocopier after 4 years we simply substitute 4 for t in the value equation given as shown below:

V (t) = 9650 - 860t

t=4

V(4)=9650 - 860(4)

V(4)=9650-3440

V(4)=$6,210

When V(t)=5780,we can determine t by making t the subject of the formula

V (t) = 9650-860t

5780=9650-860t

860t=9650-5780

860t=3870

t=3870/860

t=4.5

The original price can be computed on the basis that the photocopier was bought when t=0, I mean in year zero, hence, attributing zero to t , we can determine the original price

V (t) = 9650-860(0)

V(0)=$9,650

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Answer:

y = -1/4

Step-by-step explanation:

If the slope is o, that means that it is a horizontal line.  The line passes though the point (4, -1/4)  The horizontal line will have y as -1/4, no matter what x is.

Answer:

[tex]\sf y =\dfrac{-1}{4}[/tex]

Step-by-step explanation:

Equation of the line with slope 0 is y = c.

where c is the y-co-ordinate.

 The line with slope 0 is a horizontal line that is parallel to x-axis.

          [tex]\sf y =\dfrac{-1}{4}[/tex]

The percentage increase of the value of Tessa's stock is 49%.

Stock is a term used to describe the shares of ownership of a company. It is sometimes also called equity.

To find the percentage value change, we use the formula given below

P = (N-O)/O*100

Here, P = percentage change, N = new value, O = old value.

P = (263.73-177)/177*100

P = 86.73/177*100

P =  8673/177

P = 49%

Therefore, we can conclude that the total percentage increase of the value of Tessa's stock is 49%.

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Answer:

3.75

Explanation:

Given the equation 4x+4y = 15, we are to find the x coordinate of equation

To do this we will find the x intercept of the equation.

when y = 0

4x+4y = 15

4x + 4(0) = 15

4x = 15

x = 15/4

x = 3.75

Hence the x coordinate of the equation is 3.75

Answer:

 g(x) = f(5x)

Step-by-step explanation:

We assume that "shrink by a factor of 1/5" means that horizontal distances on the graph of g(x) are 1/5 of those on the graph of f(x).

Dividing x by a dilation factor will cause horizontal dilation of a graph. Here, that factor is 1/5, so the desired function is ...

 g(x) = f(x/(1/5))

 g(x) = f(5x)

The height of the tree which John wants to measure is equal to 64.94 feet.

What is trigonometry ?

Trigonometry is the branch of mathematics which examines the relationship between triangle sides and angles as well as the relevant functions of any angle.

It is given that John wants to measure the height of a tree. He walks 100 feet from the base of the tree and looks up. Say , point B is the base of triangle and C is the point up to which he has walk then , BC will be length of base.

i.e.,

Length of base (B) = 100 feet.

It is given that angle from ground to top of tree (say θ) is 33°

We know that tangent (tan θ) is ratio of height to the base of object. So,

tan θ = [tex]\frac{H}{B}[/tex]

tan 33° = [tex]\frac{H}{100}[/tex]

So , the height of tree will be :

H = 100 × tan 33°

H = 100 × 0.6494

H = 64.94 feet

Therefore , the height of the tree which John wants to measure is equal to 64.94 feet.

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The colored pencils does jaime have more than talisa is 24

An arithmetic operator is a mathematical function that takes two operands and performs a calculation on them.

They are used in common arithmetic and most computer languages contain a set of such operators that can be used within equations to perform a number of types of sequential calculation. Basic arithmetic operators include:

:-Addition (+)

:-Subtraction (-)

:-Multiplication (×)

:-Division (÷)

so;

     A.T.Q:-

     The colored pencils does talisa have are 34

     The colored pencils does  jaime have are 58

   ∴ by using arithmetic operator Subtraction (-) , we conclude that how more colored pencils does jaime have than talisa

 ∵ jaime's colored pencils - talisa's colored pencils

 ⇒ 58-  34

 ⇒24

 hence; jaime have 24 pencils more than talisa

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Answer:

GCF = 1

Step-by-step explanation:

factors of 18 = 1, 2, 3, 6, 9, 18

factors of 35 = 1, 5, 7, 35

the common factor to both is 1 only

then the GCF of 18 and 35 is 1

Given that points A, B, and C are the midpoints of their respective sides, A)  1/2YZ = AC is true about the figure according to SSS congruent rule.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and angles have the same measure. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "."

When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general.

However, all six dimensions must be discovered. In light of this, it is possible to determine the congruence of triangles using just three of the six values. Triangles that are congruent have equal corresponding sides and angles.

YX = 2 × AX (A = midpoint of YX)

ZX = 2 × CX (C = midpoint of ZX)

∠X and ∠X are congruent as the Reflexive property rule.

Therefore, triangle XAC is congruent to triangle XYZ (SAS similarity theorem)

Since 2AX = XY and 2XC = XZ Then 2AC = YZ which SSS congruent rule.

So, the correct option is A)  1/2YZ = AC

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The equation for the direct linear variation that models the given information is: C. r = 64.5t.

The equation of a direct linear variation can be modelled as y = kx, where the variables are x and y, while the value of k is the constant of proportionality between the variables, x and y.

Given that:

We are told that r varies directly with t. Where k is the constant of proportionality, the equation of the direct linear variation between r and t can be expressed as r = kt.

Constant of proportionality, k = r/t

Number of shirts Rebecca can fold and restock (r) = 129

Amount of time she would spend (t) = 2

Find the constant of proportionality, k:

k = r/t = 129/2

k = 64.5

To write the equation for the direct linear variation, substitute k = 64.5 into r = kt:

r = 64.5t

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Answer:

Step-by-step explanation:

solution = (4 , 5)

y = 5 / x = 4

y = 2x - 13

5 = 2(4)- 3

5 = 8 - 3

5 = 5

the equation does make sense

y = x + 1

5 = 4 + 5

5 = 5

the equation does make sense

However, the questions asks if the solution works for both equations, and the solution does work for the first equation and the second one as well. The answer is yes, the solution does work for this system of equations.

Answer:

x equals four

Step-by-step explanation:

collect like terms

then it will be minus 8 x equals minus 13 minus 19 which gives minus 32. Divide both sides by the coefficient of x i.e minus 8

Then x is less than 4

Because you divided with minus so the sign will change

The correct ans to the given graph is :

Kelly added $20 into saving each week.

How would you define a graph ?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

How is a line graphed?

Draw a horizontal axis and a vertical axis first before drawing a line graph. Because age is independent, it should be plotted on the horizontal axis. Plotting should be done using height on the vertical axis. Plot a point for each pair of values using the data that has been provided.

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