g(x)
10
8
6
4
2
fo
-10-8-64-22
-4
-6
-8
-10
f(x)
2 4 6
8 10 x
What is the equation of the translated function, g(x), i
f(x) = x²?
g(x) = (x-4)² +6
Og(x) = (x + 6)²-4
g(x) = (x-6)²-4
Og(x) = (x+4)² + 6
O

The formula that represents the arithmetic sequence is f(n) = 32-7(n-1) (optionC)

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term. For example in the arithmetic sequence 3, 9, 15, 21, 27, the common difference is 6. An arithmetic sequence can be known as an arithmetic progression.

The formula for the nth of an arithmetic sequence is a(n) = a+(n-1)d. Where d is the common difference and n is the number of terms.

In the sequence 39, 32, 25, 19, 12,. The first term is 32 and the common difference is 32-39= -7.

Therefore the formula for the sequence is formed by inserting the values of a and 7.

f(n) = 32+(n-1)-7

f(n) = 32-7(n-1)

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Answer:

f(n) = 39-7(n-1)

Step-by-step explanation:

Trust I took test

To find the 95% confidence interval for the mean Sales on days that have 12 employees working, we would need to know the population standard deviation and the sample size. The formula for a 95% confidence interval for the mean is:

(sample mean) ± (critical value) x (standard deviation / sqrt(sample size))

Without the information about sample size, standard deviation and sample mean, it's not possible to find the exact 95% confidence interval for the mean Sales on days that have 12 employees working.

Similarly, to find the 95% prediction interval for Sales on a day with 12 employees working, we would need to know the population standard deviation, sample size, and the sample mean. The formula for a 95% prediction interval for a single observation is:

(sample mean) ± (critical value) x (standard deviation of the mean) x sqrt(1 + (1/sample size))

Again, without the information about sample size, standard deviation and sample mean, it's not possible to find the exact 95% prediction interval for Sales on a day with 12 employees working.

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The slice when cube is sliced through all faces is hexagon.

A cross-section is a shape that is yielded from a solid (e.g. cone, cylinder, sphere) when cut by a plane.

For example, a cylinder-shaped object is cut by a plane parallel to its base; then the resultant cross-section will be a circle.

Given,

A cube is sliced with a plane,

The plane meets all faces of cube,

When a plane intersects a cube there is a variety of shapes of the resulting cross section.

A hexagon, If the plane meets all faces of the cube.

Hence, slice is hexagon when cube is sliced through all faces.

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Answer:

Below

Step-by-step explanation:

Perimeter = 446

446 = (13x-1) + (13x-1) + (9x+4) + (9x+4) ft      <====four sides added together

446 = 44x +6

440 = 44x

x = 10                 then width = 9(10)+4 = 94 ft     Length = (13(10)-1) = 129 ft

There are 231+d pies baked in two years.

expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An equation is made up of two expressions connected by an equal sign.

Since we have given that

Number of pies baked for bake sale last year = 231

Number of pies baked for bake sale this year = d

So, total number of pies baked in two years is given by

231 +d

Hence, there are 231+d pies baked in two years.

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The properties shown in each statement are given as follows:

1. 4m x 0 x 3m = 0 -> neutral element of the multiplication.

2. 5 + (a + 17) = (5 + a) + 17 -> associative property of addition.

The first expression is given as follows:

4m x 0 x 3m = 0.

A multiplication by zero will always result in a value of zero, hence the property is of the neutral element of the multiplication.

The second expression is given as follows:

5 + (a + 17) = (5 + a) + 17.

The change is in the order in which the terms are added, which does not change the value of the sum, hence the property is the associative property of addition.

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Dividing 4x³ + x² - 27x + 18 by 4x - 3 will result to a quotient of x² + x - 6 and a remainder of 0

The long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder.

We shall divide the 4x³ + x² - 27x + 18 by 4x - 3 as follows;

4x³ divided by 4x equals x²

4x - 3 multiplied by x² equals 4x³ - 3x²

subtract 4x³ - 3x² from 4x³ + x² - 27x + 18 will result to 4x² - 27x + 18

4x² divided by 4x equals x

4x - 3 multiplied by x equals 4x² - 3x

subtract 4x² - 3x from 4x² - 27x + 18 will result to - 24x + 18

-24x divided by 4x equals -6

4x - 3 multiplied by -6 equals - 24x + 18

subtract - 24x + 18 from - 24x + 18 will result to a remainder of 0

Therefore by the long division method, 4x³ + x² - 27x + 18 by 4x - 3 gives a quotient x² + x - 6 and a remainder of 0.

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Answer:

3/5 is 2/3 of 9.

Step-by-step explanation:

The expression √7. √7² is equivalent to [tex]7\sqrt{7}[/tex].

According to the quadratic formula, x = (-b (b2 - 4ac)) /2a gives the roots of the quadratic equation ax2 + bx + c = 0. Convert the quadratic equation into standard form, ax2 + bx + c = 0, then find the values of a, b, and c, substitute them in the quadratic formula, and simplify to find the solution to any quadratic equation.

Let's say that multiplying 5 by 5 yields the number 25. Therefore, we can state that 5 is equal to 25 squared. Similar to this, the root values of 16, 36, 49, etc. are 4, 6, and 7, respectively.

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Answer: There were 304 children and 89 adults at the public pool on that hot summer day.

Step-by-step explanation:    

Let's say the total number of people at the pool that day is x + y = 393

   The total cost of admission for all the people is $678.50

   The cost for each child's admission is $1.50 and the cost for each adult's admission is $2.50

We can use this information to set up two equations:

   x + y = 393 (Total number of people)

   1.5x + 2.5y = 678.5 (Total cost of admission)

Now we can use the first equation to solve for one of the variables. For example, we can solve for y:

y = 393 - x

We can substitute this value of y into the second equation:

1.5x + 2.5(393 - x) = 678.5

We can then solve this equation for x:

1.5x + 982.5 - 2.5x = 678.5

-x = -304

x = 304

This means that there were 304 children at the pool that day. We can use the first equation to find the number of adults:

x + y = 393

304 + y = 393

y = 393 - 304

y = 89

Therefore, there were 304 children and 89 adults at the public pool on that hot summer day.

The provided equation of the plane contains 60 as the x, y, and z coefficients.

The mathematical formula for the line that is parallel to the given plane and passes through the specified point. N is equal to s, which is equal to ai, bj, and ck.

The line's parametric equations are x = x0 + at, y = y0 + bt, and z = z0 + ct, which are obtained by formulating the line's vector equation in terms of its components. The direction numbers of the line are known as the components a, b, and c.

Initially, by solving for y, convert the provided line's equation into slope-intercept form. You obtain y = -2x+5, meaning that the slope is 2. We wish to find the slope of the line, which is 1/2 because perpendicular lines have opposite-reciprocal slopes.

7*-8 + 5*10 + 5*0 = 6

-56 + 50 + 0 = 6

-6 = 6

= 12.

Z = 5*12 = 60.

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[tex]\dfrac{6y-1}{y} -2=3[/tex]

Simplify:

[tex]6y-1-2y=3y[/tex]

[tex]4y-1=3y[/tex]

Subtract 3y from both sides:

[tex]4y-1-3y=3y-3y[/tex]

[tex]y-1=0[/tex]

Add 1 to both sides:

[tex]y-1+1=0+1[/tex]

[tex]\fbox{y = 1}[/tex]

Answer:

a4 = -3 * 4^(4-1) = -3 * 4^3 = -3*64 = -192

Step-by-step explanation:

A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is always the same. In this case, the given sequence is -3, -12, -48, -192, -768.

To find the explicit formula for this geometric sequence, we can use the following formula:

an = a1 * r^(n-1)

where:

a1 is the first term in the sequence (-3)

an is the nth term in the sequence

r is the common ratio (the ratio between any two consecutive terms)

To find the common ratio, we can divide -12 by -3, -48 by -12, -192 by -48, and -768 by -192, and in all cases we get r = 4

Therefore, the explicit formula for this geometric sequence is:

an = -3 * 4^(n-1)

This formula can generate any term of the sequence given the value of n.

So, for example, the fourth term of the sequence, -192, can be obtained by inputting n = 4 in the explicit formula:

a4 = -3 * 4^(4-1) = -3 * 4^3 = -3*64 = -192

Using the concept of similar triangles, the height of the tree is; Option D: 38 ft 6 inches.

Similar triangles are defined as triangles that have the same shape, but then their sizes may vary. This means that equilateral triangles and squares are good examples of similar objects. Thus, if two triangles are similar, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.

Thus, applying the principle of similar triangles above to the given image, if the height of the tree is h, then we have;

5/3.25 = h/25

h = (25 * 5)/3.25

h = 38.462 ft = 38 ft + 0.462 ft

Now, conversion of ft to inches gives 0.462 ft approximately 6 inches Thus, our final answer is 38 ft 6 inches.

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The linear equation for given citation will be 35/10+5/8x where x is the number.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

As given citation is thirty five to ten added to five eights of a number

It can be changed into the linear equation

35/10+5/8x.

where x is the number.

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Answer:

7.5 hours

Step-by-step explanation:

let t represent time, l represent length and n represent number of painters.

given t varies directly with l and inversely with n then the equation is

t = [tex]\frac{kl}{n}[/tex] ← k is the constant of variation

to find k use the condition t = 5 when l = 200 and n = 3 , then

5 = [tex]\frac{200k}{3}[/tex] ( multiply both sides by 3 )

15 = 200k ( divide both sides by 200 )

0.075 = k

t = [tex]\frac{0.075l}{n}[/tex] ← equation of variation

when l = 500 and n = 5 , then

t = [tex]\frac{0.075(500)}{5}[/tex] = [tex]\frac{37.5}{5}[/tex] = 7.5 hours

Answer:

[tex]\sf \frac{2A-hb}{h}=c[/tex]

Step-by-step explanation:

[tex]\sf A=\frac{1}{2}h(b+c)[/tex]

First, multiply both sides by 2.

[tex]\sf 2A=h(b+c)[/tex]

Solve the brackets.

[tex]\sf 2A=hb+hc[/tex]

Subtract h b from both sides.

[tex]\sf 2A-hb=hc[/tex]

Divide both sides by h.

[tex]\sf \frac{2A-hb}{h}=c[/tex]

Answer: Statistical Question:

What is the number of days my friends spend at camp every summer?

How many miles do the teachers at our school drive per year?

What is the number of hours sixth graders spend playing sports each week?

Not a Statistical Question:

How tall is the Eiffel Tower?

What is the distance from my school to the fire station?

The questions "How tall is the Eiffel Tower?" and "What is the distance from my school to the fire station?" are not statistical questions because they are asking for a single, specific value, rather than a range of values or a pattern among a group of data.

On the other hand, "What is the number of days my friends spend at camp every summer?", "How many miles do the teachers at our school drive per year?" and "What is the number of hours sixth graders spend playing sports each week?" are statistical questions because they are asking for a range of values or a pattern among a group of data.

Step-by-step explanation:

The circle with a 7 feet radius cut into 6 equal sectors, indicates, using 22/7 approximation for pi, that the area of 2 of the pieces is 51 and one third square feet. The correct option is option C.

C. 51 and one third square feet

A sector of a circle is a pie shaped part of a circle that is bounded by an arc and two radii of the circle.

The specified radius of the circle, r = 7 feet

The number of pieces to which the circle is cut into = 6 equal pieces (sectors)

The area of 2 of the pieces, using 22/7 as an approximation for π are found as follows;

Area of a circle, A = π × The square of the radius

Therefore; A = π × r²

A = (22/7) × 7² = 154

The area of the circle is about A = 154 square feet

The area of one of the pieces into which the circle is cut is therefore;

Area of a piece = A/6

Area of one piece = (154 square feet)/6 = 25 and two thirds square feet

The area of 2 of the pieces = 2 × (A/6) = A/3

Therefore, the area of two of the pieces = (154 square feet)/3 = 51 1/3

The area of 2 of the pieces = [tex]51\frac{1}{3}[/tex] square feet

Option C is correct

C. 51 and one third square feet

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Using the 22/7 approximation for pi, the circle with a radius of 7 feet divided into 6 equal sectors shows that the area of 2 of the sections is 51 and a third square feet. Option C is the one that is right.

51 and a third square feet in C.

Answer:

$1.83

Step-by-step explanation:

5.50÷3 = 1.8333333 = 1.83

Answer:

The probability of rolling a seven on or before the 5th roll is 5/6 or about 83.3%

Step-by-step explanation:

The probability of rolling a seven on any given roll of two dice is 1/6, since there are six ways to roll a seven (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of the 36 possible outcomes (1-6 on the first die and 1-6 on the second die).

To find the probability of rolling a seven on or before the 5th roll, we can use the cumulative probability formula which is the probability of getting a specific event on the first roll plus the probability of getting the event on the second roll plus the probability of getting the event on the third roll and so on.

So the probability of rolling a seven on or before the 5th roll is:

P(rolling a seven on the 1st roll) + P(rolling a seven on the 2nd roll) + P(rolling a seven on the 3rd roll) + P(rolling a seven on the 4th roll) + P(rolling a seven on the 5th roll)

= (1/6) + (1/6) + (1/6) + (1/6) + (1/6)

= 5/6

So the probability of rolling a seven on or before the 5th roll is 5/6 or about 83.3%

It's worth noting that this probability is independent of the previous outcomes of the rolls, so the probability of rolling a seven on or before the 5th roll stays the same even if you already rolled a seven in previous rolls.

Answer:

109

I wish you luck in your assignments.

The correct answer is the second option.

What is typing speed?

Typing speed is the measure of how many correct words are typed in a 60-second time frame.

The average typing speed is 40 words per minute or wpm.

Therefore the correct answer is the second option.

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Correct option is C, The typing speed is measured in words per minute.

The typical typing rate is 40 words per minute (wpm). Aim for a typing speed of 65 to 70 words per minute if you want to be really productive. With the appropriate approach, it's simple!

There are various typing tests available. This typing test measures your speed of typing in words per minute. Your WPM score will increase the more you practice typing and the more you measure your typing speed. Only WPM typing is the topic of certain online typing tests and typing test games. The WPM typing test has the drawback of simply teaching you how to type quickly. The WPM typing test does not demonstrate your accuracy.

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Therefore , the solution of the given problem of inequality comes out to be graph 2 shows the solution for this system.

In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are.

Here,

Given :

=> x + y ≥ 5

and

=> - 3x + 2y ≤-2

So,

=> x ≥ 5- y

=> - 3(5- y) + 2y ≤-2

=> -15 + 3y + 2y ≤-2

=> 5y ≤ 13

=> y  ≤  13/5

and

=> x ≥ 5-  13/5

=>  x ≥  12/5

Therefore , the solution of the given problem of inequality comes out to be graph 2 shows the solution for this system.

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The percentage of voters that plan to vote for the Democrat candidate is given as follows:

Number of voters for the Democrat / 540 x 100%.

A percentage is obtained applying a proportion, which is the division of the number of desired outcomes by the number of total outcomes, which is then multiplied by 100%.

A poll was conducted of 540 voters asking for which candidates they planned to vote, hence the total number of outcomes is given as follows:

540.

Then the division of the desired number by the total number is given as follows:

Number of voters for the Democrat / 540

The multiplication to write the proportion as a percentage is given as follows:

Number of voters for the Democrat / 540 x 100%.

This problem is incomplete, as the table is not given, hence the general procedure is presented to obtain the percentage of voters that plan to vote for the Democrat candidate.

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The statements that describe that actions that are helpful to our credit score includes:

The Option C is correct.

Our credit score are based on credit history including the number of open accounts, total amount of debt, history of repayment, and other elements.

To improve your credit score, some actions you can take include:

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Triangle a is a shape that is formed by connecting three points.

Triangle is a geometric figure with three sides and three angles. It is one of the basic shapes in geometry. Triangles are either right, acute, or obtuse, depending on the size of each angle. The sum of the angles in a triangle is 180 degrees. Triangles can be classified into equilateral, isosceles, and scalene triangles, depending on the length of the sides. All three types of triangles have various applications in mathematics, physics and engineering.

In order to reflect triangle a in the x axis, triangle b must be a mirror image of triangle a. To achieve this, each point in triangle a must be reflected across the x axis. This is done by multiplying the y coordinate of each point in triangle a by -1. As a result, triangle b will have the same three points as triangle a, except that the y coordinates of each point in triangle b will be the opposite of what they are in triangle a.

After reflecting triangle a in the x axis to form triangle b, the next step is to rotate triangle b around the origin 90°. This can be achieved by finding the coordinates of each point in triangle b, then rotating each point around the origin. To do this, the x coordinates of each point in triangle b remain the same, while the y coordinates are multiplied by -1. As a result, triangle c will be formed as a 90° rotation of triangle b around the origin.

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