Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
A(n)=-6+(n-1)(6)
A. 0, 18, 54
B. –6, 18, 54
C. 6, 18, 54
D. –6, 12, 48

Answer:

4 inches

Step-by-step explanation:

1 foot = 12 inches

45 feet --- 6 inches

From this we can conclude that the scale of the Blueprint is:

1 foot in actual = 1/90 foot on blueprint

If the girder is actually 30 feet long, then

30 feet --- (1/90*30*12) inches

30 feet --- 4 inches

Answer:

An equivalent expression to 54+18x, using the distributive property is 18(3+x)

Step-by-step explanation:

In the problem we have the binomial (54+18x), and we are asked to use the distributive property, this means that we can find a factor wich is distributed in both terms of the binomial.

We know that any number, or in this case any polinomial (or binomial), can be multiplied times 1 and will stay the same number, and we only need to write this 1 in a way that could resolve our problem, in particular we can say that

[tex]1=\frac{18}{18}[/tex]

then we can distribute the denominator, so we calculate:

[tex](54+18x)=1(54+18x)=\frac{18}{18}(54+18x)=18(\frac{54}{18}+\frac{18x}{18})=18(3+x)[/tex]

And the equivalent expression to (54+18x) is 18(3+x).

Answer

It is 2 scoops

Step-by-step explanation:

3⁄8 x 1⁄4 = 3⁄32 quart

3⁄4 ÷ 3⁄32 = 8 scoops

Final answer:

The number of possible batting orders a coach can make with 13 players for 9 positions is found by calculating [tex]^{13}P_9[/tex], which equals 518,918,400. Thus, the correct answer is C. 259,459,200.

Explanation:

To determine how many possible batting orders a baseball coach can make with 13 players to fill 9 positions, we use the concept of permutations since the order in which the players are arranged matters. The formula for permutations of n items taken r at a time is [tex]^{n}P_r[/tex] = n! / (n - r)!, where the exclamation point indicates a factorial. In this case, we have 13 players and want to find out the number of ways to arrange 9 of them, so we calculate-

[tex]^{13}P_9[/tex]= 13! / (13 - 9)!.

We can simplify this by calculating the factorials: 13! = 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 and 4! = 4 × 3 × 2 × 1, so [tex]^{13}P_9[/tex] = 13! / 4!.

Instead of multiplying out both factorials completely, we can cancel out the common terms: (13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (4 × 3 × 2 × 1) = (13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5) / 1.

Calculating the above gives us 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 = 518,918,400 ways to arrange the batting order. Therefore, the correct answer to how many possible batting orders can be made is C. 259,459,200.

The average fuel efficiency rating, calculated by adding the mpg ratings and dividing by five, is 32.418 mpg, rounded to the nearest hundredth as 32.42 mpg. The answer is D. 32.42 mpg.

To find the average fuel efficiency rating of the top five models, we need to calculate the mean mpg rating. To do this, we add up all the mpg ratings and then divide by the number of models:

Add the fuel efficiency ratings together: 26.3 + 28.95 + 33.6 + 35 + 38.24.

The sum is 162.09 mpg.

Divide this sum by the number of cars, which is 5: 162.09 ÷ 5.

The average is 32.418 mpg.

To record the average to the appropriate degree of precision, we consider the place values of the original data provided. The given ratings include mpg values recorded to the nearest hundredth, as in 28.95 mpg and 38.24 mpg. This means the average should also be recorded to the nearest hundredth: 32.42 mpg. Therefore, the correct answer is D. 32.42 mpg.

Answer:

The interpretation of the slope is that for each $1000 you spend, your revenue increases by $900.

Step-by-step explanation:

We have that:

The revenue y is a function of the advertising expediture x, and the relationship is given by the following function:

y = -48.3 + 9x.

However, since y is in thousands and x in hundreds, i am going to rewrite

y = -48.3 + 0.9x

This means that if you spend no money in advertising, you lose -48.3 thousands of dollars. However, for each $1000 you spend, your revenue increases by $900.

So the interpretation of the slope is that for each $1000 you spend, your revenue increases by $900.

1 mile = 5280 feet

 5280 * 2/3 =

5280 *2 = 10560

10560/3 = 3520

 it is 3520 feet long

The correct answer is:

7.8 × 10⁷

Explanation:

To write a number in scientific notation, we want the decimal behind the first non-zero digit in the number. The first non-zero digit in 78 is 7; this means we want 7.8. In order to have the decimal point behind the 7, we need to move the decimal 7 places. This is the exponent of 10 in our scientific notation, which gives us

7.8 × 10⁷

Answer:

Look at the below steps.  

Step-by-step explanation:

We have been given two intersecting lines:

The given angles are vertically opposite angles:

[tex]2x+6=96[/tex]

On simplification we get:

[tex]2x=90[/tex]

On further simplification we get:

[tex]x=\frac{90}{2}[/tex]

[tex]x=45[/tex]

Hence proved that x=45.

divide completions by percentage

345 / 0.60 = 575 pass attempts

The value of "a" is 2.

To find the value of "a," we can use the formula for the equation of a line, which is y = mx + b.

First, we need to find the slope, represented by "m," using the given points (-1, -5) and (4, 5). The slope formula is (y2 - y1) / (x2 - x1).

Substituting the coordinates, we have:

m = (5 - (-5)) / (4 - (-1))
m = 10 / 5
m = 2

Now that we have the slope, we can substitute it into the equation of the line with the point (a, 1):

1 = 2a + b

To solve for "a," we need to find the value of "b." We can substitute one of the given points into the equation and solve for "b."

Using (-1, -5):

-5 = 2(-1) + b
-5 = -2 + b
b = -3

Now we can substitute the values of "b" and "a" into the equation:

1 = 2a - 3

To isolate "a," we add 3 to both sides:

1 + 3 = 2a
4 = 2a

Dividing both sides by 2, we find:

2 = a

Therefore, the value of "a" is 2.

Solution:

The points at which Raquel Darts hit the coordinate grid having center at the origin are  (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6).

As we can see that not all points are collinear.

As line of best fit is the the line which passes through some points , may be not through the single point, or all the points.

Plotting all the options on coordinate grid i.e on a scatter plot and then determining , the  line of best fit of the darts is

y= 0.6 x + 0.6 →→Option (A), the reason being it passes through a point (9,6).

In a standard deck of cards, there are a total number of 52 different card. From those 52 cards, 4 cards are numbered as five. Therefore the probability of selecting a card of five is:

Probability = 4 / 52 = 1 / 13

Assuming that no replacement is made, so the probability changes with each draw, since the total number of cards decreases from 52 to 51 to 50 and so on. Therefore this is not a simple event.

Answer: [tex]1x^2+4x+3[/tex]

Step-by-step explanation: Given expression (x^3-x^2-17x-15)/(x-5).

We need to divide it x^3-x^2-17x-15 by x-5 using synthetic division .

In order to solve by synthetic division, we would write all the coefficients of given divisor polynomial:

And we divide them by 5 using synthetic division method.

             ______________          

      5    |     1   -1   -17   -15                       Getting first number down.

            |           5   20   -15                      Multiplying each down number by

           - - - - - - - - - - - - - - - -                    divisor 5.

                  1    4      3       0                     5×1=5  , 5×2=20, 5×2=15

                                                   Subtracting those products from coefficients.

Now, writing the final polynomial degree 1 less than 3, that is 2.

So, [tex]1x^2+4x+3[/tex] would be our quotient.                    

Answer:

D. [tex]6\pi\text{ cm}[/tex].

Step-by-step explanation:

We are asked to find the circumference of a a circle with a diameter of 6 cm.

We will use circumference of circle to solve our given problem.

[tex]C=\pi\cdot D[/tex], where,

C = Circumference of circle,

D = Diameter of circle,

Upon substituting [tex]D=6\text{ cm}[/tex] in above formula we will get,

[tex]C=\pi\cdot 6\text{ cm}[/tex]

[tex]C=6\pi\text{ cm}[/tex]

Therefore, circumference of our given circle would be [tex]6\pi\text{ cm}[/tex] and option D is the correct choice.

Answer:

✅ triangle

✅ pentagon

✅ hexagon

✅ trapezoid

❌ octagon

Step-by-step explanation: