Find the first five terms of the sequence for which:

a₁ =1/3 and d = 1/2
(Write your answers as fractions)

Answer:

The answer is A

Step-by-step explanation: if 4 is the radius you take 4 and square it

(4 times 4= 16)

16 times pie

(in this case 3.14)

equals: 50.24

The line of the best fit is shown in the picture which is approximate near the dots.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

The slope and y-intercept can be found using the formula below:

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have a given a scatter plot shows the data for NCAA quarterbacks comparing their attempted passes to completed passes.

We can draw a line of best fit y = mx + c

Thus, the line of the best fit is shown in the picture which is approximate near the dots.

Learn more about the line of best fit here:

brainly.com/question/14279419

#SPJ1

The point that is not included in the solution set for the inequality in the graph is (-1, 3).

In the information given, (h, k) is the vertex point. In the graph, the vertex point will be (1, 2). The equation will be:

y = a(x + 1)² + 2

By the point of the graph(0, 3) the value of a will be:

3 = a(0 - 1)² + 2

3 = a + 2

a = 3 - 2

a = 1

The equation this becomes:

y = 1(x - 1)² + 2.

y = x² - 2x + 1 + 2

y = x² - 2x + 3

Therefore, the point that is not included in the solution set for the inequality is (-1, 3).

Learn more about graph on:

brainly.com/question/19040584

#SPJ1

Answer:

[tex]x = \dfrac{21}8[/tex]

Step-by-step explanation:

[tex]~~~~~~~~\dfrac 1 2 -x + \dfrac 34 = x-4\\\\\\\implies \dfrac 24 + \dfrac 34 - x =x-4\\\\\\\implies \dfrac 54+4=x+x\\\\\\\implies 2x = \dfrac{21}{4}\\\\\\\implies x = \dfrac{21}{4 \cdot 2}\\\\\\\implies x = \dfrac{21}8[/tex]

Answer:

[tex]\frac{1}{13}[/tex]

Step-by-step explanation:

The total number of cards in a standard deck of cards is 52, in which there:

King: 4 cards <----------

Queens: 4 cards

Jack: 4 cards

Ace: 4 cards

Club/Diamond/Heart/Spade: 13 cards

Moreover, 26 of the 52 cards are red, and the remainder 26 are of black.

So the probability that a "king" card will be picked is [tex]\frac{4}{52}[/tex], which can be further simplified [tex]\frac{1}{13}[/tex]

Answer:

IUOIUJUIYIYIYUYUYUYIYUYUY

Deena is 420 miles from home in 12 hours.

The graph is shown below. The graph is linear

From the question, we are to determine how far Deena is from home in 12 hours

From the given linear equation,

y = 35x

We are to determine how far Deena is from home in 12 hours

That is,

x = 12 hours

Put x = 12 into the equation,

∴y = 35(12)
y = 420 miles

Hence, Deena is 420 miles from home in 12 hours.

The graph is shown below. The graph is linear

Learn more on Linear equations here: https://brainly.com/question/14323743

#SPJ1

Considering it's volume of 113 cm³, the approximate radius of the sphere is given by:

A. 3 cm

The volume of an sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

In this problem, we have that V = 113 cm³, hence the radius in cm is given as follows:

[tex]V = \frac{4\pi r^3}{3}[/tex]

[tex]113 = \frac{4\pi r^3}{3}[/tex]

[tex]r^3 = \frac{113 \times 3}{4\pi}[/tex]

[tex]r = \sqrt[3]{\frac{113 \times 3}{4\pi}}[/tex]

r = 3 cm.

Hence option A is correct.

More can be learned about the volume of an sphere at https://brainly.com/question/25608353

#SPJ1

Answer:

is 3 cm

Step-by-step explanation:

Answer:

There were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.

Let x be the number of 50-cent coins in the bag,

And y be the number of 20-cent coins.

From the problem,

we know that y = x - 5,

Since there were 5 fewer 20-cent coins than 50-cent coins.

We can also set up an equation for the total value of the coins in the bag,

⇒ 0.5x + 0.2y = 24.20

Now we can substitute y = x - 5 into the equation,

⇒ 0.5x + 0.2(x - 5) = 24.20

Simplifying, we get,

⇒ 0.7x - 1 = 24.20

⇒ 0.7x = 25.20

⇒ x = 36

So there were 36 50-cent coins in the bag.

Using y = x - 5,

We can find that there were 31 20-cent coins.

Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).

To learn more about equations visit:

https://brainly.com/question/29174899

#SPJ2

The inequalities are; 5¹/₄ tons = 10500 pounds; 1/2 ton + 3/4 ton > 2800 pounds; 2 tons > 60000 pounces; 1¹/₄tons > 20000 ounces

1) 5¹/₄ tons when converted to pounds is 10500 pounds.

Thus; 5¹/₄ tons = 10500 pounds.

2) 1/2 ton + 3/4 ton = 5/4 tons

Converting 1.25 to tons gives 2500 tons. Thus;

1/2 ton + 3/4 ton > 2800 pounds

3) Converting 2 tons to Ounces gives 64000 ounces. Thus;

2 tons > 60000 pounces.

4) 1¹/₄tons - ¹/₂ton = ³/₄ tons

Converting to ounces gives 24000 ounces

Thus; 1¹/₄tons > 20000 ounces

Read more about Inequalities at; https://brainly.com/question/25275758

#SPJ1

7-digit:9999999

9-digit: 1000000

The dimension of the original photo is 11 inches by 11 inches.

Given that, the area of the reduced photo is 64 square inches.

In the equation [tex](x -3)^{2} = 64[/tex], x represents the side measure of the original photo.

We have to determine the dimensions of the original photo.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, solve the equation for the value of x.

By square rooting on both the side, we get

[tex]\sqrt{(x-3)^{2} } =\sqrt{64}[/tex]

⇒[tex](x-3)=[/tex]±[tex]8[/tex]

⇒[tex]x=8+3=11[/tex] and [tex]x=-8+3=-5[/tex]

The length and width can not be negative.

Therefore, the dimension of the original photo is 11 inches by 11 inches.

To know more about the equation click the link given below:

https://brainly.com/question/2263981

#SPJ1

Answer: A) 11 inches by 11 inches

Step-by-step explanation:

Edg 2022

Answer:

The answer should be D.

Step-by-step explanation:

we can see that this is an absolute value function. we know that for the graph to be shifted to the left the value of the constant inside the absolute value should be positive. and the fact that it is shifted down means that there is a negative constant outside the absolute value. the equation is:

| X + 5 | - 1

Answer:

m = 50h, where m is the distance traveled in miles

Answer:

d

Step-by-step explanation:

Answer:

A=l*w

Step-by-step explanation:

so We Derive Their Formula

L=A/w

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{-2 -1}{1 +0} \implies \cfrac{ -3 }{ 1 }\implies -3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-3}(x-\stackrel{x_1}{0}) \\\\\\ y-1=-3x\implies y=-3x+1[/tex]

Answer:

0.75gal.

Step-by-step explanation:

(4gal.) (2qt) - (3gal.) (3qt) =

the easiest way to solve this would be get everything in the same units,

lets make the qt to gallons

2qt = 0.5gal                          divide the volume value by 4

3qt = 0.75gal

 (4gal.) + (0.5gal.) - (3gal.) + (0.75gal.)

= (4.5gal.) - (3.75gal.)

= 0.75gal.

The functions that are one to one are the set of ordered pairs.

It should be noted that the set of ordered pairs simply means an object that the pairs are significant.

On the other hand, a mapping diagram simply consists of two parallel columns that represents the domain and the range.

In this case, the functions that are one to one are the set of ordered pairs.

Learn more about ordered pairs on:

brainly.com/question/1208726

#SPJ1

Notice that the left side of the third equation is 2 times the left side of the first equation:

6x - 8y + 2z = 2 (3x - 4y + z)

The first equation says

3x - 4y + z = -5

while the third equation would reduce to

2 (3x - 4y + z) = 10   ⇒   3x - 4y + z = 5

but -5 ≠ 5, so there is no solution to the system.

Answer:

If using a calculator, you can calculate one number as a percentage of another by dividing the numbers and multiplying by 100.

Step-by-step explanation:

The correct number line which represents the solution set for the inequality is shown in option 2.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

Inequality is,

⇒ 2x - 6 ≥ 6 (x - 2) + 8

Now, We cam simplify as;

⇒ 2x - 6 ≥ 6 (x - 2) + 8

⇒ 2x - 6 ≥ 6x - 12 + 8

⇒ 2x - 6x ≥ - 12 + 8 + 6

⇒ - 4x ≥ 2

⇒ 4x ≤ - 2

⇒ x ≤ - 1/2

⇒ x ≤ - 0.5

Hence, The correct number line which represents the solution set for the inequality is shown in option 2.

Learn more about the inequality visit:

https://brainly.com/question/25944814

#SPJ7

Answer: The equation of a linear relationship is y = mx + b, where m is the rate of change, or slope, and b is the y-intercept (The value of y when x is 0).

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I got it right on the test

Answer:

B

Step-by-step explanation:

Answer:

you're right

Step-by-step explanation:

the answer is false because side AD and sides AE are not the same length, so AB/BD does not equal AC/CE

Answer:

Option 4

Step-by-step explanation:

                h = x units

   diameter = x units

                 r = (x/2) units

    [tex]\sf \boxed{\text{ \bf Volume of cone = $\dfrac{1}{3} \pi r^2h$}}[/tex]

                                   [tex]\sf =\dfrac{1}{3}*\pi * (\dfrac{x}{2})^2*x\\\\=\dfrac{1}{3}*\pi*\dfrac{x^2}{4}*x\\\\=\dfrac{1}{12}\pi x^3[/tex]

Answer:

19i

Step-by-step explanation:

note that [tex]\sqrt{-1}[/tex] = i

[tex]\sqrt{-361}[/tex]

= [tex]\sqrt{361(-1)}[/tex]

= [tex]\sqrt{361}[/tex] × [tex]\sqrt{-1}[/tex]

= 19 × i

= 19i