If a1=6 and a5=12, what does a3=?

Answer:

-13x²+24x+6

Hope this helps:)

The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.

According to the given question.

The total number of elements, n = 3

The number of elements to be selected at a time when repetition is  allowed, r = 5

Since, we know that " the number of ways or permutations of n things taken r all at a time, when repetition of things are allowed, is [tex]n^{r}[/tex].

Therefore,

The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed

= [tex]3^{5}[/tex]

= 243

Hence, the number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.

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Answer:

Step-by-step explanation:

The equation of a circle in standard form is (x - h)² + (y - k)² = r² ,

where (h, r) are coordinates of a center of a circle and "r" is a radius of a circle.

a² ± 2ab + b² = (a ± b)²

~~~~~~~~~~

x² + y² - 2x - 10y + 17 = 0

To rewrite the equation in standard form, need to group terms with the same variables, move the constant to the right side and complete the square for each grouping:

(x² - 2x) + ( y² - 10y) = - 17

( x² - 2x + 1 ) + ( y² - 10y + 25 ) = - 17 + 1 + 25

( x - 1 )² + ( y - 5 )² = 9

( x - 1 )² + ( y - 5 )² = 3²

The center of the given circle is

( 1 , 5 )

The radius of the given circle is

3 units

The quantity of the radioactive material which would remain 2 years from now is; 4 grams.

Since, it follows from the task content that after two year, the quantity of the radioactive substance decrease by 1 gram. Consequently, it follows from proportion that the quantity remaining in 2 years from now is; 5-1 = 4 grams.

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The interpretation of f(30) is the distance travelled after 30 minutes

The function is given as:

A function representing distance (feet) as a function of time (minutes),

This means that, the dependent variable is the distance and the time is the independent variable

This in other words means that:

x = time

f(x) = distance

So, the interpretation of f(30) is:

The distance travelled after 30 minutes

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Answer:

The number is 72.

Step-by-step explanation:

Let the number be xy.

x = y + 5

10x + y - 2(10y + x) = 0.25(10x + y)

10x - 2x + y - 20y = 2.5x + 0.25y

5.5x - 19.25y = 0

Substituting for x:

5.5y + 27.5  - 19.25y = 0

-13.75y = -27.5

y = 2.

So x = 2 + 5 = 7.

Answer:

n=2

Step-by-step explanation:

Create an equation.

9n=18

Divide 9 from both sides.

9n/9=18/9

n=2

Hope this helps!

Answer:

x(x-1)^2

Step-by-step explanation:

x(x^2-2x+1)

x(x-1)(x-1)

(x-1)(x-1)=(x-1)^2

The algebraic expression of the statement is 4x + 6

The statement is given as:

The sum of four times a number and six

Rewrite as:

The sum of 4 times a number and 6

Let the number be x

So, we have

The sum of 4 times x and 6

Evaluate the product

The sum of 4x and 6

Evaluate the sum

4x + 6

Hence, the algebraic expression of the statement is 4x + 6

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The correct option is B.

Rank

The RANK function in a Microsoft Excel spreadsheet enables users to order the various pieces of data by their numerical values. By entering an absolute value for the range of cells the user wants to rank, they can also use the rank function. If an absolute value is not specified, the program's auto-formula may cause the rank of the various cells to alter.

A spreadsheet is a computer program used for organizing, organizing, analyzing, and storing tabular data. Spreadsheets were created as electronic alternatives to paper accounting worksheets. Data typed into table cells serves as the program's input.

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Answer:

I hope I've finally done justice to it.

Step-by-step explanation:

[tex]y=-5x^2 \sqrt{x}[/tex]

[tex]y=-5x^2(x)^\frac{1}{2}[/tex]

[tex]y=-5( {x}^{2 + \frac{1}{2} }) = - 5 {x}^{ \frac{5}{2} } [/tex]

[tex] \frac{dy}{dx} = - 5( \frac{5}{2}) {x}^{ \frac{5}{2} - 1 } [/tex]

[tex]\frac{dy}{dx} = ( \frac{ - 25}{2}) {x}^{ \frac{3}{2} } [/tex]

[tex]\frac{dy}{dx} = ( \frac{ - 25}{2}) \sqrt[3]{ {x}^{2} } [/tex]

Answer-

Step-by-step explanation:

Answer:

5/52 i think

Step-by-step explanation:

there are 52 cards in desk ,with26red and black cards.There 2red and 2 blackthree and. 1 six of hearts .

.

.

.

.

.

.

.

The computation shows that the time before

they can no longer communicate will be 10 minutes

From the information, it was stated that two hikerd are wandering through heavy woods with walkie talkies and that the walkie talkies have a range c of 100 yards.

It should be noted that after t hours, the distance between the hikers will be:

d² = (0.24t)² + (0.17t)² - 2(0.24t)(0.17t) cos 109.10°

d = 0.0568

Therefore, we will find the time when d = 0.0568. This will give a time of 10 minutes.

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a. Expressing y in terms of x, y = 20/(x + 3)

b. When x = 5, the value of y is 2.5

The question has to do with inverse variation.

Inverse variation is variation in which one quantity varies inversely as the other.

Given that y is inversely as x + 3 and that y = 4 when x = 2.

Since y varies inversely as x + 3, we have

y ∝ 1/(x + 3)

y = k/(x + 3)

When y = 4, x = 3. So

y = k/(x + 3)

4 = k/(2 + 3)

4 = k/5

k = 4 × 5

k = 20

So, y = k/(x + 3)

y = 20/(x + 3)

So, expressing y in terms of x, y = 20/(x + 3)

Since  y = 20/(x + 3)

Substituting x = 5 into the equation, we have

y = 20/(x + 3)

y = 20/(5 + 3)

y = 20/8

y = 5/2

y = 2.5

So, when x = 5, the value of y is 2.5

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This is reverse percentage

8.4% = 420

÷8.4 both side

1% is now 50

1% =50

x100

100% is 5000

Check:

8.4/100 = 0.084 our decimal multiplier

5000 x 0.084 = 420

Thus, x is 5000

Hope this helps!

To solve the given quadratic equation, a² - 5 = -2, the first step we need to do is to represent it in the standard form by adding 2 to both sides.

A quadratic equation is solved using the quadratic formula, [tex]x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex], when the equation is in the standard form, ax² + bx + c = 0, where, a, b, and c, are real numbers.

In the question, we are asked for the first step in solving a² - 5 = -2.

We can see that the provided equation is quadratic in the variable a.

To solve, the equation, we first need to represent the given equation in the standard form, ax² + bx + c = 0, where, a, b, and c, are real numbers.

To represent it in the standard form, we add 2 to both sides of the equation, to get a² - 5 + 2 = -2 + 2, or, a² - 3 = 0, which is a standard quadratic equation in the variable a.

Thus, to solve the given quadratic equation, a² - 5 = -2, the first step we need to do is to represent it in the standard form by adding 2 to both sides.

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Answer:

-8

Step-by-step explanation:

Remember pemdas

7 - 3*(10:2):1 =

7-3*5:1=

7-15:1=

7- 15=

-8

Answer:

-8

Step-by-step explanation:

7-3(10:2):1

We always solve what's in parenthesies first.

7 - 3*5:1

Multiplication and division have equal priority, so we solve that part from left to right:

7 - 15:1 =

= 7 - 15 =

= -8

331.5 inches²  is the area of the octagon, rounded to the nearest square inch.

What is octagonal in shape?

Solving for an area of a regular octagon, we can make use of the formula shown below:

Area = 1/2 × apothem × perimeter

In this problem, the following values were given such as:

Apothem = 10 inches

Perimeter = 66.3 inches

Put the values in the formula

Area = 1/2 × 10 × 66.3

Area = 331.5 inches²  

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Answer: C). 332 in.2

Step-by-step explanation:

on edg

In the hypothesis, based on the 90% confidence interval, (0.02, 0.12), there is convincing evidence that the new formula of laundry detergent is better because the interval is entirely above 0

Let's define the null hypothesis and alternative hypothesis first.

H0:p1-p2=0

Ha:p1-p2>0

Also, 90% CI is (0.02,0.12), we know that if the 0 of the null hypothesis is not in the confidence interval then we reject the null hypothesis.

In the given scenario 0 is not within the given interval, hence we reject the null hypothesis and accept the claim that new detergent A cleans better.

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The quantity of meat and cheese sold by the deli according to the description accounts in the task content are; 4.5 and 2.5 pounds respectively.

The quantity of meat sold by the deli as represented by the variable X in the task content can be calculated by solving the systems of equations.

The quantity of cheese sold by the deli as represented by the variable y in the task content can be calculated by solving the systems of equations.

Consequently, solving the system of equations by means of substitution, we have;

y = (30.50-4x)/5

Hence, we have;

11x + 14((30.50-4x)/5) = 84.50

x = 4.5 pounds of meat and

y = 2.5 pounds of cheese.

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Proficiency in statistics is an important skill for a data analyst because it is needed in  identifying patterns and correlations in data.

Data analysis can be regarded as the  process of collecting as well as modeling, and analyzing data so as to be able to extract insights that support decision-making.

Some Types of Data Analysis are:

It should be noted that Proficiency in statistics is an important skill for a data analyst because it is needed in  identifying patterns and correlations in data.

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Using it's concept, we have that the probability that both the first digit and the last digit of the three-digit number are even numbers is 2/27.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering that there are six numbers, out of which 4 are odd and 2 are even, we have that:

Hence the desired probability is:

p = 1/3 x 2/3 x 1/3 = 2/27.

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Correct option is D) and E)

(3,7π/6),(3,11π/6)

Point of intersection is the point where two lines or two curves meet each other.

The point of intersection of two lines of two curves is a point.

If two planes meet each other then the point of intersection is a line.

The term "point of intersection" refers to the intersection of two lines. The equations a1x+b1y+c1=0 and a2x+b2y+c2=0, respectively, are used to represent these two lines. The two lines' intersection point is shown in the following figure. The intersection of three or more lines can also be located.

let

5 + 4 sin(θ) = −6 sin(θ)

Then get

θ= -1/2

Then you can make it

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I understand that the question you are looking for is:

On the interval [0, 2π), which points are intersections of r = 5 4 sin(θ) and r = −6 sin(θ)? check all that apply.

A) -3,7/6

B) (-3,11/6)

C) (3,7/6)

D) (3,11/6)

The equation of the line of best fit, using the least square method is v = 2.19t + 6.7, making the 2nd option as the right choice.

In the question, we are asked to find the equation of the line of BEST FIT for the given scatter plot.

We let the time be the independent variable x, and velocity is the dependent variable y.

We find the line of best fit using the least square method.

First, we calculate the mean:

Now, we find the slope of the line of best fit, using the formula:

m = {∑(x - μ(x))(y - μ(y))}/{∑(x - μ(x))²}.

Taking value from the tables, which is attached, we get:

m = 239.35/109.2683333 = 2.190479096.

Now, we calculate the y-intercept of the line of best fit, using the formula:

b = μ(y) - m.μ(x),

or, b = 20.5 - 2.190479096*6.283333 = 6.736489681.

Now, the equation of the line of best fit, in the form of y = mx + b, can be written as, y = 2.190479096x + 6.736489681, which on approximation, and making y as v, the velocity, and x as t, the time, we get: v = 2.19t + 6.7.

Thus, the equation of the line of best fit, using the least square method is v = 2.19t + 6.7, making the 2nd option as the right choice.

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[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

A linear function is an equation of the form:

[tex]\sf{y=mx+b}[/tex]

▪ [tex]\sf{m= \: slope}[/tex]

▪ [tex] \sf{b= \: y-intercept}[/tex]

First, pick any two pairs of points from the table.

[tex]\small\longrightarrow \sf{(x_1,y_1)(-1.13)}[/tex]

[tex]\small\longrightarrow \sf{(x_2,y_2)=(0,10)}[/tex]

Using these points, find the slope.

[tex]\small\longrightarrow \sf{m= \dfrac{y _{2 } - y_1}{x_2-y_1} }[/tex]

When x=0, y=10, therefore, the y-intercept, b=10.

[tex]\leadsto[/tex] Substitute m=-3 and b=10 into the slope-intercept form given above:

[tex]\small\longrightarrow \sf{m=m = \dfrac{10 - 13 }{0 -( - 1) } = - \dfrac{3}{1} = - 3}[/tex]

▪ [tex]\small\longrightarrow \sf{y= -3x+10}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\large\boxed{\bm{y= -3x+10}}[/tex]

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=562\\ r=5 \end{cases}\implies 562=\cfrac{\pi (5)^2 h}{3}\implies 1686=25\pi h \\\\\\ \cfrac{1686}{25\pi }=h\implies 21.47\approx h[/tex]

Answer: i believe the answer is 26

Step by step explanation

Total no. of observation = (12+13) = 25

Median = Average of 18/2 observation + (18/2+1)

=1/2 (12th observation + 13 observation)

1/2 × (25 +27) = 1/2 × 52

=26

The length of the function x = 2y is 2√5 units

According to the given question.

We have a function

x = 2y

Since, we know that the length of the function in the interval [a, b] is given by

l =    [tex]\int\limits^a_b\sqrt{1+(\frac{dx}{dy}) ^{2} } \,dy[/tex]

Where, l is the length of the function.

Now, differentiating the given function x = 2y w.r.t y.

Therefore,

dx/dy = 2

So, the length of the given function x = 2y  from y = -1 to y = 1 is given by

l =   [tex]\int\limits^1_{-1}{\sqrt{1+2^{2} } } \,dy[/tex]

⇒ l =   [tex]\int\limits^1_{-1} {\sqrt{1+4} } \,dy[/tex]

⇒ l =   [tex]\int\limits^1_{-1}{\sqrt{5} } \,dy[/tex]

⇒ l = √5[1 - (-1)]

⇒ l = √5(2)

⇒ l = 2√5

Hence, the length of the function x = 2y is 2√5 units.

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