Harry asked a sample of 4 people how many siblings they had. Here are their responses:

0, 0, 1, 3

The mean is x-bar = 1 sibling.

What formula gives the standard deviation?

[tex]\begin{array}{c|c|c}\underline{\quad (x,y)\quad}&\underline{\quad y=2x\quad }&\underline{\quad Answer\quad }\\(-1, a_o)&a_o=2(-1)&a_o=-2\\(0, a_1)&a_1=2(0)&a_1=0\\(1, a_2)&a_2=2(1)&a_2=2\\(2, a_3)&a_3=2(2)&a_3=4\\(3, a_4)&a_4=2(3)&a_4=6\\(4, a_5)&a_5=2(4)&a_5=8\end{array}[/tex]

Answer:

2(2r + 1)(2r - 5)

Step-by-step explanation:

Given

8r² - 16r - 10 ← factor out 2 from each term

= 2(4r² - 8r - 5)

To factorise the quadratic

Consider the factors of the product of the coefficient of the r² term and the constant term which sum to give the coefficient of the r- term.

product = 4 × - 5 = - 20 and sum = - 8

The factors are + 2 and - 10

Use these factors to split the r- term

4r² + 2r - 10r - 5 ( factor the first/second and third/fourth terms )

= 2r(2r + 1) - 5(2r + 1) ← factor out (2r + 1) from each term

= (2r + 1)(2r - 5), so

4r² - 8r - 5 = (2r + 1)(2r - 5) and

8r² - 16r - 10 = 2(2r + 1)(2r - 5) ← in factored form

The factored form of the given quadratic equation 8r² - 16r - 10 will be 2(2r + 1)(2r - 5) .

A quadratic equation is the second-order degree algebraic expression in a variable.

The standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

It is Given that

8r² - 16r - 10

= 2(4r² - 8r - 5)

To factorize the quadratic

Consider the factors of the product of the coefficient of the r² term and the constant term which sum to give the coefficient of the r- term.

The factors are + 2 and - 10

Use these factors to split the r- term

4r² + 2r - 10r - 5

= 2r(2r + 1) - 5(2r + 1)

= (2r + 1)(2r - 5),

4r² - 8r - 5 = (2r + 1)(2r - 5)

and

8r² - 16r - 10 = 2(2r + 1)(2r - 5)

The factored form of the given quadratic equation 8r² - 16r - 10 will be 2(2r + 1)(2r - 5) .

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Answer:

[tex]\large\boxed{a.\ -44}[/tex]

Step-by-step explanation:

[tex]\dfrac{y}{4}+8=-3\qquad\text{subtract 8 from both sides}\\\\\dfrac{y}{4}+8-8=-3-8\\\\\dfrac{y}{4}=-11\qquad\text{multiply both sides by 4}\\\\4\!\!\!\!\diagup^1\cdot\dfrac{y}{4\!\!\!\!\diagup_1}=(4)(-11)\\\\y=-44[/tex]

Answer:

a.  -44.

Step-by-step explanation:

y/4 + 8 = -3

Subtract 8 from both sides:

y/4 = -3 - 8

y/4 = -11

Now multiply both sides by 4:

y = 4 * -11 = -44 (answer).

Answer:

5 but its probaly not right bc im just looking for pointsStep-by-step explanation:

Answer:

parameter

Step-by-step explanation:

Answer:

b 125

Step-by-step explanation:

first you know that you have 2 and 5 as similar numbers you both square them so that they become a ratio of area which is 4/25 after you do 4/25=20/x and you do cross multiply then you find 125. hope that helped understand.

Answer:

B.

Step-by-step explanation:

o find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.

Answer:

2000 m/h

Step-by-step explanation:

speed = distance/time

Mila's distance was (2/3)·(750 m) = 500 m, so her speed was ...

(500 m)/(1/4 h) = 2000 m/h

Mila swam 500 meters in 0.25 hours. Hence, her average speed was 2000 meters/hour.

To calculate Mila's average speed, first we need to calculate the distance she swam. Mila swam 2/3 of Logan's distance, which is 2/3 * 750 meters = 500 meters.

Now, we need to find out how long she swam in hours as her time was given in quarters of an hour. As Mila swam for 1/4 of an hour, this translates to 1/4 * 60 minutes = 15 minutes, or 0.25 in hours.

Speed is calculated as distance/time, therefore Mila's average speed is 500 meters/0.25 hours = 2000 meters/hour.

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Answer:

ZX

Step-by-step explanation:

A diameter is a chord of a circle that passes through the center of the circle.

A chord of a circle is a segment inside the circle whose endpoints are on the circle.

Chords of the circle:

ZY, ZX, YW, UV

Of all those chords, only two pass through the center of the circle:

ZX, YW

Of the two diameters, only one is a choice:

ZX

Answer: B. ZX

Answer:

zx

Step-by-step explanation:

A pex

Answer:

b = √(c^2 - a²)

Step-by-step explanation:

Start with the given c = √a^2 + b^2.  Squaring both sides, we get:

c² = a² + b².

We want to iosolate b² and then b.

So:  subtract a² from both sides, resulting in:

c² - a² = b²

Taking the square root of both sides, we get:

√b² = √(c² - a²)

and so:

b = √(c^2 - a²)

To solve the Pythagorean theorem equation for b, isolate b on one side by first squaring both sides. Move the a^2 term to the other side of the equation, then take the square root of both to solve for b. The solution is b = √(c^2 - a^2).

The formula mentioned, c = √a^2 + b^2, represents the application of the Pythagorean theorem for right-angled triangles. To solve this equation for b, you would have to isolate b on one side. Start by squaring both sides of the equation, which gives: c^2 = a^2 + b^2. Then, move a^2 to the other side of the equation to isolate b^2 assuming c^2 > a^2. This gives you: b^2 = c^2 - a^2. Then, take the square root of both sides, which gives: b = √(c^2 - a^2).

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Answer:

You add them together and divide it by how many number there are.

Step-by-step explanation:

For example lets say we need to find the average of 12, 15, 18, and 24.

You would do 12+15+18+24

You will get a sum of 69

Then since there are 4 numbers you do 69 divided by 4 and get a quotients of 17.25.

Therefore 17.25 is the average of all four numbers.

Answer:

81

Step-by-step explanation:

3 digits ^4 number options

3^4=81

Check the picture below.

[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ a=3\\ b=2 \end{cases}\implies \cfrac{(x-0)^2}{3^2}+\cfrac{(y-0)^2}{2^2}=1\implies \cfrac{x^2}{9}+\cfrac{y^2}{4}=1[/tex]

For this case we must indicate the graph corresponding to the following equation:

[tex]y = 2e ^ x[/tex]

Then, we evaluate the equation for[tex] x = 0[/tex]

[tex]y = 2e ^ 0[/tex]

We have by definition, any number raised to zero results in 1.

So:

[tex]y = 2[/tex]

Now we evaluate the equation for x = -1

[tex]y = 2e ^ {-1}\\y = \frac {2} {e}\\y = 0.736[/tex]

We already have two points to graph:

[tex](0,2)\\(-1,0.736)[/tex]

Observing the options, we realize that the correct option is option C.

It should be noted that graphs A and D, by definition, do not correspond to the exponential function.

Answer:

Option C

The  fraction of the animals at the shelter are dogs 74/100 or 37/50

A relative value indicating hundredth parts of any quantity.

Given:

74% of the animals at an animal shelter are dogs.

We know the percent is considered as 100.

If we need to estimate anything in percent we compare it with 100%.

So,  fraction of the animals at the shelter are dogs be,

=74% of 100%

=74/100*100/100

= 74/100

=37/50

Hence,  fraction of the animals at the shelter are dogs be is 74/100 or37/50.

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The answer is 4. All of the above I googled it

Answer:

[tex]\sqrt[6]{200}[/tex]

Step-by-step explanation:

First of all, you need to know that you cannot multiply those radicals without having a common index (the little number outside the radical that sits in the curve of the radical).  One is a 3 and the other, without being stated outright, is understood to be a 2.  BUT we can make them like.  The index of a radical is the denominator of the exponential equivalent.  

[tex]\sqrt[3]{5}=5^{\frac{1}{3}}[/tex] and

[tex]\sqrt{2}=2^{\frac{1}{2}}[/tex]

See how the indexes are now the denominators of the rational exponents.  We can make them like by finding the LCM of 3 and 2...which is 6:

[tex]5^{\frac{1}{3}}=5^{\frac{2}{6}}[/tex] and

[tex]2^{\frac{1}{2}}= 2^{\frac{3}{6}}[/tex]

Now that the indexes are like, we rewrite them as radicals again:

[tex]\sqrt[6]{5^2}*\sqrt[6]{2^3}[/tex] which, simplified, is

[tex]\sqrt[6]{25}*\sqrt[6]{8}[/tex]

Now we can find the product which is

[tex]\sqrt[6]{200}[/tex]

The product of ∛5 ×√2 is approximately 2.41. The correct option is b) [tex]\sqrt[6]{200}[/tex], which matches the calculated value.

To find the product ∛5 × √2, we first take the cube root of 5 (∛5) and then multiply it by the square root of 2 (√2).

∛5 ≈ 1.71 (approximately, rounded to two decimal places)

√2 ≈ 1.41 (approximately, rounded to two decimal places)

Now, let's calculate the product:

∛5 × √2 ≈ 1.71 × 1.41 ≈ 2.41 (approximately, rounded to two decimal places)

Now, let's check the options:

a. [tex]\sqrt[6]{10}[/tex] ≈ 1.72 (approximately, rounded to two decimal places)

b. [tex]\sqrt[6]{200}[/tex] ≈ 2.41 (approximately, rounded to two decimal places) <-- Matches our calculated value.

c. [tex]\sqrt[6]{500}[/tex] ≈ 2.80 (approximately, rounded to two decimal places)

d.[tex]\sqrt[6]{100000}[/tex] ≈ 5.62 (approximately, rounded to two decimal places)

The correct answer is option b)[tex]\sqrt[6]{200}[/tex].

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Step-by-step explanation:

A number cubed is equal to the product of 52 and the square of the number.

Answer:

  the last choice shown here: F'(0, -4), G'(-3, -1), H'(-2, 2), I'(0, -2)

Step-by-step explanation:

The translation vector tells you that the new coordinates are found by adding -4 to each of the old coordinates. When you realize that the answer choices differ in their values for H' and I', you can conclude that you only need to find one of those to determine the correct answer.

  H' = H + (-4, -4) = (2-4, 6-4) = (-2, 2) . . . corresponds to the last choice shown

_____

When you subtract 4 from each of the coordinates of the other points, you find they also match the last answer selection.

Final answer:

The translation of the figure along the vector ⟨−4,−4⟩ results in the vertices F'(0,-4), G'(-3,-1), H'(-2,2), and I'(0,-2).

Explanation:

The student is asking about a translation of a geometric figure in the coordinate plane. To translate a figure, we add the translation vector to each vertex of the figure. In this case, the translation vector is ⟨−4,−4⟩, which means we subtract 4 from the x-coordinate and subtract 4 from the y-coordinate of each vertex of the figure.

Therefore, the translated figure will have vertices F'(0,-4), G'(-3,-1), H'(-2,2), and I'(0,-2).

Answer:

216°

Step-by-step explanation:

Both chords are the same length, so the left and right arcs are both 72°.  The whole circle is 360°, so:

72° + 72° + x = 360°

x = 216°

Answer:

B.

Step-by-step explanation:

the denominator you want is 16 so 4(4) is 16, which makes 3(4) 12 so 12/16. 7/16 is already perfect. 8(2) is 16 therefore 5(2) is 10 which makes 10/16.

The total number of seats in all 7 rows is 24

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that  there are 16 rows and each row has either 20 or 24 seats.

Therefore,

7 x 24 = 168

9 x 20 = 180

If the total number of seats in all 16 rows is 348,

168 + 180 = 348

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Answer:

144, 36, 9, 2 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

The recursive formula allows us to find a term in a sequence from the previous term.

Given

[tex]a_{n}[/tex] = [tex]\frac{a_{n-1} }{4}[/tex]

Given the fourth term we require to work back to the third term , second and so on. Rearrange the formula to give

Multiply both sides by 4, then

[tex]a_{n-1}[/tex] = 4[tex]a_{n}[/tex]

Given a₄ = 2 [tex]\frac{1}{4}[/tex], then

a₃ = 4 × a₄ = 4 × 2[tex]\frac{1}{4}[/tex] = 9

a₂ = 4 × a₃ = 4 × 9 = 36

a₁ = 4 × a₂ = 4 × 36 = 144

The first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied with that constant term to form a geometric progression.

The recursive formula allows us to find a term in a sequence from the previous term.

Given

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

Given the fourth term, we require to work back to the third term, second, and so on. Rearrange the formula to give.

Multiply both sides by 4, then

a[tex]_{n-1}[/tex] = 4a[tex]._n[/tex]

Given a₄ = 2, then

The first four terms will be calculated as given below:-

a₃ = 4 × a₄ = 4 × 2 = 9

a₂ = 4 × a₃ = 4 × 9 = 36

a₁ = 4 × a₂ = 4 × 36 = 144

Therefore, the first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.

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Answer: Option C

Step-by-step explanation:

By definition, a relation is considered a function if and only if for each input value x there is only one associated output y value.

To verify if the graph of a relation is a function, trace on the graph vertical lines parallel to the y axis. If one of these vertical lines cuts the graph in 2 or more points, then the relationship is not a function

By definition, a function is considered a one-to-one function if and only if there is no equal output value and, for two different input values.

For example, the following ordered pairs do not correspond to a one-to-one function, because the output value y = 6 is associated with two input values ​​x = 1 and x = 3

(1, 6) (3, 6)

To verify if the graph of a relation is a function, draw on the graph horizontal lines parallel to the x axis. If one of these horizontal lines cuts the graph in 2 or more points, then the relationship is not a one-to-one function.

When you draw vertical lines on the plot shown, you will see that they always intersect at a single point. Therefore the relationship is a function

When drawing horizontal lines on the displayed graph you will notice that they always intersect at a single point. Therefore the function is a one-to-one function

the answer is C

Answer:

  $1,000 at 2%; $1,800 at 4%

Step-by-step explanation:

Let x represent the amount invested at 2%. Then x+800 was invested at 4% and the total interest earned was ...

  x·2% + (x+800)·4% = 92

  x·6% + 32 = 92 . . . . . . . . . simplify

  x·0.06 = 60 . . . . . . . . . . . . subtract 32; write 6% as a decimal

  x = 60/0.06 = 1000 . . . . . divide by the coefficient of x

$1000 was invested at 2%; $1800 was invested at 4%.

Answer:  272

Step-by-step explanation:

f(x) = 4x         g(x) = 3x - 5

(g × f)(x) = (4x)(3x - 5)

             = 12x² - 20x

(g × f)(-4) = 12(-4)² - 20(-4)

               = 12(16) + 80

               = 192 + 80

              = 272

Answer:

1 : 1000

In the real life, it measures as:

62 mm = 62000 mm = 6.2 m

54 mm = 54000 mm = 5.4 m

It ask how large is it, I don't know if you want area or primeter, so I will give you both of them.

Area:

6.2 x 5.4 = 33.48 m^2

Primeter:

(6.2 + 5.4)2 = 23.2 m.

Perimeter of the square backyard=56m

Perimeter of a square=4*side

Side=

56=4*side

56/4=side

side=14 cm

Area of a square=side*side

=14*14

=196cm^2

So,the area of the square backyard is 196m^2.

Answer:

A=196

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

4th option

Step-by-step explanation:

The given expression is:

[tex]\frac{1}{1+\sqrt{3}}[/tex]

In order to simplify this expression we have to multiply and divide it with the conjugate of the denominator i.e multiply and divide the entire expression with [tex]1-\sqrt{3}[/tex], as shown below:

[tex]\frac{1}{1+\sqrt{3}}\\=\frac{1}{1+\sqrt{3}} \times \frac{1-\sqrt{3}}{1-\sqrt{3}}\\=\frac{1-\sqrt{3}}{(1)^{2}-(\sqrt{3})^{2}}\\\\ =\frac{1-\sqrt{3}}{1-3}\\\\ =\frac{1-\sqrt{3}}{-2}\\\\ =\frac{-1(1-\sqrt{3})}{2}\\\\ =\frac{-1+\sqrt{3}}{2}[/tex]

Thus, 4th option gives the correct answer.

Answer:

The right option is D -1+√3/2

Step-by-step explanation:

To find the quotient of the sure function 1/1+√3, we will rationalize the surd function by multiplying the numerator and the denominator of the surd by the conjugate of its denominator.

Given he denominator to be 1+√3, the conjugate of 1+√3 is 1-√3

Multiplying by 1-√3 will result in the following;

1/1+√3×1-√3/1-√3

= 1-√3/(1+√3)(1-√3)

= 1-√3/1-√3+√3-√9

= 1-√3/1-√9

= 1-√3/1-3

= 1-√3/-2

= -(1-√3)/2

= -1+√3/2

The right option is D -1+√3/2

Answer:

15.5 in

Step-by-step explanation:

Use property of secant and tangent segments in the circle:

If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant.

In your case,

Tanget - x in

External secant - 10 in

Total secant - 10+14 in

So,

[tex]x^2=10\cdot (10+14)\\ \\x^2 =10\cdot 24\\ \\x^2 =240\\ \\x\approx 15.5\ in[/tex]

Answer:

The value of slope m = -1

Step-by-step explanation:

x = -2 + 4t

and y = 1 + 4t

Solving the both equations

x +2 = 4t

=> t = (x+2)/4     eq(1)

y-1 = 4t

=> t = (y-1)/4      eq(2)

Putting eq(1) = eq(2) as left hand side of both equations are same

(x+2)/4 = (y-1)/4

Cross multiplying

4(x+2) = 4(y-1)

4x + 8 = 4y -4

4x +4y = -4 -8

4x + 4y = -12

4(x+y) = -12

x+y = -12/4

x+y = -3

y = -x -3

The slope intercept form of line is:

y = mx + b

where m is the slope. Comparing with y = -x-3

The value of slope m = -1

The slope of the line defined by the parametric equations x=-2+4t and y=1+4t is mathematically given as

m = -1

Question Parameter(s):

the parametric equations x=-2+4t and y=1+4t

Generally, the equation for the Equations   is mathematically given as

x=-2+4t

y=1+4t

Therefore

t = (x+2)/4..1

t = (y-1)/4 ...2

 Hence

(x+2)/4 = (y-1)/4

4(x+2) = 4(y-1)

y = -x -3

In conclusion, slope intercept

y = mx + b

Hence

y = -x-3

The slope is m = -1

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Answer:

  n(n+1)

Step-by-step explanation:

Only the last two formulas work for n=1; only the last formula works for n=2.

For n=1

  3n = 3 ≠ 2

  n² -1 = 0 ≠ 2

  n² +1 = 2

  n(n+1) = 2

For n=2

  n²+1 = 5 ≠ 6

  n(n+1) = 6 . . . . . this last formula works for the given sequence