Solve the following:
-5² + 10²
(2 × (-5) × 3) + 3³
Give your answer in simplest form.

The value of the standard deviation is σ = 2.20. Using probability distribution, the required standard deviation is calculated.

The formula for the standard deviation of the given probability distribution is

σ = √∑([tex]x_i^2[/tex] × [tex]P(X_i)[/tex]) - μₓ²

Where the mean μₓ = ∑[[tex]x_i[/tex] × [tex]P(X_i)[/tex]]

It is given that,

x: $2, $3, $5, $10

P(X=x): 0.55, 0.26, 0.11, 0.08

Step 1: Calculating the mean:

we have μₓ = ∑[[tex]x_i[/tex] × [tex]P(X_i)[/tex]]

⇒ μₓ = 2 × 0.55 + 3 × 0.26 + 5 × 0.11 + 10 × 0.08

∴ μₓ = 3.23

Step 2: Calculating the standard deviation:

x: 2, 3, 5, 10

x²: 4, 9, 25, 100

P(X=x): 0.55, 0.26, 0.11, 0.08

([tex]x_i^2[/tex]) × [tex]P(X_i)[/tex]: 4 × 0.55 = 2.2; 9 × 0.26 = 2.34; 25 × 0.11 = 2.75; 100 × 0.08 =8

∑[([tex]x_i^2[/tex]) × [tex]P(X_i)[/tex]]: 2.2 + 2.34 + 2.75 + 8 = 15.29

Therefore,

The standard deviation, σ = √∑([tex]x_i^2[/tex] × [tex]P(X_i)[/tex]) - μₓ²

⇒ σ = [tex]\sqrt{15.29-(3.23)^2}[/tex]

      = [tex]\sqrt{15.29-10.43}[/tex]

∴ σ = 2.20

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[tex]\textbf{Heya !}[/tex]

use the slope-formula:-

[tex]\sf{\cfrac{y2-y1}{x2-x1}}[/tex]

put-in the values

[tex]\sf{\cfrac{-2-1}{1-(-3)}}[/tex]

[tex]\sf{\cfrac{-3}{1+3}}[/tex]

[tex]\sf{\cfrac{-3}{4}[/tex]

[tex]\sf{-\cfrac{3}{4}}[/tex]

`hope it's helpful to u ~

The function transformations are:

Transformations involve translating, reflecting, rotating and dilating a function across the coordinate plane

The parent function of a quadratic function is represented as:

y = x^2

When the function is stretched horizontally by a factor of k, where k is between 0 and 1, we have:

y = (x/k)^2

Assume k = 1/4. we have:

y = (4x)^2

This means that the function (c) y = (4x)^2 is stretched horizontally by a factor of 1/4

When the function is stretched vertically by a factor of k, where k is greater than 1, we have:

y = k(x)^2

Assume k = 4. we have:

y = 4x^2

This means that the function (d) y = 4x^2 is stretched vertically by a factor of 4

Translating the function left is represented as:

y = (x + k)^2

Assume k = 2. we have:

y = (x + 2)^2

Reflecting the function across the x-axis is represented as

y = -(x + 2)^2

When the function is compressed vertically by a factor of k, where k is between 0 and 1, we have:

y = -k(x + 2)^2

Assume k = 1/2. we have:

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

Translating the function up is represented as:

y = -1/2(x + 2)^2 + k

Assume k = 4. we have:

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

Hence, the function (a) y = -1/2(x + 2)^2 + 4 is translated to the left by 2 units, reflected across the x-axis, compressed vertically by a factor of 1/2 and translated up by 4 units

Translating the function right is represented as:

y = (x - k)^2

Assume k = 1. we have:

y = (x - 1)^2

Reflecting the function across the x-axis is represented as

y = -(x - 1)^2

Translating the function down is represented as:

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

Assume k = 2. we have:

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

Hence, the function (b) y = -(x - 1)^2 - 2 is translated right by 1 unit, reflected across the x-axis, and translated down by 2 units

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Step-by-step explanation:

the sum of all angles around a single point on one side of a line must be 180°.

because that line can be seen as the extension of the diameter of a circle, and the point would be the center of that circle. so, one side of the line represents a half-circle, which stands for 180°.

so we have

180 = 40 + 40 + (2x + 30) = 80 + 2x + 30 = 110 + 2x

70 = 2x

x = 35

Step-by-step explanation:

z = (specific score - mean) / standard deviation

in our case

z = (85 - 75)/15 = 10/15 = 2/3 = 0.666666... ≈ 0.67

as z-tables usually round the z-score to hundredths.

The z-score for the data value of 85 is 0.67.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score. A value that is one standard deviation from the mean would have a Z-score of 1.0. Z-scores can be either positive or negative, with a positive number signifying a score above the mean and a negative value signifying a score below the mean.

To find the z-score, you simply need to apply the following formula:

z = (x - μ) / σ

μ=75

σ=15

x=85

z =85-75/15

z=10/15

 =2/3

 =0,66666....=0.67

Therefore, the z-score for the data value of 85 is 0.67.

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Answer:

x = -5/2

Step-by-step explanation:

4x+2 = -8

We are solving for x

The first step in isolating x is to subtract 2 from each side

4x+2-2 = -8-2

4x = -10

Divide each side by 4

4x/4 = -10/4

x = -10/4

Simplify the fraction

x = -5/2

Answer:

Step-by-step explanation:

4x+2 = -8

4x = -10

4x/4 = -10/4

x = -5/2

Answer:

626.7 [tex]cm^{2}[/tex]

Step-by-step explanation:

Consider the figure as a circle with radius 7.5 and a rectangle with width 30 and length 15.

CIRCLE

A = pi*r*r = pi*7.5*7.5 = 56.25pi =176.7

RECTANGLE

A = l*w = 15*30 = 450

176.7 + 450 = 626.7 [tex]cm^{2}[/tex]

Answer: 626.7cm^2

Step-by-step explanation:

30 * 15 = 450

area of circle = πr^2

r = 15/2 = 7.5

[tex]7.5^2=56.25*pi=176.7[/tex]

450+176.7 = 626.7

Based on the total cost that Juan incurred to hire the roofer including the charge for parts and labor, the number of hours that was needed to complete the job was 14.50 hours.

The first thing to do is to find out the amount that went to labor:

= Final bill - cost of materials

= 1,131.5 - 450

= $681.50

Now that you have the cost of labor, you can find out the number of labor hours that were used based on the hourly rate:

= Cost of labor / Hourly rate

Solving gives:

= 681.50 / 47

= 14.5 hours

In conclusion, the number of labor hours that the roofer used to complete the work, based on the total amount charged to Juan is 14.50 hours.

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Answer:

A

Step-by-step explanation:

The solutions of a quadratic function will always be the x intercepts.  Thus, if there are two solutions, there are two x intercepts.

Answer:

C, 24 units^2

Step-by-step explanation:

The formula for area of a parallelogram is base times height.

The height of the parallelogram is 4 units

The base of the parallelogram is 6 units

4 times 6 is 24

Hope this helps:)

Answer:

C. 24 units²

Step-by-step explanation:

To calculate the area of a parallelogram we use the following formula:

A = B*h (B: base, h: height)

The base of the parallelogram is 6 units and the height is 4 units

4*6 = 24 units but, the area is presented in square units so the answer is  24 units²

The equation of the first circle is (x + 1)^2 + (y - 1)^2 = r^2 and the equation of the second circle is (x + 1)² + (y - 1)² = 16

The points are given as:

P(3, 0) and Q(0, 5)

The midpoint of PQ is

Midpoint = 0.5(3 + 0, 0 + 5)

Midpoint = (1.5, 2.5)

Calculate the slope of PQ

m = (y2 - y1)/(x2 - x1)

m = (5 - 0)/(0 - 3)

m = -5/3

A line perpendicular to PQ would have a slope (n) of

n = -1/m

This gives

n = -1/(-5/3)

n = 0.6

The equation is then calculated as:

y = n(x - x1) + y1

Where

(x1, y1) = (1.5, 2.5)

So, we have:

y = 0.6(x - 1.5) + 2.5

y = 0.6x - 0.9 + 2.5

Evaluate the sum

y = 0.6x + 1.6

Hence, the equation of the perpendicular bisector of PQ is y = 0.6x + 1.6

We have:

y = x + 2

Substitute y = x + 2 in y = 0.6x + 1.6

x + 2 = 0.6x + 1.6

Evaluate the like terms

0.4x = -0.4

Divide

x = -1

Substitute x = -1 in y = x + 2

y = -1 + 2

y = 1

Hence, the center of the circle is (-1, 1)

We have:

Center, (a, b) = (-1, 1)

Point, (x, y) = (0, 5) and (3, 0)

A circle equation is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where r represents the radius.

Substitute (a, b) = (-1, 1) in (x - a)^2 + (y - b)^2 = r^2

(x + 1)^2 + (y - 1)^2 = r^2

Substitute (x, y) = (0, 5) in (x + 1)^2 + (y - 1)^2 = r^2

(0 + 1)^2 + (5 - 1)^2 = r^2

This gives

r^2 = 17

Substitute r^2 = 17 in (x + 1)^2 + (y - 1)^2 = r^2

(x + 1)^2 + (y - 1)^2 = r^2

Hence, the circle equation is (x + 1)^2 + (y - 1)^2 = r^2

The equation of the second circle is

2x² + y² + ax + by - 14 = 0

Rewrite as:

2x² + ax + y² + by = 14

For x and y, we use the following assumptions

2x² + ax = 0    and  y² + by = 0

Divide through by 2

x² + 0.5ax = 0    and  y² + by = 0

Take the coefficients of x and y

k = 0.5a                   k = b

Divide by 2

k/2 = 0.25a           k/2 = 0.5b

Square both sides

(k/2)² = 0.0625a²           (k/2)² = 0.25b²

Add the above to both sides of the equations

x² + 0.5ax +0.0625a² = 0.0625a²    and  y² + by + 0.25b² = 0.25b²

Express as perfect squares

(x + 0.25a)² = 0.0625a² and (y + 0.5b)² = 0.25b²

Add both equations

(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²

So, we have:

2x² + ax + y² + by = 14 becomes

(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14

Comparing the above equation and (x + 1)^2 + (y - 1)^2 = r^2, we have:

0.25a = 1 and 0.5b = -1

Solve for a

a = 4 and b = -2

This means that the value of a is 4 and b is -2

We have:

a = 4 and b = -2

Substitute these values in (x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14

This gives

(x + 0.25*4)² + (y - 0.5*2)² = 0.0625*4² + 0.25*(-2)²+ 14

(x + 1)² + (y - 1)² = 16

The equation of the first circle is

(x + 1)² + (y - 1)² = 17

The radii of the first and the second circles are

R = √17

r = √16

√17 is greater than √16

Since they have the same center, and the radius of the first circle exceeds the radius of the second circle, then the second circle lies inside the first circle.

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a. See attachment for the labelled diagram

b. Using the sine ratio, distance from the hot air to pond A is 5,038.9 m, while distance from the hot air to pond B is 6,287.1 m.

c. Distance between the two ponds is 1,263.5 m.

Sine ratio, is: sin ∅ = opposite side/hypotenuse length

Tangent ratio is: tan ∅ = opposite side/adjacent length.

a. The diagram with the appropriate labels is shown in the image attached below.

b. Use the sine ratio to find the distance from the hot air to pond A (CA) and to pond B (CB):

CA = hypotenuse

∅ = 10°

Opposite = 875 m

sin 10 = 875/CA

CA = 875/sin 10

CA ≈ 5,038.9 m (distance from the hot air to pond A)

CB = hypotenuse

∅ = 8°

Opposite = 875 m

sin 8 = 875/CB

CB = 875/sin 8

CB ≈ 6,287.1 m (distance from the hot air to pond B)

c. Distance between the two ponds, BA = BD + DA.

Apply the tangent ratio to find BD and DA

tan 8 = 875/BD

BD = 875/tan 8

BD = 6,225.9 m

tan 10 = 875/DA

DA = 875/tan 10

DA = 4,962.4 m

Distance between the two ponds = 6,225.9 - 4,962.4 = 1,263.5 m.

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There are 625 different 4-digit codes only made with odd numbers.

To find the total number of combinations, we need to find the number of options for each one of the digits.

There are 4 digits, such that each digit can only be an odd number.

The total number of different combinations is given by the product between the numbers of options, so we have:

C = 5*5*5*5 = 625.

There are 625 different 4-digit codes only made with odd numbers.

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Answer:

A varicocele measures more than 2 mm in diameter.

Step-by-step explanation:

pampiniform plexus veins measuring more than. 2 mm in diameter at rest and which increased in diameter by 1 mm, and subjective color Doppler.

f(-a) is the remainder when f(x) is divided by (x+a). This can be obtained by remainder theorem for polynomials.

Given that f(x) is divided by (x+a) and leaves a reminder

Using the remainder theorem for polynomials we get,

f(x) = (x+a)·g(x) + r, where g(x) is the quotient and r is the remainder.

Put x = -a, then

f(-a) = (-a+a)·g(-a) + r

f(-a) = (0)·g(x) + r

f(-a) = r

f(-a) is the remainder.

Hence f(-a) is the remainder when f(x) is divided by (x+a).

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Given, that the sides of a triangle are [tex]$5 \mathrm{~cm}, 12 \mathrm{~cm}$[/tex] and [tex]$13 \mathrm{~cm}$[/tex] semi-perimeter [tex]$=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}$[/tex]

[tex]$$\begin{aligned}&\mathrm{s}=\frac{(5+12+13)}{2} \\&\mathrm{~s}=\frac{30}{2} \\&\mathrm{~s}=15 \mathrm{~cm}\end{aligned}$$[/tex]

Area of the triangle (according to Heron's Formula)

[tex]$$\begin{aligned}&=\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})} \\&=\sqrt{15(15-5)(15-12)(15-13)} \\&=\sqrt{15(10)(3)(2)} \\&=\sqrt{900} \\&=30 \mathrm{~cm}^{2}\end{aligned}$$[/tex]

What is  Heron's Formula?

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Answer:

Step-by-step explanation:

125 I think

Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.                      

Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.

Pythagoras theorem, [tex]x^{2} + y^{2} = (12)^{2}[/tex]       --->(1)

Given,[tex]\frac{dx}{dt}= 2feet/second[/tex]   at x=3

Put x=3 in Pythagoras theorem equation (1)

[tex](3)^{2} + y^{2} = 144[/tex]

         [tex]y^{2} = 144 - 9[/tex]

        [tex]y^{2}[/tex]  =  135

        y = 11.61

Derive equation (1) w.r.t to 't'

[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0[/tex]                ---->(2)

substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall

[tex]2(3)(2) + 2 (11.61)\frac{dy}{dt} = 0[/tex]

12 + 23.22 [tex]\frac{dy}{dt}[/tex]  = 0

                  [tex]\frac{dy}{dt}= \frac{-12}{23.22}[/tex]

                  [tex]\frac{dy}{dt} = -0.518[/tex]

Hence,  using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.  

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d² = (y2 - y1)² + (x2 - x1)²

..............

The probability solved by binomial distribution that all will survive is 0.8154.

When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.

Computation of probability of all survived people from heart attack;

A heart attack patient has a 0.04 percent chance of dying from the attack (i.e., 4 of 100 die of the attack).

What is the likelihood that each of the five patients who experience a heart attack will survive?

We'll refer to a victory in this scenario as a heart attack (p = 0.04). In other words, we are interested in the likelihood that none of our n=5 patients will die (0 successes).

Each attack has a chance of being fatal or not, with a probability of 4 percent for all patients, and each patient's result is independent.

Assume for the purposes of this example that the five individuals being examined are unrelated, of the same age, and free of any concomitant disorders.

By binomial distribution,

[tex]\begin{gathered}P(0 \text { successes })=\frac{5 !}{0 !(5-0) !} 0.04^{0}(1-0.04)^{5-0} \\P(0 \text { successes })=\frac{5 !}{5 !}(1)(0.96)^{5}=(1)(1)(0.8154)=0.8154\end{gathered}[/tex]

Therefore, with a 4 % chance that anyone will die, there is an 81.54% chance that every patient will survive the onslaught. The outcomes in this example could be 0, 1, 2, 3, 4 or 5 successes (fatalities).

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Answer:

y is equal to 24

Step-by-step explanation:

If y is directly proportional to x when x is equal to 5 and y is 12, then when you multiply 5 by 2 which is 10, y will be proportional to that when you multiply 12 by 2 which is 24

Answer:

b: 25

Step-by-step explanation:

The previous answer wowwubbzy13 uploaded is absolutely correct!

I'll set up a proportion.

If y = 12, then x = 5

--> 12:5

We want to find the y when x is 10

--> y:10

12:5 = y:10

5y = 120

y = 25

So B: 25 is the correct answer!

Answer:

0.87%

Step-by-step explanation:

→ Divide 0.87 by 10

0.87 ÷ 100 = 0.0087

→ Multiply answer by 100

0.0087 × 100 = 0.87

Answer:

7.

Step-by-step explanation:

Think of 42/6 as a division question.

42 ÷ 6.

The answer to this equation is 7.

Answer:

Step-by-step explanation:

Part A:  

CIRCLE A : Circumference is (pi)(diameter) so if they give you the circumference (21.98), divide it by 7 which gives you 3.14.

CIRCLE B: 18.84/6 = 3.14

Part B:

CIRCLE A: Area is (pi)(radius^2) so if they give you the area (38.465), divide it by radius^2 (7/2 = 3.5^2 = 12.25) = 3.14

CIRCLE B: 28.26/(3^2) = 3.14

Part C:

The value of pi stays the same for circle A and B.

Hope this helps :)

Answer: 49

Step-by-step explanation:

This polygon has 5 sides, meaning its interior angles add to [tex]180(5-2)=540^{\circ}[/tex].

[tex]3x+30+x+2x+x+20+3x=540\\\\10x+50=540\\\\10x=490\\\\x=49[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Equation of straight line in point - slope form :

[tex]\qquad❖ \: \sf \:y - y1 = m(x - x1)[/tex]

( m = slope = 4, point (5 , 17) )

[tex] \qquad◈ \: \: \sf \: y - 17 = 4(x - 5)[/tex]

[tex] \qquad◈ \: \: \sf \: y - 17= 4x - 20[/tex]

[tex] \qquad◈ \: \: \sf \: y = 4x - 20 + 17[/tex]

[tex] \qquad◈ \: \: \sf \: y = 4x - 3[/tex]

Now, it's the form of line in slope - intercept form, ( slope = coefficient of x = 4 and y - intercept = -3 )

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \qquad◈ \: \: \sf \: y \: \: int = - 3[/tex]

Answer:

B

Step-by-step explanation:

See the attached image.