e throw a fair die three times. if we observe the first throw is a 4, what is the probability that there is at least two 4s in the three throws?

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Answer: 119/6

Step-by-step explanation:

-3 1/2 can be written as -7/2

-5 2/3 can be written as -17/3

-7/2 times -17/3 = 119/ 6

The answer is:

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

Answer:

y = x + 2

Step-by-step explanation:

Use the slope-intercept form:

y=mx+b

M represents the slope of the line

B represents the y-intercept

If at a store 4% of the eggs are cracked and you buy a dozen, then the probability that at least 1 is cracked is 0.916

The probability that the egg is cracked = 4%

= 0.04

The probability that the egg is not cracked = 1 - 0.04

= 0.96

Total number of eggs = 12 eggs

The probability that the one egg is cracked = 12 × 0.04 × (0.96)^11

= 0.306

The probability that 0 eggs are cracked = 1 × 0.04^0 × 0.96^12

= 0.61

The probability that at least 1 egg is cracked = 0.306 + 0.61

= 0.916

Therefore, the probability that at least 1 egg is cracked is 0.916

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Answer:

I'm pretty sure its 3500

Answer:

3,500 meters above the ground.

Step-by-step explanation:

The working is in the picture I attached to this response.

⭐ if this response helped you, please mark it the "brainliest"!⭐

Step-by-step explanation:

when you look at that right-angled triangle that is created by the plank as Hypotenuse (the side opposite of the 90° angle), and the distance on the ground from the wall and the height on the wall (from ground to the plank) as the legs, we know that the Hypotenuse (the plank) is the radius of the trigonometric circle we can draw there, and the 15 m ground distance from the wall is

cos(our angle) × radius

15×sqrt(3) × cos(our angle) = 15

cos(our angle) = 1/ sqrt(3) = 0.577350269...

our angle = 54.73561032...°

Answer:

Step-by-step explanation:

A linear relationship is a distribution of scores where a straight line can be visualized in the middle of a maze of cases running from one corner to another.

What does the term "linear relationship " mean?

A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association).

                         Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships.

Why are relationships linear and nonlinear?

Plotting a linear relationship on a graph results in a straight line, whereas plotting a nonlinear relationship results in a curve.

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Answer:

(3a2 – 5ab + b2) + (–3a2 + 2b2 + 8ab)

Which of the following shows the sum of the polynomials rewritten with like terms grouped together?

[3a2 + (–3a2)] + (–5ab + 8ab) + (b2 + 2b2)

[3a2 + (–3a2)] + (–5ab + 2b2) + (b2 + 8ab)

[3a2 + 3a2] + (5ab + 8ab) + (b2 + 2b2)

[3a2 + 3a2] + (5ab + 2b2) + (b2 + 8ab)

The answer is A.

Step-by-step explanation:

The 33rd percentile is 75.4.

Percentile is defined as the value below which a given percentage falls under. The percentile formula is used when we need to compare the exact values or numbers over the other numbers from the given data i.e. the accuracy of the number.

To find the percentile, here are a few steps to use the percentile formula. If q is any number between zero and hundred, the qth percentile is a value that divides the data into two parts i.e the lowest part contains the q percent of the data and the rest of the data is the upper part.

We find the rank.

Rank = Percentile ÷ 100

Rank = 33 ÷ 100 = 0.33

So, the rank is 0.33.

Using the percentile formula,

Percentile = Rank × Total number of the data set

Percentile = 0.33 × 117

Percentile = 38.61 ≅ 39

Now, counting 39 values from left to right we reach 75.4, and we can say that all the values below 75.4 will come under the 33rd percentile. In other words, 33% of the values are below 75.4.

Therefore, the 33rd percentile is 75.4.

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The value of kinetic energy will be 37.5 Jules.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A ball of mass of 6kg rolls with a velocity of 10m/s and creates 300 Jules of kinetic energy.

Now,

Since, A ball of mass of 6kg rolls with a velocity of 10m/s and creates 300 Jules of kinetic energy.

Hence, The value of kinetic energy with a mass of 3kg and a velocity of 5m/s create will be;

⇒ Kinetic energy = 1/2 mv²

⇒ Kinetic energy = 1/2 × 3 × 5²

                           = 1/2 × 3 × 25

                           = 37.5 Jules

Thus, The value of kinetic energy will be 37.5 Jules.

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The measure of the required angle of the given rhombus ABCD is m∠ADC = 64°.

The given rhombus has four angles as

∠ADC, ∠DCB, ∠CBA, and ∠BAD

It has two diagonals that bisect each other at point E.

And we have ∠ABD = 32° and ∠ACD = 58°

Here, the angles ∠ABD and ∠BDC are alternate angles. Since we know that, the alternate angles are equal in measure, we can write

∠ABD = ∠BDC

⇒ 32° = ∠BDC

Since we know that the diagonals of a rhombus bisect the angles, we get

∠ADC = 2∠BDC

⇒ ∠ADC = 2 × 32° = 64°

Therefore,  the required angle of the rhombus is ∠ADC = 64°.

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Therefore the probability that  she buys at least one of the previous items is 0.1333

The area of mathematics known as probability deals with numerical descriptions of the likelihood that an event will occur or that a statement is true .A number between 0 and 1 is the likelihood of an event, where, broadly speaking, 0 signifies the event's impossibility and 1 denotes its certainty.

Given:

event A: she buys  red dress.

event B: she buys a blue dress.

event C: she buys a necklace.

the probability she will buy a red dress is 0.2,

the probability she will buy a blue dress is 0.4

there is 10% chance  she will buy a necklace =0.10

The probability she wants to buy at most one dress,

P(A or B or C) =0.2 +0.4 +0.1 -(0.08 -0.04 -0.02 +0.08)

P(A or B or C) =0.568

the probability she buys at least one of the previous items is

[tex]\frac{P(A or B or C)}{P(AorB andC)}[/tex] = [tex]\frac{0.2 * 0.1 * 0.4}{(0.2 * 0.1)+(0.1 *0.4)}[/tex]

 [tex]\frac{P(A or B or C)}{P(AorB andC)}[/tex]= 2/15 =0.133

Therefore the probability that  she buys at least one of the previous items is 0.1333

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There is enough evidence to conclude that the doctor's claim is true.

We have given that,

population mean μ = 11 pounds

sample size n = 25

sample mean x = 12 ponds

standard deviation σ = 4 pounds

so the null hypothesis is H₀ : μ = 11 pounds

and the alternative hypothesis is Hₐ : μ > 11 pounds

now we will calculate test statistics,

t = (x-μ)/(σ/√n)

 = (12 - 11)/(4/√25)

 = 1/(4/5)

t = 1.25

p-value from the z-table is 0.10565

the result is non significant at p < 0.01.

Hence the null hypothesis rejected .

Therefore there is enough evidence to conclude that the doctor's claim is true.

The level of significance is the measurement of the statistical significance. It defines whether the null hypothesis is assumed to be accepted or rejected. It is expected to identify if the result is statistically significant for the null hypothesis to be false or rejected.

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Answer:

1+i

Step-by-step explanation:

Divide by 1

(1/1+i)

(1+i)

Identify the components of the numbers and add the real and imaginary parts separately

=(1)+(1)i

=(1)+(1)i

=(1+i)

Answer:

y - 2 = - [tex]\frac{3}{4}[/tex] (x + 8)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{3}{4}[/tex] and (a, b ) = (- 8, 2 ) , then

y - 2 = - [tex]\frac{3}{4}[/tex] (x - (- 8) ) , that is

y - 2 = - [tex]\frac{3}{4}[/tex] (x + 8)

The value of angle x that extends from the given polygon is 61°.

How to find the value of x?

The angle of straight line will be 180°

119° + x = 180°

x = 180° - 119°

x = 61°

Hence, the value of x that extends from the given polygon is 61°.

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Answer:

height = 5 m

Step-by-step explanation:

the volume (V) of a cuboid ( shape of room ) is calculated as

V = A h ( A is the area of the base and h the height )

here V = 235 and A = 47 , then

47h = 235 ( divide both sides by 47 )

h = 5 m

Answer:

volume= height * length * breadth = 235

area= length * breadth = 47

Step-by-step explanation:

47*height= 235

height=5sq

The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. A plane curve created by a point moving so that its distance from a fixed point equals its distance from a fixed line is known as a parabola. A normal parabola's standard equation is y 2 = 4 an x, where an is the distance from the vertex to the focus.

Given,

Function,

y = x² - 8x + 12

The supplied equation's vertex must be located.

The equation is a parabolic equation when we look at it.

We are aware that a parabolic equation's generic form is

y = x² - 8x + 12

where the parabola's vertex's x and y coordinates are denoted by h and k.

We can determine the following by comparing the aforementioned equation with the parabola's general form:

x = 4, y = 4 and h = -8

The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).

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The simplest polynomial with the given roots will be equal to x⁴ + 5x² - 36.

A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and raising non-negative integers to power, together with uncertainty and coefficients. x² + 4x + 7 is an illustration of a single indeterminate x polynomial.

The total of terms with the pattern [tex]kx^n[/tex] forms a polynomial. Where n is indeed a positive number and k is any number. For instance, the polynomial 3x + 2x - 5 exists.

As per the given information in the question,

The given roots are 3i, -2, 2

As we know that if 3i is a root then -3i is also a root.

Then, the factored form of this polynomial will be:

p(x) = (x - 3i)(x + 3i)(x + 2)(x - 2)

= (x - (3i)²) (x² -2x + 2x - 4)

It will become: (x² + 9)(x² - 4)

It can be further expanded,

x⁴ - 4x² + 9x² - 36

x⁴ + 5x² - 36

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The equation in standard form for the circle will be;

⇒ (x + 2)² + (y - 9)² = 1

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle that has a diameter with endpoints (-2,10) and (-2,8).

Now,

Since, The circle that has a diameter with endpoints (-2,10) and (-2,8).

Hence, The radius of circle is the half of the distance between two points of the diameter.

So, Radius = 1/2 (√ (8 - 10)² + (- 2 - (-2))²

                 = 1/2 √4

                = 1/2 × 2

                 = 1

Thus, Radius (r) of circle = 1

And, The center of circle is midpoint of the endpoints of the diameter.

Hence, Centre = (- 2 + (-2))/2, (10 + 8)/2

                       = - 4/2 , 18/2

                       = (- 2, 9)

Hence, The equation of circle with center (-2, 9) and radius 1 is;

⇒ (x - (-2))² + (y - 9) = 1²

⇒ (x + 2)² + (y - 9)² = 1

Thus, The equation in standard form for the circle will be;

⇒ (x + 2)² + (y - 9)² = 1

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The length of the YZ for the two similar triangles will be 9 inches.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

Given that triangle, ABC is similar to triangle XYZ. The value of the side YZ will be calculated by the similarity property,

YZ / BC = XZ / AC

x / 3 = 15 / 5

x = ( 15 x 3 ) / 5

x = 3 x 3

x = 9 inch

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The monthly share of annual expenses is $1820/month.

The monthly Share is calculated by dividing the annualized net amount of non-monthly billed services by 12.

Nonrecurring billing:

A one-time transaction is a non-recurring payment.

There is usually only one invoice or bill involved, and it only happens once.

Frequently, the amount is greater than the sum for recurring payments.

Subscriptions that are on monthly billing are billed on the same day each month for as long as the subscription is current.

So, we have:

Annual: $4200

Living: $670

Fixed: $800

Now, calculate as follows:

4200/12 = 350

Then,

350 + 370 + 800 = $1820/month

Therefore, the monthly share of annual expenses is $1820/month.

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The correct answer is 64

Demoivre's theorem states that for all complex numbers z and all positive integers n:

z^n = (r^n) × (cos(n∅) + isin(n×∅))

where r is the magnitude of z and theta is the argument of z.

To use Demoivre's theorem to simplify (1−i)^12, we can first write (1−i) in polar form as r × cis(∅). where r is the magnitude and cis(∅) is the size complex number. is 1, the argument ∅. In this case the size of (1−i) is √(1^2 + (-1)^2) = √(2) and the argument of (1−i) can be found using the arctangent function.

∅ = arctan(-1÷1) = -45 degrees.

So (1−i) can be written as sqrt(2) × cis(-45 degrees). Applying this to Demoivre's theorem, we get:

(1−i)^12 = (√(2)^12) × (cos(-540°) + i×sin(-540°))

We can simplify this to:

(1−i)^12 = 2^6 × cis(-180°)

This can be further simplified as follows.

(1−i)^12 = 64 × (-1)

the final answer is -64.

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Answer:

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

3(x-5)=12

Use distributive property on with the 3 and parenthesis (3 times x and 3 times -5)

3x-15=12

Add fifteen to both sides (15 on the left side cancels out)

3x=27

Divide both sides by 3 (3 on the left side cancels out)

x=9

Answer: not sure on this problem too

Step-by-step explanation:

sorry, can't really help!

The area of the circle is 66.50cm²

A circle is an object in which all distances are equal from the center.

In a circle, the length of the two tangents are equal.

From the figure, BP=CP

Also, the angles between a tangent and a radius is = 90⁰

⇒<OCP=90⁰

<PCB=<PBC=(180-60)/2 = 120/2 = 60⁰

Using cosine rule,

p²=b²+c²-2bccosP

p²=8²+8²-2*8*8*cos60

p²=64+64-128*0.5

p²=128-64

p²=64

Take the square root of both sides to get

p=√64=8

Note that CB=8  .....................(given)

Cx=8/2=4cm

Using trigonometric ratio

CosC = Adjacent/Hypotenuse

Cos30 = 4/CO

CO = 4/cos30

CO = 4/0.8660

CO = 4.6cm

CO = radius (r)

Area of circle = пr²

Area = 22/7 * 4.6 * 4.6

Area = 66.50 cm²

In conclusion, the area of the circle is  66.50cm²

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The mean number of people with the genetic mutation in these groups is 80 as this follows a Binomial Distribution.

It is given that 10% of the population has a genetic mutation. We have a sample of 800 here.

Let X be the random variable that defines the number of people with the mutation in the sample.

Since every person can or can't have the mutation, this is a Binomial distribution.

Here,

n = 800

p = 0.1

According to the formula for a Binomial Distribution,

the mean = np

Therefore, the mean for the above distribution will be

800 X 0.1

= 80.

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