A bag contains 10 balls.
4 are red and 6 are blue.
2 balls are taken from the bag at random without replacement.
a) Write down the probability that there are at least 2 red balls still in the bag. (1)
b) Write down the probability that there are at least 3 red balls still in the bag. (3)
Your final line must say, P(at least 3 red) = a/b where a and b are integers.
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Total marks: 4

Answer:

15

Step-by-step explanation:

The equation of ellipse with foci (-6,-1) and (-6,-7), and co-vertices (-2,-4) and (-10,-4) is [tex]\frac{(x+6)^2}{25}+\frac{(y+4)^2}{16}=1[/tex]

What is equation of an ellipse?

The standard equation of an ellipse centered at (h, k) with a major axis parallel to the x-axis is given by:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

where the coordinates of the vertex are (h±a, 0), coordinates of co-vertex are (h, k ± b) and the coordinates of foci are (h±c, k), where a² = c² + b².

According to the given question:

Given foci of the ellipse :

(-6, -1) and (-6, -7)

Co-vertices of the ellipse :

(-2, -4) and (-10, -4)

From the given foci and vertices ,

c = -1 - (-7) /2 = 3

b = -2 - (-10) /2 = 4

c² = a² + b²

∴ a² = 3 x 3 + 4 x 4 = 25

( h, k) = (-6 - 6 /2 , -1 - 7 / 2) = (-6, -4)

Equation of the ellipse is given by:

(x - h)²/ a² + (y - k)²/b² =1

(x - (-6))²/ 25 + (y - (-4))²/16 = 1

[tex]\frac{(x+6)^2}{25}+\frac{(y+4)^2}{16}=1[/tex]

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The letters of the points that satisfy the inequalities are  points A, D, E, I

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

The given parameters are:

y<-[tex]\frac{1}{2}x +2[/tex]   and

2x+y≤8

If we plot the graphs of the first inequality,

we notice that the coordinates of the origin are (0,0) then we have

Rearrange the inequality

[tex]y > -\frac{1}{2} x=2[/tex]

At origin y=0, x=0

[tex]0+\frac{1}{2}(0) > 2[/tex]

⇒ 0+0<2                (false)

Therefore the origin is not included

In the second inequality

2x+y≤8

Coordinates of the origin are (0,0)

2(0)+(0)≤8

0+0≤8             (False)

Therefore the origin is not included.

In conclusion the points that satisfy the inequalities are points A,D,E,I

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The equation of line through the origin and (-5, 6 ) is y = [tex]-\frac{6}{5}x[/tex]

The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.

the coordinates of the origin is (0, 0) and h other coordinates are (-5, 6)

at x = 0 and y = 0

using the equation of straight line y = mx + c

0 = 0(m) + c

so c = 0

at x = -5, y = 6

6 = -5m +c

but c = 0

6 = -5m

m = -6/5

Equation of line becomes y = -6/5x

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Based on the definition of an equilateral triangle, the measure of angle KML is: d 60.

An equilateral triangle can be described as a triangle that has three sides that are equal and also equal interior angles that measures 60 degrees each.

The image shows that the three sides of triangle KML are marked equally by three strokes. This shows that the three sides of triangle KML are congruent to each other. Since they are congruent, they have equal length.

Therefore, triangle KML is an equilateral triangle that has interior angles that measures 60 degrees.

Angle KML is an interior angle of the equilateral triangle, therefore:

The measure of angle KML is: d. 60 degrees.

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Answer:

y = 0

Step-by-step explanation:

x + 2y = 2 ( subtract 2y from both sides )

x = 2 - 2y → (1)

x = - 4y + 2 → (2)

substitute x = 2 - 2y into (2)

2 - 2y = - 4y + 2 ( add 4y to both sides )

2 + 2y = 2 ( subtract 2 from both sides )

2y = 0 , then

y = 0

Answer:

A. [tex]y=11x[/tex]

Step-by-step explanation:

The graph is linear, meaning it follows the formula [tex]y=mx+b[/tex], where y and x are variables, m is the constant rate that the graph increases by, and b is the y-intercept. The graph is increasing at a rate of 55 calories burned per 5 minutes spent skateboarding, which simplifies to 11 calories per 1 minute, so m is 11. The graph's y-intercept is 0 because it runs through the origin, and there's no point in writing "11x + 0" so it's just "y = 11x"

To perform a hypothesis test we use students' t distribution.

What is a hypothesis test?

A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters thanks to hypothesis testing.

Here, we have

Given, the population mean is 13. the sample mean is 12.8, and the sample standard deviation is two. the sample size is 20.

We have to find distribution to perform a hypothesis test.

The students t distribution is used when

1- sample size less than 30. Here 20.

2-population standard deviation not given.

3-population is normal.

Hence, we concluded that to perform a hypothesis test we use students' t distribution.

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can you send a picture of the question?

The number of animals will the farmer have after 7 months including the 10 cattle are 1280.

For the stated question-

Thus, number of animals after years;

= 10 x  2⁷

= 1280

Thus, number of animals will the farmer have after 7 months including the 10 cattle are 1280.

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By solving an inequality, we will see that option a is cheaper for more than 60 miles.

We know that option A charges $25 per day plus $0.15 per mile, so the cost for x miles is given by the linear equation:

A(x) = $25 + $0.15*x

While for option B the fixed cost is $10 and the cost per mile is $0.40, so the cost equation is:

B(x) = $10 + $0.40*x

The cost of option a will be smaller when:

$25 + $0.15*x < $10 + $0.40*x

$25 - $10 < $0.40*x - $0.15*x

$15 < $0.25*x

$15/$0.25 < x

60 < x

So for 60 miles the cost is the same, for x > 60 miles the cost of option a will be smaller (because the slope is smaller).

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Therefore, coin is unfair ,It is true that the coin can be considered unfair.

Calculating or estimating how likely or "possible" something is to occur is the subject of probability. Words like "certain," "impossible," or "probable" can be used to express the likelihood of an event occurring. Probabilities in mathematics are always expressed as fractions, decimals, or percent with values ranging from 0 to 1.

Here,

Step 1: We see that a coin is tossed 100 times, but we only receive heads 27 times.

In other words, the odds of a head are 27/100 or 0.27.

It is thought that there will be an equal number of heads and tails on a fair coin (or very close, if not equal).

So, using a fair coin:

P(H)=P(T)=0.5

Step 2

But in this instance, P(H)=0.27, which is a long way from 0.5.

Therefore, coin is unfair.

It is true that the coin can be considered unfair.

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Answer:

x = 0 and y = 2

Step-by-step explanation:

5x + 3y = 6

-5x - 3y = -6

Adding the equations gives 0 = 0, so the equations are equivalent.

x = 0 and y = 2

Answer:

43 p

Step-by-step explanation:

total cost = 10 - 4.84 = 10.00 - 4.84 = £5.16

b + t = 5.16

t = 11b

b + 11b = 5.16

12b = 5.16

12 / 12 b = 5.16/12

b = £0.43

As the given polynomial -8y has only 1 term in is and hence it is classified as a monomial.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

x² 4x + 7 is an illustration of a polynomial with a single indeterminate x.

The quantity of terms allows for the classification (naming) of polynomials.

A polynomial may contain exponents, constants, and variables, but it never divides by a variable.

They may also contain one or more terms, but not an infinite quantity.

The degree can also be used to categorize polynomials (the largest exponent of the variable).

An expression with only one term is called a monomial.

The sole term in an expression needs to be non-zero in order for it to be a monomial.

Therefore, as the given polynomial -8y has only 1 term in is and hence it is classified as a monomial.

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Answer:

13

Step-by-step explanation:

You take the number of miles from weeks 5-8 and add them up. 2+3+4+4=13

Answer: log81 = 1/4

Step-by-step explanation:

Log81^3

81^x = 3

The common base is 3, so

(3^4)^x=3

3^4x = 3^1

4x = 1

x= 1/4

Entonces, la distancia entre los puntos A y B es de aproximadamente 15.

Generalmente, Para encontrar la distancia entre los puntos A y B, puedes utilizar la fórmula de la distancia euclidiana:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

En este caso, la distancia sería:

d = √((3 - (-6))² + (-7 - 5)²)

The square root of ((3 - (-6))² + (-7 - 5)²) is equal to:

=√((3 - (-6))² + (-7 - 5)²)

= √((9)² + (-7 - 5)²)

= √(81 + 144)

= √225

d ≈15

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Encontró la pregunta completa

El punto A está en (-6,5) y el punto B está en (3,-7). ¿Cuál es la distancia entre los puntos

With the help of congruency of triangles rules, we know that TSR ≅ QRS because of (B) the AAS congruence theorem.

Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.

These triangles can be moved, turned, flipped, and rotated to produce the same appearance.

When moved, they are parallel to one another.

So, we have two sets of angles and one common side.

Review the congruence situations.

SSS ⇒ Three sides in the first, three sides in the second.

SAS: two sides, including the angle of the first side.

Incorporating angle in the second.

2 angles and the side that joins them in the first, according to ASA

Two angles and the side that connects the two angles.

AAS = 2 angles in the first triangle, plus 1 side.

Second, and one side in △.

Let's read the statements again and fill in the blanks.

Step 1: Since all right angles are congruent, mTSR = mQRS = 90°.

Step 2: Since it is given, mT = mQ

Step 3: Due to the reflexive property, SR becomes RS (common side)

Step 4: Because of the AAS congruence theorem, TSR and QRS are required.

Therefore, with the help of congruency of triangles rules, we know that TSR ≅ QRS because of (B) the AAS congruence theorem.

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The correct form of a question:
Given: TSR and QRS are right angles; T ≅ Q

Prove: TSR ≅ QRS

Step 1: We know that TSR ≅ QRS because all right angles are congruent.

Step 2: We know that T ≅ Q because it is given.

Step 3: We know that SR ≅ RS is because of the reflexive property.

Step 4: TSR ≅ QRS because __________

a. of the ASA congruence theorem

b. of the AAS congruence theorem

c. of the third angel theorem

d. all right triangles are congruent

Answer:

Step-by-step explanation:

o.67891

The KN is 21.4 rounded to the nearest tenth.

The orthocenter of a triangle is the place where the perpendicular drawn from the vertices to the opposing sides of the triangle intersect each other. The orthocenter for a triangle with an acute angle is located within the triangle. The orthocenter for a triangle with an acute angle is outside the triangle.

Now we need to find the slope of JL.

From that we have to find the slope of the perpendicular line through B.

Slope of JL=  (y₂ - y₁) / (x₂ - x₁)

J (7, 8) and L (5, 2)

here x₁=  7,y₁  = 8, x₂ = 5 and y₂ = 2

=  -6 / -2

= 3

Slope of the altitude KM  =  -1/ slope of JL = -1/3

Equation of the altitude KM : (y - y₁)  =  m (x -x₁)

Here K(1,2);

(y - 2)  =  -1/3 (x -1)

(y - 2)  =  -x/3 +1/3

Now we need to find the slope of JK.

From that we have to find the slope of the perpendicular line through D.

Slope of KL=  (y₂ - y₁) / (x₂ - x₁)

J(7,8) and K(1,2)

here x₁=  7,y₁  = 8, x₂ = 1 and y₂ = 2

 = 1

Slope of the altitude JO  =  -1/ slope of JL

                                         = -1

Equation of the altitude JO : (y - y₁)  =  m (x -x₁):

 (y - 8)  =  -1 (x - 7)

Solving the equation, x = 21 and y = -6

So the orthocenter N is (21 , -6)

Now the distance of KN is = √(21 - 1)² + (-6 -2)²

                                             =√464

                                             = 21.5

Therefore, the KN is 21.5 rounded to the nearest tenth.

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Answer:6.3

Step-by-step explanation:

I got it correct on my test

Answer:

I think it's 0.5%

Step-by-step explanation:

16/32 x 100% = 0.5%

The slope of the line passing through the points  (-9, 6) and (-3, 9) is (1/2).

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is

y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

We know slope(m) = (y₂ - y₁)/(x₂ - x₁).

Given, A line passes through the points (-9, 6) and (-3, 9).

∴ Slope(m) of the line is = (9 - 6)/(- 3 + 9) = 3/6 = 1/2.

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For this we have to calculate 50% of 7,000 which is 3,500

What does a math percent mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

What is the formula for percentage?

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

first we have to calculate 70% of 10,000 which is 7,000

Then now we have to calculate 50% of 7,000 which is 3,500

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Answer:

1. D 2. C 3. C

Step-by-step explanation:

On my test

For the given similar triangle the value of x will be 9 inches.

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

Since the two triangles are similar,

Suppose the unknown side is x,

Since the ratio of the sides of the similar triangles is equal the obtained expression is,

8/6=12/x

x=12×6 / 8

x=9 inches

Thus, for the given similar triangle the value of x will be 9 inches.

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