7th grade math help me pleasee

The number of ways to draw four marbles from the bag is 330.

The number of ways to draw four marbles if two must be red and two must be white from the bag is 150.

The number of ways to draw four marbles if all must be the same color from the bag is 20.

To find the number of ways the concept of combination is used. The formula for finding combination is as follows,
\(^nC_r=\frac{n!}{r!(n-r)!}\)

Where C is for combination, n is number of terms out of which r is selected terms, and ! is a sign of factorial.

Now, finding the number of ways to draw four marbles from the bag,

Total number of marbles = 5 + 6 = 11

Here, n = 11 and r = 4, so putting the values in the formula,

\(^{11}C_4=\frac{11!}{4!(11-4)!}\\\\=\frac{11\times10\times9\times8\times7!}{4\times3\times2\times1\times7!} \\\\=330\)

Similarly, now finding the number of ways to draw four marbles if two must be red and two must be white from the bag,

Here, n = 5 for red and r = 2 and n = 6 and r = 2, so putting the values in the formula,

\(^{5}C_2\times^{6}C_2=\frac{5!}{2!(5-2)!}\times\frac{6!}{2!(6-2)!}\\\\=\frac{5\times4\times3!}{2\times1\times3!}\times \frac{6\times5\times\times4!}{2\times1\times4!}\\\\=150\)

Similarly, now finding the number of ways to draw four marbles if all must be the same color from the bag,

Here, n = 5 for red and r = 2 and n = 6 and r = 2, so putting the values in the formula,

\(^{5}C_4+^{6}C_4=\frac{5!}{4!(5-4)!}+\frac{6!}{4!(6-4)!}\\\\=\frac{5\times4!}{4!\times1!}+\frac{6\times5\times\times4!}{4!\times2\times1}\\\\=5+15\\\\=20\)

Therefore, The number of ways to draw four marbles from the bag is 330 and the number of ways to draw four marbles if two must be red and two must be white from the bag is 150 and the number of ways to draw four marbles if all must be the same color from the bag is 20.

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Step-by-step explanation:

I) 9+9+9+9=36

Ii)radius is 4.5 L=2piR= 2pi(4.5)= 9pi

Iii) A=piR^2= pi(4.5)^2 = 20.5pi

IV) 9×9 =81

V) 81-20.5pi = 16.597

Answer:

this is a required answer.

76 degrees Fahrenheit was found to be equal to approximately 24.4 degrees Celsius using the formula of conversion.

To convert Fahrenheit to Celsius, you can use the following formula:

Celsius = (Fahrenheit - 32) x 5/9

Plugging in 76 degrees Fahrenheit, we get:

Celsius = (76 - 32) x 5/9

Celsius = 44 x 5/9

Celsius = 220/9

Celsius ≈ 24.4

Therefore, 76 degrees Fahrenheit is approximately 24.4 degrees Celsius.

On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.

On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.

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The null hypothesis (H0) states that the average age is equal to or greater than 30.8 years, while the alternative hypothesis (Ha) states that the average age is less than 30.8 years.

In hypothesis testing, we set up the null hypothesis (H0) and the alternative hypothesis (Ha) to investigate a claim or conjecture. In this case, the conjecture is that the average age of a senior surgical resident in the United States is less than 30.8 years old.

The null hypothesis (H0) assumes that the average age is equal to or greater than 30.8 years, and any difference observed in the sample is due to random chance or sampling variability. Therefore, the null hypothesis can be stated as:

H0: The average age of senior surgical residents in the United States is greater than or equal to 30.8 years.

The alternative hypothesis (Ha) represents the claim or the opposite of the null hypothesis. In this case, the alternative hypothesis states that the average age is less than 30.8 years, indicating that there is a significant difference or evidence against the null hypothesis. Therefore, the alternative hypothesis can be stated as:

Ha: The average age of senior surgical residents in the United States is less than 30.8 years.

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Answer:

Step-by-step explanation:

100000³ = 100000 × 100000 × 100000

100000 × 100000 × 100000 =

10000000000 × 100000 =

1e+15 or 1.000.000.000.000.000

Answer:

If a tangent segment and a secant segment intersect outside a circle, then the square of the measure of the tangent segment equals the product of the measures of the secant segment and its external portion.

42^2 = (18 + x)(18)

1,764 = 18(x + 18)

x + 18 = 98

x = 80

So the diameter of the reservoir is 80 meters.

The diameter of the reservoir shown above can be calculated based on the intersecting secant-tangent theorem as: 80 meters.

A diameter is a straight line segment that crosses the center of a circle thereby connecting two points on its circumference and it is twice the length of the radius of a circle.

To find the diameter (x), apply the intersecting secant-tangent theorem which states that:

AB² = AC(x + CA)

Substitute:

42² = 18(x + 18)

1,764 = 18x + 324

1,764 - 324 = 18x

1,440 = 18x

1,440/18 = x

x = 80 meters.

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Answer: y => 12

y is greater than or equal to 12

Step-by-step explanation:

So they give you the function of y = 2x + 4 and the domain of all real numbers is greater than or equal to 4.

In simple term, the domain is x => 4, x is greater than or equal to 4.

Using that we can substitute the x in the function by 4.

y = 2(4) + 4

y = 8 + 4

Which gave us the answer of 12.

Since the domain can be anything greater than 4 or 4. We can expect the

same for the range.

Then the range will be 12 or greater than 12. For example, 13, 14, 15, 16...

Ex. y = 2(5) + 4

y = 10 + 4

y = 14

Ex. y = 2(4.5) + 4

y = 9 + 4

y = 13

Answer: no it does matter because it just the same numbers repeating

Step-by-step explanation:

Answer:

9. C

10. C

Step-by-step explanation:

Answer:

x= -3 and x= -1

Step-by-step explanation:

when x= -3 y= |-3+2|-1 = |-1|-1 = 1-1=0

and when x= -1 y = |-1+2|-1 = |1|+1=0

This sign |x| means that all values inside it are positive

Answer:

3.8

Step-by-step explanation:19 divided by 5 equals 3.8

Answer:

Step-by-step explanation:

Answer: 1/6.

Step-by-step explanation:

3/18 is just 1/6 because you have to divide the numerator and denominator by 3.

Answer:

It will be 14 I think because you're adding them all up and that's what you get so. Maybe it's right.

Answer: 3

Step-by-step explanation: Order them from greatest to least and then pick the number that is right in the middle of it which is the median. Glad to help!

Answer:

7.5

Step-by-step explanation:

the slope m is a measure of the rate of change

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (6, 45 ) and (x₂, y₂ ) = (9, 67.5 )

m = \(\frac{67.5-45}{9-6}\) = \(\frac{22.5}{3}\) = 7.5 ← rate of change

Answer:

a

Step-by-step explanation:

Lily would need 40.64 centimeters of copper wire for her experiment.

Given data ,

We may use the conversion factor that 1 inch is equivalent to 2.54 centimeters to convert 16 inches to centimeters .

From the unit conversion ,

1 inch = 2.54 inches

Consequently, 16 inches is equivalent to :

40.64 centimeters are equal to 16 inches at 2.54 centimeters per inch.

Hence , Lily would thus want 40.64 centimeters of copper wire for her experiment.

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S is not a basis for R3 because: c. S is linearly dependent and does not span R3.

A basis for a vector space is a set of vectors that are linearly independent and span the space.

Let's check if S = {(1, 1, 1), (0,1,1), (1,0,1), (0, 0, 0)} satisfies this definition of the basis or not.

Here, we have to find if the set is linearly dependent or not. If the set is linearly dependent, then it can't be a basis. To check the linearity of the set, we will set the equation for the linear combination of vectors of set S.

Then α1(1, 1, 1) + α2(0,1,1) + α3(1,0,1) + α4(0, 0, 0) = 0

For the above equation to hold true, α1 + α3 = 0α1 + α2 = 0α1 + α3 = 0

By solving the above equations, we get

α1 = -α3α2 = -α1α4 = 0

The above equation shows that α4 = 0 means there is always a trivial solution which makes it linearly dependent.

Therefore, it is not a basis.

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The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A.

The above statement is True.

Eigenvalue:

An eigenvalue is a special set of scalar values ​​associated with the most probable system of linear equations in a matrix equation. Eigenvectors are also called eigenvalues. It is a non-zero vector which can be modified by at most its scalar factor after applying a linear transformation.

According to the Question:

If the geometric multiple of the eigenvalues ​​is greater than or equal to 2, the linearly independent set of eigenvectors is no longer unique to the multiple as before. For example, for the diagonal matrix A=[3003], one could also choose the eigenvectors [11] and [1−1], or any pair of two linearly independent vectors.

Sometimes vectors are simply expanded to vector times matrix. If this happens, this vector is called the eigenvector of the matrix and the "stretch factor" is called the eigenvalue. Example: Given a square matrix A, λ is the eigenvalue of A, and the corresponding eigenvector x is

Ax = λx.

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The length of the third side of the triangle with a perimeter of 7x + 8 is 2x + 3

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

A triangle is a polygon that has three sides. The perimeter of a triangle is the sum of all the three sides.

Hence:

Perimeter of triangle = side 1 + side 2 + side 3

A triangle has a perimeter of 7x + 8. the first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.

Hence:

Perimeter of triangle = side 1 + side 2 + side 3

7x + 8 = 3x + (2x - 5) + side 3

7x + 8 = (5x - 5) + side 3

side 3 = 7x + 8 - (5x - 5)

side 3 = 2x + 13

The length of the third side is 2x + 3

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Answer:

m<1 = 175 degrees

Step-by-step explanation:

3x + 10 = 2x + 15

-2x - 10 = -2x - 10

x = 5

180 - 5 = 175 degrees

If the alternative hypothesis is that the proportion of items in population 1 is larger than the proportion of items in population 2, then the null hypothesis should be that there is no significant difference in the proportion of items between population 1 and population 2.

Based on the information provided, the null hypothesis should be:

The null hypothesis is that the proportion of items in population 1 is less than or equal to the proportion of items in population 2.

This is denoted as H₀: P₁ ≤ P₂. The alternative hypothesis, as you mentioned, is that the proportion of items in population 1 is larger than the proportion of items in population 2, which is represented as H₁: P₁ > P₂.

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Answer:

The diameter is 1 unit.

Step-by-step explanation:

The formula for circumference of a circle of diameter d is C = (3.14)d, where 3.14 is a close approximation of π (pi).

Here the circumference is given and is 3.14 units.  Because C = 3.14d,

the diameter of this circle is 3.14/3.14, or simply 1 (unit).

Robert W. Fogel, in his famous article, used data from one year, 1890, to make inferences about a longer time period, 1850-1890. He did so through the use of statistical methods, including regression analysis and comparative economic growth analysis.

The basic idea behind this approach is to use the data from 1890 as a snapshot of the state of the economy at that time and to use this information to make inferences about the longer time period. The assumption behind this approach is that the data from 1890 is representative of the economy over the entire period 1850-1890, and that the underlying trends and patterns that existed in 1890 were also present in the earlier period.

Fogel used a combination of economic theory, demographic data, and historical information to validate his assumptions and to support his conclusions. He also conducted extensive sensitivity analysis to ensure that his results were robust to different assumptions and data sources.

In conclusion, while using data from one year to draw conclusions about a much longer time period might seem unconventional, it was a valid approach used by Robert W. Fogel in his research and allowed him to make important contributions to our understanding of the economic history of the United States.

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Answer:

Y≤ -2x+8 basically isolate y by itself by subtracting 2x on both sides. Y ≥ -x+4 same thing here subtract x on both sides

Step-by-step explanation:

Answer:

Width = 50 m and Length = 100 m

Step-by-step explanation:

Wire length = 300 m = Perimeter of the rectangle

width = x

length = 2x

perimeter of a rectangle = 2( l + w )

300 m = 2( 2x + x )

300 m = 2( 3x)

300 m = 6x

300m/6 = x

50 m = x

Hence, width = x = 50 m , length = 2x = 2(50) = 100 m

Answer:

10^-5

10^-5 = 1/100,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{1}{100000}=\frac{1}{10^{5}}=10^{-5}\\\\\\\frac{1}{a^{m}}=a^{-m}\)

1. The most likely color for the taxi = green

2. The probability that the taxi is blue = 0.25

Let us assume that tg represents the taxi was green and tb represents the taxi was blue;

Also yg represents the taxi appeared green and yb  represents the taxi appeared blue.

9 out of 10 athenian taxis are green

So, P(tg) = 0.90

And, P(tb) = 1 - P(tg)

                = 1 - 0.90

                = 0.10

As under the dim lighting conditions, discrimination between blue and

green is 75% reliable,

P(yb | tb) = 0.75.

So, P(yg | tb) = 1 - P(yb | tb)

                     = 0.25

Similarly P(yg | tg) = 0.75

Thus, P(yb | tg) = 1 - P(yg | tg)

                         = 0.25

P(tb | yb) = P(tb, yb) / P(yb)

               = [P(yb | tb) P(tb)] / [P(yb, tg)P(tg) + P(yb | tb) P(xb)]

               = 0.25

Thus the probability that the taxi is blue = 0.25

P(tg | yb) = 1 - P(tb | yb)

              = 0.75

We can observe that P(tb | yb) > P(tb) but the posterior P(tb | yb) is smaller than 0.5, since the prior P(tb) is very small. Thus, the taxi was most likely green.

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The complete question is:

Suppose you are a witness to a nighttime hit-and-run accident involving a taxi in Athens.All taxi cars in Athens are blue or green. You swear under oath that the taxi was blue.Extensive testing shows that, under the dim lighting conditions, discrimination between blue and green is 75% reliable.

1. is it possible to calculate the most likely color for the taxi? (*hint:* distinguish carefully between the proposition that the taxi *is* blue and the proposition that it *appears* blue.)

2. what is the probability of the taxi being blue, if you know that 9 out of 10 athenian taxis are green?