6. Three cards are drawn from an ordinary deck and not replaced. What is the
probability of getting 3 spades?

Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

Answer:

Below

Step-by-step explanation:

From 7 to 10 AM is THREE hours (if the times are all on the same day)

It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

To multiply the square roots V7 and V2, we can combine the numbers inside the square roots and simplify the result.

V7 * V2 = V(7 * 2) = V14

Multiplying the numbers under the square roots, we get 7 * 2 = 14. Therefore, the product of V7 and V2 is V14.

This means that the square root of 14 is the result of multiplying V7 and V2. However, it is important to note that V14 cannot be further simplified because 14 does not have any perfect square factors.

In summary, the product of V7 and V2 is V14. It is worth mentioning that when multiplying square roots, we can multiply the numbers inside the square roots and keep the square root symbol intact, unless the numbers inside have perfect square factors that can be simplified further.

It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

for such more question on simplest form

https://brainly.com/question/4077992

#SPJ8

Answer:

Step-by-step explanation:

f(10) = 110×0.8855¹⁰

You can do the math.

Answer:

32.6045597492

Step-by-step explanation:

110(.8855)^10

the answer is communicative

Answer:

I think its commutative

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Answer:

67

Step-by-step explanation:

First off, we find a pair of x and y that suits the equation

x = 2 ; y = 1 => 3 x 2 + 4 x 1 = 10

So, we need to find the gradient of the line that goes through (0;0) and (2;1)

(I'll use the slope one for short)

= \(\frac{y2-y1}{x2-x1} =\frac{1-0}{2-0} = \frac{1}{2}\)

So, the gradient is 1/2.

The interquartile range or the standard deviation can be used to measure the spread of data depending on the outlier present.

It is possible to measure spread using the interquartile range or the standard deviation. The presence of extreme outliers should warrant the observer using the interquartile range for the measurement of spread.

However, if there are no extreme outliers in the dataset you are working with, then it is recommended that you use the standard deviation for the purpose of measurement.

Learn more about outliers here:

https://brainly.com/question/29546240

#SPJ1

I cannot interpret or analyze visual graphs. However, I can provide some general guidance on how to approach the questions:

a. To determine the prices of soda and/or taco based on the Budget Constraint BC2, you need to find the points where the budget line BC2 intersects with the axes (taco and soda quantities). The prices can be derived from the slope of the budget line, where the slope represents the rate at which one good can be traded for another.

b. To find the combination of taco and soda quantities that optimizes Ali's utility, you need to look for the point where the indifference curve (IC) is tangent to the budget line (BC). This point represents the maximum level of utility Ali can achieve within his budget constraint. It's the point where the marginal rate of substitution (MRS) between tacos and soda is equal to the price ratio of tacos to soda.

The corresponding values of g(x) \(g(x)=-3(\frac{1}{2} )^x\) are -12, -6, -3, and -1.5.

A graph of each of the point of g(x) is shown in the image below.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the corresponding y-values of g(x) for each x-values given in the table as follows;

When the x-value = -2, the corresponding y-values of g(x) is given by:

\(g(-2)=-3(\frac{1}{2} )^{-2}\)

g(-2) = -3 × 4

g(-2) = -12.

When the x-value = -1, the corresponding y-values of g(x) is given by:

\(g(-1)=-3(\frac{1}{2} )^{-1}\)

g(-1) = -3 × 2

g(-1) = -6.

When the x-value = 0, the corresponding y-values of g(x) is given by:

\(g(0)=-3(\frac{1}{2} )^{0}\)

g(0) = -3 × 1

g(0) = -3.

When the x-value = 1, the corresponding y-values of g(x) is given by:

\(g(1)=-3(\frac{1}{2} )^{1}\)

g(1) = -3 × 0.5

g(1) = -1.5.

Read more on function here: https://brainly.com/question/10687170

#SPJ1

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer: 31 is No   35 is Yes    28 is No     36 is Yes

Answer:

1. 7 to the square root of 3

2. negative square root of 3

Step-by-step explanation:

1. simplify 0.7 x 10 square of 3

2. Calculate: you get 7 to the square root of 3

1. simplify -0.125 x 8 to the square root of 3

2. Calcaute: you get negative square root of 3

The factors of the expression 0.7√300 and -0.125√192 will be 7 x √3 and - 1 x √3, respectively.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expressions are given below.

0.7√300 and -0.125√192

Simplify the expressions, then we have

0.7√300 and -0.125√192

7√3 and - √3

Factorize the expression, then we have

7 x √3 and - 1 x √3

More about the factorization link is given below.

https://brainly.com/question/6810544

#SPJ2

Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

Read more on midpoint here: brainly.com/question/17918978

#SPJ2

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

For more such questions on future value

https://brainly.com/question/24703884

#SPJ8

The solution of the Jordan's system is 3/2 and -1.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y = 2x² + 3..............(1)

y – x = 6

y= 6 +x ..............(2)

Put the value from (2) in equation (1) we get

y = 2x² + 3

6+ x  = 2x² + 3

2x² + 3 -6 -x = 0

2x² - x - 3 = 0

2x² -3x + 2x -3= 0

x( 2x-3) +1 (2x-3)= 0

(2x- 3)(x+1)= 0

x= 3/2, -1.

Hence, the value is 3/2, -1.

Learn more about Equation here:

https://brainly.com/question/29657992

#SPJ1

The Question you have attaches seems to incomplete/ inappropriate.

the complete question is

Jordan is solving this system of equations: y = 2x2 + 3 and y – x = 6. Which statements are true about Jordan’s system? Check all that apply.

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

According the question,

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

Where x represents the quantity of additional tours that the tourist wants to add to their travel package.

The function f(x) represents the total cost of the travel package plus the additional cost of the extra tours.

Learn more about Equation here:

https://brainly.com/question/29538993

#SPJ1

The study is classified as an observational study, and the problem is given as follows:

A.

This is a convenience sample with voluntary​ response, which has a high chance of leading to bias.

Experiments are studies in which there are two groups, with different features, and then the effect of a feature is studied.

For an observational study, there are no changes, just a question is asked, as is the case for this problem.

Convenience samples lead to bias as many people that share characteristics can answer.

More can be learned about observational studies at https://brainly.com/question/13193533

#SPJ1

Answer:

The answer is "\(\bold{\left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}7&-2\\ -\frac{1}{2}&\frac{7}{2}\end{array}\right]}\)".

Step-by-step explanation:

\(\bold{\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}6&5\\ 19&8\end{array}\right]}\)

Solve the L.H.S part:

\(\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\\\\\\left[\begin{array}{cc}a+2c&b+2d\\3a+4c&3b+4d\end{array}\right]\)

After calculating the L.H.S part compare the value with R.H.S:

\(\left[\begin{array}{cc}a+2c&b+2d\\3a+4c&3b+4d\end{array}\right]= \left[\begin{array}{cc}6&5\\ 19&8\end{array}\right]} \\\\\)

\(\to a+2c =6....(i)\\\\\to b+2d =5....(ii)\\\\\to 3a+4c =19....(iii)\\\\\to 3b+4d = 8 ....(iv)\\\\\)

In equation (i) multiply by 3 and subtract by equation (iii):

\(\to 3a+6c=18\\\to 3a+4c=19\\\\\text{subtract}... \\\\\to 2c = -1\\\\\to c= - \frac{1}{2}\)

put the value of c in equation (i):

\(\to a+ 2 (- \frac{1}{2})=6\\\\\to a- 2 \times \frac{1}{2}=6\\\\\to a- 1=6\\\\\to a =6 +1\\\\\to a = 7\\\)

In equation (ii) multiply by 3 then subtract by equation (iv):

\(\to 3b+6d=15\\\to 3b+4d=8\\\\\text{subtract...}\\\\\to 2d = 7\\\\\to d= \frac{7}{2}\\\)

put the value of d in equation (iv):

\(\to 3b+4 (\frac{7}{2})=8\\\\\to 3b+4 \times \frac{7}{2}=8\\\\\to 3b+14=8\\\\\to 3b =8-14\\\\\to 3b = -6\\\\\to b= \frac{-6}{3}\\\\\to b= -2\)

The final answer is "\(\bold{\left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}7&-2\\ -\frac{1}{2}&\frac{7}{2}\end{array}\right]}\)".

The 55th term of the arithmetic sequence is 131.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, the nth term of the sequence is aₙ= -1+3(n−1)

Here, the 55th term in the sequence is

a₅₅= -1+3(55-1)

= -1+132

= 131

Therefore, the 55th term is 131.

To learn more about an arithmetic sequence visit:

https://brainly.com/question/10396151.

#SPJ9

Answer:

8/5

Step-by-step explanation:

Answer:

\(3x + 6y = 1200\) is the correct linear equation.

Step-by-step explanation:

Given:

Time taken to manufacture an office chair = 3 hours

Number of office chairs produced = \(x\)

Time taken to manufacture an office desk = 6 hours

Number of office desks produced = \(y\)

Let us calculate, Total Time taken to manufacture \(x\) chairs.

Suppose we manufacture 2 chairs, time taken = 3 hours + 3 hours i.e. = 6 hours

Suppose we manufacture 3 chairs, time taken = 3 hours + 3 hours + 3 hours i.e. = 9 hours

Now, we are manufacturing \(x\) number of chairs so we have to add 3 for \(x\) number of times:

OR

simply multiply 3 with \(x\).

i.e. Total time taken in producing \(x\) chairs = 3\(x\) hours

Similarly Total time taken in producing \(y\) desks = 6\(y\) hours

We have a total of 1200 hours to produce this type of office chairs and desks:

So, 1200 = Total time taken in producing \(x\) chairs + Total time taken in producing \(y\) desks

Putting the values, we get the following:

\(3x+6y=1200\) is the correct linear equation for the situation.

Step-by-step explanation:

log8 64 = a

cut log and base^a

64 = 8^a

8^a = 64

or a = 2

Answer:

\(8^a = 64\), which gives \(a=2\).

Step-by-step explanation:

When you see \(\log_8(64)=a\), think: \(a\) is the number such that \(8^a = 64\). Mathematical intuition gives us that \(a=2\) immediately, but we can also work this out more methodologically:

\(8^a = 64\\(2^3)^a = 2^6\\2^{3a} = 2^6\\3a = 6\\a = 2\)

And this solution suffices.