A deck of cards has 3 blue, 4 black, and 6 purple cards. Draw 2 cards without replacing any cards. What is the probability of both cards being blue?

The probability when a couple has 6 children at at least one of them is a boy is 63/64

First step

Probability  of all 6 girls=(1/2)^6

Probability  of all 6 girls = 1/64

Second step is to determine the probability at least one of them is a boy

Let at least one boy means not all girls

Hence:

P(all girls)+P(not all girls)=1

P(at least 1 boy)=1-P(all girls)

P(at least 1 boy)=1-1/64

P(at least 1 boy)=63/64

Inconclusion The probability when a couple has 6 children at at least one of them is a boy is 63/64

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Answer:

Astain = Apaint

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Step-by-step explanation:

By solving the system of linear equations formed from the scenario given, we find that the ice rink sold 34 general admission tickets and 61 youth tickets during the afternoon skating session.

This problem is a simple linear algebra problem. We can represent the total number of tickets with the variable x (for the general admission tickets) and y (for the youth tickets). The scenario provides us with two equations:

To solve the system of equations, we can multiply the first equation by 8 to have both equations involving '8y', which gives us 8x + 8y = 760.

Subtracting the first modified equation from the second gives: 2x = 68. Therefore, solving for x gives us x = 34. That means, there were 34 general admission tickets sold.

Substitute x=34 into x + y = 95, we get 34 + y = 95, which simplifies to, y = 61. That means, there were 61 youth tickets sold.

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The inverse of f(x) = ∛(x-4) is  f(x)³ + 4.

The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.

Given:

We have the equation,

f(x) = ∛(x-4)

Let y = ∛(x-4)

In order to find the inverse function, we have to solve for y :

y =  ∛(x-4)

y³ = (x-4)

x = y³ + 4

or, x = f(x)³ + 4

Therefore,  f(x)³ + 4 is the inverse function.

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Answer:

Median is decreased by the outlier or Outlier made median lower.

Step-by-step explanation:

First we calculate median of the data without an outlier:

Data in Ascending or increasing order ,

105 , 108 , 109 , 113 , 118 , 121 , 124

Now there are 7 terms so

Median = [tex]\frac{7+1}{2}^{th}\:term[/tex] = 4th term = 113

Now we find median of the data with outlier:

Data in ascending or descending order,

61 , 105 , 108 , 109 , 113 , 118 , 121 , 124

here no of terms are 8.

So, Median = [tex]\frac{(\frac{8}{2})^{th}+(\frac{8}{2}+1)^{th}}{2}[/tex]

                   = [tex]\frac{4^{th}+5^{th}}{2}=\frac{109+113}{2}[/tex]

                   = 111

So, Median is decreased by the outlier or Outlier made median lower.

To determine the equation of a line given two points, calculate the slope and then use one point to write the equation in slope-intercept form. The equation of the line through (3, -6) and (-3, 0) is B. y = -x - 3.

To find the equation of the line that contains the points (3,
-6) and (
-3, 0), we need to calculate the slope (m) of the line using the slope formula:

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

Plugging in the given points:

m = (0 - (-6)) / (-3 - 3)

m = 6 / -6

m = -1.

With the slope now known, we can use one of the points and the slope to write the equation of the line in point-slope form (y - y1) = m(x - x1) and then convert it to slope-intercept form (y = mx + b). Let's use the point (-3, 0):

y - 0 = -1(x + 3)

y = -1x - 3.

Therefore, the correct equation of the line is B. y =
-x - 3.

Answer:

6/20 = 3/10

Step-by-step explanation:

Her brother gets the first treat.  There are 2 grape treats out of 3+2 = 5 total; this is a probability of 2/5.

Maggie gets the second treat.  There will still be 3 cherry treats left, but only 5-1 = 4 treats remaining; this is a probability of 3/4.

Together this gives us 2/5(3/4) = (2*3)/(5*4) = 6/20 = 3/10

Answer:

3/10 or 6/20

Step-by-step explanation:

To find the number of quarters, solve the system of equations. Kat has 14 quarters.

To find the number of quarters Kat has, we can solve the system of equations given. The first equation states that the number of quarters (q) and the number of dimes (d) add up to 19.

The second equation represents the total value of the coins, where each quarter is worth $0.25 and each dime is worth $0.10.

By solving this system of equations, we can determine the value of q, which represents the number of quarters.

Using the first equation, we can solve for d by subtracting q from both sides: d = 19 - q.

Substituting this value of d into the second equation, we get: 0.25q + 0.1(19 - q) = 4.

Solving this equation, we find q = 14. Therefore, Kat has 14 quarters.

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Try this solution:

1. The final formula for the area of the figure is: A=A₁+A₂, where A₁ - the area of the square (its side is 18m) and A₂ - area of the triangle (the base is (8+18)m., height is 16 m.)

2. Using all the data in the formula above:

A=18*18+0.5*16*(8+18)=324+8*26=324+208=532 m².

answer: 532

Answer: yes it's correct

Step-by-step explanation: yes it's correct

The length of the rectangle will be 12 units.

The rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of ractangle = 2( length + width).

Let say,

Length = l   and   width = w

Given,

length of a rectangle is 3 times the width

l = 3w

The difference between the length and the width is 8 feet

l - w = 8

By equation 1 and 2

3w - w = 8

2w = 8

w = 4

Substitute into equation 1

l = 3(4)

l = 12 units.

So the length of the rectangle will be 12 units.

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Answer with explanation:

1)

If we divide 1/3 pounds equally among two people then each of them will get a share of:

[tex]\dfrac{1}{2}\times \dfrac{1}{3}\\\\=\dfrac{1}{6}\\\\=0.1666\ pounds[/tex]

Hence,the given answer that each will get 0.3333 pounds is incorrect.

2)

Molly wrote the following quotation to solve the problem: 2 . 1/3 = n.

This is an incorrect equation since this equation does not represent the half share of 1/3 pounds.

It represents the double amount of 1/3 pounds.

The complex number 3, in trig form, would be 3 cos 0 degrees. This is a ray from the center, right, along the x-axis, for a distance of 3 units.

Answer:

Step-by-step explanation:

3(cos(0)+isin(0))

General Idea:

The formula to find the Amount 'A' that need to be paid after ' t ' years for a Principal ' P ' with a annual rate of interest ' r ' is given below:

[tex] A= P(1+r \cdot t) [/tex]

Applying the concept:

Annie's cafe borrows $6100 at 6% for 290 days.

From the above statement we can conclude,...

[tex] P= \$6100\\ \\ r=6\%\\ \\ t=\frac{260}{365} [/tex]

Substituting the values of P, r and t in the formula, we get...

[tex] A=6100 \cdot (1+6 \% \cdot \frac{260}{365} )\\ \\ A=6100(1+\frac{6}{100} \cdot \frac{260}{365} )=6100(1+\frac{1560}{36500} ) \approx 6361 [/tex]

Conclusion:

The total amount that must be repaid after 290 days is approximately [tex] \$6361 [/tex]

To determine the time needed for an investment to double at a 5% compounded annual rate, apply the Rule of 72 by dividing 72 by the interest rate, resulting in approximately 14.4 years.

The question pertains to the time it takes for an investment to double in value with compound interest. To calculate this, we can use the Rule of 72. This rule states that you can approximate the number of years it'll take for an investment to double by dividing 72 by the annual interest rate. In this case, with a 5% interest rate, it would be calculated as 72 \/ 5, which equals approximately 14.4 years.

Here's a step-by-step explanation:

Apply the Rule of 72 by dividing 72 by the interest rate: 72 ÷ 5 = 14.4.

Therefore, it will take roughly 14.4 years for the sum of money to double at an annual compounded interest rate of 5%.

This is a quick and efficient way to estimate the power of compound interest and make informed investment decisions.

Solution: The correct option is d, i.e., Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.

Explanation:

we know that the sum of angles of a triangle is always [tex]180^{\circ}[/tex]. In ΔXYZ,

[tex]\angle X +\angle Y +\angle Z=180^{\circ}[/tex]

[tex]35^{\circ} +\angle Y +47^{\circ}=180^{\circ}[/tex]

[tex]\angle Y +82^{\circ}=180^{\circ}[/tex]

[tex]\angle Y =98^{\circ}[/tex]

In both triangles it is noticed that the sides AC and XZ are equal. In given triangles [tex]\angle A =\angle X=35^{\circ}[/tex] and [tex]\angle B =\angle Y=98^{\circ}[/tex].

By AAS rule of congruence ΔABC and ΔXYZ are congruent triangles, therefore we can transform ΔABC to ΔXYZ. For the transformation of ΔABC to ΔXYZ translate the vertex having same angle and rotate the triangle to align the sides and angles.

Since vertex X and vertex A have same angle, therefore we translate vertex X to vertex A and rotate ΔXYZ to align the sides and angles.

Hence the correct option is d.

Answer: d

Step-by-step explanation:

How many 1/3 pieces can be made from 2 pizzas, we know it is 6 and it is arrived by dividing 2 by 1/3 or multiplying by its reciprocal 3/1.

Hence to find how many 3/10 pieces can be made from 12/15 pizza, we have to divide 12/15 by 3/10 or multiplying by its reciprocal 10/3, i.e.

12/15 times 10/3= 8/3 or 2  2/3 

What does that mean? This means that while 2 three-tenths pieces can be made, 2/3of 3/10 i.e. 2/3×3/10=2/10=1/5 or one-fifth of pizza will be left out.

So the answer is 2 three-tenths pieces can be made, and one-fifth pizza will be left out.

Answer: it would be 2 3/10 pieces will be left over

For this case we have the following vectors:

[tex]a = 4i - 4j\\b = 4i + 5j[/tex]

We must find the product point of both vectors.

To do this, we multiply component by component and add the results.

We have then:

[tex]a.b = (4) (4) + (-4) (5)\\a.b = 16 -20\\a.b = -4[/tex]

Answer:

The point product of both vectors is given by:

[tex]a.b = -4[/tex]