# A bag contains 4 red marbles, 1 green one, 1 lavender one, 3 yellows, and 2 orange marbles. HINT [See Example 7.] How many sets of five marbles include at most one of the yellow ones?

266

Step-by-step explanation:

Red marbles = 4

Green marbles = 1

Lavender marbles = 1

Yellow marbles = 3

Orange marbles = 2

To pick 5 marbles with at most 1 yellow, we can pick 5 non-yellow marbles or (4 non-yellow marble and 1 yellow marble).

Picking 5 non-yellow marbles

There are 4 + 1 + 1 + 2 = 8 non-yellow marbles.

The number of ways of picking any 5 is

Picking 4 non-yellow marble and 1 yellow marble

The number of ways of picking any 4 non-yellow marbles is

The number of ways of picking any 1 yellow marble from 3 is

Number of ways for both =

Total number of picking 5 marbles with at most 1 yellow

Therefore, total number of ways = 56 + 210 = 266

## Related Questions

For four weeks in June Cameron baked 3 1/4 miles each week and swim 2 1/2 miles each week for three weeks in July he baked 4 3/4 miles each week and swim 3 1/2 miles each week how much greater was the total distance Cameron bike and swim in July compared to the total distance he bike in swim in June

For June:
Bike:
(4) * (3 1/4) = 13 miles
Swim:
(4) * (2 1/2) = 10 miles
Total:
13 + 10 = 23 miles
For July:
Bike:
(3) * (4 3/4) = 14.25 miles
Swim:
(3) * (3 1/2) = 10.5 miles
Total:
14.25 + 10.5 = 24.75 miles
The difference between both months is:
24.75 - 23 = 1.75 miles

the total distance Cameron bike and swim in July compared to the total distance he bike in swim in June was 1.75 miles greater

+ AlpQLScihp oans IbEmC-HAVOXMXB3Betzzi9sI8550WzDcwaron have a spinner divided into 8 equal sections. Each section is bered with a number 1 through 8. Salma is going to spin the spinner 1600 times. Theoretically, how many times should she land on a 1, 2, 3​

Salma should land her spinner on a 1, 2 or 3 about 600 times.

Step-by-step explanation:

Since Salma has a spinner divided into 8 equal sections, and each section is bered with a number 1 through 8, and Salma is going to spin the spinner 1600 times, to determine, theoretically, how many times should she land on a 1, 2, 3 the following calculations must be performed:

8 = 100

3 = X

3 x 100/8 = X

300/8 = X

37.5 = X

100 = 1600

37.5 = X

37.5 x 1600/100 = X

60000/100 = X

600 = X

Therefore, Salma should land her spinner on a 1, 2 or 3 about 600 times.

Hi there! :)

We can examine each answer choice individually:

A. 569 × 10² = 569 × (10 · 10) = 569 · 100 = 56,900. Therefore, this choice is incorrect.

B. 569 · 10 = 5,690. This choice is incorrect.

C. 10³ · 569 = (10 · 10 · 10) ·569 = 1000 · 569 = 569,000. This choice is correct.

D. 10² · 569 = (10 · 10) · 569 = 56,900. This choice is incorrect.

Therefore, the correct option is C.

A. 569 × 10² = 569 × (10 · 10) = 569 · 100 = 56,900.

B. 569 · 10 = 5,690.

C. 10³ · 569 = (10 · 10 · 10) ·569 = 1000 · 569 = 569,000.

D. 10² · 569 = (10 · 10) · 569 = 56,900.

Which quadratic relation has a y-intercept of 8?O y = 0.5(x + 2)(x + 4)
O y = 0.5 (x - 2)(+ 8)
O y = 0.5(x2 -2x - 16)
O y = 0.5 (x2 -2x + 16)

y = 0.5 (x^2 -2x + 16) has a y-intercept of 8.

Step-by-step explanation:

The x-coordinate of every y-intercept is zero.  To determine which of the four quadratics given here has a y-intercept of 8, we need only substitute 0 for x in each; if the result is 8, we've found the desired quadratic.

O y = 0.5(x + 2)(x + 4) becomes y = 0.5(2)(4) = 4 (reject this answer)

O y = 0.5 (x - 2)(x + 8) becomes y = 0.5(-2)(8) = -8 (reject)

O y = 0.5(x2 -2x - 16) becomes y = 0.5(-16) = -8 (reject)

O y = 0.5 (x2 -2x + 16) becomes y = 0.5(16) = 8 This is correct; that '8' represents the y-intercept (0, 8).

Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 64x2 + 81y2 = 1. $L=\iint_{R} {\color{red}9} \sin ({\color{red}384} x^{2} + {\color{red}486} y^{2})\,dA$.

Notice that Given that is an ellipse, consider a conversion to polar coordinates:

The Jacobian for this transformation is

with determinant

Then the integral in polar coordinates is

where you can evaluate the remaining integral by substituting and .

To evaluate the integral, we make a change of variables using the transformation x=u/8 and y=v/9 to transform the region into a unit circle. Then we convert the integral to polar coordinates and evaluate it.

### Explanation:

To evaluate the given integral, we can make the appropriate change of variables by using the transformation x = u/8 and y = v/9. This will transform the region R into a unit circle. The determinant of the Jacobian of the transformation is 1/72, which we will use to change the differential area element from dA to du dv. Substituting the new variables and limits of integration, the integral becomes:

L = \iint_{R} 9 \sin (612 u^{2} + 768 v^{2}) \cdot (1/72) \,du \,dv

Next, we can convert the integral from Cartesian coordinates(u, v) to polar coordinates (r, \theta). The integral can be rewritten as:

L = \int_{0}^{2\pi} \int_{0}^{1} 9 \sin (612 r^{2} \cos^{2}(\theta) + 768 r^{2} \sin^{2}(\theta)) \cdot (1/72) \cdot r \,dr \,d\theta

We can then evaluate this integral to find the value of L.

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Simplify: 3a + 5a PLS ANSWER ILL GIVE BRAINLIEST

Step-by-step explanation:

becuase the numbers are simply being added, you can just add 3+5.

for example, say a=3

3(a)+5(a)=3(3)+5(3)

9+15=24

but 3+5(a)=8(a)

8(3)=24