Find the measures of two complementary angles if one angle is

What is the probability of choosing a king in a deck of 52 cards?

nikklg [1K]

<span>K) = 4/51 since there are four aces in the deck but only 51 cards left after the king has been removed. WITH REPLACEMENT: Find the probability of drawing three queens in a row, with replacement. We pick a card, write down what it is, then put it back in the deck and draw again.</span>

8 0

3 years ago

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Diana is painting statues. She has \dfrac{7}{8} 8 7 start fraction, 7, divided by, 8, end fraction of a liter of paint remaini

anzhelika [568]

Answer:

Number of statues that can be painted are 17

Step-by-step explanation:

Initially Diana has $\frac{7}{8}$ liters of paint remaining.

Every statue requires $\frac{1}{20}$ liters of paint for painting.

We have to find how many statues we will be able to paint with this remaining paint.

To get the number of statues,

Number of statues = $\frac{Paint remaining}{Paint required for 1 statue}$

number of statues = $\frac{\frac{7}{8} }{\frac{1}{20} }$

= $\frac{35}{2}$ = 17.5

Since the number of statues is not an integer the maximum number of statues that can be painted are 17.

3 0

3 years ago

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The square root 30 lie between what two numbers

Debora [2.8K]

The square root of thirty lies between the numbers 5 and 6.

8 0

3 years ago

According to the U.S. Census Bureau, the prob ability that a randomly selected household speaks only English at home is 0.81. Th

ludmilkaskok [199]

Answer:

Step-by-step explanation:

Given that according to the U.S. Census Bureau, the prob ability that a randomly selected household speaks only English at home is 0.81.

The probability that a randomly selected household speaks only Spanish at home is 0.12.

(a) the probability that a randomly selected household speaks only English or only Spanish at home

= 0.81+0.12 = 0.93

(since these two are disjoint sets)

(b) the probability that a randomly selected household speaks a language other than only English or only Spanish at home

= 1-0.93= 0.07 (remaining)

(c) the probability that a randomly selected household speaks a language other than only English at home

=1-0.81=0.19

(d) Can the probability that a randomly selected household speaks only Polish at home equal 0.08? Why or why not?

Polish alone can never exceed 1-(0.81+0.12) i.e. 0.70

At most it can take values as 0.7 only

So no is the answer.

4 0

3 years ago

Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x.

Leni [432]

Answer:

a)

$g(2.9) \approx -6.6$

$g(3.1) \approx -3.4$

b)

The values are too small since $g''$ is positive for both values of $x$ in. I'm speaking of the $x$ values, 2.9 and 3.1.

Step-by-step explanation:

a)

The point-slope of a line is:

$y-y_1=m(x-x_1)$

where $m$ is the slope and $(x_1,y_1)$ is a point on that line.

We want to find the equation of the tangent line of the curve $g$ at the point $(3,-5)$ on $g$ .

So we know $(x_1,y_1)=(3,-5)$ .

To find $m$ , we must calculate the derivative of $g$ at $x=3$ :

$m=g'(3)=(3)^2+7=9+7=16$ .

So the equation of the tangent line to curve $g$ at $(3,-5)$ is:

$y-(-5)=16(x-3)$ .

I'm going to solve this for $y$ .

$y-(-5)=16(x-3)$

$y+5=16(x-3)$

Subtract 5 on both sides:

$y=16(x-3)-5$

What this means is for values $x$ near $x=3$ is that:

$g(x) \approx 16(x-3)-5$ .

Let's evaluate this approximation function for $g(2.9)$ .

$g(2.9) \approx 16(2.9-3)-5$

$g(2.9) \approx 16(-.1)-5$

$g(2.9) \approx -1.6-5$

$g(2.9) \approx -6.6$

Let's evaluate this approximation function for $g(3.1)$ .

$g(3.1) \approx 16(3.1-3)-5$

$g(3.1) \approx 16(.1)-5$

$g(3.1) \approx 1.6-5$

$g(3.1) \approx -3.4$

b) To determine if these are over approximations or under approximations I will require the second derivative.

If $g''$ is positive, then it leads to underestimation (since the curve is concave up at that number).

If $g''$ is negative, then it leads to overestimation (since the curve is concave down at that number).

$g'(x)=x^2+7$

$g''(x)=2x+0$

$g''(x)=2x$

$2x$ is positive for $x>0$ .

$2x$ is negative for $x$ .

That is, $g''(2.9)>0 \text{ and } g''(3.1)>0$ .

So $2x$ is positive for both values of $x$ which means that the values we found in part (a) are underestimations.

6 0

3 years ago