How much would $125 invested at 8% interest compounded continuously be worth after 16 years? Round your answer to the nearest cent. Do not include units in your answer.

The probability that at least one of them is a girl is about 0.977

The probability of an event is defined as the possibility of an event occurring against sample space.

[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]

Permutation is the number of ways to arrange objects.

[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]

Combination is the number of ways to select objects.

[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]

Let us tackle the problem.

This problem is about Probability.

Given:

The true probability of a baby being a boy P(B) = 0.534

The true probability that all of six randomly selected births in the country are boys is :

[tex]P(6B) = P(B) \times P(B) \times P(B) \times P(B) \times P(B) \times P(B)[/tex]

[tex]P(6B) = \boxed {(P(B))^6}[/tex]

The true probability that at least one of them is a girl is:

[tex]P(G\geq 1) = 1 - P(6B)[/tex]

[tex]P(G\geq 1) = 1 - (P(B))^6[/tex]

[tex]P(G\geq 1) = 1 - (0.534)^6[/tex]

[tex]P(G\geq 1) \approx \boxed {0.977}[/tex]

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation

The probability that out of the next six randomly selected births, at least one of them is a girl is 0.98.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -

P (Event A) = n(A)/n(S)

where -

n(A) → Number of outcomes favorable to event A.

n(B) → Total number of possible outcomes.

Given is the true probability of a baby being a boy. Its value is -

P(A) = 0.534

Assume that for the next six randomely selected births, the probability that it will be a baby boy is P(B). In one of the six randomely selected births, the probability that it will be a boy is 0.534. Therefore, the probability of being a boy in all the six cases will be -

P(B) = [P(A)]⁶

P(B) = 0.023

Now, for at least one of them to be girl, the probability of the event will be -

P(C) = P(B)' = 1 - 0.023 = 0.98

Therefore, the probability that out of the next six randomly selected births, at least one of them is a girl is 0.98.

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Answer:

Option B).[tex]x^{9}.(\sqrt[3]{y} )[/tex].

Step-by-step explanation:

The given expression is [tex](x^{27}y)^{\frac{1}{3} }[/tex].

We have to further simplify so that we can get the answer as shown in the options.

[tex](x^{27}y)^{\frac{1}{3} }=(x^{27})^{\frac{1}{3}}(y)^{\frac{1}{3}}[/tex]

[ As [tex](x^{a}.y^{b})^{m}=(x^{a})^{m}.(y^{b})^{m}[/tex] ]

Now ([tex](x^{27})^{\frac{1}{3}}(y)^{\frac{1}{3}}=(x^{\frac{27}{3} }).(y^{\frac{1}{3} } )=x^{9}.(\sqrt[3]{y} )[/tex]

Therefore Option B. is the answer.

Answer:

[tex]QR=4\ units[/tex]

[tex]RP=2\ units[/tex]

Step-by-step explanation:

we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

In this problem

triangle ABC is similar triangle PQR -------> given problem

so

[tex]\frac{AB}{PQ}=\frac{CA}{RP}=\frac{BC}{QR}[/tex]

we have

[tex]AB=9\ units, PQ=3\ units,CA=6\ units,BC=12\ units[/tex]

Find the length of side QR

[tex]\frac{AB}{PQ}=\frac{BC}{QR}[/tex]

substitute the values and solve for QR

[tex]\frac{9}{3}=\frac{12}{QR}[/tex]

[tex]QR=12*3/9=4\ units[/tex]

Find the length of side RP

[tex]\frac{AB}{PQ}=\frac{CA}{RP}[/tex]

substitute the values and solve for RP

[tex]\frac{9}{3}=\frac{6}{RP}[/tex]

[tex]RP=6*3/9=2\ units[/tex]

Paul had 15 onion plants.

To solve the problem, we need to calculate three-fourths of the 20 onion bulbs that Paul planted, as this represents the number of bulbs that sprouted.

First, we find three-fourths of 20 by multiplying 20 by the fraction [tex]\(\frac{3}{4}\)[/tex]:

[tex]\[ \frac{3}{4} \times 20 = \frac{3 \times 20}{4} \][/tex]

[tex]\[ \frac{3 \times 20}{4} = \frac{60}{4} \][/tex]

[tex]\[ \frac{60}{4} = 15 \][/tex]

Therefore, 15 onion bulbs sprouted, which means Paul had 15 onion plants.

Answer:

mADC = 220°

Step-by-step explanation:

In the given diagram AB and BC are tangents to the given circle O. We have to find the measure of arc ADC.

By theorem of tangents and arcs.

m∠ABC = [tex]\frac{1}{2}[/tex] [m ADC- m AC ]

Since it is given in the question

∠ABC = 40 & AC = 140°

Therefore, 40 = [tex]\frac{1}{2}[/tex] [ m ADC - 140 ]

40 × 2 = m ADC - 140

80 + 140 = m ADC

mADC = 220°

Final answer:

60 meters is significantly less than 6 kilometers, as 6 kilometers is equal to 6,000 meters.

Explanation:

To answer this, we need to compare the two measurements in the same unit. We know that 1 kilometer is equivalent to 1,000 meters, so to convert 6 kilometers to meters, we multiply by 1,000:

6 km  imes 1,000 = 6,000 m

Now we can compare the two measurements:

60 m

6,000 m

Since 60 is less than 6,000, we can conclude that 60 meters is less than 6 kilometers.

The 6th term of the geometric sequence is 3552

To find the 6th term of a geometric sequence, we need to determine the common ratio (r) first.

Given that t3 = 444 and t7 = 7104, we can use these two terms to find the common ratio.

t3 = t1 * r^(3-1)

444 = t1 * r^2

t7 = t1 * r^(7-1)

7104 = t1 * r^6

Dividing the two equations, we get:

7104/444 = (t1 * r^6) / (t1 * r^2)

16 = r^4

Taking the fourth root of both sides, we find:

r = ∛16 = 2

Now that we have the common ratio (r = 2), we can find the first term (t1) by substituting the values of t3 and r into the equation t3 = t1 * r^(3-1):

444 = t1 * 2^2

444 = 4t1

t1 = 111

To find the 6th term (t6), we substitute the values of t1 and r into the general formula for the nth term of a geometric sequence:

t6 = t1 * r^(6-1)

t6 = 111 * 2^5

t6 = 111 * 32

t6 = 3552

Therefore, the 6th term of the geometric sequence is 3552.

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Answer:

Part A: A=48  B=29 C=77  D=17  E=6   F=23  G=65  H=35  I=100

Part B: 6% of the survey respondents did not like either football or baseball.

Part C:  The survey results reveal a great dislike for baseball this is because 35% of the survey respondents dislike baseball while only 23% of the survey respondents dislike football.

The value of variable y in the equation,

2y + 2 = 9 is y = 7/2.

An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.

Given:

A phrase: Twice the difference of a number and 2 equals 9.

Let the number be y.

Then according to the question,

twice the difference of a number means,

2 x y

= 2y.

And the 2y and 2 equals 9.

That means,

we have an equation,

2y + 2 = 9

Subtract 2 from both sides,

we get,

2y = 7

y = 7/2.

Therefore, the value of y is 7/2.

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Answer: 1/4

Step-by-step explanation: In this problem, we are tossing two coins and we want to find the probability of tossing a tails and a tails. Tossing two coins are independent events because the outcome of tossing one coin does not affect the outcome of tossing the other coin.

We can find the probability of independent events by multiplying the probability of the first event by the probability of the second event. Note that we are talking about the theoretical probability because we aren't going to actually toss the coins.

If we want to find the probability of tossing a tails and a tails, we multiply the probability of tossing a tails by the probability of tossing a tails.

Now, let's find the probability of tossing a tails on the first coin. Remember that a coin has two sides which are heads and tails. Tails is one of these sides so the probability of tossing a heads is 1 out of 2 or 1/2. On the second coin the same is true so the probability is 1 out of 2 or 1/2.

Finally, we can simply multiply 1/2 by 1/2 which gives us 1/4. Therefore, the probability of tossing tails and tails is 1/4.

add them then divide by 3

16.00 + 40.00 + 130 = 186.00

186.00/3 = 62.00

 the average is 62.00

area = L x W

W=L-7

120 = L x L-7

120 = L^2-7L

L^2-7L+120 =0

(L-15) (L+8)

L=15, L=-8. It can't be a negative number so L=15

W=15-7 = 8

15*8 =120

 length = 15 inches

width = 8 inches

Answer:

The dimensions of the rectangle. Length= 15 inches and Width= 8 inches

Step-by-step explanation:

Let width of rectangle be W and length be L then

L=W+7 ---- (A)

Also given that area of rectangle = 120 square inches

=> WxL=120   -----(B)

From equation (A) and (B)

Wx(W+7) = 120

=> [tex]W^{2}+7W-120=0[/tex]

=>[tex]W^{2}+15W-8W-120=0 =>(W+15)(W-8)=0[/tex]

=> [tex]W=-15 or 8[/tex]

Since the width can not be a negative quantity , so W= 8 inches

=> L= W+7= (8+7) inches =  15 inches

Thus the dimensions of the rectangle. Length= 15 inches and Width= 8 inches

Final answer:

The conjecture for interior angles of complex polygons involves using the formula (n-2)×180 degrees for regular polygons and more complex considerations for 3D shapes like pentagonal bipyramids or square antiprisms. As the number of sides increases, calculations become more intricate and the interior angles can approach 180 degrees in very large polygons.

Explanation:

The question involves making a conjecture for the interior angles of complex polygons. A commonly used theorem related to this is that the sum of the interior angles of a polygon can be found using the formula (n-2)×180 degrees, where n is the number of sides in the polygon. For instance, to find the sum of the interior angles of a pentagon (a polygon with five sides), we calculate (5-2)×180 degrees = 540 degrees. As the number of sides increases, our calculations can become more complex, especially when dealing with non-regular polygons (where the sides and angles don't all have the same length/measure).

When considering the interior angles of complex geometries like a pentagonal bipyramid or a square antiprism, it's essential to recognize that their interior angles may involve multiple planes and hence cannot be calculated using the simple 2D polygon interior angle sum formula. These shapes involve three-dimensional calculations and often require advanced geometry or trigonometry to dissect into understandable components.

Considering large numbers of sides and complex figures, the interior angle measures can approach different limits. For example, as the number of sides I becomes very large, the interior angle measures can become very close to 180 degrees, which is suggested by the idea that for a polygon with infinitely many sides (approaching a circle), each interior angle would be 180 degrees.

Final answer:

The graph of a geometric sequence forms either an exponential decay or growth curve, depending on the common ratio, with the sequence appearing as a straight line on a semi-logarithmic scale.

Explanation:

The graph of any geometric sequence takes on a distinctive shape. If the common ratio of the geometric sequence is between -1 and 1 (excluding 0), the points of the graph will form a curve that approaches the x-axis as the number of terms increases, which is known as an exponential decay if the common ratio is positive, and an oscillating decay if it is negative. Similarly, if the common ratio is greater than 1 or less than -1, the sequence will exhibit exponential growth with each subsequent term becoming larger, and the points will diverge away from the x-axis forming an upward curve if the common ratio is positive or oscillating upward if it is negative. The graph may have a y-intercept, where it crosses the y-axis, and when graphed on a semi-logarithmic scale, the sequence with a positive common ratio will appear as a straight line.

The line [tex]\mathbf{\overline{MK}}[/tex] is a bisector of the line [tex]\mathbf{\overline{JN}}[/tex], and both lines form part of

ΔMNG and ΔKJG.

Correct response:

A two column proof is presented as follows;

Statement [tex]{}[/tex]                                     Reasons

1. [tex]\overline{NG}[/tex] ≅ [tex]\overline{JG}[/tex]                       1. Given (hash marks representing equal length)

2. ∠N and ∠J are right angles      2. Given (symbol for right angle)

3. ∠MGN ≅ ∠KGJ                       3. Vertical angle are congruent (theorem)

4. ∠N ≅ ∠J                                   4. Right angles are (all) congruent

5. ΔMNG ≅ ΔKJG                    5. Angle-Side-Angle, ASA, congruency rule

According to the ASA congruency rule, if two angles and the included

side of one triangle are the same to two angles and the included side of

another triangle, the two triangles are congruent.

∠N, side [tex]\mathbf{\overline{NG}}[/tex]∠MGN in ΔMNG are congruent to ∠J, side [tex]\mathbf{\overline{JG}}[/tex]∠KGJ in ΔKJG

Therefore;

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Part A.

Amount of money earned = Regular rate per hour * Number of working hours

M = 12 x

Part B.

Amount of wages earned = Regular rate per hour * Maximum number of regular working hours + Overtime rate per hour * Excess working hours

T = 12 * 30 + 16 * y

T = 360 + 16 y

or

T = 16 y + 360

Part C.

Given T = 408, find y:

408 = 16 y + 360

y = 3 hrs

Therefore the total hours Gary worked that week is,

x + y = 30 + 3 = 33 hrs        

(x = 30 since that is the maximum limit for regular working hours)

hello : 

help :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 )  Δ > 0  the equation has two reals solutions : x =  (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions

Answer:

Hi!

The correct answer is y =x^2 - 4x + 2

Step-by-step explanation:

The axis of symmetry is the x-coordinate vertex of the parabola.

The general form to find the axis of symmetry is:

[tex]x=-\frac{-b}{2*a} [/tex]

For y =x^2 - 4x + 2, a=1, b=−4 and c=2:

[tex]x=-\frac{-4}{2*1} = - \frac{-4}{2} = -(-2) = 2[/tex]

[tex]x = 2[/tex]