a child has toy blocks that contain the numbers 1 through 80. what is the probability that the child will pick up a number that is not a multiple of 11? give your answer in fraction form.

Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

Answer:

email or call or talk to your teacher and ask why

Step-by-step explanation:

The distance from the sun to the other focus is 5.01 × 10⁹ m.

(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;

2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.

(b) To express this in terms of solar radii, we set up a ratio;

(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2

Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.

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Complete question is;

The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.

The store has 16 board games

What are equivalent ratios?

The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.

Let x = number of legos

Let y =  number of board games

Given ratio: 9:6= 9/6

x/y = 9/6

substitute x=24

24/y=9/6

Do cross multiplication

(6*24)/9=y

16=y

or

y=16

So, the store has 16 board games

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Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

Answer:

Lowest: 78

Highest: 99

Step-by-step explanation:

Quiz 1 =A

Quiz 2 = B

B = 21 + A

2A = 57 + B

2A = 57 + (21 + A)

2A = 78 + A

A = 78

B = 21 + A

B = 21 + 78

B = 99

When Claire and Megan meet, they will be $13\frac{1}{2}$ miles away from the outpost.

Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.

This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone $9$ miles, and Megan will have gone $8\frac{1}{2}$ miles. When they meet, they will have gone a total of $17\frac{1}{2}$ miles, leaving them $13\frac{1}{2}$ miles away from the outpost.

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When Claire and Megan meet, they will be \(13\frac{1}{2}\) miles away from the outpost. This can be solved by applying the concept of speed.

Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.

This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone 9 miles, and Megan will have gone \(8\frac{1}{2}\) miles. When they meet, they will have gone a total of \(17\frac{1}{2}\) miles, leaving them \(13\frac{1}{2}\)miles away from the outpost.

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To find a plane containing the point (-5, 6, -6) and the line defined by parametric equations x(t) = 7 - 5t, y(t) = 3 - 6t, and z(t) = -6 - 6t, we can use the point-normal form of the equation of a plane.

The equation of a plane in point-normal form is given by Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane, and (x, y, z) are the coordinates of a point on the plane. We can determine the normal vector by taking the cross product of two direction vectors in the plane.

The direction vector of the line can be obtained by taking the coefficients of t in the parametric equations, which gives us (-5, -6, -6). We can choose any two non-parallel direction vectors in the plane, for example, (1, 0, 0) and (0, 1, 0). Taking the cross product of these two vectors, we get the normal vector (0, 0, -1).

Now, we can substitute the values of the point (-5, 6, -6) and the normal vector (0, 0, -1) into the point-normal form equation. This gives us 0*(-5) + 0*6 + (-1)*(-6) + D = 0, which simplifies to D = -6. Thus, the equation of the plane containing the point (-5, 6, -6) and the given line is 0*x + 0*y - z - 6 = 0, or simply -z - 6 = 0.

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1/10

Step-by-step explanation:

she ran 1 mile per 10 minutes so its 1/10

Answer: Jon collected 173 stamps.

The graph that represents the solution to the inequality is a number line with closed point at 10 with arrow pointing left

You should be aware that inequality is is a mathematical statement showing that two opposite things are not equal.  The graph is a diagram that illustrates the statement.

The given inequality is 2(b + 2) > 24

Opening the brackets to get

2b+4≥24

2b≥24-4

This implies that 2b≥20

Making b the subject

b≥20/2

b≥10

Conclusively the graph is a number line with closed point at 10 with arrow pointing left

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Answer:

7%

Step-by-step explanation:

19,795 - 18,500 = 1295

What percent is 1,295 of 18,500

X/100 = 1295/18,500 (cross multiplication)

= 7%

Answer:

first you subtract 2 from both sides

-6x>18

then you divide

-6 by 18 which is -3 and since you divided with a decimal that flips your sign so your answer is X<-3

Answer:

x<-3

Step-by-step explanation:

First, write the equation and subtract 2 on both sides.

-6x+2>20

     -2  -2

-6x>18

Divide both sides by -6.

-6x>18

/-6  /-6

x<-3

(Remember, we have to flip the sign when multiplying or diving by a negative.)

Hope this helps! Have an amazing day C:

A 99% confidence interval for the average number of free throws in practice is; CI = (211.25, 238.75)

A confidence interval is defined as the mean of your estimate plus and minus the variation in that estimate. Thus, the formula for confidence interval is;

CI = x' ± z(s/√n)

where;

x' is sample mean

s is standard deviation

n is sample size

z is z-score at confidence level

Now, z-score at confidence level of 99% is; z = 2.576

We are given;

x' = 225

Sample size; n = 43

Standard deviation; s = 35

Thus;

CI = 225 ± 2.576(35/√43)

CI = 225 ± 13.75

CI = (225 - 13.75), (225 + 13.75)

CI = (211.25, 238.75)

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The constant y(t) = (y0-5)e^(-t) + 6e^(-4t) - 4t - 1; g(t) = (y0-4)e^(-t) + 6e^(-4t) - 4t; y0 = g(t).

What is algebra ?

Algebra is a branch of mathematics in which arithmetic operations and other formal manipulations are applied to abstract symbols rather than specific numbers.

Since y(t) = 6e^(-4t) - 4t - 1 is the general solution of the non-homogeneous equation y' + y = g(t), we can write it as:

y(t) = C1e^(-t) + 6e^(-4t) - 4t - 1

Setting t = 0 and using the initial condition y(0) = y0, we get:

y0 = C1 + 6 - 4 * 0 - 1

Solving for C1, we get:

C1 = y0 - 5

So, the general solution of the non-homogeneous equation is:

y(t) = (y0 - 5)e^(-t) + 6e^(-4t) - 4t - 1

Finally, the function g(t) can be found by comparing the general solution of the non-homogeneous equation with the right-hand side of the equation:

g(t) = (y0 - 5)e^(-t) + 6e^(-4t) - 4t - 1 + y = (y0 - 5 + 1)e^(-t) + 6e^(-4t) - 4t

Therefore, g(t) = (y0 - 4)e^(-t) + 6e^(-4t) - 4t.

So, the constant y(t) = (y0-5)e^(-t) + 6e^(-4t) - 4t - 1; g(t) = (y0-4)e^(-t) + 6e^(-4t) - 4t; y0 = g(t).

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Answer:

N^2+3

Step-by-step explanation:

Hope that helps!

The total number of arrangements possible if A and B must not sit together:

=  3600

Now, According to the question:

The no. of circular arrangements of n distinct items = (n-1)!

If A,B,C,D,E,F,G and H are the 8 persons to be seated around the table and A,B the 2

particular persons who must not sit together.

The total no.of circular arrangements for 8 persons = (8-1)! = 7! = 5040 --(1)

The no. of circular arrangements possible if A and B were to sit together = 6! (considering A and B as a single pair).

But, A and B can interchange their positions.

Hence, the no. of arrangements =6!×2=720×2=1440−−−−>(2)

So, the total number of arrangements possible if A and B must not sit together, = (1) - (2)

= 5040-1440

= 3600

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Answer:

(2x+1)(x−2)(2x−5)

Step-by-step explanation:

(3x−6)(4x2−1)−(2x−4)(4x2+4x+1)

4x3−16x2+11x+10

=(2x+1)(x−2)(2x−5)

The measure of the major arc JLK will be 206°. Then the correct option is B.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

The measure of the minor arc JK will be 154°.

Then the sum of the major arc and minor arc in a circle is 360°.

Then the major arc JLK will be given as,

JLK + JK = 360°

JLK + 154° = 360°

JLK = 206°

The measure of the major arc JLK will be 206°. Then the correct option is B.

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Answer:

Both mean and median are greater for Plot A than for Plot B.

Step-by-step explanation:

Plot A :

Plot A has 0 dots above 0, 1, and 2, 1 dot above 3, 2 above 4, 2 above 5, 2 above 6, 2 above 7, 0 above 8 and 9, and 1 above 10

A : 3, 4, 4, 5, 5, 6, 6, 7, 7, 10

Mean :

(3+4+4+5+5+6+6+7+7+10) / 10 = 5.7

Median :

1/2(n+1)th term

1/2(11)th term = 1/2(11) = 5.5th term = 11/2 = 5.5

Plot B:

B : 3,4,4,5,5,5,6,6,6,7

Mean = 51 / 10 = 5.1

Median :

1/2(n+1)th term

1/2(11)th term = 1/2(11) = 5.5th term = 10/2 = 5

Answer:

Both mean and median are greater for Plot A than for Plot B.

Step-by-step explanation:

If a set s = {u1,...., up} g has the prοperty that ui*uj uj d 0 whenever i≠ j , then S is an οrthοnοrmal set. The given statement is false.

The prοperty mentiοned in the statement, which states that the inner prοduct οf any twο distinct vectοrs in the set is zerο (i.e., ui * uj = 0 fοr i ≠ j), implies οrthοgοnality. Hοwever, fοr a set tο be cοnsidered οrthοnοrmal, it must satisfy twο cοnditiοns:

1. Orthοgοnality: Each pair οf distinct vectοrs in the set must be οrthοgοnal, meaning their inner prοduct is zerο.

2. Nοrmalizatiοn: Each vectοr in the set must have a length (οr magnitude) οf 1, which is achieved by dividing each vectοr by its nοrm.

In the given statement, οnly the οrthοgοnality cοnditiοn is satisfied, but the nοrmalizatiοn cοnditiοn is nοt mentiοned. Therefοre, we cannοt cοnclude that the set is οrthοnοrmal based οn the given prοperty alοne.

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The required function is 200 (1.4)ˣ = 5, where the value of x is calculated to be -11.

The given function is y = a bˣ

x₁ = 0, y₁ = 200

x₂ = 2,  y₂ = 392

Let us determine a, b.

a b⁰ = 200

a b² = 392

a = 200

200 b² = 392

b² = 392/200 = 49/25 = 7/5 = 1.4

So, the function is y = 200 (1.4)ˣ

Now, let us determine x for y = 5,

200 (1.4)ˣ = 5

(1.4)ˣ = 0.25

Taking log on both sides,

log (1.4)ˣ = log 0.025

x log 1.4 = log 0.025

x = log 0.025/log 1.4

x ≈ -11

This means the embryo was implanted on March 10th and she visited the doctor 11 days later.

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The interval of convergence for the given power series is (2, 8).

To find the interval of convergence for the given power series. We have the power series:

∑(n=2 to ∞) ((x-5)ⁿ)/(3ⁿ)

To find the interval of convergence, we'll use the Ratio Test. For the Ratio Test, we need to compute the limit:

L = lim (n → ∞) |(a_(n+1)/a_n)|

For our series, a_n = ((x-5)ⁿ)/(3ⁿ). Therefore, a_(n+1) = ((x-5)(n+1))/(3(n+1)). Now, let's compute the ratio:

|(a_(n+1)/a_n)| = |(((x-5)(n+1))/(3(n+1))) / (((x-5)ⁿ)/(3ⁿ))|

Simplify the expression:

|(a_(n+1)/a_n)| = |(x-5)/3|

The series converges if L < 1. So we have:

|(x-5)/3| < 1

Now, we'll solve for x to find the interval of convergence:

-1 < (x-5)/3 < 1

Multiply each term by 3:

-3 < x-5 < 3

Add 5 to each term:

2 < x < 8

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The given series with partial sums sn = (n² - 1) / (3n²) has a sum of 1/3. The convergence of the partial sums to 1/3 as n approaches infinity confirms this result.

To calculate the sum of the series where the partial sums are given as

sn = (n² - 1) / (3n²), we can analyze the expression and determine its behavior as n approaches infinity.

Looking at the expression, we can simplify it as sn = (1 - 1/n²) / 3. As n approaches infinity, the term 1/n² becomes negligible, and we are left with sn = 1 / 3. This means that the partial sums converge to a fixed value of 1/3 as n becomes larger.

Since the partial sums converge to 1/3, we can conclude that the sum of the series is also equal to 1/3. This is because the sum of an infinite series is defined as the limit of its partial sums as n approaches infinity. In this case, the partial sums approach 1/3, indicating that the series converges to 1/3.

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The value of money £6 in € is €9, i.e. £6 = €9

Currency is anything that is generally accepted to have value as a medium of exchange so that it can be traded for goods and services. The trading system within an economy is based on its currency, which is usually specific to a country and issued by that country's government.

Given that, two currency rates, £1 = $1.14 and $1 = €1.32, we need to find the value of £6 in €

Since, £1 = $1.14, we can write, $1 = £1/1.14

also, $1 = €1.32

Therefore,

£1/1.14 = €1.32

£1 = €1.32 x 1.14

£1 = €1.5

Therefore,

£6 = €1.5 x 6

£6 = €9

Hence, the value of money £6 in € is €9, i.e. £6 = €9

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