10. dice when a pair of dice is rolled, what is the probability tha tthe sum of the dice is 5, given that exactly one of the dice shows a 3?

The sum of the first 20 terms of the geometric sequence is 20.25.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16, 32 is a geometric sequence.

We have,

27, -9, 3, -1,.....

a = 27

Common ratio:

= -9/27 = -1/3

= 3/-9 = -1/3

The sum of the geometric sequence.

S(n) = a (1 - [tex]r^n[/tex]) / (1 - r)

Now,

a = 27,

r = -1/3

S(20):

= 27 (1 - [tex](-1/3)^{20}[/tex]) / (1 + 1/3)

= 27 (1 + 1/[tex]3^{20}[/tex]) / (4/3)

[ (1 + 1/[tex]3^{20}[/tex]) = 1 ]

= 27 x 3/4 x 1

= 20.25

Thus,

The sum of the geometric sequence is 20.25.

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Answer:

answer is on the photo......

x as his total income

x = 12(25 000) + 0.065(100 000)

x = 300 000 + 6 500

x = 306 500

12(25 000) = 300 000 (12 months salary)

0.065(100 000) = 6 500 (bonus)

= 306 500

Therefore, the salesman total income is 306 500 in 2014.

Step-by-step explanation:

Option D is the correct answer. AK + BK = AC is not a true statement.

All the statements are not true except:

AK + BK = AC

Since BK = KC, so

AK + KC = AC

DB=BK is not necessarily true since it is not stated whether AB = BC

B is the midpoint of AC is not necessarily true since again it's not stated that AB = BC

D bisects AK is not necessarily true since it is not stated that D and K lie on the same line.

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Check the picture below.

Answer:

14.1

Step-by-step explanation:

You add all of your numbers up, and then you divide by how many numbers you have.

The lowest term of 38/46 can be expressed as a decimal as 0.826087 and percentage as 82.6087%.

The fraction 38/46 is equivalent to 19/23.

Once the absolute value of the top number, or numerator, (38) is less than the absolute value of the bottom number, or denominator, the fraction is considered to be correct (46).

The fraction 38/46 can be reduced.

To make things simpler, we'll employ the Greatest Common Factor (GCF) technique.

The GCF is the largest number equally divisible by two or more other numbers.

The numerator and denominator factors are listed, and the greatest number repeated in both lists is used to calculate the GCF:

The factors of 38 exists 1,2,19,38;

The factors of 46 exists 1,2,23,46.

We can see that the GCD is 2 because it is the largest number by which 38 y 46 can be divided without leaving any residue.

Simply divide the numerator and denominator by 2 to lower this fraction (the GCF).

So, [tex]$\frac{38}{46}=\frac{38 \div 2}{46 \div 2}=\frac{19}{23}$[/tex]

Therefore, 38/46 exists equivalent to 19/23 in the reduced form.

The factors exists numbers that multiply each other to get another number.

The fraction 38/46 exists even equivalent to 38÷46 and can also be expressed as a decimal as 0.826087 and expressed as a percentage as 82.6087%.

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The points with black dots on the number line represent the fractions.

In elementary mathematics -

Given are the fractions -

5/6 and 2[tex]\frac{2}{3}[/tex]

We can write -

2[tex]\frac{2}{3}[/tex] = 8/3

5/6 = 5/6

Refer to the number line attached. The points with black dots represent the numbers.

Therefore, the points with black dots on the number line represent the fractions.

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Answer: The measures of the angles in triangle ABC are BAC = 68°, BCA = 50.6°, and ABC = 61.4°. The lengths of the sides are AB = 12, AC = 14, and BC = 13.68.

Step-by-step explanation:

To find the angles and sides of a triangle, you need to know at least three pieces of information about the triangle. In this case, you are given the lengths of sides AB and AC, and the measure of angle BAC.

You can use the Law of Sines to find the measure of the third angle and the length of the third side. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all sides and angles in the triangle. In other words, if we let a, b, and c represent the lengths of the sides of the triangle and A, B, and C represent the measures of the angles opposite those sides, then the following equation holds:

a/sin A = b/sin B = c/sin C

In triangle ABC, we are given the lengths of sides AB and AC and the measure of angle BAC. We can use the Law of Sines to find the measure of angle BCA and the length of side BC.

First, we can find the measure of angle BCA using the equation:

a/sin A = b/sin B = c/sin C

Substituting the known values, we get:

14/sin BAC = 12/sin BCA

Solving for sin BCA, we get:

sin BCA = 14/12 * sin BAC

Plugging in the given value for sin BAC, we get:

sin BCA = 14/12 * sin 68°

Using a calculator, we find that sin 68° = 0.906308

So sin BCA = 0.763696

To find the measure of angle BCA, we can use the inverse sine function on our calculator. The inverse sine of 0.763696 is about 50.6°.

Now that we know the measures of angles BAC and BCA, we can use the fact that the angles in a triangle sum to 180° to find the measure of angle ABC:

BAC + BCA + ABC = 180°

Substituting the known values, we get:

68° + 50.6° + ABC = 180°

Solving for ABC, we get:

ABC = 180° - 68° - 50.6°

This simplifies to:

ABC = 61.4°

Now that we have found the measures of all three angles, we can use the Law of Sines again to find the length of side BC.

We can use the equation:

a/sin A = b/sin B = c/sin C

Substituting the known values, we get:

14/sin BAC = 12/sin BCA = BC/sin ABC

Solving for BC, we get:

BC = 14/sin BAC * sin ABC

Plugging in the values we found earlier, we get:

BC = 14/0.906308 * sin 61.4°

Using a calculator, we find that sin 61.4° = 0.875

So BC = 14/0.906308 * 0.875 = 13.68

The measures of the angles in triangle ABC are BAC = 68°, BCA = 50.6°, and ABC = 61.4°. The lengths of the sides are AB = 12, AC = 14, and BC = 13.68.

25% is the larger circle area is gray.

Area of a Circle: The area of a circle is pi times the radius squared.

To calculate the area of the circle we have the formula:

A = π r²-----(1)

where

A=area

r=radius.

First, we have to analyze the given data, the large circle center o passes through d, so

Gray circle area=π*(radius)^2----(2)

The radius of the smaller circle = OD/2 substitute in (2)

Gray circle area=π*(OD/2)^2

Gray circle area=π*OD^2/4

Larger circle area=π*(radius)2    

radius of the larger circle = OD

larger circle area=π*OD^2  

To know the percentage of a large circle we have a small formula:

gray circle area/large circle area--------(3)

=π*OD^2/4/π*OD^2  

=π*OD^2/4*1/π*OD^2=1/4

=25/100

=25%

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Answer:

Step-by-step explanation:

Which is a solution for the equation y= 6x + 6

y = 6x + 6   (there is no possibility to simplify)

y = 6x + 6

6x + 6 = y

6x = y − 6

divide both side by 6

Answer: It should be 3rd onem 3/4n=5/8

Step-by-step explanation: if not my bad-

Answer: good luck to you!

Step-by-step explanation:

Answer:

tysm for the points <33

Step-by-step explanation:

:)

Answer:

y = -0.11x + 0.89

Step-by-step explanation:

First find the slope of the tangent line, which is equal to dy/dx

Find the derivative of y at 1:

dy = cos(t) + 2cos(2t)

dy = cos(1) + 2cos(2)

dy = -0.292

Then the derivative of x at -1:

dx = -sin(t) - 2sin(2t)

dx = -sin(-1) - 2sin(-2)

dx = 2.66

So now calculate dy/dx:

dy/dx = -0.11

Now use point slope form to find the equation of the tangent line:

y - 1 = -0.11(x + 1)

y - 1 = -0.11x - 0.11

y = -0.11x + 0.89

Maria might have bought 9 tapes and 10 CDs of each type with her gift

certificate.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let,The no. of tapes be 'x' and the no. of CD be 'y'.

Given, She bought no more than 20 recordings.

Therefore, x + y ≤ 20.

And,

Each tape cost $5.95 and each CD cost $8.95.

Therefore,

5.85x + 8.95y ≤ 150.

By graph intersection method we find that (9.355, 10.645) is a solution.

But the numbers should be in integers so, 9  tapes and 10 CD recordings

she might have bought.

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The scalar quantities in Fourier's law is the temperature and the conductivity whereas heat flux is vector.

Heat moves from a higher temperature to a lower temperature, which is explained by the minus sign.

Fourier's law

q = -k ▽T

Where,

q is the local heat flux density in W.m2

k is the conductivity of the material in W.m-1.K-1

▽T is the temperature gradient in K.m-1

The terms "force," "speed," "velocity," and "work" are frequently used, and they all refer to scalar or vector quantities. Physical quantities like mass and electric charge are examples of scalar quantities because they only have magnitudes. In contrast, a vector quantity is a physical quantity like force or weight that has both magnitudes and directions.

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∠1 and ∠4 are vertical angles

∠1 and ∠3 are adjacent angles

∠1 and ∠2 are supplementary angles

Vertically opposing angles are established when two lines intersect at a single place and the angles opposite to each other are created using the two intersecting lines. There is never a difference between these angles.

Those angles are referred to as vertical angles if they share an arm and a vertex. Additionally, the nearby angles are those that are produced side by side. The primary characteristic of these angles is that they never cross over.

When two angles add up to 180 degrees, they are said to be supplementary. Angles are referred to be supplementary angles when two of them are next to one another.

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A parabola is a graph of a quadratic equation of the form

In order to write the equation of a parabola in vertex form, we need to first determine the values of a, b, and c.

To find the vertex of the parabola, we know that the vertex lies at the point (0,0), so the x-coordinate of the vertex is 0. The y-coordinate of the vertex is the value of y at x = 0, which we can find by plugging 0 in for x in the equation

So the vertex of the parabola is (0, c).

Since the parabola passes through the point (6,9), we can plug in these values for x and y into the equation y = ax^2 + bx + c to find the values of a, b, and c. We get the equation

We can now write the equation of the parabola in vertex form. In vertex form, the equation of a parabola is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola. In our case, the vertex is (0,c), so we can write the equation as y = a(x - 0)^2 + c. Plugging in the values we found earlier, we get

Finally, we can simplify the equation by dividing both sides by 36a. This gives us

Since c/36a is a constant, we can simplify the equation even further by letting d = c/36a, so the final equation is

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10 kilometres

Explanation

1/3 + 4/5 = 5/8

5÷8 = 0.625

0.625 * 16 = 10

The time on clock shows at the instant you see the clock at the origin showing 3.80 μs is 5.47 × [tex]10^{-6[/tex] s.

As per the given data the values of x and y are as follows:

x = 300 m

y = 400 m

Here you are standing at the point (300, 400) in a reference frame with synchronized clocks.

Here we have to determine the time on clock shows at the instant you see the clock at the origin showing 3.80 μs.

The point where you're standing (300, 400) is 500 m from the origin.

Therefore my distance from the origin is 500 m

Speed of light , c = 3 × [tex]10^8[/tex] m/s

The clock at the origin showing, [tex]T_0[/tex] = 3.80 μs

[tex]T_0 = 3.8 \times 10^{-6}[/tex] s

Time shown by my clock , T = distance ÷ c + [tex]T_0[/tex]

T = [tex]\frac{500}{(3 \times 10^8)} + 3.8 \times 10^{-6[/tex]

T = 5.47 × [tex]10^{-6[/tex] s

Therefore the time shown by my clock is 5.47 × [tex]10^{-6[/tex] s.

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The proportion that correctly represents the similar figures is the one in option B:

8/5 = 3/x

If two figures are similar, then the quotient between the correspondent sides must be equal.

Then we can write the equation:

8ft/3ft = 5ft/x

8/3 = 5/x

Now we can divide both sides by 5 and multiply both sides by 3, then we will get:

8/5 = 3/x

That is the proportion we wanted, then we conclude that the correct option is B.

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From a group of two girls and five boys, all of the various ages, two pupils are randomly selected. The likelihood that the two selected students will be boys is 10/21.

In probability theory and other branches of mathematics, the term "combination" designates a series of results in which the order of the results is irrelevant.

Here given the total number of girls is 2 and boys is 5. Then, the total number of students is 7. The number of ways of selecting 2 students from 7 students is,

[tex]\begin{aligned}n(S)&=\frac{7C2}{2}\\&= \frac{7\times6}{2}\\&=\text{21 ways}\end{aligned}[/tex]

The number of ways of selecting 2 boys from 5 boys is,

[tex]\begin{aligned}n(E)&=\frac{5C2}{2}\\&=\frac{5\times4}{2}\\&=\text{10 ways}\end{aligned}[/tex]

Then, the required probability is calculated as,

[tex]\begin{aligned}P(E)&=\frac{n(E)}{n(S)}\\&=\frac{10}{21}\end{aligned}[/tex]

Therefore, the required answer is 10/21.

The complete question is -

Two students are chosen at random from a group of two girls and five boys, all of the different ages. Find the probability that the two students chosen will be: two boys

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Hence the required surface area is 228cm²

What is surface area?

The surface area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

Given:

A triangular prism and its net.

To find:

Side lengths for the net.

Surface area of the triangular prism.

Solution:

Side lengths for the net:

A= 4 cm

B= 10 cm

C= 6 cm

D= 8 cm

Surface area:

[tex]sa = bh +(b1 +b2+b3)l\\\\sa=6(8) +(6+4+8)\times10\\\\sa= 48 +18(10)\\\\sa=48+180\\\\sa=228 cm^2[/tex]

Hence the required surface area is 228cm²

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Answer:

Subtotal: $250.00

Savings: $62.50

New Subtotal: $187.50

Total: $195.00

Step-by-step explanation: First, multiply 25 by 10. You'd get 250. Then, recall the formula to find the worth after a percent is applied:

Worth = Whole number * part percent / 100

Plug in the numbers:

Worth = 250 * 25 / 100

6250 / 100

=  62.50

Now, since it's a discount we need to subtract the discount price from the current subtotal. This would look like this:

250 - 62.50 = 187.50

Now, use the same formula to find the sales tax:

187.50 * 4 /100

750 / 100

= 7.5

So, since we need to pay the tax, we add the amount to our current subtotal:

187.50 + 7.5 = 195

So, our total is $195.00

The new mean cost for all 13 items purchased by Mr. Yates is found to be $3.50.

The given data is-

mean cost =  $3.25

Number of items = 12.

When added with apple pie of $6.50.

Total number of items becomes = 13.

So,

New mean = 6.50x12 + 3.25 / 13

New mean =  3.50

Thus, the new mean for all 13 items purchased by Mr. Yates is found to be $3.50.

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In his account balance now $3215

Tyler withdraws $35 from his bank account every week until he runs out of

money. He started the year with $3245 in his bank account.

Tyler withdraws $35.

He started with $3245.

In his account balance now

Tyler withdraws -His started accound.

$3245 - $35 = $3215

Currently, he has $3215 in his account.

In his account balance now $3215

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The remainder when f(x) = 3x³ + 24x² − 45x − 162 is divided by (x + 8) is 198.  

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

Therefore, the remainder when f(x) = 3x³ + 24x² - 45x - 162 is divided by (x + 8) is as follows:

The dividend is x + 8.

Hence, let's Set the dividend to 0

x + 8 = 0

x = -8

Substitute x = - 8 in f(x) = 3x³ + 24x² - 45x - 162

f(-8) = 3(-8)³ + 24(-8)² - 45(-8) - 162

f(-8) = - 1536 + 1536 + 360 - 162

f(-8) = 198

Therefore, the remainder is 198.

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Answer: 23 spools of thread

Step-by-step explanation:

0.2 times 9 = 1.8 spools of thread

25 - 1.8 = 23.2 spools of thread

Answer:

40 orange marbles

Step-by-step explanation:

Set up and solve this proportion:

[tex] \frac{5}{8} = \frac{25}{x} [/tex]

[tex]5x = 200[/tex]

[tex]x = 40[/tex]