Suppose we want to choose 6 letters with out replacement from 13 distinct letters. How many ways can this be done if the order of the choices is not relevant? How many ways can this be done if the order of the choices is relevant?

Answer:

R=17

Step-by-step explanation:

R=17

It says the whale has swam upwards and jumps to a heigh less then 17 and it says model the possible change in the number of feet, (R)

Thus R=17 Will Be correct

The proof that if if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0 is made by contradiction in this problem.

Proof by contradiction is different of traditional proof because it accepts a single example showing that a statement is false, instead of having the need to derive a general relationship for all input values.

For this problem, we must assume the case in which at least one of the terms is non-zero, hence we assume that A is non-zero, hence the expression would be given as follows:

A² + B² + C² = 0

A² = -(B² + C²)

This means that the square of A would be negative. However, the square of a number is always a non-negative number, hence this equation above is a contradiction.

This contradiction was used to prove that if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0.

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The edge of a block of metamaterial is 10 centimeters.

The surface area of the cube all six faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added six times to itself. The formula to find the surface area of a cube is 6a², where a is edge.

Given that, a block of metamaterial is in the shape of a cube with a surface area of 600 square centimeters.

Here, 6a²=600

a²=100

a=10 centimeters

Therefore, the edge of a block of metamaterial is 10 centimeters.

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The rate of change of surface area is 524.02 square kilometers per minutes.

The total space occupied by a three-dimensional square prism is called surface area.

Given, the decreasing rate of the base side with respect to time, ds/dt = 7 km/min

the increasing rate of height with respect to time, dh/dt = 10 km/min

At a time, t, base side, s = 4 km

and height, h = 9 km

we need to determine the rate of change of surface area with respect to time, d A/dt

from the differentiation chain rule, d A/ dt = d A /dt × ds /ds

                                                        d A /dt = d A/ ds × ds /dt ... equation 1

we know that the surface area for prism, A = 2s² + 4sh

if we differentiate with respect to s then we find d A /ds

  d/ds (A) = d/ ds (2s² + 4sh)

d A /ds = 4s + 4h +4s dh/ds ......  equation 2

now dh /ds = dh /ds × dt /dt [ using differentiation chain rule]

dh/ds = dh/ dt× dt/ds

d h/ ds = dh/dt × 1/ ds/dt

it stated earlier that dh/ dt = 10 and ds /dt = 7

dh / ds = 10/7

putting this value in equation 2, we get

d A /ds = 4s +4h + 4s ×10/7

as we know at time t, s= 4 and h = 9

d A /ds = 4 × 4 + 4 ×9 +4×4 ×10 /7

d A /ds = 74.86

putting the value  d A /ds in equation 1, we get

d A /dt = d A /ds × ds/ dt

d A/ dt = 74.86 × 7

d A /dt = 524.02 km² / min

hence, the rate of change of surface area = 524.02 square kilometers per minutes

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Answer:

  True

Step-by-step explanation:

You want to know if it is true or false that "two angles add up to 180° if and only if they are supplementary."

Two supplementary angles have a sum of 180°. That is the definition of supplementary angles. The offered statement is True.

Answer:

Marita had a $10-off coupon, so she paid $50 - $10 = $40 for the item

Step-by-step explanation:

To find the original price of the item, we need to work backwards through the discounts and find the price of the item before any discounts were applied.

We'll call the original price of the item "x."

First, we know that Marita received a 25% discount on the item, which means she paid 100% - 25% = 75% of the original price.

Then, Marita received an additional 20% discount on the sale price, which means she paid 100% - 20% = 80% of the 75% discounted price.

So, Marita paid 80% of the original price, which was reduced by a 25% discount. That means she paid 0.8 * 0.75 = 0.6 * original price = $30.

Therefore, the original price of the item was $30 / 0.6 = $<<30/0.6=50>>50.

Finally, Marita had a $10-off coupon, so she paid $50 - $10 = $40 for the item.

Answer:

54°

Step-by-step explanation:

Angles corresponding in parallel lines are the same

Based on the measurements shown in the table, the C-axis intercept of the line is equal to 100.

In Mathematics, the y-intercept of any graph such as a linear function, exponential function, polynomial function, quadratic function, etc., generally occur at the point where the value of "x" is equal to zero (x = 0).

In Mathematics, the x-intercept can be defined as the point at which the graph of a linear function, exponential function, polynomial function, quadratic function, etc., crosses the x-coordinate and the value of "y" is equal to zero (y = 0).

In this scenario, the C-axis intercept of the line simply refers to x-intercept. Therefore, we can reasonably infer and logically deduce that the C-axis intercept of the line (x-intercept) is equal to 100 while the d-axis intercept of the line (y-intercept) is equal to 200.

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After 3 years, the price of the house would be $2,494,822.48. After 5 years, the price of the house would be $2,830,530.94.

Price is the value of a product or service that an individual or business is willing to accept in exchange for a good or service. It is typically determined by the market forces of supply and demand. Prices are usually expressed in monetary terms, but can also be expressed in terms of labor time or other resources. Prices can vary widely depending on the availability of a good or service, the amount of competition, and other factors.

To calculate the price of the house after 3 years, the formula is P x (1 + r)^t. P is the initial price of the house, which is $2,300,006. R is the rate of increase each year, which is 6%. T is the number of years, which is 3. Therefore, the price of the house after 3 years is P x (1 + 0.06)^3, which equals to $2,494,822.48.
To calculate the price of the house after 5 years, the formula is P x (1 + r)^t. P is the initial price of the house, which is $2,300,006. R is the rate of increase each year, which is 6%. T is the number of years, which is 5. Therefore, the price of the house after 5 years is P x (1 + 0.06)^5, which equals to $2,830,530.94.

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Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).

An equation is a mathematical representation of two identical variables, one on each side of a "equals" sign. Common difficulties can be solved using equations. We commonly seek pre algebra help to resolve problems in real life. Pre-algebra is the fundamental building block of mathematics.

Here,

[tex](x + 2)^{2}[/tex] / [tex]a^{2}[/tex] +  [tex](y-5)^{2}[/tex] /[tex]b^{2}[/tex] -=1 is (h, k).

the ellipse's nucleus

The major axis is the larger of the two axes, which are 2a and 26.

(H, a, k) and (H, k, b) are the vertices. Vertices are those along the major axis in this case, and covertices are those along the minor axis.

[tex](x + 2)^{2}[/tex]/16 + [tex](y-5)^{2}[/tex] /20 =1

can be written as

[tex](x + 2)^{2}[/tex]/ [tex]4^{2}[/tex]   +       [tex](y-5)^{2}[/tex] /(2√/5)2

hence centre is (-2, 5), maor axis is 2 x 2√√5 = 4√√5 and minor axis

is 2 x 4 = 8

Vertices are ( 2,5 25), or ( 2,5 25) and ( 2,5 + 25), while covertices are ( 2 4, 5) and ( 6,5), respectively.

As a result of the presence of a vertical major axis, eccentricity e and focii are

(h, k ± be). e is given by the relation a2 = b2(1 − e2) i.e.

=> e = [tex]\sqrt{1 - \frac{a^{2} }{b^{2}} }[/tex]

 a2= 16 and b2= 62

=> e = 1/√5

Focii (-2,5 ± (2√5 x 1/√5)

or (-2,5±2) i.e. (-2, 7) and (-2, 3).

Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).

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Answer:

  ∠HAF ≈ 64.90°

Step-by-step explanation:

You want the angle HAF, a base angle in the isosceles triangle formed by the face diagonals of the cuboid with dimensions 6 cm, 6 cm, and 8 cm.

The lengths of the diagonals can be found using the Pythagorean theorem:

  HA² = HD² + DA²

  HA² = 6² +6² = 2·6²

  HA = 6√2 . . . cm

  FA² = FB² +BA²

  FA² = 6² +8² = 36 +64 = 100

  FA = 10 . . . cm

Diagonal FH is the diagonal of a rectangle with the same dimensions as the rectangle whose diagonal is FA:

  FH = FA = 10 . . . cm

The angle A can be found using the law of cosines:

  FH² = FA² +HA² -2·FA·HA·cos(A)

  A = arccos((FA² +HA² -FH²)/(2FA·HA))

  A = arccos((100 +72 -100)/(2·10·6√2)) = arccos(72/(120√2))

  A = arccos(0.3√2) ≈ 64.90°

Angle HAF is about 64.90°.

630,000

Step-by-step explanation:

350x60=21,000

21,000x30=630,000

Answer:

x = 45°

Step-by-step explanation:

x° + 45° + 90° = 180°

x° + 135° = 180°

x° = 180° – 135°

x° = 45°

i hope this helped

37.5% of the cars have a fuel efficiency of at least 35 miles per gallon.

To find the percentage of cars that have a fuel efficiency of at least 35 miles per gallon,

We first need to determine how many of the eight cars meet that threshold.

To do this, we can compare each car's fuel efficiency to 35 miles per gallon, and count the number that is greater than or equal to 35.

Identify the cars that have a fuel efficiency of at least 35 mpg: 42, 42, 54,

count the number of cars which is 3

divide it by 8 which is the total number of cars

Multiply the result by 100 to get the percentage, so:

3/8 * 100 = 37.5%

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On solving the provided question we can say that by logarithm the statement is true he is short.

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

He is tall, or he is short and handsome

It is not true that he is short or not handsome

by logarithm,

the statement is true he is short.

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Answer: -18

Step-by-step explanation:

Distribute the -3 to the values inside the parentheses, (x and 8) which equals -3x-24.

Then, use inverse operations by adding 24 on both sides (it will cancel on the left) to get -3x=53

Then divide -3 on both sides to get x by itself

Answer:

-18

Step-by-step explanation:

-3(x+8)=30

by dividing 3 from both sides

-(x+8)=10

by multiplying -1 for both sides

(x+8)= -10

by subtracting 8 from both sides

x = -18

The required correct options of data set after the value's removal.

1. The mean will increase.                   3. The median may stay the same.      5. The mode will stay the same.

The Index Sponsor computes the Removal Value in the same way that Fund Interests in the linked Fund are valued.

Here,
While analyzing a data set, a scientist notices one data value that is 2 IQRs below the first quartile.
As for the properties of statistics, Change in the IQR does affect the median and mode, So options 3 and 5 are correct.
And also mean will increase.

Thus, the correct options are shown above.

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Answer:

-7

Step-by-step explanation:

-2(x+5)=4

First, distributive property,

-2x-10=4

Add 10 to both sides,

-2x=14

Divide both sides by -2

-7

The solution that (4, 10) represents is that Jim purchased 4 iced teas and 10 soft pretzels at a cricket game.

The equation that describes the relationship between the

number of iced teas and the number of soft pretzels purchased is;

3x + 2y = 32

Where;

x represents the iced teas.

y represents soft pretzels at a cricket game

Now, we are told that the ordered pair (4, 10) is a solution of the equation. This means that;

x = 4 and y = 10 is a solution.

What it means is that Jim purchased 4 iced teas and 10 soft pretzels at a cricket game

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Answer:

4,2,0

Step-by-step explanation:

the rule is subtract 2 so 0 and 8 , 1 and 6 , 2 and 4 , 3 and 2 , and then finally 4 and 0

well, that number is "x", which oddly enough is the 100%, now, we also know that 30% of that is 1260, so hmmmm

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 1260& 30 \end{array} \implies \cfrac{x}{1260}~~=~~\cfrac{100}{30} \\\\\\ \cfrac{ x }{ 1260 } ~~=~~ \cfrac{ 10 }{ 3 }\implies 3x=12600\implies x=\cfrac{12600}{3}\implies x=4200[/tex]

The United States' entry into World War I led to a rise in nationalism and patriotism, as well as a shift towards a more interventionist foreign policy. This had a lasting impact on the culture and international political policies of the country.

The United States' entry into World War I marked a significant shift in the culture of the country. Prior to the war, the United States had maintained a policy of isolationism, with a focus on avoiding involvement in foreign conflicts. However, the country's entry into the war marked a shift towards a more interventionist foreign policy, as the United States began to take a more active role in international affairs.

Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials.

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Answer: A linear model is a type of mathematical equation that describes the relationship between two variables, such as median income and the number of bachelor's degrees per 1000 people. In order to estimate the number of bachelor's degrees per 1000 people for Mississippi based on the median income, you would need a linear equation that describes that relationship.

Without that equation, it's not possible to estimate the number of bachelor's degrees per 1000 people for Mississippi based on the median income.

Additionally, without more information about the data that the model was trained on, the correlation between median income and the number of bachelor's degrees per 1000 people and how accurate and reliable the model is, it's difficult to determine the goodness of this estimate. However, in general, a linear model may provide only a rough estimate, especially if the relationship between the variables is complex or non-linear.

Step-by-step explanation:

Answer:

The number of shuttles completed successfully is recorded as the score of that runner. The score is recorded in Level. Shuttles format (e.g. 9.5). The maximum laps on the PACER test is 247, which former Central Middle School student Dennis Mejia achieved, the only person to ever reach such a level.

Step-by-step explanation:

Answer:

Step-by-step explanation:

take 9 divided by 5 wich = 1.8

Answer:

false

Step-by-step explanation:

[tex]3xy^{2}[/tex]

The coefficient is 3

Hope this helps

Answer:

4 7

Step-by-step explanation: