A table of values of a linear function is shown below. Find the output when the input is n . Type your answer in the space provided.
input 1 2 3 4 n
output 9 13 17 21

a) Probability that all four are the same suit = 0.0106 b) Probability that all four are red =0.055 c) Probability each has a different suit = 0.105

Total number of cards =52

No. of cards for each suit =13

Total types of four suit =4 (heart, spades, diamonds, clubs)

Total numbers of ways = [tex]^{52}C_4[/tex] =270,725 ways

a) number of ways choosing four cards of the same suit

= [tex]^{13}C_4+^{13}C_4+^{13}C_4+^{13}C_4[/tex]

= [tex]4 \times ^{13}C_4\\[/tex]

= [tex]4 \times \frac{13!}{4!(13-4)!}[/tex]

=2860 ways

Probability that all four are the same suit is 2860/270,725 = 0.0106

b) Number of ways all four cards are red

=[tex]^{26}C_4[/tex]

= 4,950 ways

Probability that all four are red = 4950/270,725 =0.055

c)  Number of ways each card has a different suit

=[tex]^{13}C_1\times^{13}C_1\times^{13}C_1\times^{13}C_1[/tex]

= 28,561 ways

Probability each has a different suit is 28561/270725 = 0.105

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The following expressions rewritten below;

23 + 8b

No common terms or factors

= 23 + 8b

㎡ - 5g

No common terms or factors

= m² - 5g

1/8 q + 7a/3

= (3q + 56a) / 24

12k (g+h)

= 12kg + 12kh

(2x + 3)(2 - 5x)

= 4x - 10x² + 6 - 15x

combine like terms

= -10x² -11x + 6

Therefore, algebraic expressions are solved by multiplying and combining like terms.

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Answer: Shirt-$12 Hat-$5

Step-by-step explanation:

14T + 6H = 198

10T + 6H = 150

4T=48

T=12$

10(12)+6H = 150

120 + 6H =150

H = 5$

At the end, Ann saves a total amount of 3 dollars according to the money she spent and on allowance according to the percentages.

Total Allowance of Ann = 15 dollars

Spent on food by Ann = [tex]\frac{15}{100}[/tex]*50

On food = 50 × [tex]\frac{15}{100}[/tex] = 7.5 dollars

Spent on stationary = 30% of Allowance

On stationary = 30 X[tex]\frac{15}{100}[/tex] = 4.5 dollars

Therefore, Money saved by Ann = Total Allowance - Money spent

Money saved = 15 dollars - 7.5 dollars - 4.5 dollars = 15-(7.5+4.5) dollars

Money saved = 3 dollars

Therefore, money saved by Ann is 3 dollars.

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The correct answer is,

x = 39

y =21

A different type of quadrilateral known as parallelogram has both pairs of its opposite sides parallel and equal.

The figure shows a parallelogram ABCD with the parameters AB II CD and AD II BC. Furthermore, AB = CD and AD = BC.

In a parallelogram, the opponent angles are equal.. So it means that side /A is equal to side /C, let's equate the two angles and solve for x;

5y - 3 = x + 3y

2y - x = 3                            ........(1)

Also, consecutive angles of a parallelogram are supplementary,

therefore,

/C + /D = 180

x + 3y + 2x = 180

3x + 3y = 180

x + y = 60                                  .......(2)

Now, add equations (1) and (2)

(2y-x) + (y+x) = 3 + 60

3y = 63

y = 21

now put this value of y in (2) we get,

x + y = 60

x + 21 = 60

x = 39

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The required proportionality relationship between Jordan and his friend for the sit-up is y = 2x.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
Jordan recorded the number of sit-ups he completed during the first 4 track practices, we can establish the proportionality relationship between Jordan and his friend by comparing the number of sit-ups each completed during each practice.

Let's call the number of sit-ups that Jordan and his friend completed during each practice "x" and "y". Then, the number of sit-ups that his friend completed during each practice would be "2x".

The proportionality relationship between Jordan and his friend can be expressed as,

y = 2x

This means that for every 1 sit-up that Jordan completed, his friend completed 2 sit-ups, or that Jordan's friend completed twice the number of sit-ups that Jordan completed during each practice.

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Shaniece is expected to select a lime chew about 505 times in the next 1200 selections.

Based on the given results, Shaniece selected a lime chew 24 times out of 57 selections. To estimate the expected number of times she would select a lime chew in the next 1200 selections, we can use the proportion of lime chews selected in the first 57 selections:

The proportion of lime chews selected = 24/57

To estimate the expected number of lime chews in the next 1200 selections, we can multiply the proportion by the total number of selections:

expected number of lime chews in the next 1200 selections = (24/57) x 1200

The expected number of lime chews in the next 1200 selections = 505.263

Rounding to the nearest whole number, we would expect Shaniece to select a lime chew about 505 times in the next 1200 selections.

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The equation x(x - 3m) = -5m² is non-real as the discriminant of the quadratic equation will be negative.

A quadratic equation is modeled by the rule presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:

The equation for this problem is defined as follows:

x(x - 3m) = -5m²

x² - 3mx + 5m² = 0.

The parameters are given as follows:

a = 1, b = -3m, c = 5m².

Hence the discriminant is given as follows:

Δ = (-3m)² - 4(1)(5m²)

Δ = 9m² - 20m²

Δ = -11m².

-11m² is always negative, hence the discriminant is negative and the equation is non-real.

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For given linear equations, 27hx -9y = -18 and y = 1 - 6x

h will be 2.

What is a linear equation, exactly?

When the greatest power of a variable is 1, the equation is said to be linear. Another term for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There are three more constants in addition to the constant C: the variables x and y, the coefficients A and B, and the variables.

Now,

As general equation of a line is y=mx + c where m=slope and c=constant

and here given lines are  27hx -9y = -18 and y = 1 - 6x

transforming these into general equations

y=-3hx+2 where m=-3h

and y=-6x+1    where m=-6

Now As slope of parallel lines is equal

therefore, -3h=-6

h=6/3

h=2

Hence,

           h will be 2.

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Todd has done correct calculation its values is equal to 6.79, which is closer to 7.

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number on the top side, it indicates the number of equal parts taken or whole quantity and denominator is on the bottom side, it indicates the equal parts of the whole quantity.

Given that,

Two fraction numbers in the form of addition,

⇒ 3 7/8 + 2 11/12

It can be further solved as

⇒  (24 + 7)/8 + (24 +11)/12

⇒  31/8 + 35/12

Now taking LCM of (8, 12)

LCM(8, 12) = 24

making denominator same in the both terms

⇒ 93/24 + 70/24

⇒ 163/24

⇒ 6.79

Thus, the values is closer to 7

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Equation that will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b is [tex]\frac{80+22d}{d} = 32d[/tex]

For finding the equation we will first form separate equations of both company a and company b and then we will equate the formed equation to find the number of days.

Let the number of days be d.

For company a, we will first add the service charges and per day charge multiplied with number of days, and then divide the sum with number of days.

= [tex]\frac{80+22d}{d}[/tex]

For company b, we will multiply the per day charges with the number of days.

= [tex]32d[/tex]

Now, we will equate both the formed equation

[tex]\frac{80+22d}{d} = 32d[/tex]

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The population of rabbits in the year 2013 is 1186.

To predict the population of rabbits in the year 2013, we can use exponential growth. The formula for exponential growth is:

P = P₀ * e^(rt)

where:

P = final population

P₀ = initial population (950)

r = the growth rate (we need to find this)

t = time elapsed (13 years)

We can use the data from 2003 to find the growth rate:

1000 = 950 * e^(r * 3)

1000 = 950 * e^(3r)

1000/950 = e^(3r)

ln (1000/950) = 3r

r = (ln(1000 / 950)) / 3

r = 0.0171

Now that we have the growth rate, we can use it to find the population in 2013:

P = 950 * e^(0.0171 * 13)

P = 1186

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The original price of the table was $200 before the 64% discount was applied.

What is the percentage?

Percentage is a way of expressing a fraction or proportion out of 100. It is commonly used to compare two quantities, indicate the change or growth of a quantity over time, or express the probability or chance of an event occurring.

If you received a 64% discount on the sale price of a table, and the sale price is $72, we can calculate the original price of the table as follows:

Determine the percentage of the original price that corresponds to the sale price after the discount:

If the sale price is 100% - 64% = 36% of the original price, after the 64% discount.

Use the percentage found in step 1 to calculate the original price:

Let x be the original price

x * 36% = $72

0.36x = $72

x = $72 / 0.36

x = $200

Therefore, the original price of the table was $200 before the 64% discount was applied.

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Answer:

Complementary is 2 angles that add up to 90 degrees and supplementary is 2 angles that add up to 180 degrees

48+32=80 so that would be neither

101+77=178 so that would be neither

107+73=180 so that would be supplementary

Step-by-step explanation:

have a nice day.

Answer:

only here for points

Step-by-step explanation:

Anwer: EG=EF+EG => 6x+12+48=144

6x=144-12-48

6x=84

x=14

d)x=14

The measure of the angle x would be 25.2°.

What is a circle theorem?

The circle theorem is a set of mathematical rules and relationships that apply to circles and their components, such as chords, tangents, and angles. These theorems describe how the different parts of a circle relate to each other and are used to solve geometric problems involving circles. Some common circle theorems include the inscribed angle theorem, the chord-chord theorem, and the tangent-secant theorem.

By using the circle theorem, we can write

5x-7 = 119

5x = 119 + 7

5x = 126

x = 126/5

x = 25.2°

Hence, the measure of the angle x would be 25.2°.

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The measure of BC from the triangle ABC is 40.82 units.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, in triangle ABC, AB=21 units and AC=35 units.

By using Pythagoras theorem,

BC²=AB²+AC²

BC²=21²+35²

BC²=441+1225

BC²=1666

BC=√1666

BC=40.82

Therefore, the measure of BC is 40.82 units.

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Answer:

To convert 6 feet into meters, first create a conversion factor to convert from feet to meters. Make sure the original unit is in the denominator, then cancel feet. Next, multiply the original measure by the conversion factor to get 1.8288 meters, or 1.83 meters if you simplified it.

Step-by-step explanation:

The value for A∪B in probability form is 3/4. The value for A∪B in data set form is {5, 6, 8}.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The event U has data - U = {1, 2, 3, 4, 5, 6, 7, 8}

The event A has data - A = {6, 8, 10}

The event B has data - B = {5, 6, 9, 12}

The event C has data - C = {1, 3, 7}

The probability formula is -

Probability = No. of outcomes that is favorable / Total number of outcomes

The value for A∪B is -

A∪B = 3/4

The value of A∪B in data set is the values that are present in U data set and in A and B data set.

So, the value is - {5, 6, 8}

Therefore, the value is 3/4 or {5, 6, 8}.

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The function with a greater stretch factor is the function graphed and the value is 3 times greater

The function with a greater stretch factor is the function which has a greater number multiplying the function

The given equation is a(x) = 1/3 x³ while the function graphed is b(x) = x³+ 2

The stretch factor is determined by the coefficients which are

a(x): 1/3 and b(x): 1

comparing this numbers

= b(x) / a(x)

= 1 / 1/3

= 3

this shows that b(x) which is 1 is greater by 3 times.

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a. The best data type for the number of siblings would be an integer.

An example of a typical value for this variable would be 3, as someone might have 3 siblings. An integer is the best data type because the number of siblings is a whole number and can never be a fraction or a negative number.

b. The best data type for the final grade in this class would be a floating-point number. An example of a typical value for this variable would be 85.5, as a final grade may include decimal points. A floating-point number is the best data type because a final grade can have a decimal point and may include fractions.

c. The best data type for the population of Earth would be a long integer. An example of a typical value for this variable would be 7,794,798,739, as of the year 2020. A long integer is the best data type because the population of Earth is a large number and cannot be expressed using a regular integer.

d. The best data type for the population of a U.S. county would be an integer. An example of a typical value for this variable would be 100,000, as the population of a county can vary greatly. An integer is the best data type because the population of a county is a whole number and can never be a fraction or a negative number.

e. The best data type for the number of passengers on a bus would be an integer. An example of a typical value for this variable would be 20, as a bus can carry a varying number of passengers. An integer is the best data type because the number of passengers on a bus is a whole number and can never be a fraction or a negative number.

f. The best data type for one player's score in a Scrabble game would be an integer. An example of a typical value for this variable would be 45, as a score in Scrabble is calculated in whole numbers. An integer is the best data type because a score in Scrabble is a whole number and can never be a fraction or a negative number.

g. The best data type for one team's score in a Major League Baseball game would be an integer. An example of a typical value for this variable would be 7, as a team's score is calculated in whole numbers. An integer is the best data type because a team's score is a whole number and can never be a fraction or a negative number.

h. The best data type for the year a historical event occurred would be an integer. An example of a typical value for this variable would be 1776, as the year the United States declared independence. An integer is the best data type because a year is a whole number and can never be a fraction or a negative number.

i. The best data type for the number of legs on an animal would be an integer. An example of a typical value for this variable would be 4, as many animals have four legs. An integer is the best data type because the number of legs an animal has is a whole number and can never be a fraction or a negative number.

j. The best data type for the price of an automobile would be a floating-point number. An example of a typical value for this variable would be $25,000.50, as a price for a car can include decimal points. A floating-point number is the best data type because the price of a car can have a decimal point and may include fractions.

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Answer:

The third option

Step-by-step explanation:

The third option, {1, 4, 7, 10, ...} is an arithmetic sequence because you add 3 to get from 1 to 4, and then you add 3 to get to 7, and then you add another 3 to get to 10.

Answer:

287 miles

Step-by-step explanation:

20.95+ .80x =250.55

250.55-20.95=229.6

.80x=229.6

229.6/.80=x

x=287 miles

Answer:

C

Step-by-step explanation:

The spaces go F A C E. The note shown is C.

12 servings of rice require six cups of rice. In order to make 12 servings, 6 cups of rice would be needed, or 2/5 of a cup.

1. It takes 2 cups of rice to make 5 servings.

2. Divide 12 by 5 to determine how many cups of rice are required to prepare 12 servings.

3. The final product is 2.4 cups.

4. Round up to the nearest whole number, which is 6 cups, to get 12 servings.

You will require 6 cups of rice to produce 12 servings of rice. The number of servings that can be made from 2 cups of rice can be used to determine this. 5 servings can be produced from 2 cups of rice. This indicates that 2/5 of a cup of rice is needed for each serving. Divide 12 by 5 to see how many cups of rice are required for 12 servings. This results in 2.4 cups of liquid. Round the amount up to the nearest whole number, which is 6 cups, to make 12 servings. 6 cups of rice are therefore required to make 12 servings.

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The absolute value function on the graph is:

f(x) = -|x + 4| - 5

Remember that an absolute value function that has a vertex at (a, b) will be written as:

f(x) = |x - a| + b

Here the vertex is at (-4, -5), replacing that in the general formula we will get:

f(x) = |x + 4| - 5

And we also can see that the absolute value function opens downwards with slopes of 1, then there must be a leading coefficient of -1, the actual function is:

f(x) = -|x + 4| - 5

That is the graphed function.

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Answer:

the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer

Step-by-step explanation:

To factor the equation 2 - 8 + 33 = 0, we start by collecting all the terms on one side of the equation:

2 - 8 + 33 = 0

becomes

33 - 8 + 2 = 0

Next, we can rewrite this as:

33 - 6 = 0

Finally, we factor the left-hand side of the equation to get:

33 - 6 = (33 - 3) - 3 = 30 - 3 = 27 - 0

So the factored form of the equation 2 - 8 + 33 = 0 is 27 = 0.

Verification: We can verify that the factored form of the equation is correct by substituting 0 for 27 and checking that the equation holds. So, if we replace 0 for 27 in equation 27 = 0, we get:

27 = 0, which is true.

Therefore, the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer.

Answer:

TRIANGLE PROBLEM:

area : 6a^4

perimeter : 12a^2

SIMPLIFY problem:

-40c^2+26a^2+30ac

EVALUATE & FACTOR:

(q^2 - p) ( p^2 - q)

and the solved form is 240

hope it helps :)

Step-by-step explanation:

lol im an rsm kid too. but i hope these are right,

first i'm gonna start with 263 c.

AREA = 4a^2 * 3a^2 divided by 2.  

12a^4 divided by 2 = 6a^4.

AREA = 6a^4

Perimeter you can find with the pythag. th.

(4a^2) ^2 + (3a^2 ) ^2 = c^2

16a^4 + 9a^4 = c^2

, the missing side is 5a^2

therefore the perimeter is 4a^2 + 3a^2 + 5a^2 = 12a^2

ok next, im gonna do 266

the answer is -40c^2+26a^2+30ac

make sure to check this w/ symbo or mthway

ok last one!!

factored form is (q^2 - p) ( p^2 - q)

and the solved form is 240

A square of 10 cm on each side has four quarter circles drawn with centers at the four corners, then the area of the shaded region is 21.46 centimeter square

The side of the square a = 10 cm

The area of the square = a^2

Substitute the values in the equation

The area of the square = 10^2

= 100 centimeter square

There are 4 quarter circle in the figure. We know 4 quarter circle is one circle

The area of the circle = πr^2

Where r is the radius of the circle

The radius of the circle = 5 cm

The area of the circle = π × 5^2

= 78.54 centimeter square

The area of the shaded region = The area of the square - The area of the circle

= 100 - 78.54

= 21.46 centimeter square

Therefore, the area of shaded region is 21.46 centimeter square

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