if $m$ is a real number and $x^2 mx 4$ has two distinct real roots, then what are the possible values of $m$? express your answer in interval notation.

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:

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:

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

By using the concept of combinations, we have determined that there are 210 three-digit numbers that can be formed using the digits 0-6 without repeating any of them. Among them, there are 90 odd numbers and 120 numbers greater than 330.

Combinations are a fundamental concept in mathematics, particularly in the field of combinatorics, which deals with counting and arranging objects.

To solve this problem, we can use the concept of combinations, which is a way of counting the number of ways we can choose k items from a set of n items. In this case, we want to find the number of three-digit numbers we can form from the set {0, 1, 2, 3, 4, 5, 6}, without repeating any of the digits.

First, we can determine the number of ways we can choose the first digit. Since there are seven digits to choose from, we have 7 options for the first digit.

Next, we can determine the number of ways we can choose the second digit. Since we have already used one of the digits, we only have 6 options left for the second digit.

Finally, we can determine the number of ways we can choose the third digit. Since we have used two of the digits, we only have 5 options left for the third digit.

Therefore, the total number of three-digit numbers we can form is given by the product of the number of choices for each digit:

7 x 6 x 5 = 210

So there are 210 different three-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, and 6, without repeating any of the digits.

To find the number of odd numbers, we need to consider that the last digit must be either 1, 3, or 5, since these are the only odd digits in the set. We can choose the first two digits in the same way as before, and then choose one of the three odd digits for the last digit. Therefore, the number of odd three-digit numbers is:

6 x 5 x 3 = 90

To find the number of three-digit numbers greater than 330, we need to consider that the first digit must be either 3, 4, 5, or 6. We can choose the first digit in 4 ways, and then choose the remaining two digits as before. Therefore, the number of three-digit numbers greater than 330 is:

4 x 6 x 5 = 120

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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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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 length of earthworm will be 4 cm after 4 hours. And the length is 14 cm after 49 hours.

Proportions are defined when two or more ratios are made to be equal to each other.

Two quantities are said to be directly proportional if a positive change in one quantity also lead to a positive change in the other quantity.

If a is proportional to b, we denote it as a ∝ b.

Given,

Length of an earthworm, l ∝ square root of the number of hours, n, which have elapsed since it's birth.

l ∝ √n

l = k √n, for some constant k.

If a worm is 2 cm long after 1 hour, we can write it as,

2 = k × √1

⇒ k = 2

So the proportionality constant is 2.

After 4 hours,

l = k √4

l = 2 × 2 = 4 cm

If the length is 14 cm,

14 = 2 √n

√n = 14 / 2

√n = 7

n = 7² = 49 hours

Hence the length of worm is 4 cm after 4 hours. It will take 49 hours to grow to a length of 14 cm.

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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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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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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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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.

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 simplest form of the fraction equivalent to 0.7 is 7/10

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, to show the denominator of the fraction in the simplest form that is equal to 0.7

To convert 0.7 into a fraction, we have to write it in p/q form, where p and q are positive integers.

we can write .7 as 0.7/1

now to remove the decimal point we will multiply and divide by 10

therefore,

0.7/1 ×  10/10  = 7/10

Hence, the simplest form of the fraction equivalent to 0.7 is 7/10

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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$

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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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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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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Note that the body starts "with an initial velocity and moves with uniform acceleration."(Option C)

In mechanics, acceleration is defined as the rate of change of an object's velocity with respect to time. Vector quantities are accelerations. The orientation of an object's acceleration is determined by the orientation of its net force.

The distance covered by the particle in nth second

Sₙ = u + a/2(2n-1)

S₈ = 20m

S₈ = u + a/2(2x(8-1)

20 = u + 7.5a ...................()

S₉ = 22 = u + a/2(2*9-1)

22 = u + 8.5a ..................(2)

By solving equations 1 and 2 we have :

u=5m/s , a=2m/s²

Thus,

S₁₀ = u+ a/2(2*10-1)

S₁₀ = 5 + 1/2 * 2 (2 * 10-1)

S₁₀ = 5 + 19

S₁₀ = 24m

Thus, it is correct to state that the body starts with the initial velocity and moves with uniform acceleration, and the correct option is C.

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Full Question:

A body covers 20 m, 22 m, 24 m, in 8th, 9th, and 10th seconds respectively. The body starts:

from rest and moves with uniform velocity.

from rest and moves with uniform acceleration.

with an initial velocity and moves with uniform acceleration.

with an initial velocity and moves with uniform velocity.

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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There are 10 cars in a race, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.

An arrangement of particulars in a specific order is appertained to as a permutation. Then, the factors of sets are arranged in a direct or successional order. For case, the set A = ,6 has a permutation of 2, which is. There's no other way to organise the factors of set A, as you can see.

There are 10 cars in the race,

Three cars finish the race in the 1st ,2nd and 3rd order

1st finish the race have 10 chances

P(A) = 10

2nd finish the race have 9 chances

P(B) = 9

3rd finish the race have 8 chances

P(C) = 8

The number in which this can be put,

= P(A) x P(B) x P(C)

= 10*9*8

=720 ways

Therefore, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.

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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 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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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.

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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Answer:

Step-by-step explanation:

Answer:

3x² + 9x + 1

Step-by-step explanation:

5x - 2 + 3x² + 4x + 3

= 9x - 2 + 3x² + 3

= 9x + 1 + 3x²

= 3x² + 9x + 1

We have drawn the graph for the given inequality.

What is inequality?

Inequality is a mathematical statement that compares two values or expressions and shows their relative size. It is represented by the symbols >, <, ≥, or ≤, which respectively mean "greater than", "less than", "greater than or equal to", and "less than or equal to". Inequalities can also include variables and can be used to describe a range of possible values for that variable.

For the given inequality y ≤ 3/5x-5

we can draw the graph as shown below:

Hence, we have drawn the graph for the given inequality.

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the probability that it will rain on the following day, given that it rained tomorrow, is 0.75. Rounded to three decimal places, the answer is 0.750.

Given the probabilities, you can use Bayes' theorem to calculate the probability that it will rain on the following day, given that it rained tomorrow. Bayes' theorem states that: P(A|B) = P(B|A) * P(A) / P(B)

Where: P(A|B) is the likelihood that event A will occur assuming event B has already happened. P(B|A) is the probability of event B given that event A has occurred. The prior probability of event A is P(A). The prior probability of event B is P(B).

In this case, let A be the event that it rains on the following day and B be the event that it rains tomorrow.

So, P(A|B) = P(B|A) * P(A) / P(B) = 0.9 * 0.3 / P(B)

To calculate P(B), you can use the total probability theorem:

P(B) = P(B|A) * P(A) + P(B|~A) * P(~A) = 0.9 * 0.3 + 0.08 * 0.7 = 0.327

Now, you can substitute the values into the formula for P(A|B) to get:

P(A|B) = 0.9 * 0.3 / 0.327 = 0.75

So, the probability that it will rain on the following day, given that it rained tomorrow, is 0.75. Rounded to three decimal places, the answer is 0.750.

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