Here are the hottest recorded temperatures (ln^ F) for eight cities throughout North America. Complete the grouped frequency distribution for the data. In the distribution, the frequency of a class is the number of temperatures that class. (Note that we are using a class width of 5.)

Answer: AE

Step-by-step explanation:

if you look at the picture you can tell that Ae is a ray because rates tend to have 2 points and 2 sides one going on forever. that's why there's an arrow near "a"

Answer:

Equation of perpendicular line:

[tex]\boxed{\quad y=-\dfrac{1}{2}x+\dfrac{7}{2}\quad }[/tex]

Step-by-step explanation:

Generalized lope-intercept form of a line is y = mx + b    [1]

where

m = slope

b = y-intercept

Equation of the given line is y = 2x - 1           [2]

We are asked to find the equation of the line perpendicular to this and also passes through (1, 3)

The width of the floor if the length is (x - 13) units is (x+13) units.

The area of Rectangle is length times of width.

Given that area of the floor is (x²-169) sq units.

We have to find the width of the floor when  length is (x - 13) units.

Area=Length×Width

x²-169=(x-13)width

We know that (a²-b²)=(a+b)(a-b)

(x-13)(x+13)=x-13width

Divide both sides by (x-13)

x+13=width

Hence, the width of the floor if the length is (x - 13) units is (x+13) units.

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Answer:

A composite figure is made up of simple geometric shapes. To find the area of a composite figure or other irregular-shaped figure,divide it into simple, nonoverlapping figures. Find the area of each simplerfigure, and then add the areas together to find the total area of the compositefigure

Step-by-step explanation:bc of the way u gave it im showing it to u

The values of x for the given equations are:

1. The value of x = 0

2. The values of x are ±1

3. The values of x are 0 and -7/16

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

To find the values of x in each of the equations, we need to simplify them using algebraic operations:

1. 8x² = 6x² + 5x²

Combining like terms on the right-hand side:

8x² = 11x²

Subtracting 6x² from both sides:

2x² = 0

Dividing both sides by 2:

x² = 0

Taking the square root of both sides:

x = 0

Therefore, the only solution to this equation is x = 0.

2.Similarly, we can calculate values of x for this equation:

-7x² + 6 = x² - 7x²

x² = 1

Taking the square root of both sides:

x = ±1

Therefore, the solutions to this equation are x = 1 and x = -1.

3. 7x² + 9x² = -6x² - 7x

x(16x + 7) = 0

Using the zero product property:

x = 0 or 16x + 7 = 0

Solving for x in the second equation:

16x = -7

Dividing both sides by 16:

x = -7/16

Therefore, the solutions to this equation are x = 0 and x = -7/16.

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Answer:

Area of rectangle = [tex]\mbox{\large \boxed{\textrm{65 sq. inches}}}[/tex]

Step-by-step explanation:

Let square side = [tex]a[/tex]

Area of square   [tex]A = a^2[/tex]

Given [tex]A = 81[/tex]  and equating it to [tex]a^2[/tex]
[tex]a^2[/tex] [tex]= 81\;in^2[/tex]

[tex]a = \sqrt{81} = 9\;in[/tex]

Perimeter of square = [tex]4a = 4\cdot 9 = 36 \;in[/tex]

If [tex]l[/tex] = length of the rectangle and [tex]w[/tex] = width

Perimeter P of rectangle = [tex]2(l + w)\\[/tex]

Given perimeter of rectangle = perimeter of square we get
[tex]2(l + w) = 36\\\\l + w = 36/2\\\\l + w = 18[/tex]

Given

[tex]w = 5\\\\l + 5 = 18\\\\l = 18 - 5 = 13\\\\[/tex]

[tex]\\\\\textrm{Area of rectangle } = l \times w\\\\= 13 \times 5 \\\\= 65 \;sq.\;inches[/tex]

The Larger number is 8

What is a linear equation in one variable?

The fundamental equation used to represent and solve for an unknown quantity is a linear equation in one variable. It is always a straight line, and it is simply shown graphically. A mathematical statement is simply represented by a linear equation.

Given that, the sum of two numbers is 14 and the larger number is four less than twice the smaller number

let the larger number be 'a' and the smaller be 'b'

from the question,

a + b = 14 .....eq 1

a = 2b - 4 .....eq 2

By substituting eq 2 in eq 1:

2b - 4 + b = 14

3b - 4 = 14

3b = 14 + 4 = 18

b = 6

a = 2b - 4 = 2*6 - 4 = 8

Therefore, The two numbers are 8, 4

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Answer:

Step-by-step explanation:

The answer is 4x^2y+8x^3+y^2-2xy

The values of x for which f(x) = g(x) are -1 and 4

From the question, we have the following parameters that can be used in our computation:

f(x) = -2x + 4

g(x) = x^2 - 5x

Using the above as a guide, we have the following:

Using the above as a guide, we have the following:

x = -1 and x = 4

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Note that the r-value of the above data is : -0.903 (Option A)

In mathematics, the r-value typically refers to the correlation coefficient, which measures the strength and direction of the linear relationship between two variables.

With regard to the above data:

A) Find the Sum of the X values: 4 +5+8+9+13 = 39

B) Find the Sum of the Y values: 23 +12 +10 +9 +2 = 56

C) Find the Sum of x^2: 4^2 + 5^2 + 8^2 + 9^2 +13^2 = 355

D) The sum of the Y^2's: 23^2 + 12^2 + 10^2 + 9^2 + 2^2 = 858

E) Sum of x *y's: 4*23 + 5*12 + 8*10 + 9*9 + 13*2 = 339

N = number of sets = 5

Numerator of r = (E - A*B/N) = 339-39*56/5 = 339 - 436.8 = -97.8

Denominator of r = SQRT(C-A^2/N) x SQRT(D-B^2/N) =

SQRT(355-39^2/5) x SQRT(858-56^2/5) =

SQRT(50.8) x SQRT(230.8) =

7.1274 x 15.1921 =

108.2803

r = -97.8 / 108.2803

r = -0.903

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The average rate of change of the function over the interval [2,3] will be around 3.

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

For example to draw the equation y = 3x +2 this will draw a straight line in the coordinate geometry.

The rate of change is given by dy/dx

The average rate of change can be given as:

= (difference in y coordinate)/(difference in x coordinate)

= Δy/Δx

Average rate of change = ( 11 - 8 )/(3 - 2 )

                                        = 3

Hence, the average rate of change is 3

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Peter's study is an example of a cross-sectional clinical study that investigates three pre-defined groups of patients with the same neurological syndrome by examining both the average score for each group and the scores for individual patients.

Cross-sectional study that compares three groups of patients with the same neurological syndrome. In this type of study, the researcher examines the groups at a specific point in time to obtain information about the prevalence, incidence, and characteristics of the disease or condition being studied. By examining both the average score for each group and the scores for individual patients, Peter is able to draw conclusions about the relationship between the neurological syndrome and the factors being studied. This type of study can help to identify risk factors, determine the efficacy of treatments, and guide future research in the field.

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∠5 is the alternate interior angle of ∠3.

What is transversal?

A transversal is a line that, at two different points in the geometry, cuts through two lines in the same plane. Various types of angles in pairs, including consecutive interior angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.

When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairs of that transversal. Alternate interior angles are what they are called.

Line m and line n are parallel and line l is transversal.

The alternate pairs of that transversal are ∠3 and ∠5.

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The toy rocket will hit the ground after approximately 3.86 seconds.

The rocket will hit the ground when its height is equal to zero, so we can use the equation h = -4.97t^2 + 38.5t + 5.6 to find the value of t that satisfies this condition. To do this, we set h equal to zero and solve for t:

0 = -4.97t^2 + 38.5t + 5.6

-5.6 = -4.97t^2 + 38.5t

4.97t^2 - 38.5t - 5.6 = 0

This is a quadratic equation and can be solved using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 4.97, b = -38.5, and c = -5.6.

Plugging in these values, we get:

t = (-(-38.5) ± √((-38.5)^2 - 4 * 4.97 * -5.6)) / (2 * 4.97)

t = (38.5 ± √(1466.25 + 113.92)) / 9.94

t = (38.5 ± √1580.17) / 9.94

The square root of 1580.17 is 39.67, so:

t = (38.5 ± 39.67) / 9.94

t = (38.5 + 39.67) / 9.94 or (38.5 - 39.67) / 9.94

The first solution gives us a time of approximately 3.86 seconds, while the second solution is negative and therefore represents an unrealistic result.

The toy rocket will hit the ground after approximately 3.86 seconds.

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Answer:

170 feet per second

Step-by-step explanation:

To answer the question you need to find the unit rate. To find the unit rate divide the denominator with the numerator in a way that the denominator becomes 1.

5,100/30 = 170

The skydiver falls at a rate of 170 feet per second before opening the parachute.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

It takes a skydiver 30 seconds to fall 5,100 feet before opening the parachute.

Hence, Height for this is,

⇒ 5100 / 30

⇒ 170 feet per second

Thus, the skydiver falls at a rate of 170 feet per second before opening the parachute.

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The probability of the flight being overbooked is 0.38742 or 38.7%.

To calculate the probability of the flight being overbooked, we need to use a probability formula. In this case, we can use the binomial probability formula. The formula is as follows:

[tex]P(x) = ^nC_x * p^x * q^{(n-x)}[/tex]

Where:

P(x) is the probability of x number of events occurring.

n is the total number of trials.

p is the probability of success.

q is the probability of failure.

nCx is the number of ways to choose x items from a set of n items.

Let's say a plane has 8 seats. The airline sells 10 tickets for this flight. The probability of all ten passengers showing up for the flight is quite low. Based on past experience, the airline knows that only 90% of ticketed passengers usually show up for a flight. This percentage is also known as the "show-up rate."

In our case:

n = 10 (total number of passengers)

p = 0.9 (probability of a passenger showing up)

q = 0.1 (probability of a passenger not showing up)

We want to find the probability of having more than 8 passengers show up, which would mean the flight is overbooked. To do that, we need to calculate the probability of having 9 or 10 passengers show up. We can use the formula to calculate this:

P(9 or 10) = P(9) + P(10)

P(9 or 10) = ¹⁰C₉ x 0.9⁹ x 0.1¹ + ¹⁰C₁₀ x 0.9¹⁰ x 0.1⁰

P(9 or 10) = 0.38742 or 38.7%

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Complete Question:

Airlines usually overbook for a flight (sell more tickets than the numbers of available seats). They do this because they know from past experience that only 90% of ticketed passengers actually show up for the flight.

A plane has 8 seats. If the airline sells 10 tickets for this flight, what is the probability that the flight will be overbooked?

If so far the George's string is 44 inches long , then his string is not long enough , so he need to make it longer .

To find whether George's string is long enough, we first convert both measurements to same unit of measurement.

that means we convert length of the string in inches to feet by dividing it by 12 ; because  there are 12 inches in a feet  ;

⇒ (44 inches)/(12 inches/feet)  

⇒ 3.67 feet  ;

The George's string is currently 3.67 feet long and he needs a string that is 4 feet long  .

So , his current string is not long enough and he needs to make it longer. He needs to add another 0.33 feet to his string  .

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The given question is incomplete , the complete question i

George needs a string that is 4 feet long. So far his string is 44 inches. Is it long enough or does he need to make it longer ?

Answer:

Step-by-step explanation:

The exchange rate between the South African Rand (ZAR) and the Kenyan Shilling (KES) fluctuates daily. As of my training data cut off in 2021, the exchange rate was approximately 1 ZAR = 10.87 KES.

So, 30 South African Rand would be equivalent to approximately 329.10 Kenyan Shillings. However, it is important to note that exchange rates can change over time, so it is always a good idea to check a reliable source for the most up-to-date conversion rate before making any currency exchanges.

The expression to measure {x} can be written as -

{x - 10} + {2x +40} + 90 = 180

We can write the Pythagoras theorem as - The sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.

Mathematically -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right triangle ABC

We an write the expression to measure {x} as -

{x - 10} + {2x +40} + 90 = 180

Therefore, the expression to measure {x} can be written as -

{x - 10} + {2x +40} + 90 = 180

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The value of the functions at 9m is

Generally, In mathematics, a function is a rule that maps one set of values (the domain) to another set of values (the range). The values in the range are determined by applying the function to the values in the domain.

Functions can take many forms and be expressed in different ways, including:

Linear functions: a function that produces a straight line when graphed. It has the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.

Quadratic functions: a function that produces a parabola when graphed. It has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Therefore, this function

- f(x) = 4x

g(x) = 9x¹/2

for

F(x)=4x

F(9)=4*9

f(9)=36

for

g(x) = 9x¹/2

g(9)=9√9

=27

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Answer:

So the simplified expression is:

2x - 4 / (x^2 + 9x + 20)

Step-by-step explanation:

To simplify the expression, we need to simplify the numerator and denominator separately, and then simplify the entire expression.

Starting with the numerator:

4x^2 + 12x - 16

For the denominator:

The first fraction: 2x + 10 can be simplified as follows: 2x + 10 = (2)(x) + (2)(5) = 2x + 10

The second fraction: 6x + 24 over x^2 + 9x + 20

We can simplify the denominator by using partial fraction decomposition. To do that, we need to write the denominator as a sum of simpler fractions, each with a numerator that is a constant. In other words, we write:

6x + 24 / (x^2 + 9x + 20) = (A x + B) / (x^2 + 9x + 20) + (C x + D) / (x^2 + 9x + 20)

Multiplying both sides by the denominator, we get:

6x + 24 = (A x + B)(x^2 + 9x + 20) + (C x + D)(x^2 + 9x + 20)

Expanding the right-hand side, we obtain:

6x + 24 = Ax^3 + (A 9 + B) x^2 + (A 20 + B 9 + C) x + (B 20 + D)

Comparing the coefficients of the polynomials on both sides, we get the following system of linear equations:

A = 0

B = 6

C = 0

D = -24

Therefore, the partial fraction decomposition of the denominator is:

6x + 24 / (x^2 + 9x + 20) = (6x + 24) / (x^2 + 9x + 20)

Putting it all together, we have:

4x^2 + 12x - 16 / (2x + 10) / (6x + 24) / (x^2 + 9x + 20) = (4x^2 + 12x - 16) / (2x)(6x + 24) / (x^2 + 9x + 20) = 2x - 4 / (x^2 + 9x + 20)

So the simplified expression is:

2x - 4 / (x^2 + 9x + 20)

Answer:

28 cups of Flower

Ratio Table:

2,4,6,8

7,14,21,28

Step-by-step explanation:

2x4/7x4=8/28

The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution, with a probability of success of 10.5%.

The binomial distribution has certain properties, such as the mean and variance, that can be used to make inferences about the population. For example, the mean of the distribution is given by:

μ = np

where n is the sample size and p is the probability of success.

The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution. The binomial distribution describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In our case, a success is a person with diabetes, and the probability of success is the prevalence of diabetes in the population, which is 10.5%. The number of trials is 100, which is the sample size. Therefore, the distribution of the number of people with diabetes in our sample can be written as:

X ~ B(100, 0.105)

Where X is the random variable representing the number of people with diabetes in our sample, and B(100, 0.105) denotes the binomial distribution with 100 trials and a probability of success of 0.105.

In our case, the mean number of people with diabetes in our sample is:

μ = 100 x 0.105 = 10.5

This means that we expect, on average, to find 10.5 people with diabetes in our sample of 100.

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The probability that 2 or fewer tomato seeds germinate out of 10 planted, given a germination rate of 43%, is 0.586 or 58.6%.

To calculate the probability that 2 or fewer seeds germinate, we need to use the binomial distribution, where:

In this case, n = 10, p = 0.43, and we want to find the probability that 0, 1, or 2 seeds germinate. We can calculate this probability as the sum of the probabilities of each of these outcomes:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

where X is the random variable representing the number of seeds that germinate.

Using the binomial distribution formula, we can calculate the probability of each outcome:

P(X = k) = (n choose k)[tex]* p^k * (1 - p)^{(n - k)}[/tex]

where (n choose k) is the binomial coefficient, equal to [tex]n! / (k! * (n - k)!)[/tex].

Plugging in the values, we get:

P(X = 0) = (10 choose 0) [tex]* 0.43^0 * 0.57^{10}[/tex] = 0.057

P(X = 1) = (10 choose 1) [tex]* 0.43^1 * 0.57^9[/tex] = 0.205

P(X = 2) = (10 choose 2) [tex]* 0.43^2 * 0.57^8[/tex] = 0.324

Therefore,

[tex]P(X \leq 2)[/tex] = [tex]0.057 + 0.205 + 0.324[/tex] = 0.586

So the probability that 2 or fewer seeds germinate is 0.586, or 58.6%.

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Answer:

164 cm^2

Step-by-step explanation:

lets find square of triangle first

corner ABD is 90 degrees coz corner ABC is 180 degrees and EBC is 90

(sum of all angles of a quadrilateral is 360,

B = 360 - C - F - E

360 - 90 - 90 - 90 = 90)

BD = CF - DE

BD = 16 - 8 = 8 cm

S ABD = AB * BD / 2 (coz corner B is 90 degrees)

S ABD = 13 * 8 / 2 = 13 * 4 = 52 cm^2

lets find square of BEFC next

S BEFC = CF * EF ( B = C = F = E = 90 so thats a rectangle)

S BEFC = 16 * 7 = 70 + 42 = 112 cm^2

finally lets find total area

S = S ABD + S BEFC = 52 + 112 = 164 cm^2

Miss Carol's bank account is losing money at a daily rate of $15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

We must calculate Miss Carol's account balance's daily decline in order to ascertain the rate of change in her bank account.

Since Miss Carol lent her friend $65 this month, her account balance is reduced by $65, leaving her with $500 - $65 = $435.

The information that her account is losing $15 every day can then be put to use. We can write this as:

Rate of change = -$15 per day

The negative symbol signifies a declining amount on her account.

Therefore, Miss Carol's bank account is losing money at a daily rate of

$15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

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The percentage of the shipping crate when compared to the total weight of the shipment would be = 16%

The weight of two granite specimen = 22 pounds

The weight of the crate = 20 pounds

The weight of shipping crate = 8 pounds

The total weight of the whole shipment = 22+20+8 = 50 pounds.

Therefore the percentage of shipping crate as compared to the total weight;

= 8/50 × 100/1

= 800/50

= 16%

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The probability of committing type 1 error best describes notion of significance level of hypothesis test.

What is probability?

Probability is a mathematical concept used to measure the likelihood or chance of an event occurring. It is expressed as number between 0 and 1, where 0 represents an impossible event, and 1 represents certain event. The probability of an event is calculated by dividing number of favorable outcomes by total number of possible outcomes. Probability is used in various fields, including statistics, economics, finance, and science. It is used to make predictions, assess risk, and make informed decisions. Probability theory helps to explain random phenomena, such as the outcomes of a coin toss or the probability of a disease occurring in a population.

Complete Question:

Which one of the following best describes the notion of the significance level of a hypothesis test?

i) the probability of committing a type 1 error

ii) the probability of committing a type 2 error

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