Between which two integers does 7/3 lie Answer A 4 and 5 Answer B 1 and 2 Answer C 2 and 3 Answer D 3 and 4

Answer:

f(x) is the blue graph, g(x) is the red graph.

x^2 - 3x + 17 - (2x^2 - 3x + 1) = 16 - x^2

16 - x^2 = 0 when x = -4, 4

So the area between these two graphs is (using the TI-83 graphing calculator):

fnInt (16 - x^2, x, -4, 4) = 85 1/3

The two column proof is written as follows

Statement                                                           Reason

MA = XR                                           given (opposite sides of rectangle)

MK = AR                                           given (opposite sides of rectangle)

arc MA = arc RK                               Equal chords have equal arcs

arc MK = arc AK                               Equal chords have equal arcs

An arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.

If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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The probability that the total shown on the two dice after they are rolled is greater than or equal to 8 is 1/9.

For a percentage data of students who play the different game and win the prize, the expected amount to pay for prizes for that booth by the carnival committee is equals to the $218.70.

We have a booth of school carnival in past years, The percentage of students win a stuffed toy = 22%

The percentage of students win a jump rope = 16%

The percentage of students win a t-shirt

= 6%

The winning amount for stuffed toy game = $ 3.60

The winning amount for jump rope game = $1.20

The winning amount for t-shirt game

= $7.90

The remaining students do not win a prize. Now, total number of students play the game at the booth = 150

So, number of students who win stuffed toy = 22% of 150 = 33

Number of students who win jump rope = 16% of 150 = 24

Number of students who win stuffed toy

= 6% of 150 = 9

For determining the expected pay using the simple multiplication formula. Total expected pay for prizes for that booth is equals to the sum of resultant of multiplcation of number of students who play a particular game into pay amount for that game. That is total excepted pay in dollars = 3.60 × 33 + 1.20 × 24 +7.90 × 6

= 218.7

Hence required value is $218.70.

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Step-by-step explanation:

Again, using similar triangle ratios

7.2 m  is to 2.4 m  

     as   AB is to  12.0 m

7.2 / 2.4  = AB/12.0    Multiply both sides of the equation by 12

12 *   7.2 / 2.4   = AB = 36.0 meters

Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:

sin^2(a) + cos^2(a) = 1

sin^2(a) + (-5/9)^2 = 1

sin^2(a) = 1 - (-5/9)^2

sin^2(a) = 1 - 25/81

sin^2(a) = 56/81

Taking the square root of both sides:

sin(a) = ±sqrt(56/81)

Since a is in quadrant III, sin(a) is positive. Therefore:

sin(a) = sqrt(56/81) = (2/3)sqrt(14)

Answer:

Jaxon made 11 free throws over the season.

Step-by-step explanation:

If he made 5% of his free throws, we know that he will make 5% of the total number of free throws he took, which is 220:

We multiply 220 by 0.05, or 5% to find out how many free throws he made:

220*0.05 = 11

After that, we now know that Jaxon made 11 of his free throws out of 220 over the course of the season, or 5%.

The resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

Expressions in writing are made using mathematical operators such as addition, subtraction, multiplication, and division.

For instance, "4 added to 2" will have the mathematical formula 2+4.

So, we have the expression:

= x² + 10x + 24

Now, solve when x = 3 as follows:

= x² + 10x + 24

= 3² + 10(3) + 24

= 9 + 30 + 24

= 63

Therefore, the resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.

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Correct question:

Evaluate the expression when x = 3.

x² + 10x + 24

a. 81

b. 86

c. 63

d. 60

Answer:

a 1053

b 250

multiply 650 by 1.62 for part a.

for part b divide by 1.62 since pound is less than dollar

hope this helps :)

The logical assumption used is: An arithmetic sequence is a set of discrete values, whereas a line is a continuous set of values.

An arithmetic sequence is a set of numbers where, with the exception of the first term, each term is obtained by adding a fixed constant to the term before it. Every pair of following terms in the sequence has the same fixed constant, which is known as the common difference. A1 stands for the first term in an arithmetic sequence, while an is used to represent the nth term.

A solid line symbolises continuous numbers, whereas the classmate's logical presumption is that an arithmetic series comprises of discrete values. This presumption is untrue, though, as a line can effectively represent an arithmetic series.

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Answer:

see the images and explanation

Step-by-step explanation:

for the graph:

the domain 0 < x < 5

the range for each functions:

g(x) = 2x + 1

g(x) = y  ,   1 < y < 11

h(x) = 2x + 2 ,  2 < y < 12

The current in the circuit when the resistance is 12 ohms is 40 amps.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.

We can use the inverse proportionality formula to solve this problem, which states that:

current (in amps) x resistance (in ohms) = constant

Let's call this constant "k". We can use the information given in the problem to find k:

24 amps x 20 ohms = k

k = 480

Now we can use this constant to find the current when the resistance is 12 ohms:

current x 12 ohms = 480

current = 480 / 12

current = 40 amps

Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.

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Answer: there is only one number

Answer:

Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.

Espero haber ayudado :D

The probability of picking one bolt and one nut is 1/2 or 50%.

To find the probability that one is a bolt and one is a nut, we need to use the formula for calculating the probability of two independent events happening together: P(A and B) = P(A) × P(B)

Let's first calculate the probability of picking a bolt from the box:

P(bolt) = number of bolts / total number of parts = 3/6 = 1/2

Now, let's calculate the probability of picking a nut from the box:

P(nut) = number of nuts / total number of parts = 3/6 = 1/2

Since the events are independent, the probability of picking a bolt and a nut in any order is:

P(bolt and nut) = P(bolt) × P(nut) + P(nut) × P(bolt)

P(bolt and nut) = (1/2) × (1/2) + (1/2) × (1/2)

P(bolt and nut) = 1/2

Therefore, the probability of picking one bolt and one nut is 1/2 or 50%.

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the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.

To find the probability that one chosen part is a bolt and the other chosen part is a nut, we need to use the formula for probability:

Probability = (number of desired outcomes) / (total number of outcomes)

There are two ways we could choose one bolt and one nut: we could choose a bolt first and a nut second, or we could choose a nut first and a bolt second. Each of these choices corresponds to one desired outcome.

To find the number of ways to choose a bolt first and a nut second, we multiply the number of bolts (3) by the number of nuts (3), since there are 3 possible bolts and 3 possible nuts to choose from. This gives us 3 x 3 = 9 total outcomes.

Similarly, there are 3 x 3 = 9 total outcomes if we choose a nut first and a bolt second.

Therefore, the total number of desired outcomes is 9 + 9 = 18.

The total number of possible outcomes is the number of ways we could choose two parts from the box, which is the number of ways to choose 2 items from a set of 6 items. This is given by the formula:

Total outcomes = (6 choose 2) = (6! / (2! * 4!)) = 15

Putting it all together, we have:

Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 18 / 15
Probability = 1.2

However, this answer doesn't make sense because probabilities should always be between 0 and 1. So we made a mistake somewhere. The mistake is that we double-counted some outcomes. For example, if we choose a bolt first and a nut second, this is the same as choosing a nut first and a bolt second, so we shouldn't count it twice.

To correct for this, we need to subtract the number of outcomes we double-counted. There are 3 outcomes that we double-counted: choosing two bolts, choosing two nuts, and choosing the same part twice (e.g. choosing the same bolt twice). So we need to subtract 3 from the total number of desired outcomes:

Number of desired outcomes = 18 - 3 = 15

Now we can calculate the correct probability:

Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 15 / 15
Probability = 1

So the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.

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Equation that represents the total number of minutes y Emily studied for the math exam is y = 40 +x.

We can represent the total number of minutes Emily studied for the math exam using the equation,

y = 40 + x

Here, 'y' represents the total number of minutes Emily studied for the math exam, '40' represents the number of minutes she studied in the morning, and 'x' represents the number of minutes she studied later that evening.

By adding the number of minutes studied in the morning to the number of minutes studied later that evening, we can calculate the total number of minutes Emily studied for the math exam.

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The radius of the water bottle which is in cylindrical shape is approximately 2.12 cm.

A cylinder is a three-dimensional shape that consists of two congruent, parallel circular bases that are connected by a curved lateral surface. The lateral surface of the cylinder is formed by a rectangle that is wrapped around the circular bases.

A cylinder can be thought of as a circular prism, where the bases are circles and the lateral surface is curved. The height of a cylinder is the perpendicular distance between the two bases, and the radius is the distance from the center of the base to the edge of the circular base.

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. We can rearrange this formula to solve for the radius:

r = √(V/πh)

Substituting the given values, we have:

r = √(150/π(8.9))

r ≈ 2.12 cm (rounded to two decimal places)

Therefore, the radius of the water bottle is approximately 2.12 cm.

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To compute the covariance matrix of the variables in the data, the "matrix-operation" which should be used is ([tex]X^{t}[/tex] × X)/n.

The "Covariance" matrix is defined as a symmetric and positive semi-definite, with the entries representing the covariance between pairs of variables in the data.

The "diagonal-entries" represent the variances of individual variables, and the off-diagonal entries represent the covariances between pairs of variables.

Step(1) : Compute the transpose of the centered data matrix X, denoted as [tex]X^{t}[/tex]. The "transpose" of a matrix is found by inter-changing its rows and columns.

Step(2) : Compute the "dot-product" of [tex]X^{t}[/tex] with itself, denoted as [tex]X^{t}[/tex] × X.

The dot product of two matrices is computed by multiplying corresponding entries of the matrices and summing them up.

Step(3) : Divide the result obtained in step(2) by the number of samples in the data, denoted as "n", to get the covariance matrix.

This step scales the sum of the products by 1/n, which is equivalent to taking the average.

So, the covariance matrix "C" of variables in "centered-data" matrix X can be expressed as: C = ([tex]X^{t}[/tex] × X)/n.

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The given question is incomplete, the complete question is

Let X be a matrix of centered data with a column for each field in the data and a row for each sample. Then, not including a scalar multiple, how can we use matrix operations to compute the covariance matrix of the variables in the data?

Step-by-step explanation:

hope this will help you Thanks

The missing angles of the diagram are:

∠1 = 118°

∠2 = 62°

∠3 = 118°

∠4 = 30°

∠5 = 32°

∠6 = 118°

∠7 = 30°

∠8 = 118°

Supplementary angles are defined as two angles that sum up to 180 degrees. Thus:

∠1 + 62° = 180°

∠1 = 180 - 62

∠1 = 118°

Now, opposite angles are congruent and ∠2 is an opposite angle to 62°. Thus: ∠2 = 62°.

Similarly: ∠3 = 118° because it is congruent to ∠1

Alternate angles are congruent and ∠5 is an alternate angle to 32°. Thus:

∠5 = 32°

Sum of angle 4 and 5 is a corresponding angle to ∠2 . Thus:

∠4 + ∠5 = 62

∠4 + 32 = 62

∠4 = 30°

This is an alternate angle to ∠7 and as such ∠7 = 30°

Sum of angles on a straight line is 180 degrees and as such:

∠8 = 180 - (30 + 32)

∠8 = 118° = ∠6 because they are alternate angles

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The correct statement regarding the null hypothesis is: the null hypothesis claims the opposite of what the researcher believes.

The null hypothesis is the claim that no relationship exists between two sets of data or variables being analyzed. The

null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative

relationship does not exist, hence the term "null".

In research, the null hypothesis is a statement of no effect or no relationship between variables, while the alternative

hypothesis represents the effect or relationship the researcher is interested in demonstrating.

The purpose of statistical testing is to determine whether there is enough evidence to reject the null hypothesis in

favor of the alternative hypothesis.

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Therefore , the solution of the given problem of unitary method comes out to be during the 4-second period, the tram's elevation changed by 3 metres every second.

To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.

Here,

By dividing the overall elevation change (12 metres) by the total time required (4 seconds),

it is possible to determine the change in the tram's elevation every second. We would then have the average rate of elevation change per second.

=> Elevation change equals 12 metres

=> Total duration: 4 seconds

=>  12 meters / 4 seconds

=> 3 meters/second

As a result, during the 4-second period, the tram's elevation changed by 3 metres every second.

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The MAD of the hourly wages given would be $ 0.48. The range would be $ 2.00. Q1 would be $8.25. Q3 would then be $9.25. The IQR would be $1.00

Calculate the MAD:

First, find the mean of the data set:

mean = (sum of all values) / (number of values)

mean = (8.25 + 8.50 + 9.25 + 8.00 + 10.00 + 8.75 + 8.25 + 9.50 + 8.50 + 9.00) / 10

mean = 88.00 / 10 = 8.80

Then, find the mean of these absolute deviations:

MAD = (sum of absolute deviations) / (number of values)

MAD = (0.55 + 0.30 + 0.45 + 0.80 + 1.20 + 0.05 + 0.55 + 0.70 + 0.30 + 0.20) / 10

MAD = 4.10 / 10 = 0.41

Calculate the range:

range = maximum value - minimum value

range = 10.00 - 8.00 = 2.00

Find Q1 and Q3:

{8.00, 8.25, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00}

Q1 is the median of the lower half, and Q3 is the median of the upper half.

Lower half: {8.00, 8.25, 8.25, 8.50, 8.50}

Upper half: {8.75, 9.00, 9.25, 9.50, 10.00}

Q1 = median of lower half = 8.25

Q3 = median of upper half = 9.25

Calculate the IQR:

IQR = Q3 - Q1

IQR = 9.25 - 8.25 = 1.00

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The estimated regression equation for the given data is y = -30.7 + 3.409x

To develop an estimated regression equation for the given data, we need to use the method of least squares.

The formula for the slope of the regression line is given by:

b = ∑(xi - x)(yi - y) / ∑(xi - x)²

where xi and yi are the individual values of the two variables, x and y are their respective means.

The formula for the intercept of the regression line is given by:

a = y - b × x

where a is the intercept and b is the slope.

Using the given data, we can calculate the values of x, y, b, and a as follows

x = (6 + 11 + 15 + 18 + 20) / 5 = 14

y = (7 + 9 + 12 + 21 + 30) / 5 = 15.8

∑(xi - x)(yi - y) = (6 - 14)(7 - 15.8) + (11 - 14)(9 - 15.8) + (15 - 14)(12 - 15.8) + (18 - 14)(21 - 15.8) + (20 - 14)(30 - 15.8) = 306.8

∑(xi - x)² = (6 - 14)² + (11 - 14)² + (15 - 14)² + (18 - 14)² + (20 - 14)² = 90

b = ∑(xi - x)(yi - y) / ∑(xi - x)² = 306.8 / 90 = 3.409

a = y - b × x = 15.8 - 3.409 × 14 = -30.7

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The given question is incomplete, the complete question is:

Given are data for two variables, x and y. Develop an estimated regression equation for these data.

Number of red counters in the original bag is 3, and the number of green counters is 7.

Let's use algebra to solve the problem. Let U be the number of red counters and G be the number of green counters originally in the bag.

From the first part of the problem, we know that

Probability (selecting a green counter) = G / (U + G) = 3/7

Solving for U in terms of G, we get

U = (7G - 3G) / 3 = 4G/3

So we know that there were 4G/3 red counters and G green counters in the bag originally. But since the number of counters must be a whole number, we can assume that there were 4R red counters and 3G green counters originally, where R and G are both integers and R + G is the total number of counters.

After adding 2 red and 3 green counters, the number of counters in the bag is now R + 2 + G + 3 = R + G + 5.

From the second part of the problem, we know that

P(selecting a green counter) = (G + 3) / (R + G + 5) = 6/13

Solving for R in terms of G, we get

R = (13G - 9G - 15) / 7 = 4G/7 - 15/7

Since R must be an integer, we can try different values of G to see if R is an integer. For example, if G = 7, then R = 3 and the total number of counters is 10.

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The given question is incomplete, the complete question is:

There are only U red counters and G green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3/7. The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6/13. Find the number of red counters and the number of green counters that were in the bag originally

The cube roots of 216 written in the rectangular (standard) form are 3 + 3√3, -3+3√3, and 6.

In mathematics, the cube root formula is used to represent any number as its cube root, for example, any number x will have the cube root 3x = x1/3. For instance, 5 is the cube root of 125 as 5 5 5 equals 125.

3√216 = 3√(2x2x2)x(3x3x3)

= 2 x 3 = 6

the prime factors are represented as cubes by grouping them into pairs of three. As a result, the necessary number, which is 216's cube root, is 6.

Therefore, the cube roots of 216 are 3 + 3√3, -3+3√3, and 6.

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Answer:

1

Step-by-step explanation:

First of all we use the "law of sines"

to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x

and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°

180°=70°+51°+ x

x = 180°-121°

=59°

Using law of sines:

(sides are represented by small letters/capital letters are the angles)

a/sinA= b/sinB= c/sinC

We have one given side which is "9"

so,

9/sin70= x/sin59

doing the criss-cross method,

9×sin59=sin70×x

9×sin59/sin70=x

x=8.2 (answer 1)

I hope this was helpful <3

It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.

The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.

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Given statement: The rule of thumb for estimating the time of completion is 1.5 times what you originally think it will be.

Given statement is True.

The reason for this rule of thumb is that tasks often take longer than initially estimated due to unforeseen challenges, dependencies, and other factors that can cause delays.

By estimating the time of completion as 1.5 times the original estimate, you are accounting for these potential delays and allowing for a more realistic timeline.

This rule of thumb is not a hard and fast rule, and there will be cases where tasks take less or more time than 1.5 times the original estimate. However, it can be a helpful guideline for project planning and resource allocation, as it helps to ensure that sufficient time and resources are allocated to complete tasks within a realistic timeframe.

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