Sam has 3 1/4 pounds of blueberries. Ben also has some blueberries. Together, they have 4 2/3 pounds of blueberries. Create an equation to represent the number of pounds of blueberries, b, Ben has.

The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.

To find the inverse of the given function as it is not a one to one function (has the same value f(x) for more that one value of x) you restrict the domain to get a function one to one.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

f (x) = 1/3x - 2

Find its inverse as shown below,

Add 2 to x and then divide by 1/3 as shown below,

f⁻¹(x) = (x + 2) / 1/3

f⁻¹(x) = 3(x + 2)

compare with f⁻¹(x) = a (x + 2)

a = 3

Calculate the x-intercept by putting f(x) = 0

0 = x + 2

x = -2

In a quadratic function as given use the vertex to restrict the domain; restrict the domain using coordinate x of the vertex.

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Answer: No, it is not a right triangle

Step-by-step explanation:

a=17

b=16

c=26

a^2 + b^2 = c^2 (C will always be the longest side)

17^2 + 16^2 = 26^2

49 + 256 = 676

305 is not equal to 676

Answer:

to test if this is a right triangle, test the side lengths with the Pythagorean theorem

a^2 + b^2 = c^2

Step-by-step explanation:

c is the hypothenuse, the longest side of a right triangle

a and b are the legs of the right triangle.

a = 16

b = 17

c = 26

16^2 + 17^2 = 26^2 ?

256 + 289 = 676?

545 ≠ 676

NO, this triangle is NOT a right triangle

Answer:

a. -0.004
b. -sqrt(20)/70

Step-by-step explanation:

a.

We are given that y = a(x - 70)^2 + 20

And we know that x=0 and y=0

We can substitute these values into the equation:

0 = a(-70)^2 + 20

Simplifying we get:

0 = a(4900) + 20

Subtracting 20 from both sides we get:

-20 = a(4900)

Dividing both sides by 4900 we get:

a = -20/4900

a = -20/4900 = -0.004

So the value of a is -0.004

b.
We are given that y = a(x - 70)^2 + 20

And we know that x=140 and y=0

We can substitute these values into the equation:

0 = a(140-70)^2 + 20

Simplifying we get:

0 = a(70)^2 + 20

Subtracting 20 from both sides we get:

-20 = a(70)^2

Taking the square root of both sides:

sqrt(-20) = a(70)

Dividing both sides by 70:

-sqrt(20)/70 = a

a = -sqrt(20)/70

So the value of a is -sqrt(20)/70

Answer: 69

Step-by-step explanation:

Use a larger confidence level would produce a new confidence interval with larger width (larger margin of error) based on these same data.

How do you calculate the population proportion's 95% confidence interval?

We must determine p′ and q′ in order to construct the confidence interval. p′ = 0.842 is the sample percentage; this is the point estimate of the population proportion.

                               Since CL = 0.95 is the requested confidence level, the calculation is as follows: = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) = 0.025.

What does confidence interval mean?

When you conduct your experiment again or resample the population in the same way, you may anticipate your estimate to fall inside a specific range of values a certain proportion of the time. This is known as the confidence interval.

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The total number of calories burned can be represented by the inequality 10x + 15y ≥ 600

Using the following parameters:

The inequality is

10x + 15y ≥ 600

In this case, x = 30 and y = 0.

Plugging in these values into the inequality:

10(30) + 15(0) = 300

Since 300 is less than 600, Timmykat will not burn enough calories if he only bikes for 30 minutes and doesn't run at all.

In this case, x = 0 and y = 30.

Plugging in these values into the inequality:

10(0) + 15(30) = 450

Since 450 is less than 600, Timmykat will not burn enough calories if he only runs for 30 minutes and doesn't bike at all.

See attachment

Three different scenarios where Timmykat will burn at least 600 calories a day are:

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The data set's environment variable(s) are quantified on a nominal scale.

Describe data sets?

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Answer:

AB = 49

ABC = 253

BAC = 156

ABC = 311

Step-by-step explanation:

The whole circle is 360

360 - 107 - 49 = 204  

We now know the measurement of the 3 sections shown.

AB = 49

ABC = 49 + 204 = 253

BAC = 107 + 49 = 156

ACB = 107 + 204 = 311

Answer:

Option A: (5,-2)

Step-by-step explanation:

4x - 3y = 26

3x + 2y = 11

from equ 1 make x the subject formular | equ means equation

4x - 3y = 26

4x = 26 + 3y

x = (26 + 3y)/4

Substitute x = (26 + 3y)/4 into equ 2

3((13+3y)/4) + y = 11

(39+17y)/4 + y = 11

39/4 + 17y/4 + y = 11

39/4 + 17y/4 = 11

17y/4 = 11 - 39/4

17y/4 = -17/2

17/4y/17/4 = -17/2/17/4

y = -2

Substitute y = -2 into equ 2

3x + 2y = 11

3x + 2(-2) = 11

3x - 4 = 11

3x = 11 + 4

3x = 15

3x/3 = 15/3

x = 5

(x,y) = (5,-2)

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The perimeter of a two-dimensional shape is the distance around the shape. In this case, the paperboard has a semicircle cut out of it, so the perimeter of the paperboard that remains after the semicircle is removed is the distance around the remaining rectangular shape.

To calculate the perimeter of the remaining rectangular shape, you can use the formula: 2(length + width) = 2(26 in + 20 in) = 2(46 in) = 92 in.

It is important to note that the perimeter is a measure of the distance around a two-dimensional shape and it doesn't take into account the area inside the shape. Also it is measured in units, in this case inches.

I hope this helps :)

Answer:

They have to be similar because careful inspection will show all of their angles (the two triangles) are equal.

One can start with the fact that the two triangles have a common angle.

CAll it x.

x * 40 + q = 180

x + 50 + r = 180

q and r must equal 50 and 40 to satisfy the sum of the interior angles must sum to 180.

The different values of x in the equation y = 3 sin (x + π/2) to determine the values of y for different values of x.

The equation of the trigonometric graph is given by y = A sin (Bx + C).

Here, A is the amplitude, B is the angular frequency, and C is the phase shift.

Let's assume that A = 3, B = 1, and C = π/2.

Therefore, the equation of the trigonometric graph is given by y = 3 sin (x + π/2).

To calculate the value of y, we can substitute values of x in the equation.

Let's consider x = 0.

Therefore, the value of y is given by y = 3 sin (0 + π/2).

Using the trigonometric identity sin (π/2 + x) = cos x, we get y = 3 cos 0.

Since cos 0 = 1, y = 3.

Hence, the value of y for x = 0 is 3.

Similarly, we can substitute different values of x in the equation y = 3 sin (x + π/2) to determine the values of y for different values of x.

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it depends on what x is but simplified that equation is 9x+9+x

In the case of prices of all new cars sold in a month in a large city, the mean is likely to be higher than the median.

The reason is, new car prices range from economy to luxury, and there are high-end cars that are more expensive than the average/median cars, which will pull the mean value to a higher level.

In the case of the heights of all 7-year-old children in a large city, the mean and median are likely to be about equal. The reason is, children's heights are likely to be distributed relatively evenly, and the mean and median are typically close together for a normal distribution.

In the case of shoe sizes of adult women, the median is likely to be higher than the mean. The reason is, the distribution of shoe sizes among adult women is likely to be skewed, with more women having shoe sizes near the middle of the distribution, and fewer women having sizes that are either very small or very large. This will pull the median to a higher level than the mean.

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I am pretty sure the answer is 14.5

Answer:

14.5

Step-by-step explanation:

Arrange the numbers from small to big

11, 11, 12, 13, 14, 15, 16, 16, 18, 20

If the set of data is an even number, like in this case,

Take 2 of the middle numbers:

14 and 15

Add them and divide by 2:

14+15= 29

29 ÷ 2= 14.5

Answer:

We can solve this problem using the principle of counting, specifically the handshaking lemma.

The handshaking lemma states that in a group of 2n people, where each person shakes hands with exactly one other person, the number of handshaking arrangements is equal to n!.

In this case, we have 9 people, so n = 4.5. Each person shakes hands with exactly two other people, so the number of handshaking arrangements is (4.5!) / (2!)^4 = 945.

Finally, the remainder when N is divided by 1000 is 945 % 1000 = 945.

Step-by-step explanation:

Answer: x= 0.146  or  x= -5.15

(refer to the steps I wrote down, check the image)

Let H be a nontrivial subgroup of G.

Since p and q are coprime, the only possible divisors of pq are p and q. Thus we must have either |H|=p or |H|=q. Now, by Cauchy's theorem, H must contain an element of order p or q respectively. Then, by Lagrange's theorem, the order of any element in H must divide p or q, i.e. H must be cyclicThen, H has an order of m, where m is a divisor of pq. By Lagrange's Theorem, m divides both p and q. Since p and q are prime, m must be equal to either p or q. This implies that the order of H is either p or q.

Therefore, H must be cyclic, because the order of a cyclic group is always equal to its number of elements. Thus, any nontrivial subgroup of G must be cyclic.

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Complete question:If G is a group of order pq, where p and q are primes, how could I prove that any nontrivial subgroup of G must be cyclic?

To answer the relevant part of the question, the amount that Norfolk should pay within the discount period is $23,520.

The discount period is based on the credit terms.

For instance, 2/10, n/30 show the discount and credit terms.  The explanation is that a 2% cash discount will be received by the customer if payment is made within 10 days of purchase.

Furthermore, the customer's credit period expires after 30 days.  Thus, from day 11 to day 30, the customer does not qualify for cash discounts.

The catalog list price = $40,000

Trade discount = 40%

Discounted price = $24,000 ($40,000 x (1 - 40%)

Cash discount = $480 ($24,000 x 2%)

Cash payment = $23,520 ($24,000 - $480)

Thus, Norfolk Sporting Goods will pay $23,520 if it utilizes the discount.

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The vertical line that violates the vertical line test is given as follows:

x = -3.

A relation represents a function when each input value is mapped to a single output value.

For the relation graphed, we have that at x = -3, there are two closed bounds of the function, meaning that the input x = -3 is mapped to multiple outputs and thus the relation is not a function.

This also means that a vertical line traced at x = -3 would cross the graph of  the function at two points, thus violating the vertical line test.

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If a submarine is 575 feet below sea level and is ascending at a rate of 325 feet per minute, we can use that information to determine how long it will take for the submarine to reach the surface.

The distance the submarine needs to travel to reach the surface is:

Distance = Sea level - Current depth

Distance = 0 feet - (-575 feet) = 575 feet

We can use the rate of ascent and distance to find the time it will take for the submarine to reach the surface.

Time = Distance / Rate

Time = 575 feet / 325 feet per minute

Time = 1.77 minutes

So it will take the submarine 1.77 minutes to reach the surface, assuming it continues to ascend at a rate of 325 feet per minute.

Alex's set of ordered pairs would no longer define a function if any of the following actions were taken:

A set of ordered pairs defines a function if, for every element in the domain (the set of first coordinates), there is exactly one element in the range (the set of second coordinates).

For example, if Alex's set of ordered pairs is {(1,2), (2,3), (3,4)}, it would no longer define a function if a new ordered pair of (2,5) is added to it, as it would mean that there are now two different second coordinates (3,5) for the first coordinate 2. This would violate the rule that every element in the domain must have exactly one corresponding element in the range. Similarly, removing one of the ordered pairs, changing the order of the ordered pair, or changing the domain or range would cause the set to no longer to define a function.

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The percent of dry erase markers that are red is 25

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Given;

Number of black dry erase markers= 56

Number of red dry erase markers= 14

Now,

14/56=x/100

56x=1400

x=25

Therefore, the value of red marker in percent will be 25%

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We have compared the given standard distributions based on their means and standard deviations.

What is the standard deviation?

Standard deviation is a statistical measure of the spread of a dataset, defined as the square root of its variance. It is a way to quantify the amount of variation or dispersion of a set of data values.

(a) The means and the standard deviations of both distributions (1) and (2) are the same. The only difference is that there is an outlier in (2) with the value of 20 that doesn't exist in (1)

(b) The means of both distributions (1) and (2) are the same. However, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)

(c) The means of both distributions (1) and (2) are different, Distribution (2) has larger mean than Distribution (1). Also, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)

(d) The means of both distributions (1) and (2) are different, Distribution (2) has smaller mean than Distribution (1). Also, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)

Hence, we have compared the given standard distributions based on their means and standard deviations.

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The greatest prime factor of 2516 is 11, so the answer is A. 11

What is the prime factor?

A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11,

We can use the process of counting to find the sum of all the numbers in S.

For one-digit numbers, there are 2 possibilities (0 or 1).

For two-digit numbers, there are 2 x 2 = 4 possibilities (00, 01, 10, 11).

For three-digit numbers, there are 2 x 2 x 2 = 8 possibilities (000, 001, 010, 011, 100, 101, 110, 111).

For four-digit numbers, there are 2 x 2 x 2 x 2 = 16 possibilities (0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111).

So, the sum of all the numbers in S is

2 + 4(1+2+3+4) + 8(1+2+3+4+5+6+7+8) + 16(1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16)

We can simplify this expression as

2 + 4(10) + 8(36) + 16(136)

The sum of all the numbers in S is equal to 2 + 40 + 288 + 2176 = 2516.

Hence, The greatest prime factor of 2516 is 11, so the answer is A. 11

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Answer: D

Step-by-step explanation: A box of apples consists of 20 apples. Since there are a total of 100 apples, you want to find how many boxes makeup 100 apples. 100/20. Then, you would want to multiply that by the cost of each box (i.e. 5 boxes times 17). This is what is done in D when  the order of operations is followed.

The function uniqueItems takes a list of items and a maximum number of item deletions and returns the number of unique items remained in the bag.

def uniqueItems(items, m):

 uniqueItems = set(items)

 return len(uniqueItems) - m

items = [1,2,3,4,5,6]

m = 2

print(uniqueItems(items, m)) # 4

# First, we create a set using the items list to get a collection of unique items

uniqueItems = set(items)  # {1, 2, 3, 4, 5, 6}

# Then, we subtract the maximum number of items to be deleted from the length of the set to get the number of unique items remained

return len(uniqueItems) - m  # 4

The function uniqueItems takes a list of items and a maximum number of item deletions and returns the number of unique items remained in the bag.

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The inequality that can be used to solve the possible values of the number is 11 + 3/4x < 112 where the number x is x < 134 2/3

sum of 11 and three-fourths of a number is less than 112.

Let

The unknown number = x

11 + 3/4x < 112

Subtract 11 from both sides

3/4x < 112 - 11

3/4x < 101

divide both sides by 3/4

x < 101 ÷ 3/4

multiply by the reciprocal of 3/4

x < 101 × 4/3

x < 404/3

x < 134 2/3

Therefore, the inequality which represents the situation is 11 + 3/4x < 112.

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Answer: imma be honnest im just trying to get points rn.

Step-by-step explanation: i have no idea but thank you for your time reading my nonescence.