Jeremy caught 8 fish in a contest.
The mean weight of the fish was 4.3125 kg.
He forgot to make his own record of the weight of the last fish,
but the first 7 were: 4.3 kg, 5.3 kg, 6.8 kg, 2.6 kg, 3.2 kg, 4.4 kg and 4.8 kg.
What was the weight of the last fish?
kg [2]

The functions h(x) = (x - 1)² and g(x) = -(x + 1)(x -1) key aspects shown in the picture.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a function:

h(x) = (x - 1)²

The range of the function:

y ≥ 0

The function increases over the interval (1, ∞)

The function decreases over the interval (-∞, 1)

g(x) = -(x + 1)(x -1)

The range of the function:

y ≤ 1

The function increases over the interval (-∞, 0)

The function decreases over the interval (0, ∞)

Thus, the functions h(x) = (x - 1)² and g(x) = -(x + 1)(x -1) key aspects shown in the picture.

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Answer:

B

Step-by-step explanation:

Compare triangle ABC with triangle A'B'C. Let's try to prove that they're similar.

BC = 6 + 3 = 9 units

B'C = 6 units

BC/B'C' = 9/6 = 3/2 = 1.5

AC = 2 + 4 = 6 units

A'C = 4 units

AC/A'C = 6/4 = 3/2 = 1.5

These two pairs of corresponding sides have the same ratio, so that's promising.

Also notice that angle BCA = angle B'CA'. So, by SAS Similarity Theorem, we know that triangles ABC and A'B'C are similar.

By definition, similar triangles have the same corresponding angles.

Angle ABC corresponds to angle A'B'C, so they're equal. Since angle ABC = 40 degrees, then angle A'B'C = 40 degrees, as well.

Hope this helps!

Without proper context or a diagram, it's impossible to definitively state the measure of angle A'B'C. However, as an example, if angle A'B'C is in an equilateral triangle, it would be 60 degrees.

The question appears to be asking about the measure of an angle, designated as A'B'C. However, without proper context or a diagram to reference, it's impossible to definitively state what the measure of angle A'B'C is. It can be any value depending on the context. But, if A'B'C is a part of a triangle or a particular geometric shape with known properties, we can solve it based on the information given related to that specific shape.

For example, in an equilateral triangle, each angle measures 60°. So, if A'B'C is an angle in an equilateral triangle, it would most likely be 60°. Yet, without sufficient context, this is simply a hypothetical situation.

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[tex]2x + 4 = - 8 + 5x \\ 12 = 3x \\ x = 4[/tex]

Answer:   888+88+8+8+8 = 1,000

Step-by-step explanation: First of all line all your eights' up and then split them

To add eight 8's and get the number 1000 using only addition, you can express 1000 as the sum of two numbers: 800 and 200.

To add eight 8's and get the number 1000 using only addition, you can express 1000 as the sum of two numbers: 800 and 200. Here's how:

Now, you have 24 and 32, which add up to 56. Finally, add 800 and 200, which equals 1000.

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Answer:

10 metal and 20 plastic

Step-by-step explanation:

10 x 25 is 250, 20 x 10 is 200 and 250 + 200 is 450

Answer:

you would have 80 units of space

Step-by-step explanation:

to find out how much volume there is you have to multiply the base x the width x the height so that would be 8x5x2 and 8x5 is 40 and 40x2 is 80

The box has a volume of 80 cubic inches, determined by multiplying its dimensions: length (8 inches), width (5 inches), and height (2 inches).

To determine the space available for candy in the given box, we need to calculate the volume of the box. The volume of a rectangular box can be found by multiplying its length, width, and height. Here, the box measures 8 inches in length, 5 inches in width, and 2 inches in height.

To find the volume, use the formula:

Volume = Length × Width × Height

In this case, the volume is:

Volume = 8 inches × 5 inches × 2 inches = 80 cubic inches

Therefore, the box has 80 cubic inches of space available for candy.

Answer:

yea i think yea yes yes yes yes

Final answer:

Yes, repeating decimals can be expressed as fractions using a simple algebraic equation.

Explanation:

Yes, repeating decimals can be expressed as fractions. To represent a repeating decimal as a fraction, you can use a simple algebraic equation. Let's take an example:

Consider the repeating decimal 0.3333... Now, let x be the number we want to express as a fraction. We can multiply both sides of the equation by 10 in order to move the decimal point to the right and eliminate the repeating part:

x = 0.3333...

10x = 3.3333...

Now, we subtract the two equations to eliminate the repeating part:

10x - x = 3.3333... - 0.3333...

Combining like terms:

9x = 3

Finally, dividing by 9 gives us the fraction representation of the repeating decimal:

x = 3/9 = 1/3

Answer: the minimum score required for the scholarship is 29.24

Step-by-step explanation:

Since the scores are normally distributed, it follows the central limit theorem. The formula for determining the z score is

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

Since the university plans to award scholarships to students whose scores are in the top 9%, the scores that would be qualified are scores which are at least 91%(100 - 9 = 91).

Looking at the normal distribution table, the z score corresponding to the probability value of 0.91(91/100) is 1.35

From the information given,

µ = 21

σ = 6.1

Therefore,

1.35 = (x - 21)/6.1

6.1 × 1.35 = x - 21

8.235 = x - 21

x = 8.235 + 21 = 29.24

The minimum ACT Reading score required to be in the top 9% for a university scholarship is approximately 29.2, determined by using a z-score of 1.34, the mean score of 21, and the standard deviation of 6.1.

To determine the minimum ACT Reading score required to be in the top 9% of students, and hence eligible for a scholarship at a university, we utilize the concept of z-scores in a normal distribution. A z-score indicates how many standard deviations an element is from the mean.

First, we need to find the z-score that corresponds to the top 9% of the distribution. Standard z-score tables or calculators will show that the z-score for the top 9% is approximately 1.34. This z-score means the score is 1.34 standard deviations above the mean. Next, we apply the z-score formula:

Z = (X - μ) / σ

Where:
Z is the z-score (1.34 in this case),
X is the ACT score we want to find,
μ is the mean (21 for ACT Reading),
σ is the standard deviation (6.1 for ACT Reading).

We can rearrange the formula to solve for X (the ACT score):
X = Z * σ + μ

Substituting the values we have:

X = 1.34 * 6.1 + 21

X ≈ 29.214

The minimum ACT Reading score required for the scholarship is therefore approximately 29.2 when rounded to the nearest tenth.

The probabilities of interest when rolling a pair of fair six-sided dice are: P(A) the probability of the first die being a 5 is 1/6, P(B) the probability of the second die being a 3 is 1/6, P(A and B) the probability of both events occurring is 1/36, and P(B|A) the conditional probability of B given A is equal to P(B), indicating that events A and B are independent.

When rolling a pair of fair six-sided dice, each die is independent of the other. Therefore, the sample space consists of 6 x 6 = 36 equally likely outcomes. The probability that the first die is a 5, event A, is P(A) = 1/6 because there are 6 possible outcomes for the first die and only one of them is a 5.

The probability that the second die is a 3, event B, is also P(B) = 1/6 for the same reason as A, as there are 6 possible outcomes and only one of them is a 3. Now, the probability that the first die is a 5 and the second die is a 3, both events occurring simultaneously (A and B), is P(A and B) = P(A) times P(B) which equals 1/36.

The conditional probability that the second die is a 3 given that the first die is a 5, P(B|A), is simply the probability of B since events A and B are independent, so P(B|A) = P(B) = 1/6. This implies that knowing the outcome of the first die does not change the probability of the second die rolling a 3.

Given this independence, P(B|A) = P(B), and thus events A and B are indeed independent events.

[tex](a) \( P(A) = \frac{1}{6} \)\\(b) \( P(B) = \frac{1}{6} \)\\(c) \( P(A \text{ and } B) = \frac{1}{36} \)\\(d) \( P(B|A) = \frac{1}{6} \)\\(e) No, \( P(B|A) \neq P(B) \); events A and B are dependent.[/tex]

(a) P(A), the probability that the first die is a 5:

There are 6 outcomes where the first die is a 5.

[tex]\[ P(A) = \frac{\text{Number of outcomes where first die is a 5}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6} \][/tex]

(b) P(B), the probability that the second die is a 3:

There are 6 outcomes where the second die is a 3.

[tex]\[ P(B) = \frac{\text{Number of outcomes where second die is a 3}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6} \](c) \( P(A \text{ and } B) \), the probability that the first die is a 5 and the second die is a 3:[/tex]

There is only 1 outcome where the first die is a 5 and the second die is a 3, which is (5,3).

[tex]\[ P(A \text{ and } B) = \frac{\text{Number of outcomes where both A and B occur}}{\text{Total number of outcomes}} = \frac{1}{36} \][/tex]

(d) P(B|A)  the conditional probability that the second die is a 3 given that the first die is a 5:

Given that the first die is a 5, there are 6 possible outcomes for the second die, and 1 of those outcomes is a 3 (the outcome (5,3)).

[tex]\[ P(B|A) = \frac{\text{Number of outcomes where B occurs given A}}{\text{Number of outcomes where A occurs}} = \frac{1}{6} \][/tex]

(e) [tex]\[ P(B|A) = \frac{1}{6} \neq \frac{1}{6} = P(B) \]\\Since \( P(B|A) \neq P(B) \), the events A and B are dependent, not independent.[/tex]

Answer: last option

Step-by-step explanation:

Answer:

The box plot below shows the total amount of time, in minutes, the students of a ... A vertical line is drawn inside the rectangle at the point 55. ... Part B: Calculate the interquartile range of the data, and explain in a ... (2 points) ... make the "whisker" portion longer and could potentially slightly shift the box.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

5,000 Joules of work.

Step-by-step explanation:

A 1000-watt microwave does 5000 joules of work in 5 minutes.

Work is defined as the energy transferred to or from an object by applying force along a displacement.

Given that, the power of the microwave is P = 1000 watts and the time is t = 5 s.

The work done by the microwave is given by:

W = P×t

W = 1000 × 5

W = 5000 joules

Hence, a 1000-watt microwave does 5000 joules of work in 5 minutes.

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Given:

The system of equation:

[tex]x+y = -4[/tex] -------- (1)

[tex]y = x^{2} -6x[/tex] --------- (2)

To find the values of x and y.

We will use substitution method.

From (1) we get,

[tex]y = -4-x[/tex]

We will put the value of y in (1) and we get,

[tex]-x-4 = x^{2} -6x[/tex]

or, [tex]x^{2} -5x+4= 0[/tex]

Now we will apply middle term factor method.

  [tex]x^{2} -(4+1)x+4 = 0[/tex]

     [tex]x^{2} -4x-x +4 = 0[/tex]

[tex]x(x-4)-1(x-4) = 0[/tex]

       [tex](x-4)(x-1)= 0[/tex]

so, x = 4 and 1

Now,

Substitute x = 4 in (1) we get,

[tex]y = -4-4 = -8[/tex]

And putting x = 1 in (1) we get,

[tex]y = -4-1 = -5[/tex]

Hence, the solution of the given system of equation is (4,-8) and (1,-5)

Thus, Option A is the correct answer.

Answer:

8906.4 feet

Step-by-step explanation:

The worker is walking around the park which is the circumference.

The equation for the circumference is diameter times (pi)

since the diameter is 975, you multiply 975 by pi which gives you 2968.8

Because the worker walks around the park 3 times you multiply the circumference by 3 which is 2968.8 times 3 which equals 8906.4

Therefore the worker walks 8906.4 feet a day

Answer: Option "B" is correct.

Step-by-step explanation:

Since we have given that

α= 0.10

Let the population variances are equal and samples are random and independent.

Let [tex]\bar{x}[/tex] be the mean amount spent by a customer at Burger Stop.

Let [tex]\mu[/tex] be the mean amount spent by customer at Fry World.

So, it has given that

the mean amount is spent by a customer at Burger stop is greater than the mean amount spent by a customer at Fry World.

So, Hypothesis would be :

[tex]H_0:\bar{x}=\mu\\\\H_1:\bar{x}>\mu[/tex]

Hence, Option "B" is correct.

Answer:

86

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A rational number is one that can be written in the form p/q, where p and q are whole numbers. However, [tex]4\sqrt{20} =8\sqrt{5}[/tex] cannot be simplified further. It is impossible to write it in the form of p/q, so it's not A.

An irrational number is just the opposite of a rational one: it can't be written in the form p/q. Since [tex]4\sqrt{20} =8\sqrt{5}[/tex] isn't rational, it's irrational, so B is correct.

An integer is a number without any decimal values. [tex]4\sqrt{20} =8\sqrt{5}[/tex] is approximately 17.889. Clearly, this is a decimal, so it's not C.

D is wrong because we know [tex]4\sqrt{20} =8\sqrt{5}[/tex] is irrational.

Hope this helps!

Answer:

B. An irrational number

Step-by-step explanation:

4√20 can not be written in the fraction form, hence not rational

√20 is not an integer, hence 4√20 is also not at integer

Answer:

94.5%

Step-by-step explanation:

Percent decrease can be represented as

[original price] * percentage = [new price]

When trying to find the percentage, you can manipulate the equation by dividing both sides by the original price to get:

percentage = [new price] / [original price]

In this case, this is represented by 192300/203400, or 94.5%

The median home price in the West fell from $203,400 to $192,300 then the percent decrease is 5.5%

percentage, a relative value indicating hundredth parts of any quantity.

Given that In one month, the median home price in the West fell from $203,400 to $192,300.

We have to find the percent decrease.

Percent decrease =[ (difference in price)/(original price) ] ×(100)

=203,400-192,300/203,400 ×(100)

=11100/203,400 ×(100)

=5.457 %

Hence, the median home price in the West fell from $203,400 to $192,300 then the percent decrease is 5.5%

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The scarf is $20 without tax.

The scarf is 20% off of 25, 5 is 20% of 25 so all you have to do is 25 - 5 to get your answer.

25 - 5 = 20

The sale price of the scarf , not including the tax is $20.00.

A sale price is the discounted price at which goods or services are being sold.

sale price = original price - discount price

According to the given question,

the original price of the scarf is $25.00

discount price = 20%of original price

⇒ discount price =[tex]\frac{20}{100}[/tex]×[tex]25[/tex]

⇒discount price = $5.00

Therefore,

sale price  of scarf = $25.00-$5.00

Sale price of scarf = $20.00

Hence, the sale price of the scarf, not including tax is $20.00

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There are 75 birds in each section

First, lets see how many in each enclosure so we have an amount to multiply by 3

450/18 = 25 birds per enclosure.

Now lets see how many birds would be in 3 enclosures i.e. a section

25 * 3 = 75

The profit function, P(x), can be obtained by finding the difference between the revenue function, R(x), and the cost function, C(x). In this case, P(x) = -330[tex]x^3[/tex] + 9,000[tex]x^2[/tex] - 67,000x + 167,000.

The profit function, P(x), can be obtained by finding the difference between the revenue function, R(x), and the cost function, C(x). In this case, we have:

R(x) = 550[tex]x^3[/tex] - 12,000[tex]x^2[/tex] + 83,000x + 7000

C(x) = 880[tex]x^3[/tex] - 21,000[tex]x^2[/tex] + 150,000x - 160,000

To find P(x), we subtract C(x) from R(x):

P(x) = R(x) - C(x)

Substituting the given functions, we get:

P(x) = (550[tex]x^3[/tex] - 12,000[tex]x^2[/tex] + 83,000x + 7000) - (880x3 - 21,000[tex]x^2[/tex] + 150,000x - 160,000)

Simplifying, we combine like terms:

P(x) = -330[tex]x^3[/tex] + 9,000[tex]x^2[/tex] - 67,000x + 167,000

Therefore, the profit function, P(x), can be expressed as a polynomial in standard form as -330[tex]x^3[/tex] + 9,000[tex]x^2[/tex] - 67,000x + 167,000.

The profit function, P(x), is found by subtracting the cost function, C(x), from the revenue function, R(x). After performing the subtraction and simplifying, the profit function in standard form is P(x) = [tex]-330x^3 + 9,000x^2 - 67,000x + 167,000.[/tex]

To find the profit function, P(x), we must subtract the cost function, C(x), from the revenue function, R(x). Given the functions:

R(x) = [tex]550x^3 - 12,000x^2 + 83,000x + 7,000[/tex]

C(x) =[tex]880x^3 - 21,000x^2 + 150,000x - 160,000[/tex]

We perform the subtraction:

P(x) = [tex](550x^3 - 12,000x^2 + 83,000x + 7,000) - (880x^3 - 21,000x^2 + 150,000x - 160,000)[/tex]

Expand and group terms:

P(x) =[tex]550x^3 - 12,000x^2 + 83,000x + 7,000 - 880x^3 + 21,000x^2 - 150,000x + 160,000[/tex]

P(x) = [tex](550x^3 - 880x^3) + (-12,000x^2 + 21,000x^2) + (83,000x - 150,000x) + (7,000 + 160,000)[/tex]

Simplify the terms:

P(x) = [tex]-330x^3 + 9,000x^2 - 67,000x + 167,000[/tex]

The profit function, P(x), in standard form is:

P(x) = [tex]-330x^3 + 9,000x^2 - 67,000x + 167,000[/tex]

Answer:

[tex]200+48n\leq 3500[/tex]

[tex]n\leq 66.7[/tex]

Step-by-step explanation:

Let the number of cartons he can safely put on the elevator at one time=n

Total weight of Carton=48n

Since the weight of the man and the cartons combined must not be more than 3500 pounds,

Therefore,an inequality that represents the situation is:

[tex]200+48n\leq 3500[/tex]

We can solve for n if required

[tex]200-200+48n\leq 3500-200\\48n\leq 3200\\\text{Divide both sides by 48}\\n\leq66.7[/tex]

The delivery man can safely carry 66 Cartons.

Answer:

For on it depends on how many cards you have and how many 4's there are

Step-by-step explanation:

So say you had 16 cards and 3 of them were 4 the probability of you picking a 4 is 3 of 16.

Final answer:

The probability of drawing a 4 and then another 4 in sequence without replacement from a 52-card deck is 1/221, calculated by multiplying the probabilities of drawing a four on the first and second draws, 1/13 and 1/17, respective

Explanation:

The question involves calculating the probability of drawing two specific cards in sequence without replacement from a standard deck of 52 cards. The condition provided is drawing a 4 first and then drawing another 4 without putting the first card back. To solve this, consider the probability of each event happening.

For the first draw, there are 4 fours in a deck of 52 cards, so the probability of drawing a four (P(A)) is 4/52 or 1/13.

After drawing one four and not returning it, there are now 51 cards left and only 3 fours left. Therefore, the probability of drawing a four as the second card (P(B) given A) is 3/51 or 1/17.

To find the total probability of both events happening in sequence, multiply the probabilities of the individual events: 1/13 * 1/17.

Thus, the probability of drawing a 4 and then another 4 in sequence without replacement is 1/221.

Answer:

$49.20

Step-by-step explanation:

Answer:

The amount made in a month with 9 sales people = 334,734.53

Step-by-step explanation:

The amount, Y, made by a sales company in dollars is related to the number of sales people, x, at the company through the relation,

Y = 60,209.47x - 207,150.70

where Y = amount made in dollars

x = number of sales people

when x = 9, what is Y.

Y = 60,209.47x - 207,150.70

Y = (60,209.47×9) - 207,150.70

Y = 541,885.23 - 207,150.70

Y = 334,734.53

Hope this Helps!!!

Answer:

10.5 hours

Step-by-step explanation:

Given:

This week Andres will practice with his band for

[tex]1\frac{1}{2} \ means\ \frac{3}{2} \ hours[/tex] on Monday

[tex]1\frac{3}{4} \ means\ \frac{7}{4} \ hours[/tex]  on Tuesday

2 hours Wednesday.

Next week Andres will practice with his band for the same number of hours on Monday, Tuesday, Wednesday.

Question asked:

What was the total number of hours Andres will practice with his band over these 6 days?

Solution:

As she practice for two weeks, three days of each week:

On two Monday, she will practice = [tex]\frac{3}{2} + \frac{3}{2} =\frac{3+3}{2} =\frac{6}{2} =3\ hours[/tex]

On two Tuesday, she will practice = [tex]\frac{7}{4} +\frac{7}{4}=\frac{7+7}{4} =\frac{14}{4} =\frac{7}{2} \ hours[/tex]

On two Wednesday, she will practice = [tex]2+2=4 \ hours[/tex]

Total hours, she will practice over 6 days  [tex]=3+\frac{7}{2} +4[/tex]

                                                                      [tex]=7+\frac{7}{2} \\ \\ =\frac{2\times7+7}{2} \\ \\ =\frac{21}{2} \\ \\ =10.5\ hours[/tex]

Thus, Andres will practice 10.5 hours with his band over these 6 days.

The total number of hours andres will practice with his band over these 6 days is 10 1/2 hours

Given:

Day 1 = 1 1/2 hours

Day 2 = 1 3/4 hours

Day 3 = 2 hours

The total number of hours for six days = 2(1 1/2) + 2(1 3/4) + 2(2)

= 2(3/2) + 2(7/4) + 4

= 6/2 + 14/4 + 4

= 3 + 14/4 + 4

= 7 + 14/4

= (28+14) / 4

= 42 / 4

= 10 2/4

= 10 1/2 hours

Therefore, the total number of hours andres will practice with his band over these 6 days is 10 1/2 hours

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Answer:

50

Step-by-step explanation:

The factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

The factors of 250 are: 1, 2, 5, 10, 25, 50, 125, 250

Then the greatest common factor is 50.

Hope this helped

:)

Answer:

y = 6/19 = 0.316

Step-by-step explanation:

Saw this on a website

Answer:

15/23

Step-by-step explanation:

please kindly see the attached for more explanation