Fishermen have been studying how the number of dead fish in the local lake is related to the


pollution index of the lake. The number of fish deaths per year is modeled by


f(x) = 9.607x + 111.958. Which value represents the y-intercept and what does it mean in the


context of the scenario?

To prove that an integer of the form a = 4n + 3, where n is an integer, has a prime divisor of the form p = 4m + 3, where m is an integer, we can use a proof by contradiction.

Assume that a does not have a prime divisor of the form p = 4m + 3. In other words, assume that all prime divisors of a can be expressed in the form p = 4m + 1 for some integer m.

Consider the number b = a^2 - 1 = (4n + 3)^2 - 1 = 16n^2 + 24n + 8 = 8(2n^2 + 3n + 1).

Now, let's consider the prime factorization of b. Since b is divisible by 8, it must have at least one prime divisor of 2. However, since all prime divisors of a (and therefore b) are of the form 4m + 1, none of them can be equal to 2.

Therefore, there must be at least one prime divisor of b that is not of the form 4m + 1. Let's denote this prime divisor as p.

Now, let's consider the possible remainders of p when divided by 4:

If p ≡ 0 (mod 4), then p can divide 8(2n^2 + 3n + 1) without dividing a. This contradicts our assumption that all prime divisors of a are of the form 4m + 1.

If p ≡ 2 (mod 4), then p can divide 8(2n^2 + 3n + 1) without dividing a. This also contradicts our assumption.

If p ≡ 1 (mod 4), then p can divide 8(2n^2 + 3n + 1) without dividing a. Again, this contradicts our assumption.

Since all possible cases lead to a contradiction, our assumption that a does not have a prime divisor of the form 4m + 3 must be false.

Therefore, we conclude that an integer of the form a = 4n + 3 has a prime divisor of the form p = 4m + 3 for some integer m.

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Answer:

B

Step-by-step explanation:

the decay will cause loss so it's the function B

Answer:

B

Step-by-step explanation:

trust

We expressed the ratio of female students to male students as a fraction, simplified it, and obtained a final ratio of approximately 3:4.

The problem states that there are 500 students at Rockland Middle School. If 43% of the students are female, we can calculate the number of female students by multiplying the total number of students by the percentage of female students:

43% of 500 = 0.43 x 500 = 215

Similarly, the number of male students can be calculated by multiplying the total number of students by the percentage of male students:

57% of 500 = 0.57 x 500 = 285

The ratio of female students to male students can then be expressed as the fraction of female students divided by the fraction of male students:

215/285 = 0.754:1

This ratio can also be simplified by dividing both numbers by their greatest common factor (GCF), which in this case is 5:

215/5 = 43

285/5 = 57

So the simplified ratio of female students to male students is 43:57 or approximately 3:4.

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Answer:

The Smith's planted 9 trees

Step-by-step explanation:

21-12=9

Because the Smith's ending amount is 21, and their beginning amount is 12 you subtract 21-12=9

Answer:

Well, there can be two answers. One of them can be 9, since they planted 9 MORE trees on top of the 12 already there. (21-12=9) The other answer can be 33 if you count all the trees they planted. (12+21=33)

Step-by-step explanation:

Answer:

x = -3 to x = 2

Step-by-step explanation:

The function is decreasing where the slope is negative, seen when the y-values decrease as the x-values increase. Your answer is correct.

Answer:

X is - 3 to x is 2

Step-by-step explanation:

Look at the x axis, the point where the curve slopes down is the decreasing point

Where x is - 3 is a peak point, it begins to slope from there and rises when x is 3

Answer:

height of the cone is 25 cm.

Step-by-step explanation:

by using the formulas for the surface area of a cylinder and a cone to find the total surface area of the solid object.

The formula for the surface area of a cylinder is 2πr(r+h) where r is the radius and h is the height.

The formula for the surface area of a cone is πr(r+l) where r is the radius and l is the slant height.

Let's assume that the radius of the cylinder and cone is 'r'.

Now we know that :

2πr(r+30) + πr(r+l) = Total surface area

We are given that the cost of painting the total surface area is Rs. 3036 at the rate of Rs. 150 per 100 sq cm. So we can use this information to find the total surface area.

3036*100/150 = 2022 sq cm

Now we can substitute this value of total surface area in the above equation.

2πr(r+30) + πr(r+l) = 2022

Now we can solve for 'l' (slant height of the cone)

we know that the slant height of the cone is 25 cm so we can substitute this value in the above equation.

2πr(r+30) + πr(r+25) = 2022

Solving this equation, we get the height of the cone = 25 cm.

So the height of the cone is 25 cm.

a^2 +b^2 =c^2

7.

4^2+17^2=c^2

16+289=c^2

305=c^2

To undo the square you have to square root so

Sqr rt of 305 =17.46

8. 24 sqrd =576

52 sqrd=2704

2704+576=3280

Sqr rt of 3280 =57.27

The range of possible lengths for the third side in the first and the second case will be greater than 21 cm and 76 feet, respectively.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The third side of the triangle must be greater than the sum of the other two sides.

A)  4 cm and 17 cm, then the third side (a) of the triangle is given as,

a > 17 + 4

a > 21 cm

The range of possible lengths for the third side will be greater than 21 cm.

B)  24 ft and 52 ft, then the third side (b) of the triangle is given as,

b > 24 + 52

b > 76 ft

The range of possible lengths for the third side will be greater than 76 ft.

The range of possible lengths for the third side in the first and the second case will be greater than 21 cm and 76 feet, respectively.

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(a)The appropriate hypothesis test at the 0.01 significance level t-value (2.82) does not exceed the critical t-value (±3.250)

(b) A Type-1 error would occur if we rejected the null hypothesis .

(a) To conduct the appropriate hypothesis test, we can set up the following hypotheses

Null hypothesis (H₀): The mean DBP of diabetic women is equal to the mean DBP of the general public (μ = 76 mmHg).

Alternative hypothesis (H₁): The mean DBP of diabetic women is not equal to the mean DBP of the general public (μ ≠ 76 mmHg).

We can use a t-test since the population mean and standard deviation are unknown, and the sample size is relatively small (n = 10). We will compare the sample mean (85 mmHg) with the hypothesized population mean (76 mmHg) using the t-distribution.

The test statistic is calculated as follows

t = (sample mean - hypothesized mean) / (sample standard deviation / √(sample size))

t = (85 - 76) / (10 / √(10))

t ≈ 2.82

We can find the critical t-value for a two-tailed test with a significance level of 0.01 and degrees of freedom (df) equal to n - 1 (10 - 1 = 9). The critical t-value is approximately ± 3.250.

Since the calculated t-value (2.82) does not exceed the critical t-value (±3.250), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean DBP of diabetic women is different from the mean DBP of the general public at the 0.01 significance level.

b. In this example, a Type-1 error would occur if we rejected the null hypothesis (stated that the mean DBP of diabetic women is different from the mean DBP of the general public) when it is actually true. In other words, we would conclude a significant difference when there is no real difference in the population means.

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The number of ways to plan her schedule of menus for the 20 school days is 10^20.

To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time. To calculate a combination, you will need to calculate a factorial.

For each day, there are ten different choices for what she will cook that day. 20 decisions are made, one for each day with ten different possibilities for each choice.

The complete question is: A school cook plans her calendar for the month of February in which there are 20 school days. She plans exactly one meal per school day. Unfortunately, she only knows how to cook ten different meals.

How many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?

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Answer:

The percent change is 50%

Step-by-step explanation:

The savings account lost $750. When the amount lost is the same amount you have left, it signifies that the amount lost is half as much as you had.

Half of the total is represented as 50%.

Check Work:

1500 x 0.5(50%*) = 750

1,500 - 750 = 750

Answer:

20

Step-by-step explanation:

1/3 = .3

6/.3  = 20

Answer:

18

Step-by-step explanation:

6 ÷ 1/3

changing the ÷ sign into × sign and taking reciprocal of the second term

6 × 3/1

putting 1 as the denominator of 6

6/1 × 3/1

now multiplying both terms

18/1

18

Answer:

47

Step-by-step explanation:

6n + 5y + 4z

substitute the variables

6(4) + 5(3) + 4(2)

6 x 4 = 24

5 x 3 = 15

4 x 2 = 8

24 + 15 + 8

= 47

Answer:

$375.32

Step-by-step explanation:

100% - 40% = 80%

80/100 = 0.8 (multiplier)

521.28 x 0.8 = 417.024

417.024 to 417.02 (2 d.p.)

100 - 10 = (ans)/100 = 0.9

417.02 x 0.9 = 375.318

$375.32

Step 1: Find the sales price

The surfboard was marked down 40% of its original price, $521.28.

0.40(521.28) = 208.512

521.28 - 208.512 = 312.768

Step 2: Find the final price

We add the tax on the sales price, not the original price. The tax is 10% in this case.

0.10(312.768) = 31.2768

312.768 + 31.2768 = 344.0448

Final price = $344.04

---I did not round until the end in this case, but rounding at every step leads to an answer of $344.05

Hope this helps!

Answer:

D

Step-by-step explanation:

Answer:5

Step-by-step explanation:

hihihi

The z-score would be most useful if you want to know how many standard deviations from the mean a single score in a data set falls. So, the answer to the given question is option B) Az score.

The z-score is a standard score that indicates how many standard deviations an observation is from the mean. A z-score expresses the difference between a measurement and the mean in units of standard deviation. It is calculated as follows: Z-score= (score – mean) / standard deviation

The z-score is frequently utilized in statistics as an index of the likelihood that a result will occur. It is often utilized to determine whether a value is significantly different from the average. It is also known as a standard score or a normal deviate.

The z-score indicates how many standard deviations an observation is from the mean. A positive z-score indicates that the measurement is above the mean, whereas a negative z-score indicates that the measurement is below the mean. A z-score of zero indicates that the score is equal to the mean.

Hence, the answer to the given question is option B) Az score.

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Answer: 140?

I am not really sure but I think 140......

Answer: x = 8

Step-by-step explanation:

To solve the given equation, we need to simplify the following first: √-24 and √-8We know that the square of an imaginary number is negative.

Also, we can write √-24 as √(-1 × 24) = 2i√6. Similarly, we can write √-8 as √(-1 × 8)

= 2i√2. Therefore, the given equation can be rewritten as follows: √6 (2i√6 − 2i√2)We can simplify the above equation further by using the distributive law of multiplication. √6 × 2i√6 − √6 × 2i√2

= 12i - 2i√3√6

Now, we can write the final answer in the form a + bi as follows: √6(√-24-√-8)

= 12i - 2i√3√6. Therefore,12i - 2i√3√6. Hence, the solution is provided above.

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Step-by-step explanation:

1) c= 180°

22) b= 22 (vertical angle theorem)

a and c = 158 because you subtract b and 22° from 360 and you get 316 then divide by 2 to get a and c

The probability of picking a red ball is 2/3.

As given in the student question,

The probability that a randomly selected person would be a protestant and at the same time be a democrat or a republican is not given in the problem statement.

Hence, it cannot be determined without further information.

Probability is the branch of mathematics that deals with the study of uncertainty.

It provides a framework for analyzing random events that occur in the real world.

Probability helps us to estimate the likelihood of a particular event occurring. It helps us to make informed decisions when faced with uncertain outcomes.

It plays a critical role in many fields such as science, engineering, economics, and finance.

Probability formula:

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.

The formula for probability is given by:

P (A) = Number of favorable outcomes/ Total number of outcomes

where P (A) represents the probability of event A.

Example:

Suppose we have a bag containing 10 red balls and 5 blue balls.

The total number of outcomes = 10 + 5 = 15

The number of favorable outcomes = 10P (Red ball) = 10/15 = 2/3

Therefore, the probability of picking a red ball is 2/3.

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The inflow rate of water is given by the function of the volume of the

tank derived from the shape of the tank.

Response:

The given parameter are;

Shape of the tank = Conical

Rate at which water is leaking out of the tank = 7,000 cm³/min

Height of the tank = 6 m

Diameter of the tank = 4 m

Solution:

We have;

\(\dfrac{D}{h} = \mathbf{\dfrac{2 \cdot r}{h}}\)

\(r = \mathbf{\dfrac{D}{2 \cdot h}}\)

Which gives;

\(r= \mathbf{\dfrac{h}{3}}\)

\(V = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h = \dfrac{1}{3} \cdot \pi \cdot \left(\dfrac{h}{3} \right)^2 \cdot h = \mathbf{ \pi \cdot \dfrac{h}{27} ^3}\)

Which gives;

\(\dfrac{dV}{dh} = \mathbf{\pi \cdot \dfrac{h}{9} ^2}\)

By using chain rule of differentiation, we have;

\(\dfrac{dV}{dt} = \mathbf{\dfrac{dV}{dh} \times \dfrac{dh}{dt}}\)

Which gives;

\(\dfrac{dV}{dt} = \mathbf{\pi \cdot \dfrac{h}{9} ^2\times 20}\)

\(\dfrac{dV}{dt} = \pi \cdot \dfrac{200}{9} ^2\times 20 \approx 279,252.68\)

\(\dfrac{dV}{dt} = \mathbf{Inflow \ rate - Outflow \ rate}\)

Therefore;

\(Inflow \ rate = \mathbf{\dfrac{dV}{dt} + Outflow \ rate}\)

Which gives;

Inflow rate ≈ 279,252.68 + 7000 = 286,252.68 ≈ 286,253

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Answer:

2+3=5

Step-by-step explanation:

2+

3=

5

answer 2+3=5

Answer:

x=39.76693372

Step-by-step explanation:

Subtract 2187 from 3.

54.92x−2184=0

Add 2184

to both sides of the equation.

54.92x=2184

Divide each term by 54.92

and simplify.

x=39.76693372

Answer:

a) acute

the triangle is acute

The inequality which is used to represent normal "temperature-range" for  "human-body", is (d) |t − 98.6| ≤ 1.8.

The "average-temperature" of body is = 98.6° F, and it can vary by 1.8°F.

The inequality |t − 98.6| ≤ 1.8 indicates that the absolute difference between the body temperature and the average temperature is less than or equal to 1.8° F.

This means that the body temperature t can vary within a range of 1.8° F from the average temperature of 98.6° F.

Which means, the temperature cam range from :

⇒ 98.6-1.8 ≤ t ≤ 98.6+1.8,

⇒ 96.8 ≤ t ≤ 100.4;

Therefore, the correct inequality is (d) |t − 98.6| ≤ 1.8.

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The given question is incomplete, the complete question is

The average human body temperature is 98.6° F, but it can vary by as much as 1.8° F. Write an inequality to represent the normal temperature range of the human body, where t represents body temperature.

(a) |t − 1.8| ≥ 98.6

(b) |t − 1.8| ≤ 98.6

(c) |t − 98.6| ≥ 1.8

(d) |t − 98.6| ≤ 1.8

Answer: |t − 98.6| ≤ 1.8

Step-by-step explanation: If takes then takes then takes then takes then takes.

Answer:

2.4

Step-by-step explanation:

4/5 / 1/3

4/5 x 3/1

4/5x3/x1 = 12/5

22/5

12/5 = 2.4

a. The current sale price for the computer system is given as follows: $618.4.

b. The amount paid by the club members, with the discount, is given as follows: $587.48.

The prices are found applying the proportions, which are the decimal equivalent of the percentages relative to each discount.

The selling price is of:

$773.

The markdown is of 20%, hence the current sale price is 100 - 20 = 80% of the selling price, hence:

0.8 x 773 = $618.4.

Club members get an additional discount, of 5%, meaning that they pay 95% of $618.4, and the amount is obtained as follows:

0.95 x 618.4 = $587.48.

The problem is given by the image presented at the end of the answer.

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