I need help please !!!

Answer:y=x-5

Step-by-step explanation: Use (y2-y1)/(x2-x1) fill those in and get (4-1)/(9-6) which is 3/3 and that is 1 for the slope. Now fill in y=1x with a given coordinate and try to find the y-intercept so we would do 1=1(6) and we need to make the right side equal to the left so we subtract 5. Ending us with y=x-5.

Answer: x=560 miles per hour

Step-by-step explanation:

\(\displaystyle\\2.25=\\\\2\frac{1}{4}= \\\\\frac{2*4+1}{4}=\\\\\frac{8+1}{4}=\\\\\frac{9}{4}\ hours\)

The second plane left at 10:00 a.m. so, him fly was 1.25 hours:

\(\displaystyle\\1.25=\\\\1\frac{1}{4}=\\\\\frac{1*4+1}{4}=\\\\\frac{4+1}{4} =\\\\\frac{5}{4} \ hours\)

Let x represent the first plane's average rate

Hence, (x-108) represent the second plane's average rate

So,

\(\displaystyle\\\frac{9}{4}x+\frac{5}{4} (x-108)=1825\ \ \ \ (1)\\\)

Multiply both parts of the equation by 4:

\(9x+5(x-108)=7300\\\\9x+5x-540=7300\\\\14x-540+540=7300+540\\\\14x=7840\)

Divide both parts of the equation by 14:

\(x=560\ miles/hour\)

The answers are :

a. The cost of 5 kg rice if you buy 5 box of 1 kg will be equal to £ 7.

b. You need to buy 2 - 2kg rice box and 1 - 1kg box , and the cost will be £6.70.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.

It is given that a shop has three different sized boxes of rice which are 1 kg box , 1.5 kg box and 2 kg box.

a.

As per the question , you want to buy 5kg of rice. And for that you could buy five boxes of size 1 kg.

We know that , cost of 1 kg rice box = £ 1.40

So  , the cost of 5 kg rice will be :

= 5 × 1.40

= £ 7

b.

It is given that you could buy 5 kg of rice in different ways.

Let's check when the cost to buy 5 kg of rice in cheapest way will be possible.

Cost of 2kg rice is £2.65.

So , if we buy 2 - 2kg rice box then it will cost :

= 2 × £2.65 = £5.30

Now 1 kg more is needed . So, if you buy 2 - 2kg rice box and 1 - 1kg rice box then total cost will be :

= £5.30 +  £1.40

=  £6.70

This is the cheapest way possible.

Therefore , the answers are :

a. The cost of 5 kg rice if you buy 5 box of 1 kg will be equal to £ 7.

b. You need to buy 2 - 2kg rice box and 1 - 1kg box , and the cost will be £6.70.

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Answer:

130°

Step-by-step explanation:

360 = 2(50) + 2x

360 = 100 + 2x

2x = 260

x = 130

Answer:

9 weeks

Step-by-step explanation:

If a chemist wants to make 671 milliliters of the drug, then 305 milliliters of compound A are needed.

Given that:

A certain drug is made of compound A and compound B.

There are 5 milliliters of compound A used for every 6 milliliters of compound B.

So, A and B are in the ratio of 5:6.

Let a chemist will use 5x milliliters of compound A and 6x milliliters of compound B to make 671 milliliters of the drug.

So, we equate the total amount and find the value of x.

i.e. 5x + 6x = 671

=> 11x = 671

=> x = 61

Putting the value of x = 61. We get the value of compound A and compound B.

The value of compound A = 5x = 5 x 61 = 305 milliliters.

The value of compound B = 6x = 6 x 61 = 366 milliliters.

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Step-by-step explanation:

(F-32)* 5/9 = C

(83 -32) * 5/9 = 28 + 1/3

The line of reflection is the y-axis

Reflection is a geometric transformation that involves flipping an object over a line or a plane, creating a mirror image of the original object.

When a figure or polygon is reflected over the y-axis, it means that each point in the original figure is moved to a new point with the same y-coordinate but a negated x-coordinate.

Here we have

Triangle DEF has vertices at D(−3, 5), E(−10, 4), and F(−11, 8).

Triangle D′E′F′ is the image of triangle DEF after a reflection.

After reflection, the vertice E′ is located at (10, 4).  

Here the x-coordinate of E, − 10 is changed to 10  

As we know when the figure is reflected over the y-axis the sign of the x coordinate will be changes  

Hence,

The line of reflection is the y-axis

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Based on the given information and the Mean Value Theorem, we can determine that the largest possible value of f(5) is 21. The Mean Value Theorem guarantees the existence of a point within the interval (−1, 5)


To find the largest possible value of f(5) using the Mean Value Theorem, we can consider the interval [−1, 5]. Since f(x) is continuous on this interval and differentiable on the open interval (−1, 5), the Mean Value Theorem guarantees the existence of a point c in the interval (−1, 5) such that the derivative of f(x) at that point is equal to the average rate of change of f(x) over the interval [−1, 5].

Since f(−1) = −3 and f(x) is continuous on the interval [−1, 5], by the Mean Value Theorem, there exists a point c in the interval (−1, 5) such that f'(c) is equal to the average rate of change of f(x) over the interval [−1, 5]. The average rate of change of f(x) over this interval is given by (f(5) - f(−1))/(5 - (−1)) = (f(5) + 3)/6.

Now, since we are given that f′(x) ≤ 4 for all values of x, we can conclude that f'(c) ≤ 4. Therefore, we have f'(c) ≤ 4 ≤ (f(5) + 3)/6. By rearranging the inequality, we get 24 ≤ f(5) + 3. Subtracting 3 from both sides gives 21 ≤ f(5), which means the largest possible value of f(5) is 21.

By considering the given conditions, such as f(−1) = −3 and f′(x) ≤ 4, we can derive the inequality 21 ≤ f(5) as the largest possible value.

#Let the function f be continuous and differentiable for all x. Suppose you are given that f(−1)=−3, and that f

′ (x)≤4 for all values of x. Use the Mean Value Theorem to determine the largest possible value of f(5).

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Based on the provided information, we can test the claim that a higher proportion of women prefer white wine compared to men. Using a 0.05 level of significance, the statistical test suggests that there is evidence to support the claim.

To test the claim, we can use a two-sample proportion hypothesis test. The null hypothesis (H0) assumes that there is no difference in the proportions of men and women who prefer white wine, while the alternative hypothesis (Ha) suggests that there is a higher proportion of women who prefer white wine.

Calculating the test statistic and comparing it to the critical value at a significance level of 0.05, we can determine whether to reject or fail to reject the null hypothesis. In this case, with 210 out of 500 women and 120 out of 500 men preferring white wine, the test statistic is computed using the formula:

(test statistic) = (p1 - p2 - 0) / sqrt((p1(1 - p1) / n1) + (p2(1 - p2) / n2))

where p1 and p2 are the proportions of women and men preferring white wine, and n1 and n2 are the respective sample sizes.

Upon calculation, if the test statistic falls beyond the critical value, we can reject the null hypothesis and conclude that there is evidence to support the claim that a higher proportion of women prefer white wine compared to men.

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(a) To find the probability that 3 machines break in a two-week interval, we can use the Poisson distribution formula. In this case, the rate parameter λ is given as 1.5 per week, and we are interested in the number of breakdowns, which follows a Poisson distribution.

P(X = 3) = (e^(-λ) * λ^x) / x!

Plugging in the values, we have:

P(X = 3) = (e^(-1.5) * 1.5^3) / 3!

Calculate the expression to find the probability.

(b) The expected number of breakdowns in a four-week interval can be calculated by multiplying the rate parameter λ by the length of the interval. In this case, the rate is 1.5 per week, and the interval is four weeks.

Expected number of breakdowns = λ * interval

Calculate the expression to find the expected number.

(c) To find the probability of 3 breakdowns in the first two weeks and 6 breakdowns in the first 5 weeks, we can use the Poisson distribution for each interval separately. The probability of 3 breakdowns in the first two weeks is P(X = 3) as calculated in part (a). The probability of 6 breakdowns in the first 5 weeks is calculated similarly using the rate parameter for a 5-week interval.

Calculate the respective probabilities and multiply them to find the overall probability.

(d) The probability that the first breakdown occurs within the first week is equal to the rate parameter λ, which is given as 1.5 per week.

(e) The probability that the third breakdown occurs within the first 8 weeks can be calculated using the cumulative distribution function (CDF) of the Poisson distribution. We can subtract the probability of no breakdowns in the first 8 weeks and the probability of one or two breakdowns from 1 to find the probability of at least three breakdowns.

Calculate the expression to find the probability.

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There is a 0.2209 = 22.09% probability that three students will arrive during a randomly chosen office hour.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.

The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).

According to our question-

The number of successes is x.

The Euler number is e = 2.71828.

is the average over the specified range.

When a professor of statistics sets an office hour for student assistance, she discovers that on average, 3.3 students show up.

It follows that

Determine the likelihood that three students will arrive during a randomly chosen office hour.

So, P(X = 3).

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The area of the sector  2π/3 radians with diameter 10 feet 75π feet²

The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.

Diameter =  10 feet

radius = 5 feet

angle =   2π/3 radians

⇒angle= arc/radius

⇒  2π/3 radians° =arc/10

⇒ arc =2π/3 radians *10

 ⇒arc=2π/3 radians*10

⇒arc = 20/π43 feet

Area of a circle = π*r²

                        =  π*5² = π25

∵ area of complete circle is π25

∴ area of 2π/3 radians = π25/2π *2π/3 radians

                                     = 75π  answer

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Answer:

The value of f(3) = 28.26

Step-by-step explanation:

You have to do is to substitute r = 3 into the function :

\(f(r) = 3.14 \times {r}^{2} \)

\(f(3) = 3.14 \times {3}^{2} \)

\(f(3) = 3.14 \times 9\)

\(f(3) = 28.26\)

Ms. Ortiz needs to find a multiple of n that is divisible by 3, 4, or 5. To arrange the trucks in 3 rows, divide them into groups of n and place each group in a row. To arrange the trucks in 4 rows, divide them into groups of n and place each group in a row.

Assume you have n trucks that need to be sorted. Ms. Ortiz prefers a configuration with more than two rows but fewer than six rows of trucks.

If there are just two rows, each row will have n/2 trucks. Because Ms. Ortiz desires more than two rows, the number of rows might be three, four, or five.

If there are three rows, each row will contain three trucks. However, because n/3 is not a whole integer, we must find a multiple of n that is divisible by 3. 3n, for example, suggests that each row will have n trucks. To arrange the vehicles in three rows, just split them into n groups.

If there are four rows, each row will contain four trucks. However, because n/4 may not be a whole integer, we must find a n multiple that is divisible by 4. 4n, for example, suggests that each row will contain n trucks. To arrange the trucks in four rows, just split them into n groups and position each group in a row.

Each row will have n/5 trucks if there are 5 rows. However, because n/5 is not a whole integer, we must find a multiple of n that is divisible by 5. 5n, for example, suggests that each row will have n trucks. To organize the trucks in 5 rows, just divide them into n groups and arrange each group in a row.

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Answer:

If you spent $56 on candy, she'd buy 8 pounds.

Step-by-step explanation:

The derivative of of f(x) = 10 is 0

The derivative of a function is the measure of the rate of change of the function. They are fundamental to the solution of problems in calculus and differential equations.

Here the function is not changing as 10 is a constant. So, if f(x) = c where c is a constant then f'(x) = 0 as the derivative of a constant is always zero.

Mathematically:

           d(f(x))/dx = \(\lim_{h \to 0}\) (f(x+h) - f(x))/h

There  is no x to substitute for x + h so no difference is noticed:

             \(\lim_{h \to 0}\) (f(x+h) - f(x))/h =   \(\lim_{h \to 0}\) (10 - 10)/h = 0

Hence, the derivative of f(x) = 10 is 0

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diamater:

\(d=2r \\\\d=2 \cdot 16 \\\\d=32\)

circumference:

\(C=2 \pi r \\\\C=2 \cdot \p \cdot 16 \\\\C=32 \cdot \pi \\\\C \approx 100.48\)

Hope that I helped you!

Answer:

Below

Step-by-step explanation:

= 5 sqrt (4 x 3) + 3 sqrt (3)

= 5 x   2 sqrt (3) + 3 sqrt 3

 = 10 sqrt 3   +  3 sqrt 3 = 13 sqrt(3)

In this case, σ = 5 and n = 49, so the standard error of the mean is 5/√49 = 0.714.
Finally, we can look up the probability of z-scores being greater than 1.4 in a standard normal distribution table or use a calculator to find that the probability is 0.0808.
Therefore, the answer is 0.0808.

The probability that the sample mean is greater than 26 can be calculated using the standard error of the mean formula, which is σ/√n, where σ is the population standard deviation and n is the sample size.

To solve this problem, we'll use the z-score formula for a sample mean:

z = (x- µ) / (σ / √n)

where x is the sample mean, µ is the population mean, σ is the population standard deviation, and n is the sample size.

In this problem, we are given the following values:
µ = 25
σ = 5
n = 49

We want to find the probability that the sample mean is greater than 26, so x = 26. Now, let's find the z-score:

Next, we need to standardize the sample mean using the z-score formula, which is (x - µ) / (σ/√n), where x is the sample mean, µ is the population mean, σ is the population standard error, and n is the sample size.
In this case, x = 26, µ = 25, σ = 5, and n = 49, so the z-score is (26 - 25) / (5/√49) = 1.4.

Now we'll use a z-table to find the probability of getting a z-score of 1.4 or greater. From the table, the probability of getting a z-score up to 1.4 is 0.9192. Since we want the probability of getting a z-score greater than 1.4, we'll subtract this value from 1:

1 - 0.9192 = 0.0808
Therefore, the probability that the sample mean is greater than 26 is 0.0808. The correct answer is: 0.0808

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Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

The equation of the line that goes through the points (−3,−4) and (9,7) can be written in the form 5x - 12y = -75.

To find the equation:

The available points are (3,5) and (9,10).

The line's slope is given by:

\(\mathrm{m}=\frac{(10-5)}{[9-(-3)]}=\frac{5}{12}\)

The equation is as follows:

\(\begin{aligned}&y-5=\left(\frac{5}{12}\right)[\mathrm{x}-(-3)] \\&\mathrm{y}-5=\left(\frac{5}{12}\right)(\mathrm{x}+3)\end{aligned}\)

Solve it to obtain the equation:

\(\begin{aligned}&12 y-60=5 x+15 \\&5 x-12 y=-75\end{aligned}\)

Therefore, the equation is 5x - 12y = -75.

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The correct question is given below:
Find an equation of the line through the points (−3,5) and (9,10) and write it in standard form Ax+By=C, with A>0.

Here the diameter = dm

Formula of circumference for circle: 2πr  or  πd

                                        where "d" is diameter and "r" is radius

For this question:

circumference:

Answer:

B is the answer

Step-by-step explanation:

Answer: 20.6

Step-by-step explanation:

The third term is 245 and the first term is 5 -> To get from the first term to the third term, we multiply it by 49.

Since in a geometric sequence, the difference between each term has to be a constant multiplier or a sequence of multipliers -> We can find the second number to be 5 x 7 = 35

So, this geometric sequence is 5 ; 35 ; 245 and so on.

-> The common ratio of this sequence is 7. (and sorry if the things above don't make sense)

Answer:

7

Step-by-step explanation:

Given:

Let the second term be "x".

⇒ 5, x, 245...

Thus, the following equations:

To find the common ratio between the three terms, we need to find the value of "x". Simplify both the equations to obtain the values of (something). Then compare both the values.

⇒ [5 × (something)] = x

⇒ [5 × (something)]/5 = x/5

⇒ (something) = x/5

⇒ x × (something) = 245

⇒ [x × (something)]/x = 245/x

⇒ (something) = 245/x

Now, let's compare both the results of (something).

⇒ x/5 = 245/x

⇒ x² = 5 x 245

⇒ x² = 1225

⇒ x = √1225 = 35

Substitute the second term into the sequence.

⇒ 5, x, 245 = 5, 35, 245

Looking at the sequence formed, we can tell that 7 is being multiplied to each term. Thus, 7 is the common ratio.