Question 2 A cuboid made from metal plates with the dimensions x, 3x and y cm has a surface area 450 cm? a) Find the volume of the cuboid as a function of x. b) Given that x can change, find a maximum

Answer:

There are 2/3 of 1/5 cups in 2/15 cups of cookie dough.

Step-by-step explanation:

1/5=3/15

Divide 2/15 by 3/15 using keep, change, flip rules

2/15x15/3=30/45=6/9=2/3

When comparing the data, a measure of center which should be used to determine which location typically has the cooler temperature is: B. Mean, because Sunny Town is skewed.

In Mathematics, skewness can be defined as a measure of the asymmetry of a box plot (box-and-whisker plot) or histogram and as such, a box plot (box-and-whisker plot) or histogram has a normal distribution when it is symmetrical.

By critically observing the histogram which represent Sunny Town, we can logically deduce that it is skewed.

In conclusion, we can reasonably infer and logically deduce that the data distribution is skewed to the left because the mean is less than the median and this area would have a cooler temperature.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

925×1000 it is the correct answer for it

Answer:

the answer is 8

Step-by-step explanation:

1. plug in 5 where there is an x: 4(5-3)+5(5)-\(5^{2}\)

2. solve everything out and cancel: 4(2)+25-25

3. 4(2)=8

Step-by-step explanation:

Given that:

Evaluate 4(x-3)+5x-x^2 for x = 5

⇛4(5-3)+5(5)-5²

⇛4(2) + 25 - 5*5

⇛8 + 25 - 25

⇛8 - 0

⇛8 Ans

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Similar questions

Evaluate the expression 3 4/5x − 2 1/2 for x = −5.

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Answer:

\(\frac{b}{a}\) is the total time taken to clean the house.

Step-by-step explanation:

Given that:

Betsy cleans \(\frac{a}{b}\) of the house.

Time taken = 1 hour

To find:

Time taken to clean the whole house = ?

Solution:

We can use unitary method here to solve this problem.

We are given that \(\frac{a}{b}\) of the house is cleaned in 1 hour.

We have to find that a total of 1 house will be cleaned in how much time.

(1 house because Betsy's house can be considered as a single unit).

To find this we will divide 1 hour with \(\frac{a}{b}\).

Now, Let us solve this mathematically:

\(\frac{a}{b}\) of the house is cleaned in = 1 hour

1 of the house will be cleaned in =  1 hour divided by \(\frac{a}{b}\)

\(\dfrac{1}{\dfrac{a}{b}}\ hours\\\Rightarrow \dfrac{1 \times b}{a}\ hours\\\Rightarrow \dfrac{b}{a}\ hours\)

So, the answer is:

\(\frac{b}{a}\) is the total time taken to clean the house.

58º + 56º = 114º

180º - 114º = 66º

The quotient of \(x^{4} +5x^{3} -3x-15\) and \(x^{3} -3\) is (x+5).

Given expression  \(x^{4} +5x^{3} -3x-15\) and \(x^{3}-3\) and we have to find the quotient of the first expression.

Quotient is any quantity produced by dividing two numbers. It can be of simple numbers or expressions also. Remainder is a number or expression that is left after division.

To find the quotient of \(x^{4}+5x^{3} -3x-15\), we have to divide the expression by \(x^{3}-3\).

We know that,

Divident=Divisor*quotient+remainder

\(x^{4}+5x^{3}-3x-15\)=(\(x^{3}-3\))*(x+5)+0

By equating from the given formula we can find that the value of quotient is  (x+5).

Hence the quotient of \(x^{2} +5x^{3} -3x-15\) by dividing it by \(x^{3} -3\) is (x+5).

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Question is incomplete as the expressions are incomplete. They should be like \(x^{4} +5x^{3} -3x-15\) and \(x^{3} -3\)

Answer:

\((2, \frac{7}{2} )\)

Step-by-step explanation:

The midpoint between two points is:

\((\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )\) when the given points are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the points (1,6) and (3,1)

\(= (\frac{1+3}{2} , \frac{6+1}{2} )\\= (\frac{4}{2} , \frac{7}{2} )\\= (2, \frac{7}{2} )\)

Therefore, the midpoint between (1,6) and (3,1) is \((2, \frac{7}{2} )\).

I hope this helps!

The solution is, the value is 126 degrees.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

The sum of adjacent side of the rectangle is 180 degrees

Hence <1 + <4 = 180 degrees

Given

<4 = 54 degrees

<1 = 180 - <4

<1 = 180 - 54

<1 = 126degrees

Hence the value of <1 is 126 degrees

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Answer:

The formula for the circumference of a circle is C = 2πr or C= πd where r represents length of r and d represent length of diameter. The length of a diameter is 2r which is why C= πd. Using this formula, we know that r= 4cm. Thus, C= 2(4)π = 8π ≈ 25.13 centimeters.

Step-by-step explanation:

(a) The average rate the water leaves the tub between t=1 and t=2 is -3 m^3/min.

(b) The average rate the water leaves the tub between t=1 and t=1.1 is -23.1 m^3/min.

(c) The estimated exact rate at t=1 is -2 m^3/min.

(d) The average rate the water leaves the tub between t=1 and t=1+h is -2 - h m^3/min.

(e) The result when h=0 in part (d) is -2 m^3/min.

(a) To find the average rate the water leaves the tub between t=1 and t=2, we need to calculate the change in volume divided by the change in time. The change in volume is f(2) - f(1) = (4 - 2^2) - (4 - 1^2) = 1 m^3. The change in time is 2 - 1 = 1 min. Therefore, the average rate is 1 m^3/min.

(b) Similarly, for t=1 to t=1.1, the change in volume is f(1.1) - f(1) = (4 - 1.1^2) - (4 - 1^2) ≈ 0.69 m^3. The change in time is 1.1 - 1 = 0.1 min. The average rate is 0.69 m^3/0.1 min ≈ 6.9 m^3/min.

(c) At t=1, we can estimate the exact rate by calculating the derivative of the function f(t) = 4 - t^2 with respect to t. The derivative is -2t, so at t=1, the rate is -2 m^3/min.

(d) When h is a very small number, we can approximate the average rate by taking the derivative at t=1. The derivative is -2t, so the average rate between t=1 and t=1+h is approximately -2 m^3/min.

(e) When we substitute h=0 in the answer to part (d), we get -2 m^3/min, which is the exact rate of water leaving the tub at t=1.

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Answer:

42

Step-by-step explanation:

trust me i had the same answer and it was right

The probability that the randomly choosen sample contains less than 2 guppies is:

P  = 0.234

The probability will be equal to the sum between the probability of selecting 0 guppies and 1 guppi.

35% of the fish in the tank are guppies, then the probability of not selecting one of them is:

p = (0.65)^7  = 0.049

And the probability of selecting one is:

q = (0.65)^6*(0.35)*7 = 0.185

Then the probability that the sample contains less than 2 guppies is:

P = p + q = 0.049 + 0.185 = 0.234

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Answer:

500000000

Step-by-step explanation:

50,000 percent is or 1,000,000 is 500000000. I hope this is correct. I did the answer by multiplying them together.

The probability that the alleged father was not the father is: 0.024, or 2.4% and The probability that the alleged father could be the father is: 0.953, or 95.3%.

To calculate the probability that the alleged father was not the father, we first need to calculate the z-score for a pregnancy length of 240 days and for a pregnancy length of 306 days. The z-score formula is:

where x is the pregnancy length, mu is the mean pregnancy length, and sigma is the standard deviation of pregnancy length.

For a pregnancy length of 240 days, the z-score is:

For a pregnancy length of 306 days, the z-score is:

To calculate the probability that the alleged father was not the father, we need to find the area under the normal distribution curve to the left of the z-score for a pregnancy length of 240 days and to the right of the z-score for a pregnancy length of 306 days, and then add these probabilities together. Using a standard normal distribution table or calculator, we find that the probability to the left of z = -3.08 is approximately 0.001, and the probability to the right of z = 2.00 is approximately 0.023. Therefore, the probability that the alleged father was not the father is:

To calculate the probability that the alleged father could be the father, we need to find the area under the normal distribution curve between the z-scores for a pregnancy length of 240 days and a pregnancy length of 306 days. Using a standard normal distribution table or calculator, we find that the probability between z = -3.08 and z = 2.00 is approximately 0.953. Therefore, the probability that the alleged father could be the father is:

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Answer:

you would need to cross multiply 37/45 = x/100

Step-by-step explanation:

The first part represents the 37 dollars out of the original 45 and the second part represents x= the unknown percent out of 100 percent.

Answer:

Ok

Step-by-step explanation:

Answer:

2>-4

Step-by-step explanation:

The answer is D. positive numbers are always greater than negative numbers.

Answer:

The graph below shows a proportional relationship between xxx and yyy.

What is the constant of proportionality, \dfrac{y}{x}

x

y

​

start fraction, y, divided by, x, end fraction ?

Step-by-step explanation:

Answer: Option A

Step-by-step explanation:

6x - 12 > -6

6x > 6

x > 1

The correlation coefficient between the number of questions right and the number of questions wrong is -2.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the variables are the number of questions right and the number of questions wrong for each student.

To calculate the correlation coefficient, you need to have data for both variables for each student. Let's assume we have the following data for three students:
Student 1: 8 right, 2 wrong
Student 2: 5 right, 5 wrong
Student 3: 2 right, 8 wrong
Step 1: Calculate the mean of the number of questions right (meanX) and the mean of the number of questions wrong (meanY). In our example:
meanX = (8 + 5 + 2) / 3 = 5
meanY = (2 + 5 + 8) / 3 = 5
Step 2: Calculate the deviations from the mean for both variables. This is done by subtracting the mean from each individual value.
For student 1:
deviationX = 8 - 5 = 3
deviationY = 2 - 5 = -3
For student 2:
deviationX = 5 - 5 = 0
deviationY = 5 - 5 = 0
For student 3:
deviationX = 2 - 5 = -3
deviationY = 8 - 5 = 3
Step 3: Calculate the product of the deviations for each student.
For student 1:
product of deviations = deviationX * deviationY = 3 * -3 = -9
For student 2:
product of deviations = deviationX * deviationY = 0 * 0 = 0
For student 3:
product of deviations = deviationX * deviationY = -3 * 3 = -9
Step 4: Calculate the sum of the product of deviations.
sum of products of deviations = (-9) + 0 + (-9) = -18
Step 5: Calculate the standard deviation of the number of questions right (sdX) and the standard deviation of the number of questions wrong (sdY). This is done by taking the square root of the sum of the squares of the deviations from the mean divided by the number of data points minus 1.
In our example:
sdX = √[((3^2) + (0^2) + (3^2)) / (3 - 1)] = √[(9 + 0 + 9) / 2] = √[18 / 2] = √9 = 3
sdY = √[((-3^2) + (0^2) + (3^2)) / (3 - 1)] = √[(9 + 0 + 9) / 2] = √[18 / 2] = √9 = 3
Step 6: Calculate the correlation coefficient (r). This is done by dividing the sum of the product of deviations by the product of the standard deviations.
In our example:
r = sum of products of deviations / (sdX * sdY) = -18 / (3 * 3) = -18 / 9 = -2
The correlation coefficient between the number of questions right and the number of questions wrong is -2. The negative sign indicates a negative linear relationship, meaning that as the number of questions right increases, the number of questions wrong decreases, and vice versa.

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I will create a continuous random variable called "Temperature" that represents the temperature readings in a city during a given day. Let T be the temperature in degrees Celsius.

The temperature follows a normal distribution with a mean of 25 degrees Celsius and a standard deviation of 3 degrees Celsius.

Mathematically, we can represent the continuous probability distribution of the Temperature random variable as follows:

T ~ N(25, 3^2)

This notation indicates that T follows a normal distribution with a mean of 25 and a variance of 3^2 (which gives us the standard deviation of 3). The normal distribution is a commonly used probability distribution to model continuous random variables, and it is appropriate for many real-life scenarios, including temperature measurements.

The created random variable, "Temperature," represents the variability of temperature values observed in the city. The mean of 25 degrees Celsius indicates the expected average temperature, while the standard deviation of 3 degrees Celsius describes the spread or variability around the mean. This continuous probability distribution allows us to estimate the likelihood of observing temperature values within certain ranges and analyze the characteristics of the temperature distribution in the city.

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Answer: straight to the point the answer is {t| 0<t<14}

Step-by-step explanation:

Answer:

361 tiles and $2,147.95

Step-by-step explanation:

19x19 to find tile area

361 x 5.95 to find cost

The value of the given 8/9 / 3 1/5 is 18/5.

We are given that;

8/9 / 3 1/5

Now,

By cross multiplication

= 8/9 / 16/5

= 9/8 * 16/5

= 9/1 * 2/5

= 18/5

Therefore, by the algebra the answer will be 18/5.

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Answer:

330 miles

Step-by-step explanation:

198/3 = 66; this shows how fast the car is going per hour

66 * 5 = 330; this is how far the car goes in 5 hours

a. We can model X as having a Bin(23, p) distribution with p = 0.5 because if there is no advantage of starting on the outer lane

b. For a 95% confidence interval the lower bound of 0.432 and an upper bound of 0.831.  For a 98% confidence interval the lower bound of 0.398 and an upper bound of 0.865.

c. Based on the 95%  and 98% CI, we can say that we are  confident that the races won by skaters starting in the outer lane.

d. The CI constructed in Question 2(e) is the least credible

(a) Since there is no benefit to beginning on the outer lane, we can model X as having a Bin(23, p) distribution with p = 0.5., then the probability of winning a race starting in the outer lane is the same as the probability of losing, which is 0.5.

We can think of each race as a Bernoulli trial, where success is defined as winning the race starting in the outer lane, and failure is defined as losing the race starting in the outer lane. Since the outcome of each race is independent and the probability of success is constant for each trial, X follows a binomial distribution.

(b) Using the normal approximation to the binomial distribution, we have:

The sample proportion of races won by skaters starting in the outer lane is p' = X/n = 12/23.

The standard error of p' is SE(p') = sqrt((p'(1-p'))/n) = sqrt((12/23)*(11/23)/23) ≈ 0.145.

For a 95% confidence interval, we can use the formula: p' ± 1.96 SE(p'). This gives a lower bound of 0.432 and an upper bound of 0.831.

For a 98% confidence interval, we can use the formula: p' ± 2.33 SE(p'). This gives a lower bound of 0.398 and an upper bound of 0.865.

(c) Based on the 95% CI, we can say that we are 95% confident that the true proportion of races won by skaters starting in the outer lane is between 0.432 and 0.831. Since the interval does not include the value 0.5, we can conclude that skaters starting in the outer lane are indeed faster with a 95% level of confidence.

Based on the 98% CI, we can say that we are 98% confident that the true proportion of races won by skaters starting in the outer lane is between 0.398 and 0.865. Since the interval does not include the value 0.5, we can conclude that skaters starting in the outer lane are indeed faster with a 98% level of confidence.

(d) The CI constructed in Question 2(e) is the least credible because it assumes that the sample proportion p' is close to the true proportion p, which may not be the case if the sample size is small or the true proportion is close to 0 or 1.

The CIs constructed in Question 2(c) and Question 3(b) use the normal approximation to the binomial distribution, which is valid for large sample sizes and when the success-failure condition is satisfied.

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Answer:

Step-by-step explanation:

Answer:

(- 1, 6 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ \(\frac{1}{2}\) (x₁ + x₂ ), \(\frac{1}{2}\) (y₁ + y₂ ) ]

Here (x₁, y₁ ) = A(- 3, 5) and (x₂, y₂ ) = B(1, 7) , thus

midpoint = [ \(\frac{1}{2}\) (- 3 + 1 ), \(\frac{1}{2}\) (5 + 7) ] = (- 1, 6 )

Answer:

(9, 9) this is where they intersect at

Step-by-step explanation:

Answer:

the cost for each drink = $2.54

Step-by-step explanation:

The statement formed a simultaneous equation :

3x + 6y = $21.12

4x + 9y = $30.41

solving simultaneously,you have that ; x = 2.54, y = 2.25