4cos^2(x)-7cos(x)+3
Please help and explain how you did it :)

To solve this problem, we need to use some basic math skills and conversion factors. We know that there are approximately $1.4 times 10^9$ cubic kilometers of water on earth, and that only about $2.5% $ of this water is freshwater.

To find out how much freshwater there is on earth, we can start by converting $2.5\%$ to a decimal by dividing it by 100. This gives us 0.025.
Next, we can multiply the total amount of water on earth by the decimal representing the percentage of freshwater:
$1.4\times10^9 \text{ km}^3 \times 0.025 = 3.5\times10^7 \text{ km}^3$
Therefore, there are approximately 3.5 million cubic kilometers of freshwater on earth. This may seem like a large amount, but it is actually a very small percentage of the total water on earth. It is important to conserve and protect this valuable resource for future generations.
In conclusion, problem solving requires understanding the given information, converting units and percentages, and performing simple calculations to arrive at a solution.

For more questions on conversion factors

https://brainly.com/question/24545553

#SPJ11

Answer:

Step-by-step explanation:

The best way to answer this is to graph it before using the quadratic formula. The graph is shown below.

Notice that the minimum doesn't come anywhere near the x axis. That means when you use the quadratic formula, you  are going to get the square root of a negative number. Check out the discriminate.

√(b^2 - 4*a * c)

a = 1

b = 6

c = 10

√(36 - 4*1*10

√36 - 40

√-4

2*i

So there is no point going any further. You have no real roots.

Answer:

Step-by-step explanation:

Are these two figures similar? If so, what is the scale factor? Justify your answer.

the sides of the large figure are 3 times those of the small figure, therefore same angles and sides in a 1:3 ratio

Answer:

Metric

"Metric" means a unit, or measurement.

Hope this helps, have an awesome day! ♣

Can I have brainliest?

a. The confidence interval with 95% confidence level for the average money spent by a shopper on the day of the study is between $91.31 and $105.69.

b. The confidence interval with 90% confidence level for the average money spent by a shopper on the day of the study  is between $92.83 and $104.17.

c.  The confidence interval calculated in part (b) narrower than the one calculated in part (a) because we want to be more confident that the true population mean falls within the interval.

d. If 100 shoppers were interviewed randomly, the 95% confidence interval's width would be narrowed than what was determined in section (a). This is due to the fact that as sample size rises, the standard error (/n) reduces.

a) We can use the formula for a confidence interval for a population mean with known standard deviation:

CI = x ± z*(σ/√n)

where x is the sample mean, σ is the population standard deviation (in this case, the sample standard deviation is used as an estimate), n is the sample size, and z is the critical value from the standard normal distribution corresponding to the desired confidence level.

For a 95% confidence level, z = 1.96 (from the standard normal distribution). Plugging in the values given:

CI = 98.5 ± 1.96*(20.75/√50) = (91.31, 105.69)

Therefore, we are 95% confident that the true average amount spent by a shopper on the day of the study is between $91.31 and $105.69.

b) Following the same formula, for a 90% confidence level, z = 1.645 (from the standard normal distribution):

CI = 98.5 ± 1.645*(20.75/√50) = (92.83, 104.17)

Therefore, we are 90% confident that the true average amount spent by a shopper on the day of the study is between $92.83 and $104.17.

c) The confidence interval calculated in part (b) is narrower than the one calculated in part (a) because a higher confidence level requires a wider interval to capture the true population mean with more certainty.

In other words, a 95% confidence interval will be wider than a 90% confidence interval because we want to be more confident that the true population mean falls within the interval.

d) If 100 shoppers were interviewed instead of 50, the width of the 95% confidence interval would be narrower than that calculated in part (a). This is because the standard error (σ/√n) decreases as the sample size increases, which leads to a narrower confidence interval.

To learn more about confidence interval visit: https://brainly.com/question/31320326

#SPJ11

Answer: X = 6

Step-by-step explanation:

The confidence interval of 2.25 to 2.38, calculated based on a sample of 49 measurements of tensile strength with a mean of 2.45 and a standard deviation of 0.25, is derived using the t-distribution. This is because the population standard deviation is not explicitly stated and the sample size is relatively small.

Based on the information, a sample of 49 measurements of tensile strength has a mean of 2.45 and a standard deviation of 0.25. The calculated 95% confidence interval for the measurements is 2.25 to 2.38.

To determine whether it is a t-distribution or a z-distribution, we need to know the sample size and whether the population standard deviation is known or unknown.

In this case, since the sample size is 49 and the population standard deviation is not explicitly stated, we can assume it is unknown.

Therefore, the appropriate distribution to use for calculating the confidence interval is the t-distribution.

Hence, the confidence interval of 2.25 to 2.38 is calculated using the t-distribution, not the z-distribution.

To know more about t-distribution refer here:

https://brainly.com/question/31116907#

#SPJ11

Answer:

8(3j - 2).

Step-by-step explanation:

24j-16

GCF = 8

so the answer is

8(3j - 2).

Answer:the slope of smaller triangle

Step-by-step explanation:

Part A:

The correct option is C.

The graph represents the function:

Part B:

The average rate of change is 1

Part A:

The graph is represents the function:

Part B:

The average rate of change on the interval -3 < x < -1 is

The slope of the line passing through the points (2,2) and (5,3) is m = 1/3

The points are (2,2) and (5,3)

The slope of the line is the change in y coordinate with respect to the change in x coordinate

Slope of the line m = \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

Where m is the slope of the line

\((x_{1},y_{1})\) are the coordinates of the first point

\((x_{2} ,y_{2} )\) are the coordinates of the second point

Substitute the values in the equation

Slope of the line m =\(\frac{3-2}{5-2}\)

m = 1/3

We know the slope intercept form

y= mx+c

Substitute the values in the equation

2 = (1/3)2+c

2 = 2/3 + c

c = 2-(2/3)

c = 4/3

The the equation will become

y = (1/3)x + 4/3

Draw the graph using the equation

Hence, the slope of the line passing through the points (2,2) and (5,3) is m = 1/3

Learn more about slope of the line here

brainly.com/question/16180119

#SPJ1

For the given coordinates the area of the triangle will be 248.5 square units.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,triangle TABLE has vertices M(-7,-1) A(5,6) L(2,-3)

x₁,y₁=(-7,-1)

x₂,y₂=(5,6)

x₃,y₃=(2,-3)

We must utilize the triangle's vertices to calculate the area of the triangle in order to obtain the equation,

S=1/2[-7(6-(-3)+5(-3-(-1)+2(-1-(6)]

S=248.5

Thus, for the given coordinates the area of the triangle will be 248.5 square units.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ1

The relative maximum point is (0, 3) and the relative minimum points are (-1, 2) and (1, 2).

To find the relative maximum and minimum points of the function f(x) = x^4 - 2x^2 + 3, we need to find the values of x where f'(x) = 0.

f'(x) = 4x^3 - 4x = 4x(x^2 - 1)

Setting f'(x) = 0, we get x = 0, ±1 as critical points.

To determine the nature of these critical points, we need to use the second derivative test.

f''(x) = 12x^2 - 4

At x = 0, f''(0) = -4 < 0, so this critical point is a relative maximum.

At x = 1, f''(1) = 8 > 0, so this critical point is a relative minimum.

At x = -1, f''(-1) = 8 > 0, so this critical point is also a relative minimum.

Therefore, the relative maximum point is (0, 3) and the relative minimum points are (-1, 2) and (1, 2).

To learn more about critical points, refer below:

https://brainly.com/question/29144288

#SPJ11

If the population is not normally distributed, a larger sample size is needed for accurate results. However, if the population is normally distributed, a smaller sample size can be sufficient.

If the underlying population of study is not normally distributed, the sample size should be larger to ensure accurate results. This is because a larger sample size helps to reduce the impact of any non-normality in the population.

If the population is normally distributed, the sample size can be smaller while still providing accurate results. This is because the assumption of normality allows for smaller sample sizes to accurately represent the population.

In summary, if the population is not normally distributed, a larger sample size is needed for accurate results. However, if the population is normally distributed, a smaller sample size can be sufficient.

Let us know more about sample size : https://brainly.com/question/32492771.

#SPJ11

The solution to the expression (12x³ + 9x² - 3) / 3x is (4x³ + 3x² - 1) / x

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

Given the expression:

(12x³ + 9x² - 3) / 3x

To solve, we need to factorize the numerator to get:

= 3(4x³ + 3x² - 1) / 3x

= (4x³ + 3x² - 1) / x

The solution to the expression is (4x³ + 3x² - 1) / x

Find more on equation at: https://brainly.com/question/2972832

#SPJ1

To solve these questions, we will use the properties of the normal distribution and the given mean and standard deviation.

Given:

Mean (μ) = 78 minutes

Standard deviation (σ) = 12 minutes

1. Proportion of eighth-graders completing the assessment examination in 72 minutes or less:

We need to find P(X ≤ 72), where X represents the time taken to complete the assessment examination.

Using the z-score formula: z = (X - μ) / σ

For X = 72:

z = (72 - 78) / 12 = -0.5

Looking up the z-score in the standard normal distribution table, we find that the cumulative probability corresponding to z = -0.5 is approximately 0.3085.

Therefore, the proportion of eighth-graders completing the assessment examination in 72 minutes or less is approximately 0.3085.

2. Proportion of eighth-graders completing the assessment examination in 82 minutes or more:

We need to find P(X ≥ 82), where X represents the time taken to complete the assessment examination.

Using the z-score formula: z = (X - μ) / σ

For X = 82:

z = (82 - 78) / 12 = 0.3333

Looking up the z-score in the standard normal distribution table, we find that the cumulative probability corresponding to z = 0.3333 is approximately 0.6293.

To find the proportion of eighth-graders completing the assessment examination in 82 minutes or more, we subtract the cumulative probability from 1:

1 - 0.6293 = 0.3707

Therefore, the proportion of eighth-graders completing the assessment examination in 82 minutes or more is approximately 0.3707.

3. Proportion of eighth-graders completing the assessment examination between 72 and 82 minutes:

We need to find P(72 ≤ X ≤ 82).

Using the z-score formula, we calculate the z-scores for both values:

For X = 72:

z1 = (72 - 78) / 12 = -0.5

For X = 82:

z2 = (82 - 78) / 12 = 0.3333

Using the standard normal distribution table, we find the cumulative probabilities corresponding to z1 and z2:

P(Z ≤ -0.5) ≈ 0.3085

P(Z ≤ 0.3333) ≈ 0.6293

4. To find the proportion between 72 and 82 minutes, we subtract the cumulative probability of the lower bound from the cumulative probability of the upper bound:

0.6293 - 0.3085 = 0.3208

Therefore, the proportion of eighth-graders completing the assessment examination between 72 and 82 minutes is approximately 0.3208.

To find the number of minutes at which 90% of all eighth-graders complete the assessment examination, we need to find the corresponding z-score for a cumulative probability of 0.90.

Using the standard normal distribution table, we look for the z-score that corresponds to a cumulative probability of 0.90, which is approximately 1.28.

Using the z-score formula: z = (X - μ) / σ

Substituting the values, we have:

1.28 = (X - 78) / 12

Solving for X, we find:

X - 78 = 1.28 * 12

X - 78 = 15.36

X ≈ 93.36

Therefore, approximately 90% of all eighth-graders complete the assessment examination within 93.36 minutes.

To know more about Probability visit-

brainly.com/question/31828911

#SPJ11

Answer:

6

Step-by-step explanation:

12=3(2)+6

12=6+6

The coordinates of the circumcenter of the triangle with the given vertices is; (-3, -3).

The circumcenter of a given triangle can be determined by determining the center of its sides as given by the coordinates of the vertices.

For the x-coordinate of the circumcenter;

Hence, the x-coordinate of the circumcenter is given as the x-midpoint of vertices;

Similarly, For y;

Read more on circumcenter:

https://brainly.com/question/8055762

Answer: 946 ml

Step-by-step explanation: 1 pint= 473.2

2*

473.2= 946.4

=946 ml

To calculate probability of having the disease given two positive test results, P(A|BB).Using Bayes' theorem, P(A|BB) = (P(A) * P(BB|A)) / P(BB) P(A|BB) = (0.05 * 0.98^2) / (0.05 * 0.98^2 + 0.95 * 0.01^2) = 0.838.

To calculate the posterior probability that the selected individual has the disease given two positive test results, we can use Bayes' theorem.

Let's define the following events:

A: Individual has the disease

B: Test result is positive

According to the problem, the probability of having the disease, P(A), is 0.05. The probability of a positive test result given the disease, P(B|A), is 0.98. The probability of a positive test result given no disease, P(B|not A), is 0.01 (since the test correctly detects the absence of the disease 99% of the time).

We want to calculate the probability of having the disease given two positive test results, P(A|BB).

Using Bayes' theorem, we have:

P(A|BB) = (P(A) * P(BB|A)) / P(BB)

Since the two test results are independent, we can calculate the probability of both tests being positive as:

P(BB) = P(B) * P(B)

Substituting the values, we can calculate the posterior probability:

P(A|BB) = (0.05 * 0.98^2) / (0.05 * 0.98^2 + 0.95 * 0.01^2)

Performing the calculations, the posterior probability that the selected individual has the disease given two positive test results is approximately 0.838, or 83.8%.

To learn more about Bayes' theorem click here : brainly.com/question/29598596

#SPJ11

Answer: 12

Step-by-step explanation:

the formula is y=mx+b where mx is the slope and b is the y intercept

The diameter of this circle has length of 65 when it is inscribed in a circle is a quadrilateral.

The straight line that runs through the center of a round shape or object from one point on one edge to another: The diameter is twice as large as the radius. The pond is six feet across. Both definitions hold true for the diameter of a sphere.

We note that 25²+60²=65² and 39²+52²=65²

Let \(\bar{AB}\)=25, \(\bar{BC}\)=39, \(\bar{CD}\)=52, \(\bar{DA}\)=60

Let \(\bar{BD}\)=x and ∠DAB=y

x²=25²+60²-3000cos(y)

x²=39²+52²-4056cos(180-y)

We obtain by performing some computation x²=4225-3000cos(y) and x²=4225-4056cos(y).

4056cos(y)=3000cos(180-y)

cos(180-y)=-cos(y)

So, by substituting we get 4056cos(y)= -3000cos(y)

cos(y)=0 or y=90.

∠BAD=90 and ∠BCD=90.

The diameter of a right triangle inscribed in a circle is the hypotenuse.

This means that the diameter is √4225=65

Therefore, the diameter of this circle has length of 65.

To know more about diameter, visit:

https://brainly.com/question/5501950

#SPJ4

Answer:

least is -14/3, -5.1, and greatest is -4

Step-by-step explanation:

In negative the numbers are completely different than the positive, its the opposite in positive numbers the higher the number is the greater it is, in negative the lower number it is the greater it is.

Answer:

8(x+3) is the answer

Step-by-step explanation:

The equation is 6(x + 3) = 60. Then the solution of the equation is 3.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The product of 6 and the sum of a number and 3 is 60.

Let the number be 'x'. Then the equation is written as,

6(x + 3) = 60

Simplify the equation, then the value of the variable 'x' will be calculated as,

6(x + 3) = 60

x + 3 = 60 / 6

x + 3 = 10

x = 10 - 3

x = 3

The equation is 6(x + 3) = 60. Then the solution of the equation is 3.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ5

Let X and Y be jointly continuous random variables with joint density function f(x,y)=c(y2−x2)e−2y,−y≤x≤y,0<y<∞. c = 1/4 so that f is a density function.

Throughout the complete range of potential X and Y values, the joint density function must integrate to 1.

The interval [-y, y] for  0 < y < ∞ defines the range of potential values for X and Y. The joint density function integral over this region must therefore be equal to 1.

Integrating the given density function, we have:

∫∫c(y2−x2)e−2y dxdy

= c ∫∫(y2−x2)e−2y dxdy

= c ∫y2e−2y dy − c ∫∫x2e−2y dxdy

= c [−2ye−2y − (−2/2)e−2y]|y=0 to ∞

= c [2 − (−1)]

= c(3)

Therefore, c = 1/4 so that the joint density function integrates to 1.

Complete Question:

Let X and Y be jointly continuous random variables with joint density function f(x,y)=c(y2−x2)e−2y,−y≤x≤y,0<y<∞. Find c so that f is a density function.

To learn more about range visit:

https://brainly.com/question/30389189

#SPJ4

Answer:

Step-by-step explanation:

The expression 191 divided by 3 equals 63.66666666666667 (approximately 64)

The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

The equation would be:

C is the total cost and m is the miles driven.

We know that:
Charge of the truck: $35

Charge per mile: $2.50

Then, form the equation as follows:

C = 35 + 2.50m

Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

Know more about equations here:

https://brainly.com/question/2972832

#SPJ1