For a normal distribution with a mean equal to µ = 3 and standard deviation equal to σ = 2, find P(x>4)a. 0.69b. 0.31c. 1d. 0e. 0.67

Yes, there is a proportion relationship between the number of bushel and acres of land. The relationship is the number of busher is directly proportional to the number of acres of land.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

direct proportion is given as y= kx

Where y and x are the variables and k is constant.

If the bushel of orange is given by x and the acres of land by y

then x= ky

for the expression to be correct the value of k should be thesame

when x= 720 and y = 4

k= x/y

k= 720/4= 180

when x= 1260 and y= 7

k= x/y

k= 1260/7

k= 180

therefore the x is directly proportional to y

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Answer: y= 3/2x - 6

Step-by-step explanation:

The equation is y=mx + b

The y-intercept is when x = 0, so on the table y-intercept = -6

The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2

to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}\)

now, the y-intercept occurs when x = 0, recheck the picture below.

(1) The perimeter of AXYZ ≈ 23.54.

(2) the height of AXYZ is approximately 5.37.

What is the perimeter of the triangle?

In geometry, the perimeter of a triangle is the total length of the boundary or the outer edge of the triangle. It is the sum of the lengths of all three sides of the triangle.

1. To determine the perimeter of ΔXYZ, we need to find the lengths of all three sides and add them together.

Using the distance formula, we have:

Side XY: √[(10-2)² + (9-5)²] = √64 + 16 = √80 ≈ 8.94

Side YZ: √[(6-10)² + (1-9)²] = √16 + 64 = √80 ≈ 8.94

Side ZX: √[(6-2)² + (1-5)²] = √16 + 16 = √32 ≈ 5.66

The perimeter of ΔXYZ = 8.94 + 8.94 + 5.66 ≈ 23.54 (rounded to the nearest hundredth).

2. To determine the height of ΔXYZ, we need to first select a base. Any side of the triangle can be chosen as the base, but for simplicity, let's choose side YZ.

The height of the triangle is the perpendicular distance from vertex X to side YZ.

To find the height, we can use the formula for the area of a triangle:

Area of AXYZ = 1/2 * base * height

We already know the base (YZ), and we can calculate the area of the triangle using the coordinates of the three vertices:

Area of ΔXYZ = 1/2 * |(10-2)(1-5) - (6-2)(9-5)| = 1/2 * |-32 - 16| = 1/2 * 48 = 24

Now we can solve for the height:

24 = 1/2 * 8.94 * height

height = 24 / (1/2 * 8.94) ≈ 5.37

So the height of ΔXYZ is approximately 5.37. The process for finding the height of this triangle is the same as for any other triangle, but the coordinates of the vertices and the length of the sides are different.

Hence, (1) The perimeter of AXYZ ≈ 23.54.

(2) the height of AXYZ is approximately 5.37.

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The scalar triple product u⋅(v×2 w) of the given vectors u=i+2j−2k, v=j−2k, and w=i−3k is 6.

To calculate the scalar triple product, we first need to compute the cross product of vectors v and 2w. The cross product v×2w is calculated as follows:

v×2w = (j−2k)×(2(i−3k))

              i         j        k

v            0        1       -2

2w         2        0     -6

v×2w = i(1*(-6))-j(2*(-2)) + k(-1*2)

         = -6i + 4j-2k

Now, we can calculate the scalar triple product u⋅(v×2w) by taking the dot product of vector u with the result obtained above:

u⋅(v×2w) = (i+2j−2k). (-6i + 4j-2k)

              = ((1*(-6)) + (2*4) + ((-2)*(-2))

              = -6 + 8 + 4

             =  6

Therefore, the scalar triple product u⋅(v×2w) is equal to 6.

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This question is incomplete

Complete Question

Joe needs to transfer 28 quarts of oil into gallons containers joe calculated that he needs 112 containers but he made a mistake in his calculations identify and correct his error

Joe's error:

28 quarts × 4 quarts/ 1 gallon

= 28 quarts/1 × 4 quarts/ 1 gallon

= (28 × 4)/ ( 1 × 1) = 112 gallons

Answer:

7 gallons is the correct answer

Joe needs to transfer 28 quarts of oil into 7 gallons

Step-by-step explanation:

Joe's error:

28 quarts × 4 quarts/ 1 gallon

= 28 quarts/1 × 4 quarts/ 1 gallon

= (28 × 4)/ ( 1 × 1) = 112 gallons

Correcting Joe's error, we have:

4 quarts = 1 gallon

28 quarts = x

Cross Multiply

4 quarts × x = 28 quarts × 1 gallon

x = 28 quarts × 1 gallon/ 4 quarts

x = 7 gallons

= 28 quarts/x gallons × 1 gallon/4 quarts

= (28 × x)/ ( 1 /4) = 7 gallons

Therefore, Joe needs to transfer 28 quarts of oil into 7 gallons

Answer:

x = 55

Step-by-step explanation:

1. We can use exterior angle theorem to find the value of x. The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two remote angles in that same triangle.

2. (Solving)

Step 1: Simplify both sides of the equation.

Step 2: Subtract 2x from both sides.

Step 3: Subtract 39 from both sides.

Step 4: Divide both sides by -1.

Step 4: Check if solution is correct.

Therefore, x = 55.

A total of 336 tubs of cookie dough were sold in all.

A ratio or figure stated as a fraction of 100 is called a percentage. The sign "%" is frequently used to indicate it as a percentage or a component of a total.

So, the number of tubs sold in each week can be represented by the following sequence:

Week 1: 100

Week 2: 0.8(100) = 80

Week 3: 0.8(80) = 64

Week 4: 0.8(64) = 51.2 ≈51

Week 5: 0.8(51) = 40.8≈41

To find the total number of tubs sold in all 5 weeks, we can add up the number of tubs sold in each week:

Total = 100 + 80 + 64 + 51 + 41

Total = 336

Therefore, a total of 336 tubs of cookie dough were sold in all.

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The required measure of the angle ∠spq of a rhombus is 110°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For rhombus,
m∠spr=(2x + 15)°
m∠qpr=(3x−5)°

And,
m∠spr = m∠qpr
2x + 15 = 3x - 5
x = 20

Now,
∠spq = m∠spr + m∠qpr
        = 2x + 15 + 3x - 5

        = 5x + 10
        = 5(20) + 10
        = 110°

Thus, the required measure of the angle ∠spq of a rhombus is 110°.

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Answer:

2, -7, 3 are your answers! :).

Step-by-step explanation:

The opposite of a positive would be it's negative form, and the opposite of a negative would be it's positive form.

Answer:

the little box would indicate that it is a 90 degree angle.

Answer: 50

Step-by-step explanation: to find CXF all you need to do is 90-40

Answer:

HCF=15    LCM=6,300

Step-by-step explanation:

Answer:

HCF = 15

LCM = 6300.

Step-by-step explanation:

Write them out as a product of their prime factors:

180 = 2*2*3*3*5

150 = 2*3*5*5

315 = 3*3*5*7

Picking out the factors common to all 3 list of prime factors:

The GCF = 3*5 = 15.

To find the LCM we pick out all the numbers except if there are repeated number we only use them once, So for example  we only take 2*2 for the calculation as there is a pair of 2's in 180 and 150 factors and there is an extra 2 in 180 - so we only take 2 of the 3 2's.

LCM = 2 * 2 * 3 * 3 * 5 * 5 * 7

= 6300.

Answer:

I think the answer would be 33. I am not exactly sure though.

When a plane is inclined at a 45-degree angle and intersects a cylinder's base along its diameter with radius "r," it results in the division of the cylinder into two identical right circular cones.

Imagine a cylinder with a radius "r."

The plane passes through the cylinder's base, creating a line that bisects the circular base into two equal halves.

This intersection between the inclined plane and the cylinder forms a cross-section that resembles an isosceles right triangle.

By symmetrically splitting the cylinder along its central axis, the inclined plane generates two congruent right circular cones, each with a 45-degree angle at its apex. The curved line formed by the intersection represents the boundary between the two cone halves.

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Answer: 810

Step-by-step explanation:

Answer: B. I and ll only

Step-by-step explanation:

The graph appear to show a sinusoid is Graph  I and II only.

A smooth, repeating oscillation characterises a sinusoidal function. Sine is an oscillation that is smooth and repeated, thus the name "sinusoidal." A pendulum swinging, a spring bouncing, or a guitar string vibrating are a few examples of commonplace objects that can be described by sinusoidal functions.

A sinusoidal function has a smooth periodic graph as its representation.

The graph repeats itself at every predetermined interval and is continuous along the x-axis.

We can tell from the graph that has been given to us that it is a sinusoidal graph || since it resembles a graph of sines.

Moreover, since graph I|I is not continuous, it cannot be a graph of sinusoidal graph.

Moreover, graph I represents a sinusoidal graph because it resembles a sine function graph.

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Answer:

6 hours

Step-by-step explanation:

4 pages=2 hours

8 pages=4 hours

12 pages=6 hours

2 + 7 < 18 inequalities represent the number of remaining hours Mr. Roy could be scheduled to work this week.

The term "inequality" in mathematics refers to a relationship among two expressions or values which are not similar to one another.

Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols " >, < , ≤ ,or ≥ ".

If x is 2, then 2+7 should equal 9, which is less than the amount Roy wanted to work, and would be the best option for him since he wanted to work for less than 18 hours.

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The complete question is as follows:

Mr. Roy is scheduled to work less than 18 hours this week. he has already worked 7 hours. if x is the remaining number of hours. Mr. Roy could work this week which inequalities represent the number of remaining hours Mr. Roy could be scheduled to work this week? select all that apply

A 2+7 > 18

B 2 + 7 < 18

C 2 +18 > 7

DI > 11

EI < 11

Answer:

1/14

Step-by-step explanation:

slope = difference of y over difference of x

= (-3-(-4)) /(8 -(-6)) = 1/14

A sample statistic is a statistical finding based on small sample size.

A sample is only a small portion of the population. Let's imagine you were interested in determining the average income for all Americans in your population. Instead of knocking on every door in America because of time and money constraints, you decide to question 1,000 random people. Your sample consists of these a thousand persons.

Once you have your sample, you will obtain a statistic of some sort. Actually, a statistic is just a piece of data; in this case, it's the average salary. A sample statistic is one that is drawn from a portion of data or a population and contains statistical information (such as an average, median, or other types of statistics).

Your sample statistic might change greatly based on the things you select from the population because you are only working with a small portion of the total population. In actuality, there is some uncertainty in the majority of sample statistics.

It's extremely unlikely that the knowledge you gather from a few items will paint a complete picture or provide you with a precise explanation of what is happening in the population as a whole. While margins of error, confidence intervals, and many other statistical tools can help us quantify uncertainty, statistics is really just scientific guesswork.

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i dont know my friend so try asking someone better than cause i have no brain for this type of math

The results of the expressions given are:

Part 1:

1)  -2

2) 12

3) 2

4) 11

5) -7

6) 7

7)  0

8)  0

9) - 6

10) - 10

Part 2:

1) 12

2) - 2

3)  2

4)  11

5) 5

6) 0

7) - 28

8) 0

9) - 17

10) -2

We solve the equations respecting the level of hierarchy:

Part 1:

1) -7+5= -2

2) 7+5 = 12

3) 7+ (-5) = 7 - 5 = 2

4) 2+9 = 11

5) 2+(-9) = 2 - 9 = -7

6) -2+9 = 7

7) 8+(-8) = 8 - 8 = 0

8) -5+5 = 0

9) -3+(-3) = - 3 - 3 = - 6

10) -5+(-5) = - 5 - 5 = - 10

Part 2:

1) 7- (-5) = 7 + 5 = 12

2) -7- (-5) = - 7 + 5 = - 2

3) 7- (+5) = 7 - 5 = 2

4) 2- (-9) = 2 + 9 = 11

5) -5- (-10) = - 5 + 10 = 5

6) 5-5 = 0

7) -8- (+20) = - 8 - 20 = - 28

8) -3- (-3) = - 3 + 3 = 0

9) -5- (+12) = - 5 - 12 = - 17

10) 8- (+10) = 8 - 10 = -2

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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Answer:

Frank is correct, because (see explanation below)

Step-by-step explanation:

Let's separate into two cases:

Case 1: Blue marble

\(\frac{6}{7}\) (There are 6 blues in the bag and 7 marbles in total in the bag, we put the 6 in the numerator because we want a blue marble first.)

Case 2: Green marble

\(\frac{1}{6}\) (There is only 1 green in the bag and 6 marbles remaining in the bag, because we already took 1 blue out in Case 1. We put 1 in the numerator because we want the green marbloe only.)

Multiply Case 1 with Case 2 because they are a combination:

\(\frac{6}{7} * \frac{1}{6} = \frac{1}{7}\)

Therefore Frank is correct.

To solve this problem, we need to use the Central Limit Theorem (CLT) since we have a large number of independent images (80) and we want to calculate the probability of the total size falling within a certain range.

The CLT states that the sum of a large number of independent and identically distributed random variables approaches a normal distribution, regardless of the shape of the original distribution.

In this case, the sum of the sizes of the 80 images will also follow a normal distribution. The mean of the sum is the product of the average size of one image (0.6 megabytes) and the number of images (80), which is 48 megabytes (0.6 * 80).

The standard deviation of the sum is the product of the standard deviation of one image (0.4 megabytes) and the square root of the number of images (square root of 80), which is approximately 3.5777 megabytes (0.4 * sqrt(80)).

Now we can standardize the range of interest using the formula for standardizing a variable:

Z = (X - μ) / σ

where Z is the standardized value, X is the value of interest, μ is the mean, and σ is the standard deviation.

For the lower bound of 47 megabytes:

Z1 = (47 - 48) / 3.5777

For the upper bound of 50 megabytes:

Z2 = (50 - 48) / 3.5777

Now, we can use a standard normal distribution table or a calculator to find the probabilities associated with these standardized values.

P(47 ≤ X ≤ 50) = P(Z1 ≤ Z ≤ Z2)

By looking up the values of Z1 and Z2 in the standard normal distribution table or using a calculator, we can find the corresponding probabilities.

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\(\\ \sf\longmapsto \dfrac{sin40.sin120}{sin110-sin340}\)

\(\\ \sf\longmapsto \dfrac{sin(90-50).sin(90+30)}{sin(90+20).sin(360-20)}\)

\(\\ \sf\longmapsto \dfrac{cos50.cos30}{cos20.(-sin20}\)

\(\\ \sf\longmapsto \dfrac{cos50cos30}{-sin20cos20}\)

\(\\ \sf\longmapsto -\dfrac{cos30cos50}{sin20cos20}\)

Using Pythagorean theorem, the side of the ladder will reach 22.45 ft far up now.

Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.

c² = a² + b²

If a 45 foot ladder is set up against the side of a house so that it reaches up 27 feet, then the distance between the base of the ladder and the base of the side of the house is the difference between the square of the two values.

c = 45 ft

a = 27 ft

b² = c² - a²

b² = (45 ft)² - (27 ft)²

b² = 2025 - 729

b² = = 1296

b = 36 ft

If Latanya grabs the ladder at its base and pulls it 3 feet farther from the house, then the distance becomes b + 3 = 39 ft.

Using Pythagorean theorem, determine how far up the ladder is on the side of the house.

c = 45 ft

b = 39 ft

a² = c² - b²

a² = (45 ft)² - (39 ft)²

a² = 2025 - 1521

a² = 504

a = 6√14

a = 22.45 ft

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Using a 95% confidence level, we can calculate a confidence interval for the difference of the population means. The results of the test and interval will help us interpret if there is a substantial difference between the two sources and where we would choose to purchase textbooks.

a. To determine if there is a significant difference in the price of textbooks from the campus bookstore and Amazon.com, we would use a two-sample t-test for independent samples.

This test compares the means of two independent samples to determine if there is a significant difference between them. In this case, our null hypothesis would be that there is no difference in the mean price of textbooks between the two sources, while the alternative hypothesis would be that there is a difference.

b. Using a 95% confidence level, we can calculate a confidence interval for the difference of the population means. Based on the sample data provided, the mean price of textbooks at the campus bookstore was $66.56, while the mean price at Amazon.com was $76.49.

The difference between the two means is $9.93. Using a two-sample t-test with a 95% confidence level, we find that the calculated t-value is 2.64 with 18 degrees of freedom. The 95% confidence interval for the difference in population means is (1.67, 18.19). This means that we can be 95% confident that the true difference in population means falls within this range.

c. Based on our results, we can conclude that there is a significant difference in the mean price of textbooks between the campus bookstore and Amazon.com. Additionally, since the confidence interval does not include zero, we can infer that this difference is not due to chance. Overall, we can say that textbooks are generally more expensive at Amazon.com compared to the campus bookstore.

However, it is worth noting that the sample size is relatively small, so it is possible that the results may not be representative of the entire population of textbooks.

Therefore, when deciding where to purchase textbooks, other factors such as convenience, availability, and additional costs (such as shipping) should also be taken into consideration.

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Answer:

30%

Step-by-step explanation:

18/60 = .3 × 100% = 30%

Answer:

135/8

Or

16.875

Step-by-step explanation:

(3²-2²)(⅔)^-3

(9-4)(3/2)³

5(27/8)

135/8

16.875