graph the system below and write its solution.

y=1/4x-3
-x+4y=-4
Note that you can also answer "No solution" or "Infinitely many" solutions.

a) The probability that the specific engineer Jane and the specific manager Mary are on the committee is 2/45

b) The probability that the most experienced and least experienced engineers are on the committee is 2/45

The term called probability in math is known as the probability is the likelihood or chance that an event will occur

And it is calculated by using the general form that can be written as,

=> Probability = Expected/Total outcome

Here we know that if 2 managers were randomly selected from  10 managers, then the probability will be 2/10

AS we know that if 4 engineers were randomly selected from 18 managers, then the probability will be 4/18

On the other hand the probability that engineer Jane or manager Mary is on the committee will be calculated as,

=> 2/10 x 4/18

=> 8/180

When we simplify this then we get the value of the probability as 2/45.

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The ratio of the variation between the group means and the variance within the groups is used to determine the f-statistic in an ANOVA test.

The ratio of variation between group means and variance within groups is used to determine the f-statistic in an ANOVA test. The difference between each group's means is measured, and the average of these differences is used to calculate the variance between the group means. Calculating the variance for each group and then averaging these variances yields the variance within the groups. The f-statistic is determined by dividing the variation between the group means by the variance within the groups. This statistic shows whether or not the variations in group means are noteworthy. The null hypothesis can be rejected if the f-statistic is greater than a predetermined threshold, indicating that the differences between the group means are statistically significant.

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If E(X) = 6 and E(Y) = 10, and the random variables are independent variables, the value of E(X | Y) is 6

Given, E(X) = 6 and  E(Y) = 10.

It is also given that X and Y are independent variables.

So, if two random variables X and Y are independent, which means that if knowing the value of one of them does not change the probability of occurring of the other one. In other words, if X and Y are independent, we can write:

                           P(Y | X) = P(Y)

So, in the question, we are asked to determine the value of E(Y | X).

                        ∴ E(X | Y) = E(X)

                        ∴ E(X | Y) = 6

Hence, the value of E(X | Y) is 6

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No, the function in the first column is not an eigenfunction of the operator in the second column.

In order for the function in the first column to be an eigenfunction of the operator in the second column, it must satisfy the equation Aφ = λφ, where A is the operator, λ is an eigenvalue, and φ is the eigenfunction. However, in this problem, the function in the first column is 5y5 y2d2/dy2 yx7−xy−7, and the operator in the second column is x3(∂3/∂x3) y3(∂3/∂y3). Since these do not satisfy the equation, the function in the first column is not an eigenfunction of the operator in the second column.

The complete question is :

Determine if the function in the first column is an eigenfunction of the operator in the second column.

5y5 y2d2/dy2 yx7−xy−7 x3(∂3/∂x3) y3(∂3/∂y3)

sinθcos3ϕ ∂2/∂θ2 ∂2/∂ϕ2

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Answer: B. 15x+7

Step-by-step explanation:

since you are calculating the total # of ice cream cones sold, you must add the two equations together: 8x+16+7x-9=

After you simplify this equation, you will have your answer.  

If 12.5 cups of milk  and 15 cups of flour is required to make the cup , then  the total number of cups required to make the biscuit is 27.5   .

To make biscuits, we need a certain amount of ingredients, including milk and flour.

In this case, the number of cups of milk required is = 12.5  and

the number of cups of flour required is = 15 cups ;  

The total number of cups required to make biscuits is the Addition of the cups of milk and flour, which is 12.5 cups + 15 cups = 27.5 cups.

Therefore , 27.5 cups of milk and flour is required .

The given question is incomplete , the complete question is

If 12.5 cups of milk  and 15 cups of flour is required to make the cup then find the total number of cups required to make the biscuit .

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The expected number of rolls until the first pair of consecutive sixes appears is 36.

This can be calculated using a geometric distribution, where each roll is considered a Bernoulli trial with success defined as rolling two sixes in a row, and failure defined as not rolling two sixes in a row. The probability of success in any given roll is 1/36, since there are 36 possible outcomes for rolling two dice and only one of them results in two sixes.

Using the formula for the expected value of a geometric distribution, we can calculate the expected number of rolls until the first success as:

where p is the probability of success in a single roll (1/36) and E is the expected number of rolls until the first success. So the expected number of rolls until the first pair of consecutive sixes appears is 36.

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Lady Macbeth exemplifies the traditional role of a woman by showing her hospitality, generosity, graciousness, and support to her guests.

At the banquet in Macbeth, Lady Macbeth fulfills a traditional feminine role in several ways. Firstly, she demonstrates her hospitality and generosity by welcoming the guests and providing them with food and drink. Secondly, she shows her nurturing nature by urging Macbeth to be more hospitable and to provide the guests with more generous servings. Thirdly, she shows her graciousness and hospitality by offering the guests timely compliments. Lastly, she shows her caring and supportive nature by encouraging Macbeth to be more gracious and generous. Altogether, Lady Macbeth exemplifies the traditional role of a woman by showing her hospitality, generosity, graciousness, and support to her guests.

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The temperature at 6 P.M. would be - 29 °F.

Given is that Casho spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -10.4°F. Between 9 am and noon, the temperature rose 9.5°F. Between noon and 3 pm, the temperature went down 10°F. Between 3 pm and 6 pm, the temperature went down 18.6°F.

Temperature at 9 A.M. = - 10.4°F.

At noon, the temperature would be = - 10.4°F + 10°F = - 0.4°F

At 3 P.M., the temperature would be = - 0.4°F - 10°F = - 10.4°F

At 6 P.M., the temperature would be = - 10.4°F - 18.6°F = - 29 °F

Therefore, the temperature at 6 P.M. would be - 29 °F.

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Using the properties of similarity, we say that;

Statements ΔPMK~ΔLMQ and Reason is SAS~.

When two figures have the same shape but differ in size, they are said to be similar figures. In other words, two figures are said to be comparable when they have many characteristics but aren't necessarily identical.

Similar figures are two shapes with the same dimension or common ratio but a different size or length, such as triangles, polygons, quadrilaterals, etc.

If two triangles are comparable, then any pairs of triangles with the same corresponding angles are also comparable.

Triangles have proportional sides on all matching sides.

In this, two sides are in equal ration and angle between these two lines is congurant. So using the properties of similarity, we say that; Statements ΔPMK~ΔLMQ and Reason is SAS~.

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She will pay $44.10 altogether for the jeans

A sales tax is a tax paid to the government for the sales of certain goods and services.

Since the pair of jeans cost $42.00 and the sales tax is 5%.

Sales pax = 5/100 * $42.00 = $2.10

Total cost = $42.00 + $2.10 = $44.10

Therefore, she will pay $44.10 altogether for the jeans

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The statistical decision you could make from this information is that the two variables are dependent and unlikely to occur by chance.

In a chi-square test of independence, a p-value of 0.0000 means that the probability of observing the data or a more extreme result given that the null hypothesis is true is very small. In this case, the p-value is less than the level of significance (0.05), which means that you would reject the null hypothesis.

Based on this information, you could make the statistical decision that there is evidence to suggest that there is a relationship between the two variables being tested and that this relationship is unlikely to have occurred by chance. This means that you would conclude that the variables are dependent on each other and not independent.

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Answer:

4/3x + 9/2y

Step-by-step explanation:

2x + 3y - 2/3 x + 1 1/2y

1 1/2 = 3/2

2x + 3y - 2/3x + 3/2y

= 6/3x + 6/2y - 2/3x + 3/2y

= 4/3x + 9/2y

The ratio of the volume of the triangular prism to the volume of the cuboid is 3: 20

The base of the triangular prism is a right triangle with legs 5 cm, 4 cm

∴ b = 5 cm and h = 4 cm

∵ Its height is 9 cm

∴ H = 9 cm

Substitute them in the rule of the prism above

∴ V = 90 cm³

The dimensions of the base of the cuboid are 6 cm and 5 cm

∴ L = 6 cm and W = 5 cm

∵ Its height is 20 cm

∴ H = 20 cm

→ Substitute them in the rule of cuboid

V = 6 × 5 × 20

V = 600 cm³

Find the ratio between them

∵ V: V = 90: 600

= 3 : 20

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Find the ratio of the volume of the triangular prism

to the volume of the cuboid.

The system of equations are solved

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

A = x³ + 9

On simplifying the equation , we get

A = x³ + 9

So , it cannot be further factorized

b)

A = x² - 12

On simplifying the equation , we get

A = x² - 12

So , it cannot be further factorized

c)

A = 9x² - 16

On simplifying the equation , we get

A = ( 3x + 4 ) ( 3x - 4 )

On factorizing the equation ,

A = ( 3x )² - ( 4 )²

Hence , it is a difference of perfect squares

d)

A = 4x² + 9

On simplifying the equation , we get

A = ( 2x )² + ( 2 )²

So , it cannot be further factorized

e)

A = x³ + 8

On simplifying the equation , we get

A = ( x )³ + ( 2 )³

Hence , it is a perfect cube

f)

A = 25x² - 64

On simplifying the equation , we get

A = ( 5x + 8 ) ( 5x - 8 )

On factorizing the equation ,

A = ( 5x )² - ( 8 )²

Hence , it is a difference of perfect squares

g)

A = x² - 100

On simplifying the equation , we get

A = ( x + 10 ) ( x - 10 )

On factorizing the equation ,

A = ( x )² - ( 10 )²

Hence , it is a difference of perfect squares

h)

A = 216x³ - 27

On simplifying the equation , we get

A = ( 6x )³ + ( 3 )³

Hence , it is a perfect cube

i)

A = 8x³ - 512

On simplifying the equation , we get

A = ( 2x )³ - ( 8 )³

Hence , it is a perfect cube

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You can construct one triangle with a 2-inch side, a 4-inch side, and a 5-inch side.

This is because of the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the 2-inch side is less than the sum of the 4-inch and 5-inch sides, and the 4-inch side is less than the sum of the 2-inch and 5-inch sides, so the conditions of the triangle inequality theorem are satisfied. Therefore, it is possible to form a triangle with these side lengths.

Answer:

13800

Step-by-step explanation:

First we suppose the cost price is X, so 15%x is lost

x-15%x=10200

85%x=10200

   x=12000

Now want 15% profit, so 100%+15%=1.15

12000x1.15=13800

Answer: There are 29 freshman in the class

Step-by-step explanation:

Sophmore = x

Freshman = x+16

x + (x + 16) = 42

x + x + 16 = 42

2x + 16 = 42

2x = 26

x = 13

Sophmore = x = 13

Freshman = x + 16 = 29

Answer:

29 freshmen

Step-by-step explanation:

Freshmen = 16 + x

Sophomores = x

Equate the number of freshmen(16 + x ) and the number of sophomores( x ) to 42( the total number of students in the class)

(16 + x ) + x = 42

16 + 2x = 42

2x = 42 - 16

2x / 2 = 26/2

x = 13

Therefore, the number of freshmen

= 16 + x

= 16 + 13

= 29

The values for x and y for the geometric system formed by two similar triangles are 9 / 2 and 15 / 4, respectively.

In this question we find the case of a geometric system formed by two similar triangles. Two triangles are similar when their angles are congruent and sides are not congruent though proportional. The situation represented in the figure is described by proportion formula:

5 / (5 + y) = 4 / 7 = 6 / (6 + x)

Now we proceed to find the values for x and y by algebra properties:

5 / (5 + y) = 4 / 7

5 · 7 = 4 · (5 + y)

35 = 20 + 4 · y

15 = 4 · y

y = 15 / 4

6 / (6 + x) = 4 / 7

6 · 7 = 4 · (6 + x)

42 = 24 + 4 · x

18 = 4 · x

x = 18 / 4

x = 9 / 2

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Answer: 1:5

Step-by-step explanation:

If the number of people who wear glasses are 1/5 of the population, the the entire population would be 5/5. In this case, your ratio would be 1/5:5/5, but when you simplify that, you’d get 1:5

I hope this helps!

Answer:

y = (x - 6)^2 + 10.

Step-by-step explanation:

y = x^2 - 12x + 46

y = (x - 6)^2 - 36 + 46

y = (x - 6)^2 + 10.

Probability that the sample mean is less than 850 if a sample of size 95 is taken from a population with a mean of 1035 and a standard deviation of 362 IS 4.941

The Central Limit Theorem says that no matter what the distribution of the population is, as long as the sample is “large,” meaning of size 30 or more, the sample mean is approximately normally distributed. If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size.

sample mean is less than 850

sample of size 95

mean of 1035

standard deviation of 362.

find the probability

μX−=μ=1035 and σX=σ/√n=362/√95 =37.44

P(850>X) =  (850 -1035)/ 37.44

               = 4.941

probability that the sample mean is less than 850 if a sample of size 95 is taken from a population with a mean of 1035 and a standard deviation of 362 IS 4.941

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Answer:

because yftythdetv y yvh bb jhh

Answer:

65

Step-by-step explanation:

basically 65% =

65/100 of the thing you're multiplying with

so,

65/100 x 100 = 65

Answer:

7. (4, -6)

8. (1, 4)

Step-by-step explanation:

7.

substitution is when we use one equation to express one variable by the other, and then use that in the second equation to solve for this other variable.

with that value we go back into the first equation and solve for the first variable.

x + y = -2

x = -2 - y

4x + 2y = 4

2x + y = 2

here we use now the x = 2 - y :

2(-2 - y) + y = 2

-4 - 2y + y = 2

-4 - y = 2

-6 - y = 0

y = -6

x = -2 - -6 = -2 + 6 = 4

8.

elimination is when we transform the equations, so that after adding both equations the sum contains only one variable, for which we can then solve. and then we use that in any of the original equations to solve for the other equation.

in our case we don't need any transformation. just by adding both equations we eliminate x and can solve for y.

-5x + 6y = 19

5x - 3y = -7

------------------------

0 3y = 12

y = 12/3 = 4

now we use that in any of the original equations. e.g. the second :

5x - 3×4 = -7

5x - 12 = -7

5x = 5

x = 1

79.1 mL is equal to 0.0791 liters with correct significant figures.

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.

79.1 mL is equal to 0.0791 litres. To convert millilitres to litres, we divide the number of milliliters by 1000:

79.1 mL / 1000 = 0.0791 liters

So, 79.1 mL is equal to 0.0791 litres with correct significant figures.

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Answer: a

Step-by-step explanation: add 2 + 3 +28

An integral for the volume of the solid obtained by rotating the region bounded by the curves y = 1/(1 x2), y = 0, x = 0, and x = 2 about the

line x = 2 is v = 2.pi.∫(0,2) (2-x/1+[tex]x^{2}[/tex]).dx

we will use the method of cylindrical shells here as per the limits given to calculate the volume,

let us first find the volume of a cylindrical shell with thickness dx at a distance of x from y axis,

dV = 2.pi(2-x).y.dx

where (x,y) is a point on the curve y=1/1+[tex]x^{2}[/tex]

v = 2.pi.(2-x)(1/1+[tex]x^{2}[/tex]).dx

Therefore the total volume would be,

v = 2.pi.∫(0,2) (2-x/1+[tex]x^{2}[/tex]).dx

v = 2.pi.[2tan-1 x -(1/2).ln(1+[tex]x^{2}[/tex])] at 0,2

v = 2.pi.[2tan-1(2) - ln 5/2]

v = 4 .pi.tan-1(2) - pi.ln5

therefore volume = 8.8 approximately.

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If ten slices are cut from the cheese. each slice has a width of 1 cm , then the maximum possible volume of the remaining block is 729 cm³ .

The maximum possible volume of the remaining block of cheese can be found by considering the slices to be the minimum possible thickness, which is 1 cm. So, after each slice is cut, the dimensions of the cheese decreases by 1 cm.

the dimensions of the block of cheese is :  10 cm by 13 cm by 14 cm  .

number of slices cut is = 10 slices .

the dimension change by the 10 cut of cheese slices are as follows :

(10,13,14) → (10,13,13) → (10,12,13) → (10,12,12) → (10,11,12) → (10,11,11) → (10,10,11) → (10,10,10) → (9,10,10) → (9,9,10) → (9,9,9) .

So , after cutting 10 slices the dimensions of the remaining block is 9 cm by 9 cm by 9cm .

the volume of the remaining cheese  block is = 9×9×0 = 729 .

Therefore , the maximum possible volume of the remaining block is 729 cm³ .

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The length of the diagonal of the rectangle is 11.7 units.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that the area of a rectangle is 44 square units. Its length measures 11 units.

Area = L x W

44  = 11 x W

W = 4 units

D² = W² + L²

D = √ ( 11² + 4 ²)

D = √ ( 121 + 16)

D = 11.7 units'

Therefore, the measure of the diagonal is 11.7 units.

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The equation for the given information is L = -1.5D + 35.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let L represent the water level after D days.

From the question, m = -1.5, b = 35, hence:

L = -1.5D + 35

Hence, the equation for the given information is L = -1.5D + 35.

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