Find the product of 27x60 then explain how you would use mental math to find the product of 27x600

Answer:

no. who eat lunch special = 12

no. who eat dessert = 6

Step-by-step explanation:

Let x = no. who eat lunch special

y = no. who eat dessert

(1)    8x + 2y = 108             (2)    6x + 3y = 90

 Divide thru by 2                         Divide thru by 3

      4x + y = 54                          2x + y = 30

     -2x - y = -30

       2x = 24

         x = 12                               2(12) + y = 30

                                                    24 + y = 30

                                                            y = 6

Answer: (6,2) (0,-2) (-3,-4)

Step-by-step explanation:

If you find the other coordinate pair groups on the graph, there is at least one that doesn't land on the line on the graph.

In the top left, (-6,-5) is not on the graph. If it had been (-6,-6) then it would've been correct, but it isn't.

In the bottom left, (0,-3) isn't on the graph. Instead, (0,-2) is.

In the bottom right, (3,-4) isn't on the graph, but (-3,-4) is.

(5x-7)(x-9)

Factoring is the inverse of the distributive property. This means that we want to find the factors, not the product.

Partial Factoring

The expression we are given has already been factored to an extent. Both terms are split into 2 different factors. This was done by factoring out the greatest common factor (GCF) from both terms. In the first term, the GCF was 5x, and in the second, the GCF was -7.

Complete Factoring

Even though it was partially factored, we can factor it more. When given the situation:

The expression can be factored into:

You can add (subtract in this case because 7 is negative) the values from outside the parentheses together. This term can then be multiplied by the value within the parentheses.

Thus, 5x(x+9) -7(x+9) can be factored into:

Remember this trick only works when both terms share a factor like (x-9).

The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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Answer:

Null Hypothesis: H0:μ ≤ 16.8

Alternative Hypothesis: Ha: μ > 16.8

Step-by-step explanation:

We are told that affer testing the hypothesis (at the 5% level of significance), that the average price-earnings ratio increased from the past value of 16.8.

It means that the past value was not more than 16.8.

This follows that the null hypothesis is given as;

H0:μ ≤ 16.8

And since it has been discovered that the ratio increased from the past value of 16.8, the alternative hypothesis is;

Ha: μ > 16.8

Answer: x=1, y=1, z=-1

Step-by-step explanation:

From the first and 3rd equation, 2x+9y=11.

The first equation is also 4x+16y-4z=24, so add that to the second equation, and you get 6x+27y=33.

Solving, we get x=1 and y=1, meaning that z=-1.

The perimeter of the water wheel  \(8\sqrt{10}\)

The correct option is (A)

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. To derive the formula, let us consider two points in 2D plane A( x, a) and B(y, b).

So, the distance between two points be: \(\sqrt{(y-x)^{2}+(b-a)^{2}}\)

As water wheel is designed in the shape of regular octagon.

To find the perimeter of the  water wheel.

Since the water wheel is in the shape of regular octagon all sides are equal.

Using Distance Formula,

D= \(\sqrt{(4-3)^{2}+(0-3)^{2}}\)

  = \(\sqrt{10}\)

So, the side of regular octagon will be \(\sqrt{10}\).

Perimeter of Regular Octagon = 8 x side

                                                   = \(8\sqrt{10}\)

Hence, the perimeter of the water wheel  \(8\sqrt{10}\)

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Answer:

A

Step-by-step explanation:

\(\begin{align}\sf\:\Phi_1 &= \iint_{S_1} (-2u^6\cos(v) - 2u^3\sin(v)) \, du \, dv \\ &= \int_{0}^{1} \int_{0}^{2\pi} (-2u^6\cos(v) - 2u^3\sin(v)) \, dv \, du \end{align} \\\)

Answer:

(-6,0)

Step-by-step explanation:

An equation of a line can be modeled as y = mx + b where m is slope and b is y-intercept.

For the line r, we can model the equation as y = mx + 3 since the line intersects y-axis at (0,3) as seen in the attachment.

For the line t, we can model the equation as y = mx - 6 as the problem gives y-intercept for line t equal to -6. Hence, the line t intersects y-axis at (0,6)

Next, we have to find the slope of line t by finding the slope of line r in the attachment. Apply the rise over run by counting the steps, you can see in the attachment that I put to learn how to count rise and run of a line. Also note that the value in attachment here is a scalar quantity, meaning only magnitude, no direction.

So we will have the slope of -1 since a line graph is heading down so the output decreases as input increases. Therefore, we know that m = -1 for both lines. Therefore, for the line t, we can model the new equation to:

\(\displaystyle{y=-x-6}\)

Then we find the x-intercept of the line by letting y = 0. Thus,

\(\displaystyle{0=-x-6}\\\\\displaystyle{x=-6}\)

Therefore, the x-intercept of line t is at (-6,0).

Answer:

(-6,0)

Step-by-step explanation:

We need to determine the equation of line r first to find the x-intercept of line t.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

\(slope = \frac{y_2 - y_1}{x_2 -x_1}\)

For line r passing through (3, 0) and (0, 3), the slope is:

\(slope = \frac{3 - 0}{0 - 3} = -1\)

Since line t has the same slope as line r, its slope is also -1.

The equation of a line in slope-intercept form (y = mx + b) is determined by its slope (m) and y-intercept (b).

We know that the slope (m) of line t is -1, and the y-intercept (b) is -6. Substituting these values into the slope-intercept form, we get:

y = -x - 6

To find the x-intercept, we set y = 0 and solve for x:

0 = -x - 6

Adding x to both sides:

x = -6

Therefore, the x-intercept of line t is (-6,0).

Answer:

42

Step-by-step explanation:

Rectangle: A = 6 x 5 = 30

Triangle: A = 1/2(6 x 4) = 12

Area of figure: 30 + 12 = 42

Answer:

Your question is missing some parts

and the degree seems off is it 90⁰

Answer:

90

Step-by-step explanation:

The average of a set of numbers is the sum of the numbers, divided by the count of the numbers.

Thus, the average of 85, 88 and 97 is

85 + 88 + 97

------------------- = 270/3, or 90

         3

Answer:

90

Step-by-step explanation:

Answer:

) The number of men who attended the sessions can be obtained by summing up the number of males in each session:

Total number of men = 12 + 18 + 17 = 47

Therefore, 47 men attended the sessions.

b) The number of people who attended Session 3 can be obtained by summing up the number of males and females in Session 3:

Total number of people in Session 3 = 17 (males) + 5 (females) = 22

Therefore, 22 people attended Session 3.

c) The sample size refers to the total number of attendees across all sessions. We can calculate it by summing up the number of males and females in each session:

Sample size = (12 + 8) + (18 + 9) + (17 + 5) = 69

Therefore, the sample size is 69.

d) To calculate the probability that a randomly selected person is male, we need to divide the number of males by the sample size:

Probability of selecting a male = Number of males / Sample size = 47 / 69 ≈ 0.6812

Therefore, the probability that a randomly selected person is male is approximately 0.6812 (rounded to four decimal places).

e) To calculate the probability that a randomly selected person attended Session 3, we need to divide the number of people who attended Session 3 by the sample size:

Probability of attending Session 3 = Number of people in Session 3 / Sample size = 22 / 69 ≈ 0.3188

Therefore, the probability that a randomly selected person attended Session 3 is approximately 0.3188 (rounded to four decimal places).

f) To calculate the probability that a randomly selected person is male and attended Session 3, we need to divide the number of males in Session 3 by the sample size:

Probability of being male and attending Session 3 = Number of males in Session 3 / Sample size = 17 / 69 ≈ 0.2464

Therefore, the probability that a randomly selected person is male and attended Session 3 is approximately 0.2464 (rounded to four decimal places).

Based on the residual plot given, the statement that describes if the model is good is B. The regression line is a good model because the residuals are randomly distributed.

For a model to be considered ideal or good, the residuals from the model should be randomly distributed in an equal manner around the regression line.

The residual plot shows that the residuals are randomly distributed which means that the regression line is a good model.

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Step-by-step explanation:

The value of the digit 1 in the number 213,456 is 10,000.

For the polynomial functions f(x) = 3x - 2 and g(x) = x² + 1, then function (f + g)(x) is calculated to be

A polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation, such as the quadratic equation or the cubic equation.

The equation in the problem has integers as below

f(x) = 3x - 2: integer value here is 1

g(x) = x² + 1 integer value here is 2

In both conditions, the integer values are positive hence both are polynomial functions

(f + g)(x) is addition of the two polynomials

f(x) = 3x - 2 + g(x) = x² + 1

= 3x - 2 + x² + 1

= x² + 3x - 1

hence (f + g)(x) = x² + 3x - 1

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Answer:

d² - 24d + c = (d - 12)² - 144 + c

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

C

Step-by-step explanation:

The lines c and d are not parallel.

The correct answer is A. No, because 26 and 21 are not congruent.

In order for two lines to be parallel, the corresponding angles formed by a transversal should be congruent. However, in this case, angles 26 and 21 are not congruent, as indicated by their different measures of 40° and 140°, respectively.

Therefore, we can conclude that lines c and d are not parallel. The congruence of angles 22 and 23, mentioned in option B, or the congruence of angles 22 and 26, mentioned in option D, does not provide sufficient information to determine the parallelism of lines c and d.

The key factor in determining parallel lines is the congruence of corresponding angles, which is not met in this scenario.

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By definition, the mode/s is/are the value/s that appear most frequently in a data set.

Ordering the given data set, we have:

We see that the most repeated values are 40 and 84. We conclude that the modes are 40 and 84.

40 and 84

Answer:

\(\boxed{6,3}\)

Step-by-step explanation:

\(0,7 \times 9\)

\(= \frac{7}{10} \times 9\)

\(= \frac{63}{10}\)

\(= 6,3\)

Answer:

6.3

Step-by-step explanation:

Because you use a cacluator.

Answer:

she have to try two times

1) Gathering the data

E (5,1.5) Circumcenter

H (4.3,2.3) incenter

I (3.6, 2.6) is the centroid.

2) Examining the figure we can see point C and B as the vertices of the

triangle, to find the radius let's use the distance formula between point E and C

E(5, 1.5) and C(3,5)

Since the radius is a line segment from the origin to the circumference then the distance BC = radius of the circumscribed triangle

Radius = 2.28

The surface area of the cube is 1536 ft².

We have,

The cube can be seen as 6 square areas in the net.

So,

The surface area of the cube.

= 6 x area of one square surface.

Now,

Side = 16 ft

Area of one square surface.

= side²

= 16²

= 256 ft²

Now,

The surface area of the cube.

= 6 x area of one square surface.

= 6 x 256

= 1536 ft²

Thus,

The surface area of the cube is 1536 ft².

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Considering the definition of perpendicular line, the equation of of perpendicular line is y= -3/4x + 5/2.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 3y= 4x +7. Expressed in the form y = mx + b, you get:

y= (4x +7)÷ 3

y= 4/3x -+7/3

The line has a slope of  4/3. If you multiply the slopes of two perpendicular lines, you get –1, then:

4/3× slope perpendicular line= -1

slope perpendicular line= (-1)÷ 4/3

slope perpendicular line= -3/4

So, the perpendicular line has a form of: y= -3/4x + b

The line passes through the point (6, -2). Replacing in the expression for parallel line:

-2= (-3/4)×6 + b

-2= -9/2 + b

-2+ 9/2= b

5/2= b

Finally, the equation of of perpendicular line is y= -3/4x + 5/2.

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Answer:

321.50 dollars.

Step-by-step explanation:

Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.

This is a tricky math problem that requires some conversions and calculations. First, we need to convert feet to meters, because Dena lives in a country that uses the metric system. According to the search results   , one foot is equal to 0.3048 meters. So, 120 feet is equal to 120 x 0.3048 = 36.576 meters.

Next, we need to multiply the length of the wallpaper by the price per meter to get the total cost. The total cost is 36.576 x 8.79 = $321.38.

Finally, we need to round the total cost to the nearest half dollar. This means we need to look at the cents part of the cost and see if it is closer to 0, 50 or 100. In this case, 38 cents is closer to 50 than to 0 or 100, so we round up the cost to $321.50.

Therefore, Dena will have to pay $321.50 for the wallpaper. That's a lot of money for some paper that will probably peel off in a few years! Maybe she should consider painting her walls instead.

Answer:

i dont know im sorry

Step-by-step explanation:

answer

306.87 degrees and 666.87 degrees.

steps

4tanθ+5=0.

Subtract 5 from both sides to get 4tanθ=-5.

Divide both sides by 4 to obtain tanθ=-5/4.

θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:

θ = -53.13 + 360 = 306.87 degrees

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

Equation with tangent function.

Title: Solving an equation involving tangent function

Synopsis: We will solve the equation 4tanθ+5=0 on the interval [0,360).

Abstract: To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation. We start by subtracting 5 from both sides, giving us 4tanθ=-5. Then we divide both sides by 4, obtaining tanθ=-5/4. Finally, we take the arctangent (or inverse tangent) of both sides to find θ, remembering to specify the interval [0,360).

Numbered list:

Start with the equation 4tanθ+5=0.

Subtract 5 from both sides to get 4tanθ=-5.

Divide both sides by 4 to obtain tanθ=-5/4.

Take the arctangent (or inverse tangent) of both sides to find θ.

Specify the interval [0,360) when giving the solution.

Analogy: Solving this equation is like solving a puzzle where you need to rearrange the pieces to get the right picture.

One-sentence summary: We solve the equation 4tanθ+5=0 by subtracting 5, dividing by 4, taking the arctangent, and specifying the interval [0,360).

To solve the equation 4tanθ+5=0, we need to isolate the variable (θ) on one side of the equation.

Subtracting 5 from both sides gives us: 4tanθ = -5

Dividing both sides by 4: tanθ = -5/4

Taking the arctangent (or inverse tangent) of both sides, we get: θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

However, we need to specify the interval [0,360), which means we need to add 360 degrees to the negative solution, giving us 306.87+360 = 666.87 degrees (which is equivalent to 306.87-360 = -53.13 degrees in this interval).

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

Sure, here's just the math:

4tanθ + 5 = 0

Subtracting 5 from both sides:

4tanθ = -5

Dividing both sides by 4:

tanθ = -5/4

Taking the arctangent (or inverse tangent) of both sides:

θ = arctan(-5/4)

Using a calculator, we find that θ is approximately -53.13 degrees or 306.87 degrees.

Since we need to specify the interval [0,360), we add 360 degrees to the negative solution:

θ = -53.13 + 360 = 306.87 degrees

Therefore, the solutions to the equation 4tanθ+5=0 on the interval [0,360) are approximately 306.87 degrees and 666.87 degrees.

ChatGPT

The directional derivative of f(x, y, z) = \(xy+z^{3}\) at the point (2, 3, 1) in the direction of a vector making an angle of 3π/4 with the gradient of f at that point is √2 (3cos(3π/4) + 2sin(3π/4)).

To find the directional derivative of f(x, y, z) = xy + z^3 at the point (2, 3, 1) in the direction of a vector making an angle of 3π/4 with the gradient of f at that point, we need to calculate the gradient of f at that point and then use it to find the dot product with the given direction vector.

The gradient of f at the point (2, 3, 1) is given by ∇f(2, 3, 1) = (y, x, 3z^2) = (3, 2, 3).

The direction vector in the direction of 3π/4 with the gradient can be found as follows:

Let \(d = (cos(3\pi /4), sin(3\pi /4), 0)\)

The directional derivative of f in the direction d at the point (2, 3, 1) is given by

∇f(2, 3, 1) . d = \((3, 2,3).(cos(3\pi /4), sin(3\pi /4),0)\)

= \(3cos(3\pi /4)+2sin(3\pi /4)\)

= √2 (3cos(3π/4) + 2sin(3π/4))

So the directional derivative of f in the direction of a vector making an angle of 3π/4 with the gradient of f at (2, 3, 1) is √2 (3cos(3π/4) + 2sin(3π/4)).

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