Evaluate the expression

(x + 3)(y - 2) , if x = -2, and y= 6

Answer: 33

Step-by-step explanation:

There are lots of things you have to remember in parallel lines with transversal lines (the lines that cut through the parallel lines). In this picture, the angles shown are co-interior angles. Co-interior angles add up to 180°.

Given this, we can make and solve the following equation:

\((x + 20) + (4x-5) = 180\\x + 20 + 4x - 5 = 180\\5x + 15 = 180\\5x = 165\\x = 33\)

If there are any steps you don't understand, I can go through it again, so please tell me :)

The Volume of the right cone (V) that has a diameter of 6 units and a height of 11 units is calculated as: 33π units³.

The volume of a right cone can be determined by applying the following formula:

Volume of a right cone (V) = 1/3 * πr²h, where:

r represents the radius of the right cone

h represents the height of the right cone

Given the following:

radius (r) = 6/2 = 3 units

Height (h) = 11 units

Plug in the values:

Volume of the right cone (V) = 1/3 * π * 3² * 11

= 1/3 * π * 99

= π * 33

Volume of the right cone (V) = 33π units³

Learn more about the volume of cone on:

https://brainly.com/question/1082469

#SPJ1

Answer:

k = \(\frac{fr^2}{90}\)

Step-by-step explanation:

f = k \(\frac{90}{r^2}\) ( multiply both sides by r² to clear the fraction )

fr² = 90k ( divide both sides by 90 )

\(\frac{fr^2}{90}\) = k

Answer:

Below

Step-by-step explanation:

Set up a ratio:

7 is to 9   as  8 is to ?

7/9 = 8/?

? = 8 * 9/7 = 72/7  = 10  2/7

Answer:

a. Yes

b. 3x+7

c. 105 cm

Step-by-step explanation:

a. a(1)+b=10

   a(2)+b=13

when you solve this by elimination or simultaneously: a=3 and b=7

∴ f(x)=3x+7

b. f(x)=3x+7

c. 3(35)+7=112 cm

The answer to work for part a) is 2. The value that is used in hypothesis testing to compare a test statistic to the rejection region is known as a critical value. The critical value differs depending on the level of significance selected for the test and the test’s degree of freedom.

The value that is used in hypothesis testing to compare a test statistic to the rejection region is known as a critical value. The critical value differs depending on the level of significance selected for the test and the test’s degree of freedom. For this particular question, the critical value can be calculated using the Z-distribution formula since the sample size is greater than or equal to 30.

Thus, the answer to work for part a) is 2.

Explanation: Given that the population standard deviation is known to be 1.28 screens, The sample size is 89 with a sample mean of 10.59 screens. The hypothesis test can be represented as follows:

H0: µ ≤ 5 Ha: µ > 5

To determine whether there is sufficient evidence to conclude that the mean number of screens per household is greater than 5, a Z-test can be used. The test statistic is calculated as follows:

Z = (X - µ) / (σ / sqrt(n))

Where X = 10.59,

µ = 5,

σ = 1.28,

n = 89.

Substituting the values in the above equation, we get

Z = (10.59 - 5) / (1.28 / sqrt(89))

= 33.97

Since the alternative hypothesis is one-tailed, the critical value for the test can be calculated using the Z-distribution formula as follows:

Critical value = Zα

where α is the level of significance. For instance, for a 5% level of significance, α = 0.05, and the corresponding critical value is 1.64. Since the calculated test statistic is greater than the critical value, the null hypothesis can be rejected at a 5% level of significance.

Hence, there is sufficient evidence to conclude that the mean number of screens per household is greater than 5.

To know more about degree of freedom visit: https://brainly.com/question/32093315

#SPJ11

The solution for the given expression -0.5x-3.69=x-1.9-2.3 is x= 0.34

The given problem is related to an algebraic expression which is the thought of expressing numbers utilizing letters or letter sets without indicating their real values, which is made up of factors and constants, at the side of logarithmic operations (expansion, subtraction, etc.). Expressions are made up of terms.

since the  given expression is :

-0.5x-3.69=x-1.9-2.3

=>-0.5x-x=-1.9-2.3+3.69

=>-1.5x=-0.51

=>x=0.34

To know more about algebraic  expression refer to the  link https://brainly.com/question/24875240?referrer=searchResults.

#SPJ4

Answer:

x=52 m1= 40 m2= 140

Step-by-step explanation:

x-12+x+88=180 since they are linear pair

2x+76=180 collect like terms

2x=180-76

2×÷2=104÷2

×=52

give me a heart and good rate please<3

The standard deviation of a sampling distribution of sample means is often referred to as the standard error of the mean. In this case, with a standard deviation of 3.1 for the sampling distribution of sample means, the best interpretation is that it represents the variability or dispersion of the sample means around the population mean.

More specifically, it quantifies the average amount of deviation or spread that is expected between the sample means and the true population mean. In other words, it provides an estimate of the typical or expected error in using a sample mean as an estimate of the population mean.

Therefore, the standard deviation of 3.1 in the sampling distribution suggests that, on average, the sample means are expected to deviate from the true population mean by approximately 3.1 units.

Learn more about standard deviation here:

https://brainly.com/question/475676

#SPJ11

In a haplodiploid system, the relatedness of a son to a maternal aunt is 75%.

In a haplodiploid system, males develop from unfertilized eggs and are haploid, while females develop from fertilized eggs and are diploid. This means that sons inherit all of their genetic material from their mother, including her alleles from both her haploid sets of chromosomes. Maternal aunts, on the other hand, share one set of haploid chromosomes with their nephew (the son), as they are the sister of his mother. Therefore, the relatedness between a son and his maternal aunt in a haplodiploid system is 0.75 or 75%.

In a haplodiploid system, the relatedness of a son to a maternal aunt can be calculated using the following steps:

1. Determine the relatedness of the son to his mother: In haplodiploid systems, sons are haploid and inherit their single set of chromosomes from their mother. This means that they are 100% related to their mother, as they share all her genes.

2. Determine the relatedness of the maternal aunt to the son's mother: The maternal aunt is a sister of the son's mother. In haplodiploid systems, sisters share 75% of their genes, as they get half of their genes from their mother and the other half from their father (who, as a haploid male, gives all his genes to his daughters).

3. Calculate the relatedness of the son to his maternal aunt: To determine the relatedness of the son to his maternal aunt, multiply the son's relatedness to his mother (100%) by the maternal aunt's relatedness to the son's mother (75%).

Relatedness of son to maternal aunt = (1.0) * (0.75) = 0.75 or 75%

So, in a haplodiploid system, the relatedness of a son to a maternal aunt is 75%.

Learn more about haplodiploid system here: brainly.com/question/31081669

#SPJ11

Step-by-step explanation:

it clearly consists of 2 rectangles and 1 triangle (as you tried correctly to point out by drawing the separating lines).

we only need to calculate all 3 areas and add them up for the total.

the area of a rectangle is

length × width

so, in our 2 cases we have

6 × 2 = 12 km²

5 × (3 + 2 + 3) = 5×8 = 40 km²

the area of a triangle is

baseline × height / 2

in case of a right-angled triangle the 2 sides enclosing the 90° angle can be used as baseline and height.

so, in our case

6 × (5 + 2 + (3 + 2 + 3 - 2)) / 2 = 6×(7 + 6)/2 = 3×13 = 39 km²

in total, the whole area is

12 + 40 + 39 = 91 km²

#1) (15-5) + 3² + 10

Parenthesis→ 10 + 3² + 10

Exponents→ 10 + 9 +10

Addition→ 29

#2) 2² + (2×2) - 2

Parenthesis→ 2² + 4 - 2

Exponents→ 4 + 4 -2

Addition→ 8 - 2

Subtraction→ 6

#3) 4² - (4×3) + 6 - 5

Parenthesis→ 4² - 12 + 6 - 5

Exponents→ 16 - 12 + 6 - 5

Subtraction→ 4 + 6 - 5

Addition→ 10 - 5

Subtraction→ 5

#4) (6÷3) + 5² - 2 × 2 + 1

Parenthesis→ 2 + 5² - 2 × 2 + 1

Exponents→ 2 + 25 - 2 × 2 + 1

Multiplication→ 2 + 25 - 4 + 1

Addition→ 27 - 4 +1

Subtraction→ 23 + 1

Addition→ 24

#5) 45 ÷ 9 + 11 × 3 - (3×2) + 3²

Parenthesis→ 45 ÷ 9 + 11 × 3 - (6) + 3²

Exponents→  45 ÷ 9 + 11 × 3 - 6 + 9

Division→ 5 + 11 × 3 - 6 + 9

Multiplication→ 5 + 33 - 6 + 9

Addition→ 38 - 6 + 9

Subtraction→ 32 + 9

Addition→ 41

#6) 60 - (3×5) + 10² + 4 ÷ 2 - 7

Multiplication→ 60 - 15 + 10² + 4 ÷ 2 - 7

Exponents→ 60 - 15 + 100 + 4 ÷ 2 - 7

Division→ 60 - 15 + 100 + 2 - 7

Subtraction→ 45 + 100 + 2 - 7

Addition→ 147 - 7

Subtraction→ 140

The correct answer is B. created in an iterative and incremental manner.

Unlike traditional Work Breakdown Structures (WBS), evolutionary WBSs are developed in an iterative and incremental manner. This means that they are built and refined over time as the project progresses, allowing for adjustments and additions to be made as new information becomes available. The evolutionary WBS is not organized in a standard manner across all projects (A) and it is not specifically designed for comparison to past projects (C). Therefore, the answer is B. created in an iterative and incremental manner.

Learn more about Work Breakdown Structures here: brainly.com/question/30455319

#SPJ11

To find the sum of 6k by adding each term together, we can simply add 6k + 6k + 6k + 6k + 6k + 6k which gives us a total of 36k.

To verify this result using the summation capabilities of a graphing utility, we can use the sigma notation (Σ) to represent the sum. The sigma notation is defined as Σ6k where k starts at 1 and goes up to 6. This means we are adding 6k, six times.

To input this into a graphing utility, we can use the summation feature. For example, on a TI-84 calculator, we can press the "Math" button, select "1:sum(", and enter the expression "6k" followed by a comma and then the values of k that we want to sum from (1) and to (6). This gives us the result of 36k, which matches our previous calculation.

Learn more about graphing utility:

https://brainly.com/question/29260419

#SPJ11

Answer:

1.6* 2,100,000= 3,360,000

2015-2012= 3

3,360,000*3= 10,080,000

Might be wrong but hope this helped!

Step-by-step explanation:

the answer to your problem is m= -5/2

Answer:

-2.5

Step-by-step explanation:

The slope formula \(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\) tells us the formula for any slope with 2 given points. We have to plug in the numbers from our 2 ordered pairs to get \(\frac{-4 - 1}{2 - 0}\), which simplifies to \(\frac{-5}{2}\) and can be written as -2.5

The slope of this equation is -2.5

Answer

Option C

y = 3x

The equation that best represents the relationship between x and y

Explanation

We are asked to find the equation that best represent the relationship between x and y, to do this, we need to note that ordered pairs are written as (x, y)

(3, 9)

(6, 18)

(7, 21)

(10, 30)

So, testing each of the equations given, we will pick the one where all the answers match

Option A

y = x^2

when x = 3, y = 3^2 = 9

when x = 6, y = 6^2 = 36 which is not equal to 18

Option B

y = 4x - 7

when x = 3, y = 4(3) - 7 = 12 - 7 = 5 which is not equal to 9

Option C

y = 3x

when x = 3, y = 3(3) = 9

when x = 6, y = 3 (6) = 18

when x = 7. y = 3(7) = 21

when x = 10, y = 3(10) = 30

We can see that all the answers match the answers obtained.

Hope this Helps!!!

Answer:

Equation A) y = \(x^{3} + 2x^{2} - 1\) is Graph E

Equation B) y = \(2x^{2} - x -3\) is Graph A

Equation C) y = \(\frac{1}{x} +1\) is Graph B

Equation D) y = \(2-3x^{2} -x^{3}\) is Graph D

The mnemonic device that is introduced to help us remember how sine, cosine, and tangent are related to the sides of a triangle is called SOH-CAH-TOA.  

The abbreviations SOH-CAH-TOA stands for:

Sine = Opposite/Hypotenuse

Cosine = Adjacent/Hypotenuse

Tangent = Opposite/Adjacent

The mnemonic device is particularly helpful when it comes to understanding and applying trigonometric ratios to right-angled triangles.

Let's evaluate the trigonometric ratios using the given terms:

Given that10 17. sin A = Opposite/Hypotenuse

19. tan A = Opposite/Adjacent

18. cos A = Adjacent/Hypotenuse

20. csc A = Hypotenuse/Opposite

21. sec A = Hypotenuse/Adjacent

22. cot A = Adjacent/Opposite

Learn more about Trignometric ratios:

brainly.com/question/24349828

#SPJ11

Density –The frequency with which something exists with a given unit of area.

Definition of density: A material's density is determined by how closely it is packed. As the mass per unit volume, it has that definition. Symbol for density: D or Formula for Density: Where is the density, m is the object's mass, and V is its volume, the equation is: = m/V.

How much "stuff" is contained in a specific quantity of space is determined by its density. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb) (Au). Styrofoam blocks are less dense than bricks. Mass per unit volume serves as its definition.

Learn more about density here

https://brainly.com/question/6838128

#SPJ4

Answer:

It’s linear

Explanation:

Answer:add all the numbers together then divide the answer by 10

Step-by-step explanation:

The center of the circle, and consequently the central point of the resort's swimming pool, is located at the intersection of the two legs of the right triangle, approximately 60 feet from one vertex and 120 feet from the other.

The upscale resort has ingeniously designed its circular swimming pool to encompass a central area containing a restaurant. This central area takes the form of a right triangle with legs measuring 60 feet and 120 feet, while the hypotenuse, the longest side of the triangle, spans approximately 103.92 feet. The vertices of the triangle neatly coincide with points on the circumference of the circular pool.

Due to the properties of a right triangle, the hypotenuse is also the diameter of the circle. This means that the circular pool is precisely constructed around the right triangle, with its center located at the midpoint of the hypotenuse.

To determine the exact coordinates of the center of the circle, we can consider the properties of right triangles. Since the legs of the right triangle are perpendicular to each other, the midpoint of the hypotenuse coincides with the point where the two legs intersect.

In this case, the center of the circle is the point of intersection between the 60-foot leg and the 120-foot leg of the right triangle.

For more such questions on center

https://brainly.com/question/1506955

#SPJ8

The maximum area of the rectangle inside the ellipse is 2ab.

Given that,

Ellipse = x2 / a2 + y2 / b2 = 1

we know the general coordinates of any point in an ellipse of the equation

x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)

So, we take general vertices of rectangles as

(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)

So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ

So, its area will be ab4sinθcosθ (Length x Breadth)

Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A

Now A=2absin2θ

Now as the area is the maximum given in the question, we have to differentiate it with respect to θ

dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)

Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ =  π / 2 and θ=π / 4

So now we to put θ=π / 4 in the equation of area which is A=2absin2θ

We get as A=2absin2π / 4=2absinπ / 2=2ab

Hence the max area of the rectangle inside the ellipse is 2ab.

To know more about rectangles visit: brainly.com/question/29123947

#SPJ4

Answer:

250 cards

Step-by-step explanation:

Let the number of baseball cards he originally had be x.

He sold 20% of the baseball cards after week one. This means that after week one the number of cards he had was:

x - (20/100 * x) = x - 0.2x = 0.8x

During week two he bought 20% more cards than he had after week one. This means that after week two, he had:

0.8x + (20/100 * 0.8x)

= 0.8x + (0.2 * 0.8x)

= 0.8x + 0.16x = 0.96x

He now has 10 fewer cards. This means that:

x - 10 = 0.96x

Collecting like terms:

x - 0.96x = 10

0.04x = 10

=> x = 10/0.04 = 250

He had 250 cards originally.

Answer:

Step-by-step explanation:

d = diameter = 12ft

r = d/2 = 12/2 = 6ft

Slant height = 13ft

Surface area of cone = π r 2 + π L r

Where L is the slant height of the cone π = 22/7

SA = 22/7×6×6+22/7×13×6

SA = 113.14+245.142

SA = 358.28ft^2

If one bundle of shingle covers 32 ft.²

Hence,358.28ft^2  = 358.28ft^2/32 ft.²

= 11.196

= 11.2 bundles