How to simplify the expression

Answer:

3/5

Step-by-step explanation:

We know two points on the line

(-1,2) and (4,5)

So we can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 5-2)/(4 - -1)

   (5-2)/(4+1)

   3/5

Answer:

h = √72 in.

Step-by-step explanation:

Height of the cone using pythagorean theorem, a² + b² = c², where:

a = h

b = ½(6) = 3 in.

c = 9 in.

Plug in the values

h² + 3² = 9²

h² + 9 = 81

h² + 9 - 9 = 81 - 9

h² = 72

h = √72

Check the picture below.

Answer:

Area of annulus is 40.85cm² to 2d.p

Step-by-step explanation:

Area of shaded part=Area of bigger circle -Area of smaler circle

Area of annulus= πR²- πr²= π(R²-r²)

A=3.142(7²-6²)

A=3.142(49-36)

A=3.142×13

A=40.846cm²

A=40.85cm² to 2d.p

Answer:

Step-by-step explanation:

2x + x = 90

     3x = 90

       x = 30

The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

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Answer:

41.93 degrees

Step-by-step explanation:

Answer:

397.9

Step-by-step explanation:

         If there are 16 sections, we can divide the total number of people attending by the number of sections.

6,367  / 16 ≈ 397.9

         Please note you cannot, or should not, have .9 of a person. This means we will round to 398 people in each section. It depends on what the context of your answer is.

Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

To show that the angle bisector of an equilateral triangle is perpendicular to the base​, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.  

After getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.

We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.

Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.

Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.

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Answer:

Here you go

Step-by-step explanation:

A

T

F

T

F

AND NOW Ā

Ā

F

T

F

T

FOR B

B

T

T

F

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FOR B COMPLIMENT

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The truth table for the logic expression is shown below

From the question, we have the following parameters that can be used in our computation:

________

(A AND B)

When expanded, we have

________   ___    ___

(A AND B)  = A   +  B

So, we have

                _______

A B (A AND B)

0     0                0

0     1                1

1      0               1

1      1                1

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The owner bought the trumpet for $682.5.

Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus its cost to make or purchase for resale) by the cost of that unit. A markup percentage is a number used to determine the selling price of a product in relation to the cost of actually producing the product. The number expresses a percentage above and beyond the cost to calculate the selling price.

Formula: Markup % = (selling price – cost) / cost x 100

where markup = 30%

cost = $525

30 = (SP - 525) / 525 x 100

30 x 525 = (SP - 525) x 100

15750 = 100SP - 52500

15750 + 52500 = 100SP

68250 = 100SP

SP = 682.5

Therefore the selling price is $682.5

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The distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

The bearing is defined as the angle measured clockwise from the north direction. A ship is anchored off a long straight shoreline that runs north and south.

From two observation points miles apart on shore, the bearings of the ship are 52 degrees and 134 degrees respectively. To find the distance from the ship to each of the observation points, we can use trigonometry.

Let's call the distance from the north observation point to the ship x, and the distance from the south observation point to the ship y. The bearings from the north and south observation points can be drawn as follows:

[asy]

unitsize(1cm);

pair O = (0,0), N = (-2,0), S = (2,0), A = (-2,1), B = (2,-1);

draw(O--N--A,Arrow);

draw(O--S--B,Arrow);

\(label("$52^\circ$", N + 0.3*dir(52), NE);\)

\(label("$134^\circ$", S + 0.3*dir(134), SE);\)

draw(O--A--B--cycle,dashed);

\(label("$x$", (N+A)/2, W);\)

\(label("$y$", (S+B)/2, E);\)

[/asy]

We can use the tangent function to find x and y, since we have the angle and opposite side.

From the north observation point, we have:

\($$\tan(52^\circ) = \frac{x}{2}$$$$x = 2\tan(52^\circ) \approx 2.95$$\)

From the south observation point, we have:

\($$\tan(134^\circ) = \frac{y}{2}$$$$y = 2\tan(134^\circ) \approx 9.88$$\)

Therefore, the distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

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On solving the given system of equations, we found the values of the variables x and y as 4 and 3 respectively.

What is meant by the system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system. A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations.

The given system of equations is:

2x + 2y = 14

4x - 2y = 10

To solve this, we have to first get rid of one variable.

Here the coefficient of variable y is the same.

So adding the equations, we get

6x = 24

x = 4

Now substituting this value of x in any one of the equations we get y.

2*4 + 2y = 14

8 + 2y = 14

2y= 6

y = 3

Therefore on solving the given system of equations, we found the values of the variables x and y as 4 and 3 respectively.

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The formula that defines the sequence is f(n) = f(n-1) + 4

The recursive function rule is expressed as;

f(n) = f(n-1)  + d

where

d is the common difference

Given the following sequence

2, 6, 10, 14, 18..

Determine the common difference

d = 6-2 = 10-6

d = 4

Substitute to have

f(n) = f(n-1)  + d

f(n) = f(n-1) + 4

Hence the formula that defines the sequence is f(n) = f(n-1) + 4

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The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

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Answer:

340

Step-by-step explanation:

area of triangle

12 × 10 = 120/.5 = 240

area of rectangle

10×10= 100

then you add together

100+240= 340

Answer:

4/9 is the answer

Step-by-step explanation:

you're welcome

The company sales in year 14, given the rate of increase and the amount made in sales would be C $3,656,872.

In the first year, the sales of the company were $ 475, 000 and this sales is scheduled or predicted to grow at 17 %.

This means that the company sales in year 14 would be :

= Initial sales x ( 1 + rate ) ^ number of years

Initial sales = $ 475, 000

Rate = 17 %

Number of years = 14 years

The company sales in year 14 is:

= 475, 000 x ( 1 + 17 %) ¹⁴

= $3, 656, 872

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Answer:

1st: x=60°

2nd: x=140°

Step-by-step explanation:

We have:

the angle of tangency  is half of the measure of the arc formed on the same side.

so

For 1st

x=½*120°

x=60°

For 2nd

y and 110° is in linear pair

y+110=180

y=180-110

y=70°

Now by using above theorem:

y=1/2*x

x=2*y=2*70

x=140°

Answer:

1. x = 60

2. x = 140

Step-by-step explanation:

An angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.

1. x = 1/2(120) = 60

2. ∠x = 180 - 110 = 70

∠x = 1/2(arc x)

70 = 1/2(arc x)

arc x = 70 x 2 = 140

The Area of the shaded portion is: 72 square inches

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ *  17 * 13 = 110.5 square inches

Area of smaller triangle =  ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

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The term that  best describe this graph attached is

does not have an outlier

An outlier is a data point that significantly deviates from the general pattern or trend of a dataset. It is an observation that is noticeably different from other data points in terms of its magnitude or value.

Outliers can be either unusually high (positive outliers) or unusually low (negative outliers) compared to the rest of the data.

The graph is not exactly uniform even though it is not skewed

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Answer:

(4.4, -4.6) and (4.4, -1.4)

Step-by-step explanation:

Got a 100 on plato

Coordinates are usually denoted by (x,y) the x-value and y-value.

This has to do with the system which makes use of numbers or coordinates in order to find the location of a point.

Please note that your question is incomplete so I gave you a general overview to get a better understanding of the concept.

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18.9% is the answer

Step-by-step explanation:

volume of a cylinder = πd²/4 x h

where d is diameter and h is height of cylinder.

thus

vol of A is

\(vol \: of \: a \: = \pi \times \frac{ {d}^{2} }{4} \times h \\ = \pi \times \frac{ {16}^{2} }{4} \times 19 \\ = \pi \times 4 \times 16 \times 19 \\ = 3818.24\)

and

\(vol \: of \: b = \pi \times \frac{ {20}^{2} }{4} \times 15 \\ = \pi \times 5 \times 20 \times 15 \\ = 4710\)

difference in vol of a and b is

\(diff \: = vol \: of \: b \: - vol \: of \: a \\ = 4710 - 3818.24 \\ = 891.76\)

this volume will remain empty after container A is pumped into container B.

this volume as a percentage of total volume of B is

\(\% = \frac{diff \: vol}{total \: vol} \times 100 \\ = \frac{891.76}{4710} \times 100 \\ = 18.9\%\)

Answer:

$321.6915

Step-by-step explanation:

original price= $399.00

20% off $399 is $319.2

$319.2-$15.00=$304.2

0.75% of 304.2 is 2.2815

5% of 304.2 is 15.21+2.2815=17.4915+304.2=321.6915

hope this helps

A percentage is a way to describe a part of a whole. The final cost of the television is $321.69.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that a 55" flat screen television is regularly priced at $399.00. Now, It is on sale for 20% off. Therefore, the cost of the flat screen is,

Cost after discount = $399 - 20% of $399

= $399 - 0.20($399)

= $319.2

The cost after the application of the coupon of $15.00 off on any purchase over $100.00. Therefore, the new cost will be,

New Cost = $319.20 - $15.00

                 = $304.2

Since the tax on the cost is 5.75%, therefore, the cost after the application of the tax is,

Cost after the tax = $304.2 + 5.75% of $304.2

                             = $304.2 + 0.00575($304.2)

                             = $321.69

Hence, the final cost of the television is $321.69.

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Therefore , the solution of the given problem of probability comes out to be AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)

The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance can be represented by any number between 0 and 1, in which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

(a) The voting box contains a total of seven slips, four of which are for candidate A and three for candidate B. Thus, there are 35 events that can occur from 7 choose 4 (or 7 choose 3) options.

Each vote can be represented by a letter, with A standing for a vote for candidate A and B for candidate B, so that all outcomes can be listed. These are the potential results:

AAAA

AAAB

AABA

ABAA

BAAA

AABB

ABAB

BABA

BBAA

ABBB

BABB

BBAB

BBBA

(b)

For instance, the following results could occur if the slips were removed in the following order:

A (1 vote for contender A) (1 vote for candidate A)

AA (2 ballots for candidate A) (2 votes for candidate A)

AAB (2 ballots for candidate A, 1 vote for candidate B) (2 votes for candidate A, 1 vote for candidate B)

AAAB (3 ballots for candidate A, 1 vote for candidate B) (3 votes for candidate A, 1 vote for candidate B)

AAAAB (4 ballots for candidate A, 1 vote for candidate B) (4 votes for candidate A, 1 vote for candidate B)

AAAABB (4 ballots for candidate A, 2 votes for candidate B) (4 votes for candidate A, 2 votes for candidate B)

AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)

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The percentage of buyers is approximately 68.26% of buyers of new houses paid between \($149,000\) and \($151,000\) .

We are given that the prices of the new homes are normally distributed with a mean of \($150,000\) and a standard deviation of $1000.

Using the 68-95-99.7 rule, we know that: approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the data falls within two standard deviations of the mean, approximately 99.7% of the data falls within three standard deviations of the mean.

In order to determine the proportion of customers who spent between $149,000 and , we must first determine the z-scores for these values:

z1 = (149,000 - 150,000) / 1000 = -1 z2 = (151,000 - 150,000) / 1000 = 1

Now, we can determine the proportion of data that falls between z1 and z2 using the z-table or a calculator. The region to the left of z1 is 0.1587, and the area to the left of z2 is 0.8413, according to the z-table. Thus, the region bounded by z1 and z2 is:

0.8413 - 0.1587 = 0.6826

We can get the percentage of consumers who spent between by multiplying this by 100% is  \($149,000\)  and \($151,000\):

0.6826 x 100% = 68.26%

Therefore, the standard deviation of customers who paid between is \($149,000\) and \($151,000\)  for this model of new homes.

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So there are 479,001,600 different 12-letter arrangements that can be formed using the letters in the word CARTOGRAPHER.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To determine the total number of different 12-letter arrangements that can be formed using the letters in the word CARTOGRAPHER, we can use the formula for permutations of n distinct objects, where n is the number of objects to be permuted. In this case, we have 12 distinct letters to permute, so the formula is:

n! / (n - r)!

where n = 12 and r = 12 (since we want to permute all 12 letters). Substituting these values into the formula, we get:

12! / (12 - 12)!

= 12! / 0!

= 12!

Therefore, there are 12! different 12-letter arrangements that can be formed using the letters in the word CARTOGRAPHER. This is equivalent to:

12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 479001600

So there are 479,001,600 different 12-letter arrangements that can be formed using the letters in the word CARTOGRAPHER.

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