The lengths of the three sides of a triangle (in feet) are consecutive even integers. If the perimeter is 60 feet, find the value of the shortest of the three side lengths.

The value of x=20, according to the given question.

What is meant by equation?

A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.

According to the given data in the question,

We know that y varies directly with x like that,

y=kx..................(1)

y=12 when x=15.

Now, we have to find the value of x when y=16.

Then, putting the given values of x & y in the eq. (1), and determine the value of k.

12=k(15)

[tex]k=12/15\\k=4/5\\[/tex]

Now, putting the value of k in the second statement in eq.(1), where only y's value is given.

[tex]16=\frac{4}{5}x\\ x=16*\frac{5}{4} \\x=20[/tex]

Hence, the value of x=20.

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Answer:

Joseph's present age=3 yrs

David's present age=9 yrs

Step-by-step explanation:

Let Joseph's present age be x.

David's present age=3x

__________________

Ater 3 yrs,

Joseph's age=x+3

David's age=2(x+3)

Also, we can add 3 to David's present age to get age After 3 yrs. So, David's age after 3 yrs would also be 3x+3.

Now, balance them.

3x+3=2(x+3)

3x+3=2x+6

x=3

D"s prsent age=9

J's present age=3

Using the probability of adults of having tattoo, critical value is 1.76 and margin of error is 0.0353 and a 95% confidence interval for the proportion of all adults that have a tattoo is (0.2347, 0.3053)

In the given question,

In a poll of 489 adults, 132 of then said they have a tattoo.

We have to find critical value and margin of error, and then construct a 95% confidence interval for the proportion of all adults that have a tattoo.

From the question

Total number of adults = 489

The adults that have tattoo = 132

So the proportion in the sample is

p = 132/489

p = 0.269

p ≈ 0.27

Now finding the proportion of adults not having tattoo.

q = 1−p

q = 1−0.27

q = 0.73

Now finding the critical value(z).

The value of z from the standard table for 95% confidence interval.

We can write 95% as 0.95

Z = [tex]z_{\alpha /2}[/tex]

Z = [tex]z_{0.95 /2}[/tex]

Z = [tex]z_{0.475}[/tex]

From the standard table of z

Z = 1.96.

Now finding the margin error.

Margin Error(E) = [tex]Z\times\sqrt{\frac{pq}{n}}[/tex]

As we know that Z = 1.96, p = 0.27, q = 0.73, n = 489

Now putting the value

E = [tex]1.76\times\sqrt{\frac{0.27\times0.73}{489}}[/tex]

Simplifying

E = [tex]1.76\times\sqrt{\frac{0.1971}{489}}[/tex]

E = [tex]1.76\times\sqrt{0.000403}[/tex]

E = 1.76×0.0201

E = 0.0353

Now finding a 95% confidence interval for the proportion of all adults that have a tattoo.

Confidence Interval = p−E< P < p+E

Confidence Interval = 0.27−0.0353< P < 0.27+0.0353

Confidence Interval = 0.2347< P < 0.3053

Hence, critical value is 1.76 and margin of error is 0.0353 and a 95% confidence interval for the proportion of all adults that have a tattoo is (0.2347, 0.3053)

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Answer:

green 45 times or 40 a note

The credit sale after state and local tax payable is 2562$.

Percentage is a measurement to find value of given number out of hundred.

Given that,

The credit sale before sales taxes = 2800$,

The rate of state sale tax = 6%,

And rate of local sale tax = 2.5%

The sale after state tax = 2800-2800×6/100=2800-168=2632,

The sale after local tax=2800-2800×2.5/100=2800-70=2730

The credit sale after state and local tax= 2800-168-70=2562.

The required credit sale =2562$.

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The value of WV is 9x - 10

A line segment can be defined as the part of a straight line which is bound by two distinct end points, and is known to be made up of every point on the line that between its endpoints.

From the information given, we can say that WY is a line with V as its midpoint with segments WV and VY.

We have;

This is represented as;

WV + VY = WY

Then;

WV = WY - VY

substitute the values

WV = 5x + 19 - (29 - 4x)

expand the bracket

WV = 5x + 19 - 29 + 4x

collect like terms

WV = 9x - 10

Hence, the value is  9x - 10

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An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The change in Shamar's bank account after 7 months is

x - 98.

Where x is the amount in the account initially.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount in the account = x

Amount deducted every month = $14

The change in the account after 7 months.

= x - 7 x 14

= x - 98

Thus,

The change in Shamar's bank account after 7 months is

x - 98.

Where x is the amount in the account initially.

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Answer The answer is 96 but as a fraction 96 8/13

Step-by-step explanation: There are 1256 rubber bands and 13 games to distribute them according to the problem; therefore, to divide to give an equal amount per each group for each game, you would give out 96 rubber bands each time, so 96 is the answer or 96 8/13.

A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?

f(x) = 1500(1.15)x

f(x) = 1500(115)x

f(x) = 1500(2.15)x

f(x) = 1500(215)x

Answer:

A

Step-by-step explanation:

Stock used to sell for $105.81 ten years ago.

[tex]CAGR = ((\frac{EV}{BV} )^{\frac{1}{n}}-1)*100[/tex]

Here, CAGR = Compounded Annual Growth Rate = -2.3%

               EV = Ending Value = x

               BV = Beginning Value = $83.80

                  n = No. of years = 10

Putting the values in the equation,

[tex]-2.3 = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)*100[/tex]

[tex]\frac{-2.3}{100} = ((\frac{83.80}{x} )^{\frac{1}{10}}-1)[/tex]

[tex]\frac{-2.3}{100}+1 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]\frac{100-2.3}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]\frac{97.7}{100}= (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex]0.977 = (\frac{83.80}{x} )^{\frac{1}{10}}[/tex]

[tex](0.9777)^{10} = \frac{83.80}{x}[/tex]

[tex]\frac{83.80}{x}=0.792[/tex]

[tex]x = \frac{83.80}{0.792}[/tex]

x = 105.81

Hence, the beginning value is $105.81.

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Answer:

If you let 'n' to represent a number then '-9 times a number' can be written as -9n

'less then' means subtraction:  12 less then -9 times a number  becomes -9n - 12 (the subtraction in the equation is written in the opposite way as written in words)

'8 minus 4 times the number ' becomes 8 - 4n

So, the equation is:  -9n - 12  =  8 - 4n

Get all the variables to one side. If you add  9n  to both sides:

   -9n + 9n - 12  =  8 - 4n + 9n

   -12  =  8 + 5n

Subtract 8 from both sides:

   -12 - 8  =  8 - 8 + 5n

   -20  =  5n

Divide both sides by 5:

   -20 ÷ 5  =  5n ÷ 5

   -4  =  n

Now, check the answer:   -9n - 12  =  8 - 4n

              -9(-4) - 12  =  36 - 12  = 24                 8 - 4(-4)  =  8 + 16  = 24        They check!

Step-by-step explanation:

Hope this helps! :)

The height of the building, using similar triangles, is given by:

36 feet.

Similar triangles are two triangles that share these two features, which are listed as follows:

The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.

From the similar triangles, the equivalent side lengths are presented as follows:

Hence the proportional relationship that models this situation is presented as follows:

3/18 = 6/h.

Applying cross multiplication, the height of the building is obtained as follows:

3h = 18 x 6

h = 6 x 6 (simplifying by 3)

h = 36 feet.

The diagram is given by the image shown at the end of the answer.

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A summation, also known as a sum, is the result of arithmetic addition of numbers or quantities.

The value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.

Any of the following algebraic expressions should be used: addition, subtraction, multiplication, and division. Bring the variable to the left and all the remaining values to the right to find the value of x.

From the given information, we get

x - y = 6 ...............(1)

"if five times the smaller number is two times the larger number"

from the above information, we get

5y = 4x + 2

5) To simplify the value of y:

y = (4x +2) / 5 ...............(2)

Substitute  y = (4x +2) / 5 in (1), then we get

x - (4x + 2) / 5 = 6

5x / 5 - (4x + 2) / 5 = 6

simplifying the above equation, we get

(5x - 4x - 2) / 5 = 6

x - 2 = 5 x 6

x -2 = 30

x = 32

Substitute the value of x in (2)

y = 4(32) + 2 / 5

simplifying the above equation, we get

y = 130 / 5

y = 26

From (1), we get

x - y = 6

substitute the value of x and y in the above equation,

32 - 26 = 6

6 = 6

6) T is the 10s digit

X is the one's digit

The two digit number is 10T + X

It is 7 times the sum of the digits, so the 2 digit number is 7 times as large as the sum of the digits

10T + X = 7(T+X)

By using distributive law

10T + X = 7T + 7X

10T + X - 7T - 7X = 0

simplifying the above equation, we get

3T - 6X = 0

3(T - 2X) = 0

T - 2X = 0

T = 2X

The tens digit is 3 more than the one's digits, so

T = X + 3

Then we have  

T = 2X = X  + 3

Subtracting X from both sides,

T - 3 = X  + 3 - 3

X = 3

The Tens digit is 6.

The number is 63.

The sum of the digits is 9.

9 × 7 = 63.

Therefore, the value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.

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The equation that could be used to determine x, the number of purses Paula must sell to pay for the new equipment is;

A. 5.00x - 2.25x = 5000

We are told the materials costs $2.25 per purse.

She sells the materials for $5 each.

If the number of materials she purchased was x, it means that;

Selling price - Cost price = 5.00x - 2.25x

Now, we are told that she wants to invest $5000 for some new equipment. This means that she must realize at least $5000 in profit from the sales she is making of the materials.

Since the formula for profit is;

Profit = Selling Price - Cost Price

Then, we will have;

5.00x - 2.25x = 5000

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Answer:  5.00x - 2.25x = 5000

Step-by-step explanation:

Answer: -52

Step-by-step explanation: multiply by breaking apart a factor (-13) x 4

Answer:

28561

Step-by-step explanation:

Find the Exact Value:

Raise -13 to the power of 4.

28561 is the answer.

If traveling with the current certain boat went 9 mph against the same boat it only went 1 mph the speed of the current  is 4km/h  and no current is 5km/h.

Let b represent  the speed of the boat

Let c represent  the speed of the current

Downstream:

b + c = 9

Upstream:

b - c = 1

Subtraction

2c = 9-1

2c = 8

Divide both side by 2c

c = 8/2

c = 4 km/h (current)

No current

b = 9 - 4

b = 5 km/h

Therefore the speed is 4km/h and no current is 5km/h.

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Answer:7,800

Step-by-step explanation:

Answer:

Option B (3,510ft) would be correct.

Step-by-step explanation:

The volume of a rectangular prism is defined as the space occupied within a rectangular prism. A rectangular prism is a polyhedron that has two pairs of congruent and parallel bases. It has 6 faces (all are rectangular),12 sides, and 8 vertices. As the rectangular prism is a three-dimensional shape (3D shape), the unit that is used to express the volume of the rectangular prism is cm3, m3 and so on. In mathematics, any polyhedron, having all such characteristics can be referred to as a Cuboid.

The expression [tex](\frac{1}{4^{-3 } } )^{-2}[/tex] is less than 1.

The sign to change to make the expression greater than 1 is changing the sign of the exponential value which will make the new expression as

[tex](\frac{1}{4^{-3 } } )^{2}[/tex]

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).

In other words, an algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.)

Therefore, let's simplify the expression to know if it's equals to 1, greater than 1 or less than 1.

[tex](\frac{1}{4^{-3 } } )^{-2}[/tex]

using law of indices,

[tex](\frac{1}{4^{-3 } } )^{-2}[/tex] = 1 × [tex](4^{-3} )^{2}[/tex]

4⁻⁶  = 1 / 4⁶ = 1 / 4096

Hence,

1 / 4096 = 0.00024414062

Therefore,  the value is less than 1.

Let's change one sign to make the expression greater than 1.

Therefore, the expression will be [tex](\frac{1}{4^{-3 } } )^{2}[/tex]

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Answer:

Step-by-step explanation:

ABC = the draw of the square means that the angle is right

We can now say that the other two angles are acute because the sum of the interior angles of a triangle is 180 degrees

BCA = acute

CAB = acute

The volume of liquid contained by cone is 105 inches cube.

What is volume?

It can be defined as the total content which can be held inside a container.

Main body:

the volume of a cone = [tex]\frac{1}{3}\pi r^{2} h[/tex]  , where r = radius and h = height of cone

diameter = 10 , so radius = d/2 = 5 inches

V = [tex]\frac{1}{3}\pi 5*5*4[/tex]

V = 3.14 *5*5*4*1/3

v≈105 inches cube

Hence the volume is 105 inches cube.

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The equation of the parabola which passes through the point (-3, -8) as described and has x-intercepts -7 and -4 as described is; y = -2 (x + 4) (x + 7).

It follows from the task content that the equation of the parabola whose x-intercepts are -7 and -4 and has the point, (-3, -8) on it be determined.

Since the equation of a parabola in the factored form usually takes the form;

y = a (x - f) (x - g) in which case when f and g are x-intercepts of the parabola.

Therefore, we have; y = a (x - (-4)) (x - (-7))

y = a (x + 4) (x + 7)

Hence, to find the value of a, we set y = -8 and x = -3 so that we have;

-8 = a (-3 + 4) (-3 + 7)

-8 = 4a

a = -2.

Therefore, the equation of the parabola is; y = -2 (x + 4) (x + 7).

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Answer:

Step-by-step explanation:

Correct answer is A 5

The probability that a student's mark is more than 75 is 0.0947 and in a class of 50 students, 5 students should have a mark of more than 75.

In the given question,

The Mathematics marks of all the students in the class are normally distributed with mean mark 54 and standard deviation 16.

We have to find the probability that a student's mark is more than 75.

In a class of 50 students, we also have to find how many students should have a mark of more than 75.

From the question the mean = 54

Standard Deviation = 16

So the probability that a student's mark is more than 75.

Using the normal distribution

z = (x−mean)/Standard Deviation

P(x>75) = P(z>(x−mean)/Standard Deviation)

P(x>75) = 1−P(z<(75−54)/16)

Simplifying

P(x>75) = 1−P(z<21/16)

P(x>75) = 1−P(z<1.3125)

From the standard z table value

P(x>75) = 1−0.9053

P(x>75) = 0.0947

Hence, the probability that a student's mark is more than 75 is 0.0947.

Now finding in a class of 50 students, how many students should have a mark of more than 75.

Total student = 50

So the student having mark of more than 75 = Total student * probability that a student's mark is more than 75

The student having mark of more than 75 = 50 * 0.0947

The student having mark of more than 75 = 4.735

The student having mark of more than 75 ≈ 5

Hence, in a class of 50 students, 5 students should have a mark of more than 75.

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The value of TU is 21

From the question, we have

ST=3x+3 and TU=2x+9

ST = TU

3x + 3 = 2x + 9

3x - 2x = 9 - 3

x = 6

substituting the value, we get

TU = 2x + 9

= 2 (6) + 9

= 12 + 9

TU = 21

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

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The seal's new position relative to the surface of the ocean is 47 meters below.

It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.

In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres

The new position will be;

= -35 - 12

= -47

This implies that it's 47 meters below the ocean surface.

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The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)

What is the scale factor?

A scale factor is Scaling the shape of an object. it means the shape of the object remains the same but the size of the object is either increased or decreased. A scale factor greater than 1 means size is increased and less than one means size is decreased

We are given a point (0,-4)

Which is to be scaled by the factor of 2 at the center position

As the value is greater than 1 the size increase

We multiply the coordinate to find the new coordinates

We get (0,-8)

Hence, The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)

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a) The amount of money in the account at the beginning is $222,222.222.

b) The total amount of money withdrawn from the account is $400,000.

c) The amount of interest earned is $177,777.778.

It is given that we want to be able to withdraw $20,000 per year for 20 years. The account earns 9% interest annually. Let the total amount of money withdrawn in the twenty years be represented by the variable "A".

A = $20,000*20 = $400,000

Let the amount of money in the account at the beginning be represented by the variable "P".

A = P*R*T

400,000 = P*0.09*20

400,000 = P*1.8

P = 222,222.222

The interest earned is the difference between the initial and the final amount in the bank. Let the interest earned be represented by the variable "I".

I = A - P = $400,000 - $222,222.222 = $177,777.778

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Answer:

The difference is the what the sum of 2+x is

Step-by-step explanation:

suppose x=3 2+3 = 5

the difference between 5 and 2 is 3

Answer:

3

Step-by-step explanation:

y-intercept = b

The slope-intercept = y=mx+b

y=-2/5x+3

m=-2/5

b=3

If the equation was something like y=-2x-3, then the b would be -3 because you are subtracting 3.