Find the missing length indicated.

In given rectangle , value of x=8 and y=11.

What is rectangle?

   An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. a flat, four-sided shape having straight sides and right-angled internal angles. Additionally, the opposing sides are parallel and the same length.

Here let us take rectangle as ABCD.

Here the given rectangle angle of B is 90°.

We know that angles in each side of rectangle is 90°.

Here ∠C=36°+c

=> 90=36+c

=> c=90-36 = 54°.

Here consider the triangle ABC , sum of all angles in triangle is 180°.

=>4x+4+90+54=180

=>4x+148=180

=> 4x=32

=> x=32/4 = 8.

Now angle A is sum of 4x+4 and 4y+10 is 90°.

=> 4x+4+4y+10=90

=>32+4+10+4y=90

=>46+4y=90

=> 4y=90-46 =44

=> y = 44/4 =11.

Hence the value of x and y is 8 and 11.

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Answer:

I hope this helps you

Step-by-step explanation:

l=80cm,b=40cm,h=20cm

Therefore,

TSA = 2(lb+bh+hl)=2(80×40+40×20+80×20)=11200 cm

2

LSA = 2(l+b)h=2(80+40)20=4800 cm

2

The inequality to illustrate the information will be C. (c) Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100.

Inequality is a relation that defines a non-equal comparison between the given two numbers or other mathematical expressions.

Let the no. of child bikes is c and the no. of adult bikes be a.

For the building of bikes,

4c + 6a ≤ 120

For the testing of bikes,

4c + 4a ≤ 100

Checking the equations, for given 10 child bikes and 12 adult bikes in the week.

For the building of bikes,

( 4 × 10 ) + ( 6 × 12 ) ≤ 120

40 + 72 ≤ 120

112 ≤ 120 (Inequality satisfied)

For the testing of bikes,

( 4 × 10 ) + ( 4 × 12 ) ≤ 100

40 + 48 ≤ 100

88 ≤ 100 (Inequality satisfied)

Hence, the correct option is C.

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Answer:

x=2

Step-by-step explanation:

The line to be parallel and have a point at (2,-5)

here is a picture attached for better understanding

Coordinates of the fourth vertex is (-4,7).

Given:

coordinates (5,-5),(7,-9) and (-2,-7)

From the figure:

Horizontal line vertices are (7,-9) and (-2,-7) on comparing the x coordinates the x is 9 units so the top line starting from (5,-5) should  move 9 units left that is x coordinate is x = -4.

Vertical line vertices (5,-5) and (7,-9) on comparing the y coordinates the y is 14 units so the left line starting from (-2,-7) should move 14 units top that is y coordinate is y = 7.

Therefore coordinates of the fourth vertex is (-4,7).

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The estimate for the number of miles traveled is, 213.71.

What rounding the decimal number?

If the following digit in the correct location is less than 5, round the number down; if it is 5 or more, round the number up. A certain level of accuracy is required when rounding decimal values.

As given, a sailor entered a race and made a round trip of 213.709 miles.

We have to round the decimal number 213.709 to nearest hundredth.

Here the digit on thousands place is greater or equal to 5.

So, we have to increase the number on hundredths place by 1, and drop the digit in the thousandths place.

Hence, the number becomes, 213.71.

Therefore, the option C is the correct.

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The correct inequality represents the the maximum number of concert tickets Tayah can buy for the reduced price of $15.00 is 1st.

Given that the 1st ticket is of fixed price which is 25 , so it will be a constant in the equation.

Now the money she left with after buying the first ticket is :

money left = 115 - 25 = 90.

so now she she can only spent 90 dollar on the tickets which is now at rate of 15 dollars.

So the equation for this situation is :

15c  ≤ 90 , where c is the number of the tickets.

Finally the total amount of tickets spent are :

15c + 25 ≤ 115

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The vertex form equation of the parabola whose vertex is; (2, -5) as required in the task content is; y = -(x - 2) - 5.

It follows from the task content that the vertex form equation of the parabola described in the task content is to be determined.

Since the vertex form equation of a parabola takes the form;

y = a (x - h)² + k

where the graph opens upward when a > 0 and opens downward when a < 0.

Therefore, the required vertex form equation of the parabola is; y = -(x - 2) - 5.

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When the bananas cost 3 IBS for $1.10, the cost for six Bananas is $2.20.

From the information, bananas cost 3 IBS for $1.10, In this his case, the first thing to do is to calculate the price for each. This will be:

= $1.10 / 3

= $0.367

Therefore the cost for six bananas will be:

= Cost for each banana × Number of banana

= $0.367 × 6

= $2.20

The cost is $2.20.

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48630 is large should the sample be if the margin of error is to be less than $4 .

What does the term "margin of error" mean?

Margin of Error  = Z*Stdev/sqrt(n)

4 <= 0.90* 33/sqrt(n)

n >= (0.90* 33/2)^4 = 48630.17 OR 48630

So, n should be atleast 48630 so that margin of error is within $4

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[tex]\sqrt[3]{8}^{\frac{1}{4}x }[/tex] is equivalent to [tex]\sqrt[12]{8}^{x}[/tex].

What are cube roots?

In mathematics, the cube root of a number x is a number y, so y³ = x. Every nonzero real number has exactly one real cube root and one set of complex conjugate cube roots, and every nonzero complex number has three different complex cube roots.

The given equation is [tex]\sqrt[3]{8}^{\frac{1}{4}x }[/tex]

Solving by using the indices properties,

                       [tex]=\sqrt[3]{8}^{\frac{1}{4}x }\\={8}^{\frac{1}{3}\frac{1}{4}x}\\=8^{\frac{1}{12}x}\\=\sqrt[12]{8}^{x }[/tex]

Hence the solution will be [tex]\sqrt[12]{8}^{x}[/tex].

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Answer: -54

Step-by-step explanation:

Answer:

-34

Step-by-step explanation:

2(-80/4) -14

-160/8 -14

-20-14

= -34

It would require 6  pattern block triangles to create two trapezoids.

A collection of arithmetic tools called Pattern Blocks was created in the 1960s. The six shapes serve as both a recreational resource and a math learning aid, helping to build the spatial thinking abilities that are essential to understanding arithmetic. They give kids the opportunity to see how shapes may be combined and broken down into new shapes, among other things, and they introduce them to the concept of tilings. Sets of pattern blocks contain multiples of the same six shapes, square, equilateral triangle, parallelogram, trapezoid, and hexagon.

It would require 6 block triangles to create two trapezoids.

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Water evaporated from a 320 liter tank of a 3 % salt solution to obtain a 8 % salt solution is 120 liters

information from the problem

a 320 liter tank of a 3 % salt

a 8 % salt solution

Comparison deals with division to ascertain how many times greater or less a number is from the other

Using comparison of the amount of water that gave 3% salt solution the amount that will give 8% is solved a below

how many 8 are there in 3

3/8 = 0.375

The factor 0.375 is used to multiply the amount of water in 3% to find the amount of water in the 8% concentration

0.375 * 320 = 120 liters

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There can be 228 disks fit into the cylindrical container

Here it is given that the diameter of the disk is 5 inches.

Therefore, the radius of the disk is 2.5 inches.

The height of the disk is 1/4 inch,

Now the cylindrical container had a height of 4 feet

1 foot = 12 inches

Hence,

4 feet = 48 inches.

Hence, the height is 48 inches.

The radius of the container is half of 5 1/4 inches

= 2.725 inches.

The number of disks that can be fit

= Volume of the container/volume of disk

The volume of any cylinder

= π X radius² X height

Hence, the volume of the disk is

π X 2.5² X 0.25 cubic inches

= 1.5625π cubic inches

= 4.909 cubic inches

The volume of the cylinder is

π X 2.725² X 48 cubic inches

= 356.43π cubic inches

= 1119.758 cubic inches

Hence the number of disks that can fit in the container

= 1119.758/4.909

= 228.103

Since the number of disks cannot be in decimal

228 disks can be fitted in.

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Option (a) 7+3•5

Step-by-step explanation:

[tex]{ \purple{ \tt{6 + {2}^{4}}}} [/tex]

[tex]{ = \purple{ \tt{6 + 2 \times 2 \times 2 \times 2}}}[/tex]

[tex]{ = \purple{ \tt{6 + 16}}}[/tex]

[tex]{ = \purple{ \tt{22}}}[/tex]

_________________________________

[tex]{ \red{ \sf{7 + 3 \times 5}}}[/tex]

[tex]{ = \red{ \sf{7 + 15 }}}[/tex]

[tex]{ = \red{ \sf{22}}}[/tex]

Therefore,

[tex]{ \green{ \sf{6 + {2}^{4} = 7 + 3 \times 5}}}[/tex]

[tex]{ \green{ \sf{22 \: \: \: \: \: \: \: = \: \: \: \: \: \: 22}}}[/tex]

Answer:

Step-by-step explanation:

-10

Answer:

-10

Step-by-step explanation:

5 goes into -50 -10 times. So -50/5=-10.

-Hope this helped

Scientists found an animal skull during an excavation and tested the amount of carbon -14 left in it. They found that 55 percent of the carbon-14 in the skull remained.

55% of the Carbon is left in the skull.

If A₀ was the original amount of Carbon, the amount of Carbon that is remaining will be 55% of A₀  which equals 0.55A₀

Using the given equation:

[tex]A = A_{o}e^{-0.000124t}\\\\ 0.55A_{o} = A_{o}e^{-0.000124t}\\ \\0.55 = e^{-0.000124t}\\\\In(0.55) = In(e^{-0.000124t})\\\\In(0.55) = -0.000124t*In(e)\\\\In(0.55) = -0.000124t\\\\[/tex]

[tex]t = \frac{In(0.55)}{-0.000124} \\\\t = 4821[/tex]

Rounding of to nearest year, we can conclude that the animal was buried 4821 years ago.

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To divide two fractions, _multiply_ the first fraction by the _Reciprocal_ of the second fraction.

What is Fraction?

A fraction represents a portion of a whole. This whole may refer to a place or a group of places. The Latin word "fractio," which means "to break," is the source of the English word "fraction." The division of food and supplies as well as the lack of a bullion currency were among the mathematical issues that the Egyptians used fractions to solve because they were the first civilization to study fractions.

Only verbal descriptions of a portion of the whole were used to write fractions in ancient Rome. The numerator and denominator of fractions were first written in India with one number above the other, but without a line. The line used to divide the numerator and the denominator was only added by Arabs.

To divide two fractions, ______ the first fraction by the _______ of the second fraction.

The answer to the blanks are Multiply and Reciprocal respectively

Example:

1/2 ÷ 3/4

= 1/2 × 4/3

= 4/6

= 2/3

Hence, the answer to blanks are Multiply and Reciprocal respectively

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Answer:

[tex]\begin{array}{|c|c|}\cline{1-2} \sf I\:\!nput & \sf Ou\:\!tput\\\cline{1-2} \sf Muffins & \sf Cost\\\cline{1-2} 1 & 2.25\\\cline{1-2} 3 & 6.75\\\cline{1-2} 6 & 13.50\\\cline{1-2} x & 2.25x\\\cline{1-2} 12 & 27\\\cline{1-2} \end{array}[/tex]

Step-by-step explanation:

Definitions:

To determine if the relationship is linear, calculate the rate of change between the ordered pairs given in the table:

[tex]\implies \sf rate\;of\;change=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{13.50-6.75}{6-3}=\dfrac{6.75}{3}=2.25[/tex]

[tex]\implies \sf rate\;of\;change=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{6.75-2.25}{3-1}=\dfrac{4.5}{2}=2.25[/tex]

As the rate of change is the same, the relationship is linear.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

The rate of change is the slope of a linear equation.

Therefore, to create an equation, substitute the found slope (2.25) and one of the ordered pairs (1, 2.25) into the formula:

[tex]\implies y-2.25=2.25(x-1)[/tex]

[tex]\implies y-2.25=2.25x-2.25[/tex]

[tex]\implies y=2.25x[/tex]

Therefore, the output is 2.25 times the input.

If the input is x, then the output is 2.25x.

If the input is 12, then the output is 2.25 × 12 = 27.

[tex]\begin{array}{|c|c|}\cline{1-2} \sf I\:\!nput & \sf Ou\:\!tput\\\cline{1-2} \sf Muffins & \sf Cost\\\cline{1-2} 1 & 2.25\\\cline{1-2} 3 & 6.75\\\cline{1-2} 6 & 13.50\\\cline{1-2} x & 2.25x\\\cline{1-2} 12 & 27\\\cline{1-2} \end{array}[/tex]

he simplest form of quadratic equation 6y² + 5y - 4  is y = 0.5 or y = −1.33333 or in fraction y = 6 / 12 or y = −16/12.

How to solve a quadratic equation using the Quadratic Formula.

6y² + 5y - 4

using the Quadratic Formula where a = 6, b = 5, and c = -4

y =−b±(√b2−4ac) / (√2a)

y =−5±(√5²−4(6)(−4)) / √(2(6))

y =−5±(√25−(−96)) / √12

y =−5± (√121 / √12

The discriminant b²−4ac>0. So, there are two real roots.

Simplify the radical:

y = (-5 ± 11) /12

y = 6/12  y =16/12

which becomes

y = 0.5

y = −1.33333

Hence, the simplest form of quadratic equation 6y² + 5y - 4  is y = 0.5 or y = −1.33333.

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Answer:

7

Step-by-step explanation:

|−5| + 2

= 5 + 2

= 7

Hope this helps! :)

An inequality sign is not part of an algebraic equation

Option A

Explanation :

Any algebraic equation will have an equal sign

For example , Algebraic equation is

This algebraic equation have = sign

The above algebraic equation have expression 3x+2

Also the above algebraic equation have variable 'x'  and 'y'

So , an algebraic equation have = sign , variables and expression

If we have inequality sign then we call it as inequality not an equation

An inequality sign is not part of an algebraic equation

The missing value for the probability distribution can be completed by option A.

What is probability distribution?

A probability distribution is a mathematical function that calculates the likelihood that various possible outcomes of an experiment will occur.

Main body:

We know that the sum of probability distribution is always 1.

P= P(X=1) + P(X=2) + P(X=4) + P(X=8) + P(X=16) + P(X=32) + P(X=64)

1= 0.1 + 0.05 + 0.25 + 0.25 + 0.05 + P(X=32) + P(X=64)

P(X=32) +P(X=64) = 1-0.7

                             = 0.3

This condition is satisfied by option A.

hence the answer is option A.

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The probability that at least one of the numbers falling uppermost is a 1, given that the sum of the numbers falling uppermost is even is 0.3056.

Given that, a pair of fair dice is cast.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

There are six different possible outcomes for a dice, the set (S) of all the outcomes can be listed as follows:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

The probability = 11/36

= 0.3056

Hence, the probability that at least one of the numbers falling uppermost is a 1, given that the sum of the numbers falling uppermost is even is 0.3056.

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The distance between the two points in simplest radical form is [tex]6\sqrt{2}[/tex].

What is the hypotenuse of a triangle?

The longest side in a right triangle is called the hypotenuse. It is the side that is opposite to the right angle (90°).

Given two points are (8, 3) and (2, 9)

The distance between the two points (d) is given by,

[tex]d = \sqrt{(x_{2}-x_{1} )^{2} + (y_{2}-y_{1} )^{2} }[/tex]

where, [tex](x_{1},x_{2} )= (8,3)[/tex]

and,  [tex](y_{1},y_{2} )= (2,9)[/tex]

Then,

         [tex]d = \sqrt{(2-8)^{2} + (9-3 )^{2} }[/tex]

or,      [tex]d = \sqrt{36 + 36 }[/tex]

or,      [tex]d = \sqrt{72} = 6\sqrt{2}[/tex]

Hence, the distance between the two points is [tex]6\sqrt{2}[/tex] .

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The correct answer among the choices is letter d. From the following choices of ordered pair, (1, 0) is the set solution of the inequality 2x + 6y ≤ 10. Substituting the given pair order make the inequality a true statement.  To counter check answer, substituting the pair order and solving the linear inequality will result a value to support the correct answer.

a. ( 3,1 ) (x ,y)

Substitution

2x + 6y ≤ 10

2(3) + 6(1) ≤ 10

6 + 6 ≤ 10

12  ≤ 10 ( The inequality is False)

This is not the correct answer since value to solve for x and y should result to an equal or lesser value than 10.

b. (2, 2) (x ,y)

Substitution

2x + 6y ≤ 10

2(2) + 6(2) ≤ 10

4 + 12 ≤ 10

16  ≤ 10 ( The inequality is False)

This is not the correct answer since value to solve for x and y should result to an equal or lesser value than 10.

c. (1, 2) (x ,y)

Substitution

2x + 6y ≤ 10

2(1) + 6(2) ≤ 10

2 + 12 ≤ 10

14  ≤ 10 ( The inequality is False)

This is not the correct answer since value to solve for x and y should result to an equal or lesser value than 10.

d. (1, 0) (x ,y)

Substitution

2x + 6y ≤ 10

2(1) + 6(0) ≤ 10

2 + 0 ≤ 10

2 ≤ 10 ( The inequality is True)

The statement states that 2 is lesser than or equal to 10.

Hence we get the required answer.

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Your question was incomplete. Please find the missing content below.

Which of the following ordered pairs is a solution of the inequality 2x + 6y ≤ 10?a. (3, 1) b. (2, 2) c. (1, 2) d. (1, 0)

As per the division process, the cost of 1 pint ice cream is $2.74

Division:

The process of splitting a specific amount into equal parts is known as division.

Given,

Two quarts of ice cream cost $5.48.

Here we need to find the cost of 1 pint of ice cream.

Here we know that, the cost of two quart ice cream is $5.48.

Now, have to find the cost of 1 pint,

We also know that,

1 quart = 2 pint.

Therefore, the value of 1 pint is obtained by dividing the number by 2, then we get,

=> 5.48/2

=> 2.74

Therefore, the cost of 1 pint of ice cream is $2.74

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For mutually exclusive events R₁,R₂ and R₃, the value of P(R₁Q) is 3/55.

Two events are said to be mutually exclusive in probability theory if they cannot happen simultaneously or at the same time. In other terms, occurrences that are mutually exclusive are referred to as discontinuous events. If two occurrences are regarded as separate ones, there is no chance that they will happen at the same moment. Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin flip, which can result in either heads or tails but not both, serve as an obvious illustration.

Given,

Events:

P(R₁) = 0.05 P(R₂) = 0.6

For P(R₁ /Q)

P(R₁Q)

mutually exclusive event:

P(Q/R₁)P(R₁)/P(Q/R₁)P(Q₁) + P(Q/R₂)P(R₂) + P(Q/R₃)P(R₃)

(0.6)(0.05)/0.6(0.05) +0.4(0.6) + 0.8(0.35)

0.03/0.03 + 0.77 + 0.28

0.03/0.55

3/55
For mutually exclusive events R₁,R₂ and R₃, the value of P(R₁Q) is 3/55.

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