Susan has a rectangle and a right triangle.
• The length of the rectangle is 4 more than its width, w.
.
• The length of the shorter leg of the triangle is equal to the rectangle's
width.
• The length of the longer leg of the triangle is twice the length of the
rectangle.

On solving the provided question, we can say that vertices of pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1); Area = 30 sq unit

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

vertices of a convex pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1).

Area = 1/2 [ 24+3+15+0-3] - [3-30-3+9-0]

Area = 1/2| 60 |

Area of pentagon  = 30 sq unit

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The population of a city is increasing at a rate of 4% each year. In 2020, there were. 236,000 people in the city.

Given, In 2015, the population of the town decreased by 10%, so [tex]8250 x 10/100 = 825[/tex]  people left the town, bringing the population down to [tex]8250 - 825 = 7425.[/tex]

From 2015 to 2020, the population increased by 15% so [tex]7425 x 15/100 = 1113.75[/tex] people came back to the town, bringing the population to [tex]7425+1113.75 = 8538.75[/tex]

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Answer:

[tex]h = -42[/tex]

Step-by-step explanation:

First, subtract 54 from both sides.

[tex]h = 4^2 - 16 \div 4 - 54[/tex]

Then, evaluate the right-hand expression using the order of operations:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

We'll first evaluate the exponent in 4²:

[tex]4^2 = 4 \times 4 = 16[/tex]

[tex]h = 16 - 16 \div 4 - 54[/tex]

Next, we can evaluate the division:

[tex]16 \div 4 = 4[/tex]

[tex]h = 16 - 4 - 54[/tex]

Finally, perform the subtraction.

[tex]16 - 4 - 54 = -42[/tex]

[tex]h = -42[/tex]

Answer:

[tex] \sf \: h = - 42[/tex]

Step-by-step explanation:

Given equation,

→ h + 54 = 4² - 16 ÷ 4

Now the value of h will be,

→ h + 54 = 4² - 16 ÷ 4

→ h + 54 = 16 - 4

→ h + 54 = 12

→ h = 12 - 54

→ [ h = -42 ]

Hence, value of h is -42.

To solve complex fractions there are two methods -

1 - Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator and then simplify further if necessary.

2 - Multiply the numerator and denominator of the overall complex fractions and then simplify further if necessary.

What is a complex fraction?

A rational expression with a fraction in the numerator, denominator, or both is referred to as a complex fraction.

There are two ways to solve a complex fraction -

Method 1 : Take an example - (1/3-1/4)/(1/8+1/2)

Step 1 - If necessary, combine the denominator and numerator into a single fraction.

Add the numerator -

=1/3-1/4

=(4-3)/12

=1/12

Add the denominator -

=1/8+1/2

=(1+4)/8

=5/8

Combine back to form a complex fraction -

=(1/12)/(5/8)

Step 2: Multiply the numerator by the denominator's reciprocal, then divide the result by the denominator.

Step 3: Simplify the rational expression if necessary.

=(1/12)×(8/5)

=8/60

=2/15

Method 2: Take an example - [(2x+1)/(x^2-25)]/[(4x^2-1)/(x-5)]

Step 1 - Divide the LCD of the smaller fractions by the numerator and denominator of the total complex fractions.

(x^2-25)=(x+5)(x-5)

The denominator of the denominator’s fraction  has the following factor -

(x-5)

Using the highest exponent and combining all the other factors, we arrive at the LCD shown below for all the little fractions -

(x+5)(x-5)

By multiplying the LCD by the numerator and denominator -

=[{(2x+1)/(x+5)(x-5)}×(x+5)(x-5)]/[{(2x+1)(2x-1)/(x-5)}×(x+5)(x-5)]

=(2x+1)/(2x+1)(2x-1)(x+5)

Step 2 - Simplify the rational expression if necessary.

=(2x+1)/(2x+1)(2x-1)(x+5)

=1/(2x-1)(x+5)

Therefore, there are two methods to solve complex fractions.

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Answer: The odds in favor of an event happening are the ratio of the probability of the event happening to the probability of the event not happening. To find the odds in favor of an event, you can use the formula:

Odds in favor = probability of event occurring / (1 - probability of event occurring)

In this case, the event is that Adam will see a meteor in the next 10 minutes. The probability that this event will occur is 0.56. Therefore, the odds in favor of this event occurring are:

Odds in favor = 0.56 / (1 - 0.56)

= 0.56 / 0.44

= 1.27

So, the odds in favor of Adam seeing a meteor in the next 10 minutes are 1.27 to 1.

It means that Adam is 1.27 times more likely to see a meteor in the next 10 minutes than not seeing one.

Step-by-step explanation:

The odds in favor of Adam seeing a meteor in the next 10 minutes are 14 : 11

Answer:

They will meet in 1 hour

Step-by-step explanation:

(1)  d = 10t

(2)  d - 8t = 2   rearrange this equation to:  d = 8t + 2

Set equation (1) equal to equation (2):

10t = 8t + 2

Solve for t:

10t - 8t = 2

2t = 2

t = 2/2 = 1 hr

Answer: 19

Step-by-step explanation:

56-13=43

43-24=19

Answer: 19

Step-by-step explanation: 13 + 24 = 37

so (56 - 37 = 19)

Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both.

For a square whose side are 2 units long is :

= 2 + 2 x 2 + 2

= ( 2 + 2 ) x 2

= 2 x 4

= 2 x 3 + 2 = 8

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The number of hours of practice is 3 x h or 3h.

In mathematics, an expression is a sentence that contains at least one number or variable. Additionally, an expression consists of at least one mathematical operation. There is no equal to sign in an expression.

Given:

Volleyball practice is h hours long. Debbie had 3 volleyball practices last week.

Multiply the number of hours for each practice by the total number of practice to get the expression for the number of practice hours.

The mathematical operation known as multiplication is used to calculate the sum of two or more numbers.

Number of hours of practice

= hours of practice x number of practice

= 3 x h

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The inequality to find the cost of the pizza they should order is c ≤ 14. The cost is at most $14.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Trey and three of his friends are ordering a pizza and they want to spend at most $3.50 per person. An inequality to find the cost of the pizza they can order is:

c ≤ (3.50 × 4)

c ≤ 14

The cost will be at most $14.

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A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol.

A few more constant examples are :

The number of days in a week represents a constant.

Substitute:

m*o+b=18

m+b=20

Apply Zero Property of Multiplication:

b=18

m+b=20

Substitute into one of the equations:m+18=20

Rearrange unknown terms to the left side of the equation:m=20-18

Calculate the sum or difference:m=2

The solution of the system is:

b=18

m=2

The answer is b=18 m=2

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Answer:

7

Step-by-step explanation:

As we want to find the whole number, and to do so we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.

21/3 = 7

Answer:

18 + 4√15

Step-by-step explanation:

(3√5+√3)(√5+ √3)

= 3√5 (√5+ √3) + √3 (√5+ √3)

= 3√5 √5 + 3√5 √3 + √3  (√5+ √3)

=  3√5 √5 + 3√5 √3 + √3 √5 + √3 √3

= 18 + 4√15

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At a significance level of 0.05, the sample data is not consistent with the null hypothesis that the proportion of population who would respond "yes" is 0.5. The P-value of 0.0005 is less than 0.05, and also the sample proportion 0.4616 is not in the interval (0.477, 0.523) which we found as 95% Confidence interval.

Therefore, we reject the null hypothesis and conclude that the population proportion of "yes" responses is different from 0.5.

The P-value for a score test for H0: π = 0.5 can be found using the z-score and a standard normal table. The z-score is calculated as

[tex]z = \frac{x-0.5}{0.5\sqrt{\frac{x-0.5}{n} } }[/tex], that is

z = (x - 0.5) / (√(0.5(1 - 0.5) / n)

where x is the sample proportion of "yes" responses (842 / (842 + 982) = 0.4616), π is the population proportion of "yes" responses, and n is the sample size (842 + 982 = 1824).

[tex]z = \frac{0.4616-0.5}{0.5\sqrt{\frac{0.4616-0.5}{1824} } }[/tex]

= (0.4616 - 0.5)/ (√(0.5(1 - 0.5) / 1824)

This gives a z-score of -3.28.

To find the P-value, we can use the standard normal table to find the probability of observing a z-score less than -3.28. This P-value is approximately 0.0005, which is less than the commonly used significance level of 0.05. Therefore, we would reject the null hypothesis that π = 0.5.

To construct a 95% confidence interval for π, we can use the formula for a normal approximation interval:

π ± z×(√(π(1-π) / n)) that is

[tex]\pi \frac{+}{} z\frac{\pi (1 -\pi )}{n}[/tex]

Where π = 0.5, z = 1.96 (for a 95% confidence level), and n = 1824.

This gives a 95% confidence interval of (0.477, 0.523)

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The solution for the rational equation (1/(x + 1)) - (1/(x + 2)) = 1/5 is specified by the option C.

C. x = -3.79, x = 0.79

A rational equation consists of a fraction that has a polynomial numerator denominator.

The specified equation can be expressed as follows;

[tex]\dfrac{1}{x + 1} - \dfrac{1}{x+2} = \dfrac{1}{5}[/tex]

Finding the common denominator for the right hand side expression, we get;

[tex]\dfrac{ (x + 2) - (x + 1)}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]

[tex]\dfrac{1}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]

[tex]\dfrac{1}{x^2+ 3\cdot x+ 2} = \dfrac{1}{5}[/tex]

Inverting both sides of the above equation, we get the following quadratic equation;

x² + 3·x + 2 = 5

x² + 3·x + 2 - 5 = 0

x² + 3·x - 3 = 0

The quadratic formula indicates that we get;

x = (-3 ± √(3² - 4×1×(-3))) ÷ (2 × 1)

x = (-3 + √(21)) ÷ 2 and x = (-3 - √(21)) ÷ 2

x ≈ 0.79 and x ≈ -3.79

The correct option is option C

C. x = -3.79, x = 0.79

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The probability that the sixth child will be a son is 50%. Each child, regardless of gender, has an equal chance of being born.

P(son) = (5 choose 6) x (0.5^6) = 0.015625

Therefore, the probability of having a son as the sixth child can be calculated using the binomial formula as follows: P(son) = (5 choose 6) x (0.5^6) = 0.015625.

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When we construct the confidence interval their sample must have some conditions which are as follows,

Therefore , these are the conditions which the administrator should use to construct a one-sample z interval for a proportion.

When two ratios are equivalent to each other , they are said to be in a state called proportion. The proportion formula is used to see whether  the given ratios or fractions are equal or not . The proportion formula can be given as, The product of means is equal to the the product of extremes. This can be written as ad = bc.

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The x-coordinate of the centroid of the triangle ABC with vertices

A(-3, 3), B(2, 5), and C(4, -3) is 1.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

The centroid of a triangle is the common intersection point of all the medians of the triangle.

When vertices of a triangle is given the co-ordinate of the centroid are

(x₁ + x₂ + x₃)/3 and (y₁ + y₂ + y₃)/3.

Given, ΔABC has vertices A(-3, 3), B(2, 5), and C(4, -3).

Therefore, The x-coordinate of the centroid is,

Gₓ = (- 3 + 2 + 4)/3.

Gₓ = 3/3.

Gₓ = 1.

So, The x-coordinate of the centroid is 1.

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The range of the function y = √(x +5)  is y ≥ 0

The domain of a function is the set of all possible values of x

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

we have

y = √(x +5)

Remember that the radicand of the function must be greater than or equal to zero

so (x +5) ≥ 0

solve for x

x ≥ -5

The domain is the interval ----> [-5,∞)

For x= -5

y = √(-5 +5) = 0

so

The range is the interval ----> [0,∞)

y ≥ 0

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On solving the provided question, we can say that by mean score the population will be 20192

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate:Divide by how many digits there are after adding up all the digits. the total divided by the count.

A sample of 12th grade students who took the National Assessment of Education Progress year 2000 mathematics test had a mean score of 250

200/4

= 50

50*e^{-2}

the population will be 20192

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The volume of the prism is 103.32 cubic inches (optionD)

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.

The base area of the prism = 4.1×7.2 = 29.52 inches squared.

The height of the prism is 3.5 inches

Therefore volume = base area × height

volume = 29.52× 3.5 = 103.32 cubic inches.

Therefore the volume of the shape is 103.32 cubic inches.

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The equations that are equivalent to each other will be 2 + x = 5, x + 1 = 4, and - 5 + x = - 2. Then the correct options are A, B, and E.

The equivalent is the expression that is in different forms but is equal to the same value.

Simplify all the equations, then we have

A. 2 + x = 5, to simplify the equation, then we have

2 + x = 5

x = 3

B. x + 1 = 4, to simplify the equation, then we have

x + 1 = 4

x = 3

C. 9 + x = 6, to simplify the equation, then we have

9 + x = 6

x = - 3

D. x + (- 4) = 7, to simplify the equation, then we have

x - 4 = 7

x = 11

E. - 5 + x = - 2, to simplify the equation, then we have

- 5 + x = - 2

x = 3

The equations that are equivalent to each other will be 2 + x = 5, x + 1 = 4, and - 5 + x = - 2. Then the correct options are A, B, and E.

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Therefore , the solution of the given problem of parallelogram comes out to be option D 80  degrees.

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Here,

Given : The parallelogram  has M angle  =100 degree

And to Find :L angle

In a parallelogram sum of the adjacent angle is 180°, So

So ,

Using this parallelogram property ,

we find :

=>100 + L =180

=> L = 80

Thus,

We get the L value using parallelogram properties.

Therefore , the solution of the given problem of parallelogram comes out to be option D 80  degrees.

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The solution to the exponential equation 8^(x/2)/4^(x/3) = 2^(-5/2) is given as follows:

x = -6/5.

The exponential equation for this problem is defined as follows:

[tex]\frac{8^{\frac{x}{2}}}{4^{\frac{x}{3}}} = 2^{-\frac{5}{2}}[/tex]

Both 8 and 4 are powers of 2, as follows:

Applying the power of power rule (multiplying the exponents), the expression on the left side can be rewritten as follows:

[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{-\frac{5}{2}}[/tex]

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence:

[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{\frac{3x}{2} - \frac{2x}{3}}[/tex]

The subtraction is obtained as follows:

3x/2 - 2x/3 = 9x/6 - 4x/6 = 5x/6.

(as the least common factor of 2 and 3 is of 6).

Then the simplified expression is of:

[tex]2^{\frac{5x}{6}} = 2^{-\frac{5}{2}}[/tex]

As the exponential function y = 2^x is injective, the solution is obtained as follows:

5x/6 = -5/2.

10x = -12

x = -6/5.

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Answer:

The two little blue boxes are going

Step-by-step explanation:

Lets start with the 0s.

Two zeros is 0. so its

_ _ _ _ 0.

Now we add 2 and 0 which is 2.

_ _ _ 2 0

now we add 6 and 4, which is 10. We have to put the 1 above the 7 and 5 and we are going to put 0 down below

_ _ 0 2 0

now we are going to add 7 +5, but dont forget the 1! Its going to be 13. Put the 3 down below and put the 1 above the 2!

_ 3 0 2 0

Now its 2 + 1 which is 3

your answer is

33020

You had a better score relative to the rest of your class.

To compare the scores of you and your friend relative to the rest of their classes, we need to calculate the standard deviation of your score and your friend's score from the average of their respective classes.

A standard deviation of 2 means that 68% of the scores in the class fall within 1 standard deviation of the mean, or between 84 and 88 in the case of Mrs. Wilson's class. Since 88 is greater than 86 (the mean) and less than 2 standard deviations away (88-86 < 2*2=4) , so your score of 88 is better than the average score in your class.

On the other hand, 85 is less than 82 (the mean) and more than 1 standard deviation away (85-82 > 2) so your friend's score of 85 is less than the average score in their class.

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The Pythagorean triplet of 16 is (8, 15, 17).

This can be calculated using the Pythagorean theorem, which states that in any right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. Therefore, given a number, we can find a Pythagorean triplet by calculating the squares of the two legs and then finding the hypotenuse.

Formula:

a² + b² = c²

Find the square of the number.

16² = 256

Subtract the square from the number to get one leg of the triangle.

16 - 256 = -240

Take the square root of the result.

√(-240) = 8

Add the square to the number to get the other leg of the triangle.

256 + 16 = 272

Take the square root of the result.

√(272) = 15

Add the two legs together to get the hypotenuse.

8 + 15 = 23

Take the square of the result.

23² = 529

Subtract the sum of the two legs from the hypotenuse.

529 - 23 = 506

Take the square root of the result.

√(506) = 17

Therefore, the Pythagorean triplet of 16 is (8, 15, 17).

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Using the unit conversion and converting all the distance units to inches, The final answer is 7575 inches.

Divide the smaller unit's value by the quantity of smaller units required to create the larger unit. Multiply to change from a larger to a smaller unit. Divide to change from a smaller unit to a larger one. We need to convert between units in order to ensure accuracy and prevent measurement misinterpretation. For example, we do not measure a pencil's length in kilometers. In this situation, one must convert from kilometers (km) to centimeters (cm).

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics.

13 yard = 468inches

2ft = 24 inches

total 268+24+13 = 505inches

505*15 = 7575 inches

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