Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. Suppose Rich only paid the interest during his 4 years in school and the 6-month grace period. What will his monthly payments be? Round to the nearest cent.

Answer:

[tex]\sqrt{a^2+b^2}[/tex]

Step-by-step explanation:

The blue line (or, more accurately, ray) r makes up the hypotenuse of a right triangle with legs (or sides) of lengths a and b. The relationship among the three values is given by the Pythagorean theorem, which states that for any right triangle, the sum of the squares of the lengths of the legs is always equal to the square of the length of the hypotenuse.

Thus, with a and b being the lengths of this right triangle and r being the hypotenuse, the length of the blue line r expressed in terms of a and b can be written as

[tex]r = \sqrt{a^2+b^2}[/tex]

However, since the left-hand side of the equation is already provided for you, what you would write in the box would be simply [tex]\sqrt{a^2 + b^2}[/tex].

[tex]\sqrt{252\\[/tex] = 6[tex]\sqrt{7}[/tex]

We have to find the equivalent of [tex]\sqrt{252\\[/tex] so first find.

Prime factorization of 252= 2² × 3² × 7²

now, Prime factors of 252 in pairs: (2×2) × (3×3) × 7

Now, the square root of 252: [tex]\sqrt{252\\[/tex] = [tex]\sqrt{((2*2) *(3*3) *7}[/tex]

So, the square root of 252 =   (2*3)[tex]\sqrt{7}[/tex]  = 6[tex]\sqrt{7}[/tex]

Factorization of an algebraic expression means writing the given expression as a product of its factors. These factors can be numbers, variables, or an algebraic expression.

There are a few methods or tricks to remember. Reduce the expression by the greatest common factor. Check if there are perfect squares or differences of squares. Use the algebraic formulas or identities to factorize the expression.

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Tadeo volunteered for 2 hours, and Dylan volunteered for 12 hours.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Tadeo volunteered at the library 6 times as many hours over the weekend as Dylan. Together, they volunteered a total of 14 hours.

Let x represent Dylan's hours and y represents Tadeo's hours. Then the equations are given as,

y = 6x                    ...1

x + y = 14               ...2

From equations 1 and 2, then we have

x + 6x = 14

7x = 14

x = 2

Then the value of 'y' is given as,

2 + y = 14

y = 12

Tadeo volunteered for 2 hours, and Dylan volunteered for 12 hours.

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Hi there! And yay--a question my brain can finally comprehend.  ;D

So you notice that the shape is divided into two shapes, a right triangle and a rectangle.   Let's find the area of the rectangle first.

To do this, you would multiply the length of the rectangle (12 feet) by the width of the triangle (6 feet).  Instead of using those unit squares you may have used to determine the area of a small figure, you can just multiply it out to make it easy!  12 x 6 is 72.  The area of the rectangle is 72.

Now for the triangle!  12 x 10 is 120.  Remember, if a question ever puts a number near that diagonal side (that does remain without a number near it now), it's trying to trick you.  Only multiply the straight sides together.  

For a triangle though, you would always divide the area by 2.  A triangle is usually half of a square or rectangle.  120/2 = 60.

Now add 60 and 72 together to find the area of the full shape.  That's 132.  :)

Have a good night!

Z score is used to get by how many standard deviations the raw score is higher or minimum the mean. The z score is given by:

z = (x - μ)/σ

where x is the raw score, μ is the mean and σ is the standard deviation.

In a normal distribution, data is uniform distributed with no skew. When plotted on a graph, the data accompany a bell shape, with maximum values clustering around a central region and tapering off as they go far away from the center.

Normal distributions have key attribute that are easy to spot in graphs:

1. The median, mean, and mode are exactly the same.

2. The distribution is symmetric about the mean half the data fall below the mean and half greater the mean.

3. The distribution can be narrated by two values: the standard deviation and the mean.

The mean determines where the top of the curve is centered.

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According to the table the occupation listed that is projected to have the greatest total number of jobs in 2016 is option C: Home health aids with 1171 thousand jobs.

What is a table?

Mathematical tables are collections of numbers that display the outcomes of calculations made using various inputs. In order to simplify and significantly speed up computation, trigonometric tables were employed in ancient Greece and India for applications to astronomy and celestial navigation. These tables were often utilised until electronic calculators were accessible and affordable.

The table for Fastest growing occupations, 2006-16 (numbers in thousands) is given.

In the third column it can be seen that the employment number for 2016 is given.

Find the occupation listed which is projected to have the greatest total number of jobs in 2016 in column 3.

The highest number of jobs is 1171 thousand in 2016.

Therefore, according to the table the occupation is Home health aids.

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Answer: the maximum number of 50-kilogram crates that can be loaded into the shipping container is 360 crates.

Step-by-step explanation:

Let x be the number of 50-kilogram crates that can be loaded into the shipping container.

We can write an inequality to represent the maximum weight that can be loaded into the container:

x * 50 + 9500 <= 27500

To solve for x, we can first subtract 9500 from both sides:

x * 50 <= 18000

Then, we can divide both sides by 50 to find the number of crates that can be loaded:

x <= 360

So, the maximum number of 50-kilogram crates that can be loaded into the shipping container is 360 crates.

Any Parallelogram can have two pairs of parallel lines.

What are parallel lines?

Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines . Both horizontal and vertical shapes are possible.

Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.

Step by step Explaination:

A quadrilateral with one small square in each of the four corners. There is one arrow on each of the two opposite sides, and two arrows on the other two opposite sides.

Two pairs of parallel sides are one of the definitions of a parallelogram. Any parallelogram MUST therefore have two sets of parallel sides. This covers all rectangles, squares, and rhombuses.

Due to the fact that they are not considered to be parallelograms, trapezoids, kites, and triangles all lack parallel sides.

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Any Parallelogram can have two pairs of parallel lines.

What are parallel lines?

Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines . Both horizontal and vertical shapes are possible.

Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.

Step by step Explaination:

A quadrilateral with one small square in each of the four corners. There is one arrow on each of the two opposite sides, and two arrows on the other two opposite sides.

Two pairs of parallel sides are one of the definitions of a parallelogram. Any parallelogram MUST therefore have two sets of parallel sides. This covers all rectangles, squares, and rhombuses.

Due to the fact that they are not considered to be parallelograms, trapezoids, kites, and triangles all lack parallel sides.

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The shape of the object is revealed in its pre-image, while its final form and position are revealed in the image following transformation.

Changes to the graph of a parent function are referred to as transformations. Transformations can be divided into three categories: translations, reflections, and dilations.

Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image of the object is its initial shape, while the Image, after transformation, is the final shape and location of the thing.

Imaging or duplicating an object is a part of transformation geometry. Transform geometry, which incorporates translation, reflection, dilation, and rotation, is covered in the ninth-grade curriculum. You will apply these concepts or notes up till grade 12.

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They have a total of 5¹¹ grains of salt in the large store.

Before solving this Question we must know an important result,

a^(m) × a^(n) = a^(m + n)

We know that,

1 container contains 5⁷ grains of salt

also, there are 5⁴ containers in the store

Thus,

Total grains of salt in all the container = 5⁷ × 5⁴

Hence, from the above result,

5⁷ × 5⁴ = 5^(7 + 4)

= 5¹¹ grains of salt

Thus,

They have a total of 5¹¹ grains of salt in the large store.

Now, just for your information, (this is not a part of the Answer and is not required in Answer)

This is just for you to know the magnitude of salt grains,

5¹¹ = 48,828,125 grain of salt were there in the store

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Answer: The box of 8 cones costs less per cone. The cost per cone is $0.67.

Step-by-step explanation:

To find the cost per cone, we need to divide the total cost by the number of cones.

8 cones box: $5.34 / 8 = $0.67 per cone

10 cones box: $6.80 / 10 = $0.68 per cone

Therefore, the box of 8 cones costs less per cone. The cost per cone is $0.67.

The system of inequality is 0 ≤ y ≤ 20.

Inequality in math is when two expressions, equations, or values are not equal to each other. Inequalities are represented by symbols such as "<" (less than), ">" (greater than), and "≠" (not equal to). Inequalities can be used to represent real-world situations where values or expressions can be greater than, less than, or not equal to each other. For example, the inequality “x > 5” means that x is greater than 5.

The system of inequalities that Nicholas needs to solve is:

10x + 25y ≤ 500

0 ≤ x ≤ 20

0 ≤ y ≤ 20

The first equation states that the total pay from both of his jobs must be less than or equal to $500. The second and third equations state that the number of hours he works at each job must be between 0 and 20.

Solving this system of inequalities will tell Nicholas how many hours he needs to work at each job in order to meet his obligations of $500 per week.

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The derivative of sin0 is cos0. We take the derivative of the inner function, which is 0, and then multiply it by the derivative of the outer function, which is the sine function. The derivative of the sine function is the cosine function.

The derivative of sinθ is cosθ.

When θ is 0, the derivative of sin0 is cos0.

The derivative of the sine function is the cosine function. This can be expressed mathematically as the derivative of sinθ equals cosθ. This means that the rate of change of the sine of an angle is equal to the cosine of that same angle. In other words, the derivative of sin0 is equal to cos0. To calculate the derivative of sin0, we can use the chain rule and the basic derivative rules. First, we identify the base function, which is sin0. Then, we differentiate the base function by applying the chain rule. We take the derivative of the inner function, which is 0, and then multiply it by the derivative of the outer function, which is the sine function. The derivative of the sine function is the cosine function. Therefore, the derivative of sin0 is cos0.

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The value of a₆ is -128, which matches the result we obtained using the recursive definition of the sequence.

What is meant by geometric?

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is. aₙ= a₁ r⁽ⁿ⁻¹⁾. The value r is called the common ratio. It is found by taking any term in the sequence and dividing it by its preceding term.

The nth term of a geometric sequence is given as:

aₙ= a₁ r⁽ⁿ⁻¹⁾.

In which a1 is the first term.

For this problem, we have :

The first term is  a1 = 4 and aₙ = -2aₙ₋₁.

Therefore, the common ratio is q = -2.

To solve the sequence using the geometric sequence formula, we need to first recognize that the sequence is a geometric sequence with a common ratio of -2.

a₁ = 4

a₂ = -2a₁ = -8 = 4 * (-2)

a₃ = -2a₂ = 16 = 4 * (-2)²

a₄ = -2a₃ = -32 = 4 * (-2)³

a₅ = -2a₄ = 64 = 4 * (-2)⁴

a₆ = -2a₅ = -128 = 4 * (-2)⁵

The formula for a geometric sequence is aₙ= a₁ r⁽ⁿ⁻¹⁾., where a is the first term, r is the common ratio, and n is the index of the term.

In this case, a=4 and r = -2, so the formula for the nth term is aₙ=4*(-2)⁽ⁿ⁻¹⁾.

To find a6, we substitute n = 6 into the formula:

a₆ = 4 * (-2)⁽⁶⁻¹⁾

= 4 * (-2)⁵

= -128

Therefore, the value of a₆ is -128, which matches the result we obtained using the recursive definition of the sequence.

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Answer: Number 2

Step-by-step explanation:

Substitute (-2, 1) into (x, y) into each equation and see if it works.

Answer:

2/3= 0.66

Step-by-step explanation:

GIVE BRAINLIEST

u jus divide 2 by 3

have a lovely night!

Answer:Answer for the first one is just 7/9, 28/36Second one is 9/14, 3/4For the third one you multiply 12.50 by 5 which gives you 62.5

Step-by-step explanation:

Answer:We can use the formula:

Distance = Velocity x Time

To find out how far Joe has ridden on the bicycle.

First, we need to convert 15 minutes into seconds. 1 minute is equal to 60 seconds. So 15 minutes is equal to 15*60 = 900 seconds.

So the distance Joe has ridden is:

Distance = Velocity x Time

Distance = 9.0 m/s x 900 sec

Distance = 8100 meters.

Joe has ridden 8100 meters in a straight line for 15 minutes with an average velocity of 9.0 m/s south.

Step-by-step explanation:

Answer:

The answer is 45

Step-by-step explanation:

Because 63 divided by 7 is 9 so that means you do 5 x 9 which is 45

The integers 6,21 from the set will make the inequality 3(j-5)>3(7-2j) true.

Inequality is the unequal distribution of resources, opportunities, or rewards among individuals or groups in society. It can occur in many forms, such as unequal access to healthcare, education, employment, or other resources, or unequal treatment based on race, gender, ethnicity, and other factors.

The given inequality is 3(j-5)>3(7-2j). The given set is S:{−4, 4, 6, 21}.

First, we will simplify the given inequality.

3(j-5)>3(7-2j)

⇒j-5>7-2j

⇒3j>12

⇒j>4

It means that numbers greater than 4 will satisfy the given inequality.

Numbers greater than 4 in the given set are 6,21

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Answer:

Step-by-step explanation:

To find x, you first need to find the length of the base. The total length of the base is 8, so the length of the base for one triangle is 4 meaning 8/2

Pythagoras theorem = [tex]a^2 + b^2 = c^2[/tex]

In this case, a will be 4 and c will be 5. Remember that c will always be the longest side of a right-angle triangle.  

[tex]5^2 + x^2 = 4^2 \\25 +x^2 = 16 \\x^2 = 25 -16 \\x^2 = 9 \\x \sqrt{9}\\ x = 3[/tex]

True: On the graph above, f(1) = 4.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line and passes through the points (-1, -2) and (1, 4) by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-2) = (4 - (-2))/(1 - (-1))(x - (-1))

y + 2 = 6/2(x + 1)

y = 3(x + 1) - 2

y = 3x + 3 - 2

y = 3x + 1

When x = 1, the value of y is given by;

y = 3x + 1

y = f(1) = 3(1) + 1

y = f(1) = 4.

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The equation -6y + 13 + 9y + 8y - 3 has one solution when all the terms are combined.

This equation has one solution when all the terms are combined. To solve this equation, the first step is to combine like terms, which are terms that have the same variable and exponent. In this equation, there are two like terms, -6y and 9y, which can be combined to give us 3y. The next like terms are 13 and -3, which can be combined to give us 10. The final step is to group the coefficients and variable terms together and move the variable terms to one side of the equation and the coefficients to the other side. This gives us the equation 3y = 10, which can be solved by dividing both sides of the equation by 3. This gives us the solution y = 10/3.

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The inverse of the logarithmic function f(x) = log2x is the exponential function f(x) = 2^x

The inverse of a logarithmic function is an exponential function. To find the inverse of the logarithmic function f(x) = log2x, we need to switch the x and y values of the function and solve for the y. This will give us the inverse function in the form y = 2^x.

The inverse of the logarithmic function f(x) = log2x is the exponential function f(x) = 2^x.

The inverse of a logarithmic function is an exponential function, which is a function of the form y = b^x, where b is a constant. To find the inverse of the logarithmic function f(x) = log2x, we need to switch the x and y values of the function and solve for the y. This will give us the inverse function in the form y = 2^x, where 2 is the constant. This inverse exponential function expresses the relationship between the x and y values of the logarithmic function in reverse, with the x values now being the exponents and the y values being the result of the exponential function.

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Answer:

Catherine buys 3 bicycle reflectors at $10.20 each, for a total cost of 3 * $10.20 = $30.60

She buys a pair of bike gloves for $12.54

She buys a bicycle for $362.68

The total cost of these items is $362.68 + $30.60 + $12.54 = $405.82

Catherine has $460 - $405.82 = $54.18 left to spend on new biking clothes.

She can buy 2 biking clothes for $27.09 each, with her remaining money.

Step-by-step explanation:

Answer:

117

Step-by-step explanation:

7/30 like mystery  

into a decimal this is 0.2333

times this by 500 and you get 116.65

which rounds to 117

The length of the hypotenuse if the legs are 6 and 8 is 10.

What is right triangle ?

A right triangle consists of two legs and a hypotenuse. The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle. There are a couple of special types of right triangles, like the 45°-45° right triangles and the 30°-60° right triangle.

Have given ,

Let legs are a , b and hypotenuse is c.

then a = 6 , b = 8 and c = ?

We know that for a right triangle ,

[tex]a^{2} + b^{2} = c^{2}[/tex]

∵ [tex]6^{2} + 8^{2} = c^{2}[/tex]

[tex]c^{2}[/tex] = 36 + 64

[tex]c^{2}[/tex] = 100

c = 10

Hence , The length of the hypotenuse if the legs are 6 and 8 is 10.

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