what is this helppp 1/2 + 1/5

Step-by-step explanation:

80=2640

107=x

80x=2640x107

80x=282480

x=282480/80

x=$3531

Geraldine receives $14,730.

Geraldine's Stafford student loan is for $15,000, but she must pay a loan fee of 1.8%.

To determine the amount of money she will actually receive, we need to subtract the loan fee from the total loan amount.

First, let's calculate the loan fee.

To find 1.8% of $15,000, we can multiply the loan amount by 0.018 (which is the decimal representation of 1.8%).

Loan fee = $15,000 \(\times\) 0.018 = $270

Now, we subtract the loan fee from the total loan amount:

Amount received = Total loan amount - Loan fee

Amount received = $15,000 - $270 = $14,730

Therefore, Geraldine will receive $14,730 from the Stafford student loan. It's important to note that the loan fee is deducted upfront, so the actual amount disbursed to the student is reduced by that fee.

This ensures that the lender receives a portion of the loan upfront to cover administrative costs and mitigate potential risk.

The remaining amount is what the student receives to use for educational expenses or other approved purposes.

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Answer:

x^2 +3x-5

Step-by-step explanation:

f(x) = 3x + 1 and g(x) = x^2 - 6

(f+g)(x) = 3x+1+x^2 -6

Combine like terms

           =x^2 +3x-5

Answer:

150°

Step-by-step explanation:

every line is equal to 180°. To find an angle, like this one, you have to subtract 30° from 180°. Therefor the answer is 150°.

If you need a further explanation just let me know

Answer:

x = 4

Step-by-step explanation:

-6x = -24

/-6      /-6

----------------

x = 4

We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

A. 20%

Step-by-step explanation:

Hope it helps!

By using the sines law we conclude that the best approximation of the value of x is 2.9 units. Answer: 2.9 units.

What is sines law?

The Law of Sines is a trigonometric law that relates the sides of a triangle to the sine of its angles. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal to the same ratio for each of the other two sides and their opposite angles. In other words, it can be expressed as:

a/sin(A) = b/sin(B) = c/sin(C)

We can use the Law of Sines to find the length of YZ:

sin(75) / 2 = sin(50) / x

Multiplying both sides by x:

x * sin(75) / 2 = sin(50)

Dividing both sides by sin(75) / 2:

x = 2 * sin(50) / sin(75)

Using a calculator to evaluate sin(50) and sin(75), we get:

x ≈ 2.9 units

Therefore, the best approximation of the value of x is 2.9 units. Answer: 2.9 units.

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The point estimate of the population is 0.415 round to the nearest thousandth as needed the margin error is 0.189.

In statistics, for point estimation, an unknown population parameter (e.g. population mean). More formally, it is applying a point estimator to data to obtain a point estimate.

Point estimation can be contrasted with interval estimation. Such interval estimates are usually confidence intervals for frequentist inference and confidence intervals for Bayesian inference. More generally, point estimators can be contrasted with set estimators. An example is the confidence rate or confidence rate. Point estimators can also be contrasted with distribution estimators. Examples include confidence distributions, randomized estimators, and Bayesian posterior distributions.

Based on the question,

The confidence  interval of Lower bound is 0.226.

The confidence interval of Upper bound is 0.604.

X - E = 0.226.                     --------------------------- (1)

X + E = 0.604                     ---------------------------(2)

Adding equation (1) and (2),

    2X = 0.83

⇒  X = 0.83/2

⇒ X = 0.415

Putting X = 0.415 in equation (1),

0.415 + E = 0.604

⇒ E = 0.604 - 0.415

⇒ E = 0.189

Thus, the point estimate of the population is 0.415 round to the nearest thousandth as needed the margin error is 0.189.

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a) 81.86 percent of the pennies will weigh between 2.7 and 3.3g. b) 100 percent of the pennies will weigh between 2.5 and 3.7g. c) 2.28 percent of the pennies will weigh less than 2.7g. d) 15.87 percent of the pennies will weigh more than 3.3g.

To solve these questions, we will use the properties of the normal distribution and z-scores.

a) To find the percentage of pennies that weigh between 2.7 and 3.3g, we need to calculate the area under the normal curve between these two values.

First, we need to standardize the values using z-scores:

z1 = (2.7 - 3.1) / 0.2 = -2

z2 = (3.3 - 3.1) / 0.2 = 1

Next, we can use a standard normal distribution table or a calculator to find the area between these two z-scores. The area between -2 and 1 is approximately 0.8186 or 81.86%.

Therefore, approximately 81.86% of the pennies will weigh between 2.7 and 3.3g.

b) Similarly, to find the percentage of pennies that weigh between 2.5 and 3.7g, we need to standardize the values and calculate the area between the corresponding z-scores.

z1 = (2.5 - 3.1) / 0.2 = -3

z2 = (3.7 - 3.1) / 0.2 = 3

The area between -3 and 3 encompasses the entire distribution and is equal to 1 or 100%.

Therefore, 100% of the pennies will weigh between 2.5 and 3.7g.

c) To find the percentage of pennies that weigh less than 2.7g, we need to calculate the area to the left of the corresponding z-score.

z = (2.7 - 3.1) / 0.2 = -2

Using a standard normal distribution table or a calculator, we find that the area to the left of -2 is approximately 0.0228 or 2.28%.

Therefore, approximately 2.28% of the pennies will weigh less than 2.7g.

d) To find the percentage of pennies that weigh more than 3.3g, we need to calculate the area to the right of the corresponding z-score.

z = (3.3 - 3.1) / 0.2 = 1

Using a standard normal distribution table or a calculator, we find that the area to the right of 1 is approximately 0.1587 or 15.87%.

Therefore, approximately 15.87% of the pennies will weigh more than 3.3g.

Correct Question :

A group of students weighs 500 US pennies. They find that the pennies have normally distributed weights with a mean of 3.1g and a standard deviation of 0.2g

a) What percentage of pennies will weigh between 2.7 and 3.3g?

b) What percentage of pennies will weigh between 2.5 and 3.7g

c.) What percentage of pennies will weigh less than 2.7g?

d.) What percentage of pennies will weigh more than 3.3g?

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Answer: 2.5, 5.4

Step-by-step explanation:

\(-16t^2 +126t=213\\ \\ 16t^2 -126t+213=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4\)

Answer:

We know that each dog food unit costs $3, and each dog treat costs $2.

Let's define the variables:

x = units of dog food that Bill buys

y = units of dog treat that Bill buys.

The total cost of the purchase will be:

cost = x*$3 + y*$2

And we know that Bill wants to spend $30, then the equation is:

$30 = x*$3 + y*$2

Now we could isolate one of the variables in one side of the equation, for example, let's isolate the "y".

$30 - x*$3 = y*$2

$30/$2 - x*($3/$2) = y

15 - (3/2)*x = y

Now we have the linear equation:

y = -(3/2)*x + 15

To determine an ordered pair, we just can replace the x by a number, like x = 2, that would mean that Bill bought 2 units of dog food.

in this case:

y = -(3/2)*2 + 15 = -3 + 15 = 12

y = 12

This ordered pair is (2, 12)

Answer:

-18%

Step-by-step explanation:

Answer:

c. 12 pens and 15 pencils

Step-by-step explanation:

We can find the number of each box Denis bought using a system of equations.

Let x represent the number of pen boxes and y the number of pencil boxes Denis bought

First equation:

We know that the sum of the quantities of the pen and pencil boxes equals the total number of boxes altogether as

# of pen boxes + # of pencil boxes = total number of boxes

x + y = 27

Second equation:

We know that the sum of the costs of the pen and pencil boxes equals the total cost as

(price of pen boxes * # of pen boxes) + (price of pencil boxes * # of pencil boxes) = total cost

15x + 18y = 450

Method to solve:  Substitution:

We can isolate x in the first equation and plug it in for x in the second equation.  This will allow us to first find y:

(x + y = 27) - y

x = -y + 27

----------------------------------------------------------------------------------------------------------

15(-y + 27) + 18y = 450

-15y +405 + 18y = 450

3y + 405 = 450

3y = 45

y = 15

Find x:

Now we can find x by plugging in 15 for y in x + y = 27:

x + 15 = 27

x = 12

Thus, Denis bought 15 pens and 12 pencils (answer choice c.)

Check work:

We can check our work by plugging in 15 for y and 12 for x in both equations and seeing if we get 27 for the first equation and 450 for the second equation:

Checking solutions in x + y = 27:

12 + 15 = 27

27 = 27

Checking solutions in 15(12) + 18(15) = 450

15(12) + 18(15) = 450

180 + 270 + 450

450 = 450

Thus, our answers are correct.

The value of cosβ, where β is the angle formed by the terminal ray in standard position passing through the point (-7, 2√3), can be determined using trigonometric ratios.

In standard position, the terminal ray of an angle is the ray that starts from the origin (0, 0) and extends to a point on the coordinate plane. We are given that the terminal ray passes through the point (-7, 2√3). To find the value of cosβ, we need to determine the x-coordinate of the point where the terminal ray intersects the unit circle.

Since the x-coordinate of the point is -7 and the y-coordinate is 2√3, we can calculate the distance from the origin to the point using the Pythagorean theorem: r = \(\sqrt{((-7)^2 + (2\sqrt{3})^2)} = \sqrt{(49 + 12)} = \sqrt{61\).

The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. In this case, the adjacent side is the x-coordinate (-7) and the hypotenuse is the radius of the unit circle (√61). Therefore, cosβ = adjacent/hypotenuse = -7/√61.

To rationalize the denominator, we multiply the numerator and denominator by √61: cosβ =\((-7/\sqrt{61}). (\sqrt{61}/\sqrt{61}) = -7\sqrt61/61\).

Hence, the value of cosβ for the given angle is -7√61/61.

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The true statements are

i. probability is usually between 0 and 1, inclusive.

ii. an event that is likely has a probability that is close to 1.

(option i and ii).

Probability is an important concept in mathematics and statistics that allows us to quantify the likelihood or chance of an event occurring. It is often represented as a number between 0 and 1, inclusive. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain to occur.

Now, let's examine each of the statements to determine which ones are true.

The first statement, "probability is usually between 0 and 1, inclusive," is true. As mentioned earlier, probability is always represented as a number between 0 and 1, inclusive.

The second statement, "an event that is likely has a probability that is close to 1," is also true. If an event is likely to occur, it means that there is a high probability of it happening. Therefore, the probability assigned to that event would be close to 1.

Hence the correct option is (a) and (b)..

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The term for the value that occurs most often in a series of numbers is called the mode.

The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.

To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.

The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.

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The distance between A(4,6) and B (9,7) is√26 or 5.1.

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

\(d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }\)

Given the points A(4,6) and B (9,7)

Now,

x₁ = 4 ,x₂ = 9

y₁ = 6 , y₂ = 7

So,

Distance between them,

\(d = \sqrt {\left( {4 - 9 } \right)^2 + \left( {6 - 7 } \right)^2 }\)

d = √26

d = 5.099 and by rounding to the nearest tenth.

5.099 → 5.1

Hence "The distance between A(4,6) and B (9,7) is√26 or 5.1".

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x = 1 and y = -2

as an ordered pair: (1,-2)

Answer:

|a+5|=a+5

Step-by-step explanation:

if a>-5 or a= -5 |a+5|=a+5

if a< -5 |a+5|= -a-5

Answer:

\( \frac{1}{ {7}^{14} } \)

Step-by-step explanation:

\((7 {}^{2} ) {}^{ - 7} \)

Rewrite using power rule

\(( {x}^{m} ) {}^{n} = x {}^{m + n} \)

\(( {7}^{2} ){}^{ - 7} = {7}^{ - 14} \)

Now rewrite using the negative power rule,

\(x {}^{ - b} = \frac{1}{x {}^{b} } \)

\( {7}^{ - 14} = \frac{1}{ {7}^{14} } \)

Answer:

\(-3\frac{1}{2}\) and in decimal it is -3.5

Step-by-step explanation:

The simplified expression is 3.5.

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,

1.75x - 2

This can be written as,

= 175/100 x 2

= 175/50

= 3.5

Thus,

3.5 is the value.

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4,600 / 80 = 57.5 (How much for one student)

What is 13% of 57.5? 7.475. (How much tax is)

So, 57.5 + 7.475 = 64.975. (How much one student is with tax)

T - Leads to lower page occupancy. T - Helps to keep the height low. T - Can still lead to a page split when no suitable page exists for the redistribution.

F - Is favored over combined redistribution and merging since it leaves nodes with free space for future inserts.

Note: The last statement is false.

Combined redistribution and merging is favored over redistribution alone because it can better utilize the available space and reduce the overall height of the B-tree.

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The general solution of the given homogeneous differential equation is:y = ±x√(Cx² + 2)

The given differential equation is: 2xyy' + (x² - y²) = 0

We have to find the general solution of the given homogeneous differential equation. To solve the above differential equation, we will use the substitution method.

Put y = vx and y' = v + xv'

Differentiating both sides w.r.t x: y' = v + xv' ⇒ v' = (y' - v)/x

Differentiating again w.r.t x: y'' = v' + xv'' + v' ⇒ y'' = (y'' - 2y'v + v² + xv')/x

Substituting these values in the given differential equation:

2x(v)(v + xv') + (x² - v²x²) = 0

2v + 2x²v' + x - v² = 0

2x²v' + 2v/x - v³/x = -1/x

We can write the above differential equation as:

2x²dv/dx + 2v/x = v³/x - 1/x

Separating the variables and integrating both sides:

∫dx/x = ∫[v/(v² - 2)]dv/x

⇒ ln |x| + ln |v² - 2| + C

⇒ ln |x(v² - 2)| = ln |Cx|

⇒ v² - 2 = Cx² (where C is a constant)

⇒ v = ±√(Cx² + 2)

Putting the value of v in y = vx, we get:

y = x√(Cx² + 2) and y = -x√(Cx² + 2)

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The slope of the line passing through the points (-5, -4) and (-13, 2) is -3/4.

Slope is simply expressed as a change in y over the change in x.

It is expressed as

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Given the points:
(-5, -4) and (-13,2)​

Point (-5, -4):

x₁ = -5

y₁ = -4

Point (-13,2)​:

x₂ = -13

y₂ = 2

Plug the given x and y values into the slope formula and simplify.

\(m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{2 - (-4)}{-13 - (-5)}\\\\m = \frac{2 + 4}{-13 + 5}\\\\m = \frac{6}{-8}\\\\m = -\frac{3}{4}\)

Therefore, the slope of the line is -3/4.

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The solution for d in the equation v = √64d is d = v²/64

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

v = √64d

Take the square root of both sides

So, we have the following representation

v² = 64d

Divide both sides of the equation by 64

So, we have the following representation

v²/64 = d

Rewrite as

d = v²/64

Hence, the value of d is d = v²/64

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