simplify the expression p×-1p×+1​

To earn an average score of 90, the score on the fourth test needs to be 98.

The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.

Given the score of the first three tests as:

91, 84, 87.

The average is given by the following formula:

Average = Sum of scores ÷ total number of tests

Let us suppose the score of fourth test as x.

Given that A = 90:

90 = (91 + 84 + 87 + x) ÷ 4

x = 98

Hence, the score on the fourth test must be equal to 98, to get an average score of 90.

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Answer

Yes, zero is contained in the interval

Answer:

The maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Step-by-step explanation:

We are given that weight P is inversely proportional to the distance D between the supports of the beam, and for this certain type of wooden beam, we have:

P = 7200/D

To find the distance between supports needed to carry 1600 lb, we can substitute P = 1600 in the above equation and solve for D:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

So the distance between supports needed to carry 1600 lb is 4.5 feet.

To find the maximum distance between supports for the beam to support a weight of 1600 lb, we can use the same equation and solve for P = 1600:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

Therefore, the maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Answer:

Step-by-step explanation:

Given the roots of quadratic equation to be 5 and 2/3, the two factors are x-5 and x-2/3.

The variable in question are both subtracted from the root given to get the actor of the quadratic equation or polynomial. We can get the resulting quadratic function by multiplying both factors together as shown;

(x-5)(x-2/3)

= x²- 2x/3 -5x +10/3

= x²-(2x-15x)/3+10/3

= x²-17x/3 +10/3

Multiply through by 3

= 3x²-17x +10 = 0

The resulting quadratic equation for both factors will be  3x²-17x +10 = 0 and the other factor is x-2/3

Answer:

633.3

Step-by-step explanation:

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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The equations of the circles that have centers on the x-axis are;

A. (x - 2)² + (y - 0)² = 22

B. (x - 0)² + (y - 0)² = 25

The equation of a circle is; (x - h)² + (y - k)² = r², where;

(h, k) = The coordinates of the center of the circle

r = The radial length of the circle

The center of the circle is on the x-axis when the y-coordinate of the center of the circle is; k = 0, therefore, the circle that have their centers on the x-axis are the circles with the term (y - 0)²

The option of the circle that has the term (y - 0)² are the first and second option, where the v is actually a y; option A and .

The correct option is therefore;

A. (x - 4)² + (y - 0)² = 22

B. (x - 0)² + (y - 0)² = 25

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Answer:

2% 2% of the nation's children (about 1.7 million) have a parent who is in jail or prison.

The value of the coin in 2019 would be approximately $132.

To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.

Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:

Value in 2019 = Initial value * (1 + Rate)^n

where Rate is the annual increase rate and n is the number of years between 2010 and 2019.

Plugging in the values:

Value in 2019 = $40 * (1 + 0.169)^9

Value in 2019 ≈ $40 * 2.996

Value in 2019 ≈ $119.84

Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.

However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.

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Answer:

y = 50x + 100

Step-by-step explanation:

Answer:

It is linear. It is linear because it is a strait line which means that it is a function. A not linear line would look like a noodle.

Few families can survive on a single salary is true statement

Many families rely on dual incomes to make ends meet, especially in areas with high living costs.

However, there are still many families that rely on a single salary to support themselves.

While it may be challenging to make ends meet on a single salary, it is still possible for families to survive and even thrive in these circumstances.

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Answer:5, 6, 7, 8, or 9.

Step-by-step explanation:

The net force on the rocket is directed upward with a magnitude of

35 N - 25 N = 10 N

By Newton's second law, the acceleration a is such that net force is equal to the mass of the rocket times its acceleration:

10 N = (2.5 kg) a

a = (10 N) / (2.5 kg)

a = 4 m/s²

Answer:

8

Step-by-step explanation:

Substitute the values in the expression, we have:

\(\displaystyle{|-1-3|+4}\)

Evaluate:

\(\displaystyle{|-4|+4}\)

Any real numbers in the absolute sign will always be evaluated as positive values. Thus:

\(\displaystyle{|-4|+4 = 4+4}\\\\\displaystyle{=8}\)

Hence, the answer is 8. A quick note that z-value is not used due to lack of z-term in the expression.

Let's start by defining some variables:

Let's call Jamal's age "J".

Let's call Alex's age "A".

From the problem statement, we know that:

J = A - 5 (Jamal is 5 years younger than Alex)

J * A = 300 (the product of their ages is 300)

We can use the first equation to substitute J in the second equation:

(A - 5) * A = 300

Expanding the left-hand side:

A^2 - 5A = 300

Moving all terms to the left-hand side:

A^2 - 5A - 300 = 0

We can solve for A using the quadratic formula:

A = (-(-5) ± sqrt((-5)^2 - 41(-300))) / (2*1)

A = (5 ± sqrt(25 + 1200)) / 2

A = (5 ± sqrt(1225)) / 2

Since A is a positive integer, we take the positive solution:

A = (5 + 35) / 2 = 20

Now we can use the first equation to find J:

J = A - 5 = 20 - 5 = 15

Therefore, Jamal is 15 years old.

It is important to note that sharing or requesting specific keys or answers to educational materials, including guided notes, would be considered unethical and potentially a violation of academic integrity.

Guided notes are intended to assist students in actively engaging with course material and enhancing their learning experience. It is recommended that you approach your teacher or instructor for any clarification or additional resources you may need to fully understand the content.

They are in the best position to provide you with the necessary guidance and support.

Instead of seeking shortcuts or unauthorized access to answers, it is more beneficial to invest time and effort in studying, asking questions, and actively participating in your educational journey.

This approach will not only help you grasp the subject matter more effectively but also promote personal growth and knowledge development.

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The dimensions listed above are thus neither exact nor precise.

In the given question the chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively and we have to classify the following set of measurements as accurate, precise, both, or neither.

It is the "value" that a buyer is prepared to pay for an object, particularly a used or second-hand car; typically, the "real worth" of any used car is a predetermined price tag after determining its value based on its condition and usage.

The chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively. This demonstrates that the weight of chocolate chips is not comparable to their actual worth.

The dimensions listed above are thus neither exact nor precise.

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Answer:

the - are the x or y

Step-by-step explanation:

Answer: the Second one

Step-by-step explanation:

Hope this helps you

Answer:

y = -8/3x + 8

Step-by-step explanation:

Step 1:  Identify which values we have and need to find in the slope-intercept form:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

Since we're told that the y-intercept is 8, this is our b value in the slope-intercept form.

Step 2:  Find m, the slope of the line:

Thus, we can find m, the slope of the line by plugging in (3, 0) for (x, y) and 8 for b:

0 = m(3) + 8

0 = 3m + 8

-8 = 3m

-8/3 = m

Thus, the slope is -8/3.

Therefore, the the equation of the line in slope-intercept form whose x-intercept is 3 and whose y-intercept is 8 is y = -8/3x + 8.

Optional Step 3:  Check the validity of the answer:

Thus, we can check that we've found the correct equation in slope-intercept form by plugging in (3, 0) and (0, 8) for (x, y), -8/3 for m, and 8 for b and seeing if we get the same answer on both sides of the equation when simplifying:

Plugging in (3, 0) for (x, y) along with -8/3 for m and 8 for b:

0 = -8/3(3) + 8

0 = -24/3 + 8

0 = -8 = 8

0 = 0

Plugging in (0, 8) for (x, y) along with -8/3 for m and 8 for b;

8 = -8/3(0) + 8

8 = 0 + 8

8 = 8

Thus, the equation we've found is correct as it contains the points (3, 0) and (0, 8), which are the x and y intercepts.

Answer:

Data Representation refers to the form in which data is stored, processed, and transmitted. ... information, such as text, numbers, photo, or music, into digital data that can be manipulated by electronic devices.

Data representation refers to the form in which data is stored, processed, and transmitted.

ray4918 here to help

Answer/Step-by-step explanation:

5. Given that ∆FGH ≅ ∆TSU, all three angles and sides of ∆FGJ are congruent to all corresponding angles and sides of ∆TSU.

Thus:

Since, <HFG in ∆FGH corresponds to <UTS in ∆TSU, therefore:

<HFG ≅ <UTS

7. Given that ∆FGH ≅ ∆FGL, the following are the corresponding sides and angles:

FG ≅ FG

GH ≅ GL

FH ≅ FL

<FGH ≅ <FGL

<FHG ≅ FLG

<GFH ≅ GFL

Answer:

Quadrilateral: 20.5 units

Triangle: 8.6 units

Step-by-step explanation:

Quadrilateral:
We can use the following formula to find the perimeter of a quadrilateral.

Perimeter = AB + BC + CD + DA

where AB, BC, CD, and DA are the lengths of the four sides of the quadrilateral.

In your case, the coordinates of the vertices of the quadrilateral are A(-3,-1), B(-3,3), C(2,3), and D(4,-1).

Using the distance formula, we can find the lengths of the four sides of the quadrilateral as follows:

\(AB = \sqrt{(-3 - (-3))^2 + ((-1) - 3)^2} = \sqrt{16} = 4\)

\(BC = \sqrt{(-3 - 2)^2 + ((3) - 3)^2} = \sqrt{25}= 5\)

\(CD = \sqrt{(2 - 4)^2 + ((3) - (-1))^2} = \sqrt{4+16} = 2\sqrt{5}\)

\(DA = \sqrt{(4 - (-3))^2 + ((-1) - 1)^2} = \sqrt{49} =7\)

Therefore, the perimeter of the quadrilateral is:

Perimeter = AB + BC + CD + DA

= \(4+5+2\sqrt5+7=20.5\) units

Triangle

The perimeter of a triangle is the total length of all three sides of the triangle. To find the perimeter of a triangle, we can use the following formula:

Perimeter = AB + BC + CA

where AB, BC, and CA are the lengths of the three sides of the triangle.

In your case, the coordinates of the vertices of the triangle are

E(-4,1), F(-2,3), and G(-2,4). Using the distance formula, we can find the lengths of the three sides of the triangle as follows:

\(EF = \sqrt{(-4 - (-2))^2 + ((1) - (3))^2} = 2\sqrt{2}\)

\(FG = \sqrt{(-2 - (-2))^2 + ((3) - (4))^2} = 1\)

\(EG = \sqrt{(-4 - (-2))^2 + ((1) - (4))^2} = \sqrt{4 + 9} = \sqrt{13}\)

Therefore, the perimeter of the triangle is:

Perimeter = EF + FG + EG

= 4 + 1 + \(\sqrt{13}\)

=8.6 units

Therefore, the perimeter of the quadrilateral is 20.5 units and the perimeter of the triangle is 8.6 units

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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A good practice to remember when adding transitions to a presentation is to ensure that they are purposeful, consistent, and enhance the overall flow of the presentation.

Purposeful: Use transitions to guide the audience through your key points and ideas, making sure they complement the content and contribute to the overall message.
Consistent: Maintain a consistent style of transitions throughout your presentation to maintain a cohesive look and feel. Avoid using too many different types of transitions, as this may be distracting.
Enhance flow: Transitions should help create a smooth flow between slides and ideas, making it easy for the audience to follow your presentation. Avoid using abrupt or overly flashy transitions that may interrupt the natural progression of your content.

finally, Test your presentation with the transitions to make sure they enhance the overall flow and comprehension of your message.

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The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3

To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:

Since for all x > 0, we have:

Thus, by the limit comparison test:

converges if and only if converges.

We can evaluate  using the power rule of integration:

where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:

∫(1/x^4) dx from 1 to infinity = lim as b → infinity

=>

=> 0 - (-1/3)

=> 1/3

Since the integral  dx converges by comparison to a convergent integral, and its value is 1/3.

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Note: The full question is

Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1

The area of the figure we need to use Rectangle, Triangle and Circle formulas:

Identify the shape: Depending on the figure you have, it could be a rectangle, triangle, circle, or a more complex shape. If it's a composite figure, break it down into simpler shapes.
Use the appropriate formula: Each shape has a specific formula to calculate the area.
- Rectangle: Area = length × width
- Triangle: Area = (base × height) / 2
- Circle: Area = π × (radius²)
Measure the necessary dimensions: Measure the required dimensions (length, width, base, height, or radius) using appropriate units (e.g., meters, centimeters, inches).
Plug the values into the formula: Insert the measured dimensions into the corresponding formula.
Perform calculations: Carry out the necessary mathematical operations to get the area.
Include units: Express the area with the appropriate square units (e.g., square meters, square centimeters, square inches).
(For composite figures) Add or subtract areas: If the figure is composed of multiple shapes, add or subtract their areas accordingly to get the total area of the figure.

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