9+4x6-65/13 order of operations

Answer:

P =33.6 m

A = 70.56 m^2

Step-by-step explanation:

The perimeter of a square is given by

P =4s = 4(8.4) =33.6 m

The area of a square is given by

A = s^2 = (8.4) ^2 =70.56 m^2

Answer:

Perimeter = 8.4×4 = 33.6 meters

Area = 8.4^2 = 70.56 square meters

Answer:

a. \(y=-0.004591(x-33)^2+5\)

b. domain: (0, 66) range (0, 5] and they represent how the vertical and horizontal distance will vary, so the domain (x-values) tells us the horizontal distance will vary from 0 to 66 during the flight path while the range (y-values) tell us the vertical distance or height will vary from 0 to 5 during the flight path.

c. the range will certainly change if the vertex is (30, 4) as the maximum is no longer 5, but rather 4, so the new range would be (0, 4]

Step-by-step explanation:

So I'm assuming the form provided was meant to be written as: \(y=a(x-h)^2+k\) also known as vertex form of a parabola. In this case the vertex is (33, 5) so we can plug these values into the equation: \(y=a(x-33)^2+5\)

Now the only thing left to do is solve for the "a" value. We can just use a point on the graph except the vertex (since it makes the x-33 equal to zero making any value of "a" working) and we're given the point (0, 0) as a point so we can use that:

\(0 = a(0-33)^2+5\\0 = 1,089a+5\\-5 = 1089a\\-0.004591 \approx a\)

Now plug this value into the vertex form to get:

\(y=-0.004591(x-33)^2+5\)

Now using the quadratic formula: \(y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) or a graphing calculator such as desmos, to determine the zeroes occur at x = 0 and 66. Since we want to only module their flight path the domain is restricted between these values, so the domain is: (0, 66) and the range is based on the y-values or in this case the height. The height will vary from zero to 5, or (0, 5]. They simply represent how the vertical and horizontal distance will vary, so the vertical distance will vary from 0 to 5 while the horizontal distance will vary from 0 to 66.

For part "c" I'm assuming it's asking if the domain/range change if the vertex is (30, 4) in which case the range will certainly change as the maximum is now 4 and not 5, so the new range would be (0, 4] where the vertical distance or height varies from 0 to 4

The circumference formula is

Where d = 4 and pi = 3.14.

Answer:

C) Quadrant 4

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answering the presented question, we may conclude that This greater expressions scale makes it easier to see the variations between the ratings of the three college students in a extra correct and informative way.

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

The difference in look between the two charts is due to the choice of the scales on the x and y-axes. In the left chart, the y-axis starts offevolved at 800 and has a range of only 200 points, whilst the x-axis starts offevolved at 1300 and has a vary of 200 points. This compressed scale makes the variations between the ratings of the three students appear larger than they absolutely are.

On the other hand, the proper chart has a y-axis that starts at zero and has a vary of 800 points, whilst the x-axis begins at 1200 and has a range of 800 points. This greater expanded scale makes it easier to see the variations between the ratings of the three college students in a extra correct and informative way.

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This question is about to determine the conditional statement,  proposition and either that is true or false.

The explanation of each part in this question is given below:

a) The given proposition can be written as the conjunction of two conditional statements as follows:

If a = 2 (mod 8), then \((a^2 + 4a) = 4 (mod 8)\).

If \((a^2 + 4a) = 4 (mod 8)\), then a = 2 (mod 8).

b) To prove the first conditional statement, assume a = 2 (mod 8). Then, there exists an integer k such that a = 8k + 2. Substituting this value of a into \((a^2 + 4a)\), we get:

\(a^2 + 4a = (8k + 2)^2 + 4(8k + 2) = 64k^2 + 36k + 8\)

Reducing this expression modulo 8, we get:

a^2 + 4a ≡ 64k^2 + 36k + 8 ≡ 0 + 4k + 0 ≡ 4 (mod 8)

Therefore, we have shown that if a = 2 (mod 8), then (a^2 + 4a) = 4 (mod 8).

To prove the second conditional statement, assume (a^2 + 4a) = 4 (mod 8). Then, there exists an integer k such that (a^2 + 4a) = 8k + 4. Substituting this value of (a^2 + 4a) into the equation a^2 + 4a - 8k = 0, we can use the quadratic formula to solve for a:

a = (-4 ± √(16 + 32k))/2 = -2 ± √(4 + 8k)

Since a is an integer, it follows that √(4 + 8k) must be an integer as well. This implies that 4 + 8k is a perfect square. The only perfect squares that are congruent to 4 (mod 8) are those of the form 8m + 4 for some integer m. Therefore, we have:

4 + 8k = 8m + 4

k = m

Substituting k = m back into the expression for a, we get:

a = -2 + √(4 + 8k) = -2 + √(8m + 4) = -2 + 2√(2m + 1)

Since a is an integer, it follows that √(2m + 1) must be an integer as well. This implies that 2m + 1 is a perfect square. The only perfect squares that are congruent to 1 (mod 8) are those of the form 8n + 1 for some integer n. Therefore, we have:

2m + 1 = 8n + 1

m = 4n

Substituting m = 4n back into the expression for a, we get:

a = -2 + 2√(2m + 1) = -2 + 2√(8n + 1) = 2(√(2n + 1) - 1)

Therefore, we have shown that if (a^2 + 4a) = 4 (mod 8), then a = 2 (mod 8).

Since both conditional statements have been proven, the given proposition is true.

(c) The given proposition is true, as shown in the proofs of the two conditional statements in part (b).

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Answer:

The appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 is the t-statistic.

The t-statistic for testing the slope coefficient is calculated as follows:

t = (b1 - 0) / SE(b1)

where b1 is the estimated slope coefficient, and SE(b1) is the standard error of the estimated slope coefficient.

From the computer output, we see that the estimated slope coefficient for exercise time is -2.20, and the standard error of the estimated slope coefficient is 0.07.

Therefore, the t-statistic is:

t = (-2.20 - 0) / 0.07 = -31.43

This t-statistic follows a t-distribution with n-2 degrees of freedom, where n is the sample size. The sample size is not given in the output, so we cannot determine the exact degrees of freedom.

The relationship between the related rates dp/dt and dV/dt is -1.3kV^-2.3

Given :

When a certain polyatomic gas undergoes adiabatic expansion, its pressure p and volume V satisfy the equation pV^1.3 = k, where k is a constant. Find the relationship between the related rates dp/dt and dV/dt.

p * V^1.3 = k

divide by v^1.3 on both sides

p *  V^1.3 /  V^1.3 = k /  V^1.3

p = k /  V^1.3

p = k *  V^-1.3

differentiate with respect to t on both sides

dp / dt = -1.3kV^-1.3 - 1 dv / dt

dp / dt / dv / dt = -1.3kV^-2.3

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side of rhombus: 2.44 inch

Use the sine rule:

\(\sf \dfrac{sin(A)}{a} = \dfrac{sin(B)}{b}\)

=============                       Let the side be "b"

\(\rightarrow \sf \dfrac{sin(110)}{4} = \dfrac{sin(35)}{b}\)

\(\rightarrow \sf b = \dfrac{sin(35)*4}{sin(110)}\)

\(\rightarrow \sf b = 2.441549178\)

\(\rightarrow \sf b =2.44 \ in\)

Answer:

3.5 in (nearest tenth)

Step-by-step explanation:

Properties of a rhombus:

Therefore, a rhombus is made up of 4 congruent right triangles.

** see attached diagram **

To find the side length of the rhombus, we need to calculate the hypotenuse of the right triangle.

As the shorter diagonal is 4 in, the base of the right triangle is 2 in

The angles that measure 110° are the angles by the shorter diagonal.  Therefore, the base angle of the right triangle is 55°

Using cos trig ratio:

\(\sf \cos(\theta)=\dfrac{A}{H}\)

where:

Given:

\(\implies \sf \cos(55^{\circ})=\dfrac{2}{x}\)

\(\implies \sf x=\dfrac{2}{\cos(55^{\circ})}\)

\(\implies \sf x=3.486893591...\)

Therefore, the side of the rhombus is 3.5 in (nearest tenth)

Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

1/2 x + 5

Step-by-step explanation:

Haf of x = 1/2 x

then add 5     :     1/2 x + 5

Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: \(g(x) = -\sqrt{9(x - 1)} + 2\)

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.

Where:

In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;

f(x) = √x

g(x) = -√9(x - 1) + 2

\(g(x) = -\sqrt{9(x - 1)} + 2\)

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\(( \frac{6d}{d {}^{4} } ) {}^{ - 2} \\ \)

Take the reciprocal of the inside to get rid of the negative exponent.

note: reciprocal=flip it over

\(( \frac{6d}{d {}^{4} } ) {}^{ - 2} = ( \frac{d {}^{4} }{6d} ) {}^{2} \\ \)

Before we continue we can notice that the inside is reducible since we have d's in the numerator and the denominator.

note: d=d^1

\( \frac{a {}^{m} }{a {}^{n} } = a {}^{m - n} \\ \)

\(( \frac{d {}^{4} }{6d} ) {}^{2} =( \frac{1}{6} \times \frac{d {}^{4} }{d}) = ( \frac{d {}^{4 - 1} }{6} ) {}^{2} = ( \frac{d {}^{3} }{6} ) {}^{2} \\ \)

\(note \: that \\ ( \frac{ \omega}{ \eta} ) {}^{x} = \frac{ \omega {}^{x} }{ \eta {}^{x} } \)

\(( \frac{d {}^{3} }{6} ) {}^{2} = \frac{(d {}^{3}) {}^{2} }{6 {}^{2} } = \frac{d {}^{3 \times 2} }{36} = \frac{d {}^{6} }{36} \\ \)

Answer

Explanation

Given:

Using trigonometric identity, To find the exact value of tan θ

To find the exact value of cos θ

θ

Answer:

\(y = \dfrac{1}{2}x -5\)

Step-by-step explanation:

The slope intercept form of a linear equation is
y = mx + b

where m = slope and b = y-intercept

Since these are given, simply plug in to get

\(y = \dfrac{1}{2}x -5\)

Answer:

y= -4x+4

Step-by-step explanation:

so the slope is -4x

Answer:

5/2 is the slope

Step-by-step explanation:

Rise/Run= 5/2

so, slope=5/2

The annual percentage yield (APY) of Rocio is 3.11 %

What is Annual Percentage Yield?

The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest.

Given data ,

Deposit amount of Russ = $ 3200

Interest rate R = 3.1 %

And it is given that the interest rate is compounded daily , so

Interest rate R = 3.1 % / 365

                       = 0.031 / 365

                       = 0.000084

Now , The annual percentage yield (APY) is calculated as

The interest amount = 3200 x ( 1 + 0.000084 )³⁶⁵

                                 = 3200 x ( 1.000084 )³⁶⁵

                                 = 3200 x 1.031133

                                 = 3299.6272

                                 ≈ 3299.627

Therefore , the interest will be

= 3299.627 - 3200

= $ 99.627

Now , the annual percentage yield (APY) is given by

= Interest / Deposit

= 99.627 / 3200

= 0.03113

≈ 3.11 %

Hence , annual percentage yield (APY) of Rocio is 3.11 %

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The icon that points out the Essential Question that you should be able to answer by the end of the lesson is this:

C. A hand icon is shown.

A hand icon is used for the purpose of identifying the important questions that should be answered at the end of the lesson. It shows that the reader should pay careful attention to the indicated question as they may have to provide an answer to it by the end of the lesson.

Icons in reading have different meanings and understanding their purposes will lead to a more immersive reading.

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Answer:

\(3\sqrt{22}\)

Step-by-step explanation:

The product of roots with the same index is equal to the root of the product \(3\sqrt{11*2}\)

Multiply

Answer: length = 8cm

Width = 4cm

Step-by-step explanation:

Let the width of the rectangle be represented by x.

Since the length of a rectangle is twice as long as the width of the rectangle, then the length will be: = 2 × x = 2x

Note that, Area of a rectangle = Length × Width

Therefore,

2x × x = 32

2x² = 32

Divide both side by 2

2x²/2 = 32/2

x² = 16

x = ✓16

x = 4

Therefore, width = 4cm

Since length = 2x

Length = 2 × 4cm = 8cm

Check: length × width = Area

8cm × 4cm = 32cm²

The maximum daily profit the company can earn is $2,350.

It is a set of points in a coordinate plane that represents the values of the function for different inputs.

The function P(x) = −6x² + 156x + 1,000 models the daily profit of the company, where x is the number of $5 price increases for each solar panel. The graph of the function has a vertex at approximately (15, 2350), which represents the maximum point on the graph.

Therefore, the maximum daily profit the company can earn is $2,350.

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Answer:

y is just being multiplyed by -4 :)

Step-by-step explanation:

in other words -4x

Answer:

y = -4x

Step-by-step explanation:

Answer:

117959332467

Step-by-step explanation:

Answer:

SPEA should have install the new power generator.

Step-by-step explanation:

The information provided is as follows:

Consider the decision tree attached below.

The loss that will be incurred after the generator is installed is, $80,000.

Compute the loss that will be incurred if the generator is not installed as follows:

\(E(\text{Loss})=P(HL|P)P(P)\times \$7000000+P(SL|P)P(P)\times \$1000000\)

             \(=(0.07\times 0.12\times \$7000000)+(0.93\times 0.12\times \$1000000)\\=58800+111600\\=170400\)

The loss that will be incurred if the generator is not installed is $170,400.

The loss from not installing the generator is more than from installing it.

Thus, SPEA should have install the new power generator.

Amount Lucy will be paying in interest will be $38,596.2  

Using the compound amount formula to get the amount after she will pay back after 20 years expressed as:

\(A =P(1+\frac{r}{n} )^{nt}\)

Substitute the parameters into the formula;

\(A=73,250(1+\frac{0.0315}{12} )^{20(12)}\\A= $73,250 (1.8761)\\A= \$137,421.49\)

If Excel calculates the monthly payment to be $411.77, the amount paid for 20 years will be $411.77 * 240months = $98,824.8

Amount Lucy will be paying interest will be $137,421- $98,824.8 = $38,596.2  

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Answer:

Step-by-step explanation:

Sales Revenue:  $800.00

Cost of good sold:  $350,000.00

Subtract:                   $450,000.00

Sales Revenue:         $795,000.00

Cost of good sold:     $600,000.00

Subtract Sales             $195,000.00

Revenue from Cost

of goods sold.