Solve each expression using the order of operations.
64 ÷ 8 × 2 + 2 × 4 – 4 × 5

(3 + 9) × 2 ÷ 4

The greatest size grid squares she can make is; 12 inch by 12 inch.

Since, it follows from the task content that the poster at the artist's disposal is 12 inch by 30 inch, it follows that the smaller dimension of the poster is; 12inch.

It is the limiting dimension and hence, the greatest size grid squares she can make is; 12in by 12 inch.

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Answer:

Step-by-step explanation:

This is a Law of Sines problem. The expanded formula is

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex] where the capital letters are the angles and the lowercase letters are the side lengths. We only use 2 of these ratios at a time. And in order to do that, we can only have one unknown per set of ratios. I have angle A and side a, so I'll use that ratio, but I don't have angle C to help me find side c. I also don't have angle B. But I do have side b, so I'll use the A and B sin stuff and then solve for C indirectly.

[tex]\frac{sin15}{9} =\frac{sinB}{12}[/tex] to solve for angle B. Cross multiply:

[tex]sinB=\frac{12sin15}{9}[/tex]

[tex]sinB=.3450926061[/tex]  Use the inverse and sin keys on your calculator (in degree mode) to get that

B = 20.2°.  Now that we have that, we can find the measure of angle C:

180 - 15 - 20.2 = 144.8°

Now we can use the sin ratio involving the angle C, side c (our unknown), and angle A and side a:

[tex]\frac{sin144.8}{c}=\frac{sin15}{9}[/tex] and cross multiply to solve for c:

[tex]c=\frac{9sin144.8}{sin15}[/tex] gives us that

c = 20.0

Answer:

Step-by-step explanation:

hello .....

note : the slope of the line (AB) is :

m = (YB -YA)/(XB - XA)

given  :  A(9,-4) and B (1,-5)

m= ((-5)-(-4))/(1-9)

m= 1/8

Answer:

Step-by-step explanation:

If (x, 68, 85) form a Pythagorean Triple, what is the value of x?

to solve we again use Pythagoras, x is the smallest number, so 68 is a cathetus and 85 the hypotenuse

x = √(85²- 68²)

x = (7225 - 4624)

x = √2601

x = 51

Answer:

  x = 51

Step-by-step explanation:

The missing value of the Pythagorean triple can be found using the Pythagorean theorem, or it can be found by comparing the values in the triple to known triples.

A Pythagorean triple is a set of integers {a, b, c} that satisfy the equation of the Pythagorean theorem:

  a² +b² = c²

The smallest such triple is {3, 4, 5}. It is also the only triple that is an arithmetic sequence. Other triples of small integers are ...

  {5, 12, 13}, {7, 24, 25}, {8, 15, 17}

There are an infinite number of "primitive" Pythagorean triples, ones that are not multiples of another triple.

The given values of the triple have the ratio ...

  68/85 = (4·17)/(5·17) = 4/5

Only the values in the {3, 4, 5} triple and its multiples will have this ratio.

The value of x is 3·17 = 51, so the triple is {51, 68, 85}.

  x = 51

__

Additional comments

Any primitive triple will have two odd numbers.

The ratios of numbers in a primitive triple are unique to that triple. That is, the numbers are mutually prime.

For any pair of positive integers m > n, there is a Pythagorean triple {2mn, m²-n², m²+n²}. Such triples will not be primitive if m and n have the same parity.

__

The above triple can be verified using the Pythagorean theorem:

  51² +68² = 2601 +4624 = 7225 = 85²

Answer: 3 to the 3rd power equals 27

Step-by-step explanation: Because a exponent is the number times itself 3x3 equals 9 that's already 2 then 9x3 equals 27 so anything above is to much

Answer:

  31√2 feet

Step-by-step explanation:

The height can be found using the Pythagorean theorem. The height of the pyramid will be the height of the right triangle whose sides are half the diagonal of the square base, the distance from the base to the peak, and the edge from the peak back to the corner of the base.

Let h represent the height of the pyramid. The diagonal of the square base will be √2 times the side of the base. So, half the diagonal will be 17√2 ft. The Pythagorean theorem tells us ...

  h² +(17√2)² = 50²

Subtracting the constant on the left gives ...

  h² = 2500 -578 = 1992

  h = √1992 = 31√2

The height of the square pyramid is exactly 31√2 feet.

__

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Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.

En este problema debemos hallar dos segmentos de cuerda que cumple la siguiente relación, basada en el enunciado citado:

5 = (90 cm - x)/x     (1)

5 · x = 90 cm - x

6 · x = 90 cm

x = 15 cm

Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.

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The equations which completes the left-hand column of the table are;

[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]

The given expression on the right is written as follows;

First row;

[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]

The definition of the sum and difference of cosine are;

cos(a - b) = cos(a)•cos(b) + sin(a)•sin(b)

cos(a + b) = cos(a)•cos(b) - sin(a)•sin(b)

Therefore;

Second row;

cos(a - b) - cos(a + b) = 2•sin(a)•sin(b)

Which gives;

[tex] sin(a) \cdot sin(b) = \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]

Third row;

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The equation for the height exists h = 31 sin((8π)t + π/2) + 35.

The model for the height can be emanated from the general formula of the sine function, then

y = A sin(Bt - C) + D

Maximum point = 70 - 4 = 66 at t = 0

Minimum point = 4

Amplitude, A = (66 - 4) ÷ 2 = 31

D = 4 + 31 = 35

At t = 0, we have;

66 = 31 × sin(B × 0 - C) + 35

31 = 31 × sin(- C)

sin(- C) = 1

C = -π/2

1 minute = 60 seconds

1 second = 1 minute/60

15 seconds = (15/60) minutes

Period = 15 seconds = 15/60 minutes

Period = 2π/B

Therefore, 15/60 = 2π/B

1/4 = 2π/B

B = 2π/(1/4) = 8π

y = Height of the function

Let h denote the height of the wristband.

The equation for the height exists h = 31 sin((8π)t + π/2) + 35.

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The linear speed based on the information is 1326 km/h.

The radius will be:

= 6378 + 252

= 6630 km

The angular speed is 0.2. The linear speed will be:

= 6630 × 0.2

= 1326 km/h.

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The answer choice which represents a pair of complementary angles in the task content is; angles DEH and DEJ.

It follows from the concept of angle geometry that two or more angles are said to be complementary when the sum of their measures is 90°.

It follows from the task content therefore that since, DEJ = 90° and the sum of the measures of angles DEH and DEJ amounts to 90°.

Hence, the pair of angles are complementary.

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[tex]increase = 13.25 - 12.50 \\ increase = 0.75 \: dollars[/tex]

[tex]12.50 = 100\% \\ 0.75 = x\%[/tex]

[tex]12.50x = 100(0.75) \\ x = \frac{100(0.75)}{12.50} = \frac{75}{12.5} = 6\%[/tex]

I assume you meant [tex]f(x)=3(2)^x[/tex].

The transaction price for Ayayai's product and the customer loyalty points are $92500 and 37000 points respectively.

Based on the information provided about Ayayai inc., the transaction price for their product and the customer loyalty points would be allocated as follows:

                                            SSP            PA              TTP                    AA____

Product purchases       $370,000       80%         $370,000         $296,000

Loyalty points               $92,500*       20%         $370,000         $74,000__

                                      $462,500                                                 $370,000

*37,000 × 2.50 = $92,500

Note:

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Answer:

∠AFB = Acute

∠DFB = Obtuse

∠CFD = Right

Step-by-step explanation:

∠AFB is acute b/c its less than 90°

∠DFB is obtuse b/c it more than 90°

∠CFD is right b/c it's exactly 90°

(L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters. This can be obtained by forming quadratic equation for the data.

Let length be L and width be W.

Given that,

three sided fence has a length of 57m,

⇒ 2W + L = 57 m ⇒ L = 57 - 2W

the area of the land is 340 square meters

length × width = 340 ⇒ L × W = 340

(57 - 2W)W = 340

57W - 2W² = 340

2W² - 57W + 340 = 0

Solve for W using quadratic formula,

a = 2, b = -57, c = 340

W = (-b±√b²-4ac)/2a  

   = (57±√3249-2720)/4

   = (57±√529)/4

   = (57±23)/4

W = 20 m and W = 8.5 m  

For W=20, L=57-2(20) = 17

For W=8.5, L=57-2(8.5) = 40

Hence (L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters.

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If the p-value less than 0.05, the decision is to reject the Null hypothesis.

The following should NOT be used as a decision-making standard in a hypothesis test.

If the p-value less than 0.05, the decision is to reject the Null hypothesis.

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Answer:

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The given function has symmetry about the y - axis.

Symmetry of the Function

If we reflect a function's graph about the y-axis, we will get the same graph since if the function is symmetrical about the y-axis. We can reflect a function about the x- and y-axis and obtain the same graph. These two symmetry kinds are known as the even function and odd function.

The given function is,

f(x) = 2x² - 1

It is an even function since the function remains same for both x and -x.

Putting f(x) = 0, we get,

2x² - 1 = 0

2x² = 1

x² = 1/2

x = ±1/2

⇒ Axis of symmetry is, x=0

Hence, the function f(x) is symmetric about y-axis.

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The value of x = 4.71, 0.41, or 5.89 radian value

Specification:

sinxtanx + tanx -2sinx + cosx = 0

tanx = sinx / cosx

sinx (sinx / cosx) + sinx / cosx -2sinx + cosx = Multiply 0

cosx to remove the fraction

sin ^ 2 (x) + sinx -2sinxcosx + cos ^ 2 (x) = 0

sin ^ 2 (x) + cos ^ Replace with 1. 2 (x) = 1

sinx -2sinxcosx + 1 = 0

sinx (1-2cosx) = -1

1-2cosx = -1 / sinx

-2cosx = -1 / sinx -1

2cosx = 1 / sinx + 1

cosx = 1 / 2sinx + 1/2

sqr (1-sin ^ 2 (x)) = 1 / 2sinx + 1/2

Squared on both sides

1-sin ^ 2 (x) = 1 / 4sin ^ 2 (x) + 1 / 2sinx + 1/4

4sin ^ 2 (x) Multiply

4sin ^ 2 (x) -4sin ^ 4 (x) = 1 + 2sinx + sin ^ 2 (X)

4sin ^ 4 (x) -3sin ^ 2 (x) + 2sinx +1 = 0

y = sinx

4y ^ 4 -3y ^ 2 + 2y + 1 = 0

sinx = y = -1 or -0.3478

x = 270, 180-22.61 or -22.61 degrees

x = 270, 157.39 or 337 .39 degrees

or

x = 3pi / 2, 0.13pi or 1.87pi radians

or

x = 4.71, 0.41 Or 5.89 radians

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Since the four choices have solution, there is no choice that have no solutions. (Correct choice: E)

Herein we must check each choice to find if a solution exists or not by algebra properties. Now we proceed to check each case:

Choice A

1/(x - 31) = 5

1 = 5 · (x - 31)

1 = 5 · x - 155

5 · x = 156

x = 31.2

Choice B

12 · x - 11 = 0

12 · x = 11

x = 11/12

Choice C

15 - 3 · x = - 8

3 · x = 23

x = 23/3

Choice D

- x + 91 = 0

x = 91

Since the four choices have solution, there is no choice that have no solutions. (Correct choice: E)

The statement presents typing mistakes and is incomplete. Correct form is shown below:

Which equation has no solution?

A. 1/(x- 31) = 5

B. 12 · x - 11 = 0

C. 15 - 3 · x = - 8

D. - x + 91 = 0

E. Neither of all

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Answer:

Step-by-step explanation:

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Solving a quadratic function, it is found that the ball has a height of 19 feet at t = 0.72 seconds and t = 1.22 seconds.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

In this problem, the function is:

h(t) = -16t² + 31t + 5

The height is of 19 feet when h(t) = 19, hence:

19 = -16t² + 31t + 5

16t² - 31t + 14 = 0.

Then:

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The number of years it would it take for there to be one person for every square yard is 93.6 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 35 billion / 1 billion) / 0.038 = 93.6 years

Here is the complete question:
Country A has an exponential growth rate of 3.8​% per year. The population is currently 1,000,000 ,000 and the land area of Country A is ​35,000,000,000 square yards. Assuming this growth rate continues and is​ exponential, after how long will there be one person for every square yard of​ land?

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The wheelchair ramp must have a height of approximately 1.553 meters. One tree is approximately 310.309 meters taller than the other one.

In this problem we have two cases in which geometric diagrams and trigonometric functions are utilized to determine side lengths. Based on all informations presented in the images attached below, we proceed to find the side lengths:

Case A

h = (6 m) · sin 15°

h ≈ 1.553 m

Case B

Δh = 60 m /cos 36° - 60 m /cos 52°

Δh ≈ 310.309 m

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The change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters

It is important to note that the maximum height is the peak altitude the balloon reached

To find the difference, we use the formula

Change = Maximum height - recovery height

Maximum height = 5000 meters

Recovery height = 3700 meters

Substitute the values

Change = 5000 - 3700

Change = 1300 meters

Thus, the change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters

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The difference between using Area and Volume with 2D and 3D figures is that Area is a measure of square units while Volume is a measure of cubic units.

The area of an object is the measure of space occupied by the two-dimensional object (flat) in a plane. Volume on the other hand is the quantity of space occupied by the object, 3-dimensional object in this case. The unit of area is in square units. The unit of volume is in cubic units.

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Using the normal distribution, there is a 0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given, respectively, by:

[tex]\mu = 42.5, \sigma = 4.8[/tex]

The probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill is the p-value of Z when X = 48 subtracted by the p-value of Z when X = 35, hence:

X = 48:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{48 - 42.5}{4.8}[/tex]

Z = 1.15

Z = 1.15 has a p-value of 0.8749.

X = 35:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{35 - 42.5}{4.8}[/tex]

Z = -1.56

Z = -1.56 has a p-value of 0.0594.

0.8749 - 0.0594 = 0.8155.

0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.

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