For Problems 9-10, simplify the expressions using properties of operations. 9. (4x – 7.2) + (-5.3x-8) 10. (t - 1) – (-7t + 2)

The value of the formula for the sequence is,

⇒ a (n) = 5ⁿ - 2

We have to given that;

The sequence is,

⇒ 3, 23, 123, 623, 3123, ...

Now, We can formulate;

⇒ 3 = 5 - 2

⇒ 23 = 5² - 2

⇒ 123 = 5³ - 2

⇒ 623 = 5⁴ - 2

Thus, The value of the formula for the sequence is,

⇒ a (n) = 5ⁿ - 2

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The inequality graphed on the number line can be written as:

-3 ≤ x < 2

Here we can see an inequality graphed on a number line, we can see that we start with a closed circle at x = -3

A closed circle means that x = -3 is a solution.

And we can see that it ends with an open circle at x = 2, the open circle means that the point is not a solution.

Then the inequality thati is shown in the number line is written as:

-3 ≤ x < 2

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The best assessment of the linearity of the relationship between the day of the month and account balance would be "Because the residual plot has no obvious pattern, and the scatterplot appears linear, it is appropriate to use the line of best fit to predict the account balance based on the day of the month."The correct answer is option C.

When assessing linearity, it is important to examine both the scatterplot and the residual plot. The scatterplot is used to visualize the relationship between the variables, while the residual plot helps us assess the appropriateness of a linear model by examining the pattern of the residuals (the differences between observed and predicted values).

If the scatterplot appears reasonably linear, it suggests that there is a linear relationship between the variables. In this case, since the scatterplot appears linear, it supports the use of a linear model to predict the account balance based on the day of the month.

Furthermore, the residual plot is used to check for any patterns or systematic deviations from the line of best fit. If the residual plot exhibits no obvious pattern and the residuals appear randomly distributed around zero, it indicates that the linear model captures the relationship adequately.

Therefore, if the residual plot shows no obvious pattern, it provides further evidence in favor of using the line of best fit to predict the account balance based on the day of the month.

In conclusion, when the scatterplot appears linear and the residual plot shows no obvious pattern, it is appropriate to use the line of best fit to predict the account balance based on the day of the month.

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Answer:

person above

Step-by-step explanation:

the obvious

About 1407 sharks would be needed to have a margin of error of 0.25

Margin of error is used to determine by what value there is deviation from the real value. Margin of error (E) is given by:

\(E=Z_\frac{\alpha}{2} *\frac{standard\ deviation}{\sqrt{sample\ size} }\)

The 90% confidence level have a z score of 1.645. Hence for E = 0.25, standard deviation = 5.7 feet, hence:

\(0.25=1.645*\frac{5.7}{\sqrt{sample\ size}}\\ \\sample\ size=1407\)

About 1407 sharks would be needed to have a margin of error of 0.25

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Answer: 26129.6

Step-by-step explanation:

6721 x 381 = 2560701

14 + 84 = 98

2560701  / 98 = 26129.6

The measure of the angle POB is equal to 46°. Thus, option C is correct.

The cοllectiοn οf all pοints in the plane that make up a circle are all equally spaced frοm a certain pοint knοwn as the "centre," making the fοrm a clοsed twο-dimensiοnal shape. The symmetry line οf reflectiοn is fοrmed by each line that traverses the circle.

Mοreοver, it pοssesses rοtatiοnal symmetry arοund the centre fοr each angle. A circle is a circular shape that can be created by tracing a mοving pοint in a plane sο that its distance frοm a specified pοint remains cοnstant.

Given

Angle AOC = 46°  

Now, ΔAOP ≅ ΔBOP

As SSS criteria is possible

Then

By CPCT

∠AOC = ∠BOC = ∠POB

∠POB = 46°  

Thus, the measure of the angle POB is equal to 46°. Thus, option C is correct.

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Answer:

Center ( -8, 1 )

Radius ( 13 )

For solving for w, where w is a real number. The value of w would be equal to 100.

Perfect squares are those integers whose square root is an integer.

Let x-a be the closest perfect square less than x, and let x+b be the closest perfect square more than x, then we get x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).

Then, we get:

\(\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}\)

Thus,\(\sqrt{x-a} and \sqrt{x+b}\) are the closest integers, less than and more than the value of \(\sqrt{x}\). (assuming x is a non-negative value).

We have a w real number so,

\(\sqrt{w} = 10\\\)

taking square both sides

\((\sqrt{w} )^2 = 10^2\\\\w = 10 \times 10\\\\w = 100\)

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Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

An acute angle, θ, is in a right triangle such that sin of theta is equal to 3 over 8 period  The value of cot θ is (√55)/3.

To determine the value of cot(θ), Since is an angle in a right triangle and sin() = 3/8, we obtain:

cot(θ) = (√55)/3

In light of the fact that is an acute angle in a right triangle, we may calculate:

sin(θ) = 3/8

Keep in mind:

Hypotenuse = ((opposite cathetus)2 + (adjacent cathetus)2), where sin() = (opposite cathetus)/(hypotenuse)

Next, we have:

contrary cathetus = 3

Using the formula hypotenuse = 8 = (3 + neighboring cathetus)2,

In order to solve this for the nearby cathetus, we obtain:

(82 - 32) = 55 adjacent cathetus

And we are aware of:

(Cot) = (nearby cathetus) (opposite cathetus)

Next, we have:

cot(θ) = (√55)/3

The value of cot θ is (√55)/3.

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The maximum and minimum values of the function is solved

Given data ,

We can find the maximum and minimum values of the function by taking the derivative of y with respect to x and setting it equal to zero.

y = (sin x)³ - (sin x)⁶

y' = 3(sin x)² cos x - 6(sin x)⁵ cos x

Setting y' equal to zero:

0 = 3(sin x)² cos x - 6(sin x)⁵ cos x

0 = 3(sin x)² cos x (1 - 2(sin x)³)

sin x = 0 or (sin x)³ = 1/2

If sin x = 0, then x = kπ for any integer k.

If (sin x)³ = 1/2, then sin x = (1/2)^(1/3) ≈ 0.866. This occurs when x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3 for any integer k.

To determine whether these values correspond to a maximum or minimum, we can use the second derivative test.

y'' = 6(sin x)³ cos² x - 15(sin x)⁴ cos² x - 9(sin x)⁴ cos x + 6(sin x)⁵ cos x

y'' = 3(sin x)³ cos x (4(sin x)² - 5(sin x)² - 3cos x + 2)

For x = kπ, y'' = 3(0)(-3cos(kπ) + 2) = 6 or -6, depending on the parity of k. This means that these points correspond to a maximum or minimum, respectively.

For x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3, y'' = 3(1/2)^(5/3) cos x (4(1/2)^(2/3) - 5(1/2)^(1/3) - 3cos x + 2). This expression is positive for x = π/3 + 2kπ/3 and negative for x = 5π/3 + 2kπ/3, which means that the former correspond to a minimum and the latter to a maximum.

Hence , the maximum value of the function is y = 27/64, which occurs at x = 5π/3 + 2kπ/3, and the minimum value is y = -1/64, which occurs at x = π/3 + 2kπ/3

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Answer:

Step-by-step explanation:

You want the maximum and minimum values of the function ...

  y = sin³(x) -sin⁶(x)

When we substitute sin³(x) = z, we have the quadratic expression ...

  y = z -z² . . . . . a quadratic function

Adding and subtracting 1/4, we can put this in vertex form:

  y = -(z -1/2)² +1/4

This version of the function describes a parabola that opens downward and has a vertex at (z, y) = (1/2, 1/4). The y-value of the vertex represents the maximum value of the function.

The maximum value of y is 1/4.

The sine function is a continuous function with a range of [-1, 1]. Then z will be a continuous function of x, with a similar range. We already know that y describes a function of z that is a parabola opening downward with a line of symmetry at z = 1/2. This means the most negative value of y will be found at z = -1 (the value of z farthest from the line of symmetry). That value of y is ...

  y = (-1) -(-1)² = -1 -1 = -2

The minimum value of y is -2.

__

Additional comment

The range of y is confirmed by a graphing calculator.

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Answer:

E) 35°, 70°.

Step-by-step explanation:

Given that the triangle has angles of a°, 2a° and 75°.

A triangle is a polygon shape that has three sides and three angles. The sum of angles in a triangle is 180°. There are different types of triangles such as scalene triangle, isosceles triangle, equilateral triangle e.t.c.

In the triangle:

a + 2a + 75 = 180° (sum of angles in a triangle)

3a + 75 = 180

adding -75 to both sides:

3a + 75 - 75 = 180 - 75

3a = 105

a = 105/3

a = 35°

Hence 2a = 2(35) = 70°

Therefore a = 35° and 2a = 70°

Answer:

E) 35°, 70°.

Step-by-step explanation:

aye

Answer:

x = 18 , y = 42

Step-by-step explanation:

27x + 14 = 500

      -14      -14

This process above moves the +14 to the right hand side, making it negative 14

27x = 486

To find x, divide 27 by 486

x = 486/27

x = 18

600 = 12 + 14y

Move the 12 to the left hand side to remain the 14y

600 = 12 + 14y

-12     -12

588 = 14y

Divide 14 by 588

588/14 = y

y = 42

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.

Answer: The equation used to find the value of x is 5x - 4 = 3x + 10. The value of x is determined to be 7.

Step-by-step explanation:

Four less than the product of a number (x) and 5 = 5x - 4

8 more than 2 added to 3 times the number = 3x + 2 + 8 = 3x + 10

Four less than the product of a number (x) and 5 is equal to 8 more than 2 added to 3 times the number => 5x - 4 = 3x + 10

                                                         5x - 3x = 10 + 4

                                                         2x = 14

                                                         x = 14/2

                 therefore,                      x = 7

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Answer:

A

Step-by-step explanation:

Answer: m = -1/2

Use (y2-y1)/(x2-x1) to find the slope.

Answer:

Yes, you're correct.

Step-by-step explanation:

Answer:

d: (0, pi)

r: [-1/2, 1/2]

Step-by-step explanation:

9514 1404 393

Answer:

  2 2/3

Step-by-step explanation:

Let the number be represented by x. Then the problem statement is telling you ...

  4 5/9 = 2 1/3 + (5/6)x

You can isolate the x term by subtracting 2 1/3 from both sides of the equation. (The properties of equality require that the same operation be performed on both sides of the equation.)

  (4 5/9) - (2 3/9) = (2 3/9) -(2 3/9) +(5/6)x

  2 2/9 = (5/6)x

The definition of the multiplicative inverse tells you that the coefficient of x can be made to be 1 if the term is multiplied by (6/5). We must do that to both sides of the equation.

  (6/5)(2 2/9) = (6/5)(5/6)x

  (6/5)(20/9) = x . . . . simplify

  120/45 = x . . . . . . do the multiplication

  8/3 = x = 2 2/3 . . . . . . . reduce the fraction

The number is 2 2/3.

_____

Additional comment

The number we're looking for is multiplied by 5/6 and the result has 2 1/3 added to it. To find the number, we "undo" these operations, in reverse order. We undo the addition by subtracting the amount that was added. We undo the multiplication by multiplying by the inverse of that factor.

This is the sort of logic that you would use to fill in the blank for ...

  7 = 1 + 3×___

You probably recognize that this breaks down into two problems:

  7 = 1 + ___ . . . . . (6 goes in the blank)

and

  6 = 3×___

You may notice that for all of these problems, a good knowledge of addition and multiplication facts is useful.

Let that be x

\(\\ \rm\hookrightarrow 5/6x+7/3=41/9\)

\(\\ \rm\hookrightarrow 5/6x=41/9-7/3=41-21/9=20/9\)

\(\\ \rm\hookrightarrow 45x=120\)

\(\\ \rm\hookrightarrow 9x=24\)

\(\\ \rm\hookrightarrow 3x=8\)

\(\\ \rm\hookrightarrow x=8/3\)

Answer:

8.5

Step-by-step explanation:

18=2x+1

-1        -1

_______

17=2x

_    _

2     2

8.5=x

Answer: Joe would have 7 apples.

Step-by-step explanation:

Joe had 2 apples, and he got 5 more. Because of this, we have to do 2 + 5.

2 + 5 = 7

Joe would have 7 apples.

Answer:

0 or 0.62921348314 (if done by the calculator)

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 89 on the left side and the dividend 56 on the right side like this:

8 9 ⟌ 5 6

Step 2:

The divisor (89) goes into the first digit of the dividend (5), 0 time(s). Therefore, put 0 on top:

0

8 9 ⟌ 5 6

Step 3:

Multiply the divisor by the result in the previous step (89 x 0 = 0) and write that answer below the dividend.

0

8 9 ⟌ 5 6

0

Step 4:

Subtract the result in the previous step from the first digit of the dividend (5 - 0 = 5) and write the answer below.

0

8 9 ⟌ 5 6

- 0

5

Step 5:

Move down the 2nd digit of the dividend (6) like this:

0

8 9 ⟌ 5 6

- 0

5 6

Step 6:

The divisor (89) goes into the bottom number (56), 0 time(s). Therefore, put 0 on top:

0 0

8 9 ⟌ 5 6

- 0

5 6

Step 7:

Multiply the divisor by the result in the previous step (89 x 0 = 0) and write that answer at the bottom:

0 0

8 9 ⟌ 5 6

- 0

5 6

0

Step 8:

Subtract the result in the previous step from the number written above it. (56 - 0 = 56) and write the answer at the bottom.

0 0

8 9 ⟌ 5 6

- 0

5 6

- 0

5 6

Answer: -pi/4 and 3pi/4

Step-by-step explanation:

Whenever you're given an inverse trig function like this, think "tangent of what gives me -1?" There are multiple ways in which you can solve this; knowing how tangent work, guess checking sin/cos to get -1, or using a calculator. The only way tangent can be an integer is if the sine and cosine of the angle are equal.

The only spots on the pi circle where this happens is pi/4, 3pi/4, 5pi/4, and 7pi/4. Answers B and D are correct

Answer:

b

Step-by-step explanation:

just did it on edg 2020

Since both angles are vertical angles, we need to set them equal to each other.

\(2(x + 10) = 3x - 30\\\\2x + 20 = 3x - 30\\\\5x + 20 = 30\\\\5x = 50\\\\x = 10\)

The final answer is x = 10.

Answer:

3x + n+6

Step-by-step explanation:

The required expression to represent the situation is; 3n+18

According to the question;

Hence, it follows that, the absolute value of the sum of a number and 6 is; |n + 6|.

Hence, 3 times the absolute value is;

Hence, upon evaluation; the expression is; 3n + 18

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The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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