Find the 8th term of the geometric sequence whose common ratio is 3/2
and whose first term is 2.

Answer:

C. 0.045

Step-by-step explanation:

The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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The critical value for a confidence level of 98% with a sample size of 32 is given as follows:

t = 2.4528.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 32 - 1 = 31 df, is t = 2.4528.

(df is one less than the sample size).

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Examining the figure, the correct options are

Two angles are said to be congruent when they are equal to each. The symbol to represent congruency is ≅

The following angles are congruent in the figure

Corresponding angles refers to angles that are in a position that are in matching position to another angle.

Corresponding angles are said to be equal when there are parallel lines intersected across by a line called transversal line.

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Answer:

  A.  23

Step-by-step explanation:

All of the right triangles are similar, so we can write the proportion ...

  (short leg)/(long leg) = CD/CB = CB/CA

  CD = CB²/CA = 32²/44 ≈ 23 3/11

The length of CD is about 23 units.

Answer:

a

Step-by-step explanation:

Maureen's pension would be $50,035.20.

What is Percentage?

To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

First, we need to calculate the average of Maureen's three highest salaries:

Average = (107,000 + 107,800 + 108,198) / 3

Average = 322,998 / 3

Average = 107,666

Next, we need to calculate 1.56% of this average:

Percentage = 1.56% * 107,666

Percentage = 1,667.84

Finally, we multiply this percentage by the number of years worked to find the pension:

Pension = 30 * 1,667.84

Pension = 50,035.20

So, Maureen's pension would be $50,035.20.

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Consider the given radical,

Factorize the number,

Consider the following properties,

Then the radical can be simplified as,

Thus, the radical is simplified as,

Answer:

NO because 7+5=12

The sum must be larger (not equal to) the longest side. If it's exactly the same, there's no room to for the shorter two sides to angle up to form a triangle.

Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

Answer:

N = 20

Step-by-step explanation:

5/3 = 1 2/3

20/12 = 1 8/20

They are equivalent

Angle L's in the triangle LMN is,

⇒ L = 72.54°

We have to given that;

A triangle LMN is shown in figure.

And, The sides are,

Since, We know that;

A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.

Since, We know that;

⇒ sin L = Opposite / Hypotenuse

And, cos L = Base / Hypotenuse

Two rays after combined into an angle have a single terminal. And, latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Now, We can use trigonometry formula to find the value of angle l we get;

⇒ sin L = Opposite / Hypotenuse

⇒ sin L = LM / LN

⇒ sin L = 18/60

Taking arc sin both side, we get;

⇒ L = 72.54°

Therefore, The value of measure of angle L is triangle LMN is,

⇒ L = 72.54°

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The two possible solutions of the given quadratic equation are -

x =  +√6 +5 and x =  -√6 +5

For the given question;

(x - 5)² - 6 = 0

Bring constant on other side.

(x - 5)² = 6

Taking square root both side.

√ (x - 5)² = √6

(x - 5) = ±√6

Separate the constant and variables.

x =  ±√6 +5

There are two possible solution.

x =  +√6 +5 and x =  -√6 +5

Thus, the two possible solutions of the given quadratic equation are -

x =  +√6 +5 and x =  -√6 +5.

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Answer:

D

Step-by-step explanation:

Answer:

2.83 inches

Step-by-step explanation:

Let y equal the length of the drawing in inches. Use a proportion to solve for the missing length.

Answer:i took the test

Step-by-step explanation: 76879686

Answer:

198, 2088, 2286, 306

Step-by-step explanation:

i think those should be right in order of questioning, i got a bit confused by the way it was presented

Answer: exponential pattern

Step-by-step explanation:

The numbers in the given sequence form an exponential pattern. The pattern is:

10, 12, 16, 28, 54, 100, 172

A. Ram spent $18 on six pens and six books. The grand total is $72.

B. The cost of each pen is $9.

C. The variable is called x.

What is an equation?

A set of variables, constants, and mathematical operations such as addition, subtraction, multiplication, or division balanced by the equal sign is known as an equation. The equation's left-hand side (LHS) is on the left side, and its right-hand side (RHS) is on the right side (RHS).

Here, we have

Given: the equation 6x + 18 = 72:

A. The issue is that Ram spent $18 on six pens and six books. The total amount he paid is $72.

B. The following equation will be used to demonstrate this:

6x + 18 = 72

Compile similar terms.

6x = 72 - 18

6x = 54

On dividing,

x = 54 / 6.

x = $9

Hence, each pen will set you back $9.

C. The variable's value is x = 9.

Hence, the pen's price is 9.

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If the two angles are complementary, then their sum is 90 degrees.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

If the two angles are complementary, then their sum is 90 degrees.

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Quadrilateral JKLM has sides with equal lengths (√85), and the slopes of opposite sides are equal. However, it is not a special type of quadrilateral like a rectangle or a square.

To describe quadrilateral JKLM, let's first plot the given points J(9, 7), K(2, 1), L(0, -8), and M(7, -2) on a coordinate plane:

J(9, 7) K(2, 1)

L(0, -8)   M(7, -2)

To find the slopes and lengths of each side of the quadrilateral, we can use the distance formula and the slope formula.

Slope of JK:

Slope (m) = (change in y) / (change in x)

m(JK) = (7 - 1) / (9 - 2) = 6/7

Length of JK:

Length (d) = √[(x2 - x1)^2 + (y2 - y1)^2]

d(JK) = √[(9 - 2)^2 + (7 - 1)^2] = √(49 + 36) = √85

Slope of KL:

m(KL) = (-8 - 1) / (0 - 2) = -9/2

Length of KL:

d(KL) = √[(0 - 2)^2 + (-8 - 1)^2] = √(4 + 81) = √85

Slope of LM:

m(LM) = (-2 - (-8)) / (7 - 0) = 6/7 (same as slope of JK)

Length of LM:

d(LM) = √[(7 - 0)^2 + (-2 - (-8))^2] = √(49 + 36) = √85

Slope of MJ:

m(MJ) = (7 - (-2)) / (9 - 7) = 9

Length of MJ:

d(MJ) = √[(7 - 9)^2 + (-2 - (-8))^2] = √(4 + 36) = √40

Based on the calculations, we can describe quadrilateral JKLM as follows:

The slope of JK and LM is 6/7.

The slope of KL is -9/2.

The slope of MJ is 9.

The length of each side (JK, KL, LM, MJ) is √85.

The quadrilateral is not a rectangle or a square since the slopes of opposite sides (JK and LM) are not perpendicular.

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The probability that a defective component will be detected only by the first inspector is 0.19

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

The probability that all three defective components in a batch escape detection by both inspectors is 0.

It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.

Therefore P(A)=P(B)=81%=0.81

At least one inspector does not detect a defect on 38% of all defective components.

Therefore, bar P(A∩B)=0.38

As we know:

bar P(A∩B)=1-P(A∩B)=0.38

P(A∩B)=1-0.38=0.62

A defective component will be detected only by the first inspector.

P(A∩barB)=P(A)-P(A∩B)

=0.81-0.62

P(A∩barB)=0.19

The probability that a defective component will be detected only by the first inspector is 0.19

Part (B) A defective component will be detected by exactly one of the two inspectors.

This can be written as: P(A∩barB)+P(barA∩B)

As we know:

P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)

Substitute the respective values we get:

P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)

=0.81+0.81-2(0.62)

=1.62-1.24

P(A∩ barB)+P(bar A∩B)=0.38

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

Part (C) All three defective components in a batch escape detection by both inspectors

This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)

As we know bar P(A∩B)=P(bar A∪ bar B)=0.38

From part (B): P(bar A∩B)+P(A∩bar B)=0.38

This can be written as:

P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0

The probability that all three defective components in a batch escape detection by both inspectors is 0

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Answer:

WR ≈ 13.862

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

WR² + RT² = WT²

WR² + 12.1² = 18.4²

WR² + 146.41 = 338.56 ( subtract 146.41 from both sides )

WR² = 192.15 ( take the square root of both sides )

WR = \(\sqrt{192.15}\) ≈ 13.862 ( to the nearest thousandth )

Answer:

hold on

Step-by-step explanation:

do you have options?

So on solving the provided question we can say we can plotting data by x = 0.83; y = 0.79; z = 0.83

Here, we have,

The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables.

Diagrams created by hand or on a computer are also acceptable.

Move 2 units to the right after starting at the origin before going 3 units up.

The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points.

The pink dot with the letter P thus stands for 2.3.

Before creating a line chart, you need first generate a number line for each value in your data collection.

Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.

x = 0.83

y = 0.79

z = 0.83

xa = 0.85

ya = 0.85

za = 0.85

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Answer:

8

Step-by-step explanation:

let x be the number , then

\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )

3x = 108 ( divide both sides by 3 )

x = 36

the number is 36, so

\(\frac{2}{9}\) × 36 = 2 × 4 = 8

The two ninths of the number is 8

We know that Three quarters of a number is  \(\frac{3}{4}\)  times of a number

Hence we will assume the number x ,

                     \(\frac{3}{4} of x = 27\)

                     \(x = 27 X \frac{4}{3}\)

                       \(x = 36\)

Now as we know the number is 36

Therefore , the two ninths of the number assumed as y

We will multiply the number 36 by 2 and then divide by 9

Hence,

                           \(y = 36 X \frac{2}{9}\)

                               \(y = 8\)

Thus, the two ninths of the number 36  is 8                            

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The equivalent expressions to \(24^{-7}\) are given as follows:

C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)

F. \((24^3 \times 24^4)^{-1}\)

Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.

The exponent in the denominator can be moved to the numerator with the changed signal, hence:

\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)

Applying the power of power rule, we multiply the powers, hence:

\((24^7)^{-1} = 24^{-7}\)

When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:

\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)

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Answer:

3.50x-15= y

Reason:

In the equation y would be the total price and x would be the amount of watermelons. The slope is 3.5- and the y intercept is -15.

y = mx + b

m/slope = 3.50

b/y-intercept = -15

x = amount of watermelons

y = total cost