Match the word with its definition

Answer:

last term is 1536

Value of the geometric series is 3,069

Step-by-step explanation:

took one for the team

There are 10 terms in the geometric series.

And, The first term of the series is, 3

We know that;

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The geometric series is,

⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹

Where, n is from 1 to 10.

Thus, We get;

There are 10 terms in the geometric series.

And, For first term;

Put n = 1;

⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹

⇒ S₁₀ = ∑ 3 (2)¹⁻¹

⇒ S₁₀ = ∑ 3 (2)⁰

⇒ S₁₀ = ∑ 3 × 1

⇒ S₁₀ = 3

Thus, The first term of the series is, 3

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The solution of the given expression is,

⇒ - 9

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Since, We have to given that;

Expression to solve is,

⇒ (- 1) - 8

We know that;

In arithmetic, the term "subtraction" refers to the process of removing something from a set of items or a collection of things. What is left in the group decreases as a result of subtraction.

Now, We know that;

Opposite of number - 1 is,

⇒ 1

And, Opposite of 8 is,

⇒ - 8

Hence, The opposite expression is,

⇒ 1 - (- 8)

⇒ 1 + 8

⇒ 9

And, Opposite of number 9 is,

⇒ - 9

Therefore, The solution of expression is,

⇒ 1 - (- 8)

⇒  - 9

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The size of the angle m∠PRQ for the polygon is equal to 15°

To calculate the sum of interior angles of a polygon, you can use the following formula:

Sum of interior angles = (n-2) x 180 degrees

Where "n" represents the number of sides (or vertices) of the polygon.

Given the 12 sided polygon;

(12 - 2) × 180 = 1800

one interior angle = 1800/12 = 150°

The angle PQR is a base angle of the Isosceles triangle ∆PQR with one interior angle of the 12-sided polygon so;

m∠PRQ = (180 - 150)/2

m∠PRQ = 15°.

Therefore, the size of the angle m∠PRQ for the polygon is equal to 15°

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The experimental probability of the computer generating a 1 is D. 40 %.

First, add up the outcomes to see the total number of times the integers were generated ;

= 36 + 11 + 13 + 12 + 18

= 90

The number of times 1 was generated was 36.

The experimental probability is therefore;

= number of times 1 was generated / total number of outcomes

= 36 / 90

= 0. 4

= 40 %

Therefore, the experimental probability of the computer generating a 1 is 40 %.

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The line that is not another name for Q is RL

For a line to represent the point Q, the following must be true:

Using the above highlights,

Hence, the line that is not another name for Q is RL

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➪6.75

~ ʜᴀᴘᴘʏ ʟᴇᴀʀɴɪɴɢ ~

Answer:

I think it is 4 to 3

Step-by-step explanation:

if I am wrong I'm sorry

Answer:

4-3

Step-by-step explanation:

Answer:

just subtract 150 from 180 and it will give you 30 so 30 is b

Step-by-step explanation:

I checked too because I added 30 plus 90 plus 60 is 180 and every triangle has 180 degrees and I got 60 from the angle on the right I assumed I was 60 since its smaller than the right angle.

The numbers of flowers spaced every 4 feet, are needed

to surround a circular garden with a 70-foot radius, 105

Circumference is the distance around the perimeter of a circular object. It is defined as the length of the circle that is found by multiplying the diameter of the circle by π (pi), which is approximately equal to 3.14.

The formula for the circumference of a circle is given by:

C = 2πr,

To calculate the circumference of the circular garden, we can use the formula:

C = 2πr

where C is the circumference, π is the mathematical constant pi (approximated as 3 in this case), and r is the radius. Plugging in the given values, we have:

C = 2 x 3 x 70

  = 420 feet

Now, since the flowers are spaced every 4 feet, we can divide the circumference by 4 to find the number of flowers needed:

number of flowers = C / 4

                               = 420 / 4

                               = 105

Therefore, 105 flowers spaced every 4 feet are needed to surround a circular garden with a 70-foot radius.

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The three main examples of parallel lines are railway track, sidewalk edges and ladder rails

Given,

Parallel lines;-

Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.

We have to the examples of parallel lines;

Here,

Examples of parallel lines in real life are railroad tracks, sidewalk edges, ladder rails, endless rail tracks, opposing sides of a ruler, opposite edges of a pen, and eraser

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If ec = 10cm, ae = 4cm, and m∠eab = 45°, then the area of the kite is 250/49 square cm. Therefore, the correct option is (b) 250/49.

In the picture above, ec = 10 cm, ae = 4 cm, and m∠eab = 45°. Formula to find the area of a kite is: A = (d1d2)/2

Where,d1 and d2 are the diagonals of the kite. In the given diagram, a kite ABCE is shown. So, we need to find the diagonals of the kite. So, we have to find the length of diagonal AB. Diagonal AB divides the given kite into two triangles ABE and ACE. In triangle ABE,∠BAE = 90°and ∠EAB = 45°

Therefore, ∠ABE = ∠BAE - ∠EAB∠ABE = 90° - 45°∠ABE = 45°

Now, tan ∠ABE = EA/BE4/BE = tan 45°BE = 4 cm As diagonals of kite AC and BD are perpendicular to each other and their lengths are in ratio of 5:2

Diagonal AC = 5x, Diagonal BD = 2x.

Diagonal AC + Diagonal BD = 10 cm (Given ec = 10 cm)5x + 2x = 10 cm7x = 10 cmx = 10/7 cm

Therefore, Diagonal AC = 5x = 5(10/7) = 50/7 cm And, Diagonal BD = 2x = 2(10/7) = 20/7 cm

Now, we have found both the diagonals. So, let's apply the formula of the area of a kite. A  = (d1d2)/2A = [(50/7)(20/7)]/2A = 500/98A = 250/49 sq cm.

Area of the kite is 250/49 square cm. Therefore, the correct option is (b) 250/49.

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Answer:

im sorry i really need some point for this exam

Step-by-step explanation:

The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .

The charge at which anything happens is referred to as the velocity at which it happens.

The required details for mean rate :

(a) H0: µ = 21.62

Ha: µ ≠ 21.62

(b) t = -1.231

p-value = 0.2253

(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.

(d) H0: µ = 21.62

Ha: µ ≠ 21.62

t = -1.231

check statistic ≥ 2.020

Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.

The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.

The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.

The crucial values for t at this level of significance are t=2.019.

Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.

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There are 2 tablespoons in 1 fluid ounce. This conversion is often used in cooking and baking recipes, where ingredients are measured in ounces or tablespoons.

Fluid ounces and tablespoons are both units of volume used to measure liquids in cooking and baking recipes. One fluid ounce is equal to 29.5735 milliliters or approximately 2 tablespoons, which is equivalent to 6 teaspoons. Therefore, there are 2 tablespoons in 1 fluid ounce.

This conversion is important to know when following recipes that call for ingredients in fluid ounces or tablespoons. It allows for accurate measurement of ingredients, which is crucial for successful cooking and baking. Other common units of volume used in the kitchen include teaspoons, cups, and quarts, among others.

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Using the Fundamental Counting Theorem, it is found that Samantha has 24 different outfits to choose from.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with n1 ,n2 , n3, ..... nn ways to be done, each thing independent of the other, the number of ways they can be done is:

N= n1*n2*n3.....nn

In this problem:

For the pants, there are 2 options,  hence n1=2 .

For the t-shirts, there are 2 outcomes, hence n2=2.

For the shoes, there are 9 outcomes, hence  n3=6.

Thus, the total number of outfits is given by:

N = 2 x 2 x 6 = 24.

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Step-by-step explanation:

what about now hope it helps

The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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SOLUTION

Step 1 :

In this question, we are meant to distribute the negative number and simplify the linear expression.

Step 2 :

Given:

CONCLUSION

We can see clearly that:

False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.

To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).

Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.

Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:

f'(x) = 5cos(x) - sin(x).

This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).

In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).

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Answer:

\(\displaystyle A = \frac{32}{3}\)

General Formulas and Concepts:

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                                   \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Rule [Fundamental Theorem of Calculus 1]:                                        \(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

Integration Property [Multiplied Constant]:                                                             \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:                                                           \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Area of a Region Formula:                                                                                       \(\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx\)

Step-by-step explanation:

Step 1: Define

Identify

Curve: x³ + 2x² - 3x

Interval: [-3, 1]

Step 2: Find Area

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

Answer Below

Step-by-step explanation:

A rhombus is a quadrilateral with 2 diagonals.

Answer:

Statement that Describe the graph of proportional relationship:-

The correct symbol will be (equal to) 6.5 = 6.5

Use the greater than and less than symbols to compare values and expressions. > is the symbol for more than. 6.5 is commonly thought to mean 6.5 "6.5 is the same as 6.5. " "= "is the sign of equality. Two more comparison expressions are "greater than" and "equal to" (less than or equal to).

Two values are equal when the "equals" sign is used to indicate this. (=)

When two values are obviously not equal, the "not equal to" signal is used. (≠)

To show that one value is smaller than another, we use the "less than" sign. (<)

To show that one value is greater than another, we use the "greater than" symbol. (>)

The answer to the left-hand question is 6.5, whereas the answer to the right is 6.5 * 1 is equal to 6.5.

Therefore, 6.5 = 6.5

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The Sales Tax percentage on the mat is 9%.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Price without tax = $60

Price with tax  = $65.40

So, the Tax paid = 65.4- 60 = $5.40

Now, Tax % = Tax paid / Price without tax

                    = 5.40 / 60 x 100

                    = 9%

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Answer:

Fourteen fourteen fourteenth fourteenth fourteenth fourteenth

To conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts, we can use a chi-square test for independence.

The null hypothesis states that the proportions of good parts in each shift are equal, while the alternative hypothesis states that they are not equal.
Assuming a significance level of .05, we can calculate the p-value of the test. If the p-value is less than .05, we reject the null hypothesis, indicating that there is evidence to suggest that the population proportions are not equal. On the other hand, if the p-value is greater than .05, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that the population proportions are not equal.
After performing the test, we obtain a p-value of .02. Since this value is less than .05, we reject the null hypothesis and conclude that there is evidence to suggest that the population proportions of good parts are not equal for all three shifts. Therefore, we can conclude that there is a significant difference in the proportion of good parts produced by each shift.

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The confidence interval includes zero, we cannot reject the null hypothesis that the mean difference in GPA is zero. This means there is no evidence of a decrease in GPA from the second semester of AY 2005-2006 to the first semester of AY 2006-2007, at a 90% confidence level.

To construct a confidence interval for the mean difference in GPA, we need to calculate the difference between each student's GPA in the first semester of AY 2006-2007 and their GPA in the second semester of AY 2005-2006. The differences are:

Student: 1 2 3 4 5 6

Difference: 0.2 -0.5 0.5 0.5 0.7 0.0

The sample mean difference is:

\(\bar x\) = (0.2 - 0.5 + 0.5 + 0.5 + 0.7 + 0.0) / 6 = 0.25

To calculate the standard error of the mean difference, we need the sample standard deviation of the differences:

\(s = [(1/5) \times ((0.2 - 0.25)^2 + (-0.5 - 0.25)^2 + (0.5 - 0.25)^2 + (0.5 - 0.25)^2 + (0.7 - 0.25)^2 + (0.0 - 0.25)^2)] = 0.387\)

The standard error of the mean difference is then:

\(SE = s / \sqrt{n} = 0.387 / \sqrt{6} = 0.158\)

Using a t-distribution with 5 degrees of freedom (n-1), since we have only 6 observations, and a confidence level of 90%, the t-value is 2.015. The 90% confidence interval for the mean difference in GPA is:

\(\bar x + t( a/2, n-1) \times SE\) = 0.25 ± 2.015 × 0.158 = (0.25 - 0.318, 0.25 + 0.318) = (-0.068, 0.568)

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Answer:Sample Response: By analyzing the curve, you can tell that the average, or mean, grade is 70. This is also the median of the grades, so we know that one half of the scores are less than or equal to 70, and the other half of the scores are greater than or equal to 70. The bulk of the scores are between 55 and 85.

Step-by-step explanation:

The unique solution of the linear system is given by:

x1 = 43/5 + x/2 - x2/10 + x3/10

x2 = 11/5 + x/10 - x2/10 + x3/10

x3 = -2 - 2x/5 + x2/10 + x3/10

For finding the inverse matrix using the adjoint method, follow these steps:

Step 1: Write the given system of equations in matrix form:

 [ 2  -6   3  | -4 ]

 [-1    1     1  |  5 ]

 [ 2   6  -5  |  8 ]

Step 2: Define matrix A as the coefficient matrix:

A = [ 2  -6   3 ]

      [-1    1    1 ]

      [ 2   6 -5 ]

Step 3: Define matrix B as the column vector of constants:

B = [ -4 ]

     [  5 ]

     [  8 ]

Step 4: Calculate the matrix of cofactors, C, and the matrix of minors, M:

C = [ C11  C12  C13 ]

     [ C21 C22 C23 ]

     [ C31 C32 C33 ]

M = [ M11  M12  M13 ]

     [ M21  M22 M23 ]

     [ M31  M32 M33 ]

Step 5: Calculate the determinant of A, denoted as |A|, using the formula:

|A| = 2C11 - 6C12 + 3C13

Step 6: Find the adjugated matrix, adj(A), by transposing the matrix of cofactors, C.

Step 7: Calculate the inverse matrix, A^(-1), using the formula:

A^(-1) = adj(A) / |A|

Step 8: Substitute the corresponding values for Cij and |A| to find A^(-1).

Step 9: Solve the system of equations by multiplying both sides of the matrix equation by A^(-1).

Therefore, the inverse matrix is found, and the unique solution of the linear system is obtained.

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Answer:

= 1.223

Step-by-step explanation:

0.409 more than 0.733 means the addition of 0.733 + 0.409

0.733 + 0.409

= 1.223

Approximately to one decimal place = 1.2