2 COLLUM PROOFS 1 question

The value of θ for the given trigonometric equation are 37° and -63°.

Given trigonometric equation is,

4tan²θ + 5tanθ = 6

We have to find the value of θ.

The value of θ is in the range [0, 360).

This is in the form of a quadratic equation.

4tan²θ + 5tanθ - 6 = 0

Discriminant = 25 - (4 × 4 × -6) = 121

tan θ = (-5 ± √121) / 8

tan θ = (-5 ± 11) / 8

tan θ = 6/8 = 3/4 and tan θ = -16/8 = -2

The value of θ are tan⁻¹ (3/4) and tan⁻¹(-2).

The value of θ are approximately 37° and -63°.

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The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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Answer:

$4

Step-by-step explanation:

divide $28 by 7 toys

you should get $4

Answer:

4 since 28 divide 7 is 4 so $4

Answer: B. Additive Inverse

Answer:

294

Step-by-step explanation:

14 x 9 = 126

so the area of your rectangle is 126.

15 - 9 = 6

so 6 is the width, 14 is the height.

14 x 6 = 84

now you have to multiply is by 2, because there is still another Triangle on the other side.

84 x 2 = 168

Now you take 168 and 126 and add your areas, and you have found the complete area!

168 + 126 = 294

I hope this helps! :)

Brainliest please??

The line of best fit for the data is approximately y = -1.07x + 92.87: A) True.

In order to determine a linear equation for the line of best fit that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the latitude would be plotted on the x-axis of the scatter plot while the average temperature would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the latitude and average temperature, a linear equation for the line of best fit is given by:

y = -1.07x + 92.87

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Answer:

The first one

Step-by-step explanation:

The attachment shows different types of polygons that have 3 more sides then the other.

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

Now depending on these we have following five possibilities:

Case 1: Triangle and hexagon

If first polygon is triangle with three angles, the second will have 6 angles and the second polygon will be hexagon.

Case 2: Quadrilateral and heptagon

If first polygon is quadrilateral with 4 angles, the second will have 4+3 =7 angles and the second polygon will be heptagon.

Case 3: Pentagon and Octagon

If first polygon is pentagon with 5 angles, the second will have 5+3=8 angles and the second polygon will be octagon.

Case 4: Hexagon and Nonagon

If first polygon is hexagon with 6 angles, the second will have 6+3=9 angles and the second polygon will be nonagon.

Case 5: Heptagon and Decagon

If first polygon is Heptagon with 7 angles, the second will have 7+3=10 angles and the second polygon will be decagon.

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Answer:

THE PRODUCT IS THE PRODUCT OF THE NUMBER THAT REPRESENTS A NUMBER OF ANY NUMBER WITH PRODUCT

HOPE IT HELPS!

The final answer is after substituting : ∫ x^3(7 + x^4)^5 dx = (7 + x^4)^6 / 24 + C.

Let u = 7 + x^4, then du/dx = 4x^3, or dx = du/(4x^3). Substituting this into the integral, we get:

∫ x^3(7 + x^4)^5 dx = (1/4)∫ u^5 du

= (1/4) * u^6 / 6 + C

= u^6 / 24 + C

= (7 + x^4)^6 / 24 + C

So the final answer, after substituting back in for u, is:

∫ x^3(7 + x^4)^5 dx = (7 + x^4)^6 / 24 + C.

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Answer:

345/7

Step-by-step explanation:

h=345/7 tell me if its right

Answer:

Answer is 18 degree as per the question

Answer: A. 18°

Step-by-step explanation:

Your formula is 108°+54°+X=180°
To find X, add 108° & 54°. The sum is 162°.
Next you need to subtract your sum from 180°.
180°-162°=18°
X=18°

The area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.

Given that, the dimensions of a rectangle (x-1) and (x+3).

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Here, the area of a rectangle

= (x+3)×(x-1)

= x²+3x-x-3

= x²+2x-3

Hence, the area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the area of a rectangle with the dimensions (x-1) and (x+3).

Answer:To conduct a hypothesis test using the p-value approach, the general steps are as follows:

State the null hypothesis (H₀) and the alternative hypothesis (H₁) based on the research question or claim.

Choose an appropriate statistical test based on the type of data and the research question.

Collect the necessary data and calculate the test statistic.

Determine the significance level (α) for the test, which will dictate the critical value or the region of rejection.

Calculate the p-value, which represents the probability of observing the obtained test statistic or more extreme values under the null hypothesis.

Compare the p-value to the significance level (α) to make a decision.

If the p-value is less than α, reject the null hypothesis in favor of the alternative hypothesis.

If the p-value is greater than or equal to α, fail to reject the null hypothesis.

Step-by-step explanation:

Answer:

angles are 30,60 and 90

Step-by-step explanation:

apply rule <30 = 1 <60 = ✓3 <90 = 2

Answer:

  4

Step-by-step explanation:

You want to know the leaf unit corresponding to data value 0.014 when values are rounded to thousandths.

The leaf unit for data values in a stem-and-leaf plot is the least-significant digit of the data value, when all data values are expressed to the same precision.

The least significant digit of 0.014 is 4. The leaf unit is 4.

<95141404393>

It is more unusual to have a day with a high temperature of 55 F. A high temerature of 55 F in July is 2.2 std deviation below the mean and a high temperature of 55 F in January is only 1.889 std deviation above the mean.

Which month is more unusual to have a day with a high temperature?

Here z score =(X-mean)/std deviation

Therefore for temperature 55 F ; zscore for January =(55-38)/9=1.889

And for temperature 55 F ; zscore for July =(55-77)/10=-2.2

As z score reflect that 55 F is farthest from the mean of July in terms of std deviation

It is more unusual to have a day with a high temperature of 55 F. A high temperature of 55 F in July is a 2.2 std deviation below the mean, and a high temperature of 55 F in January is only a 1.889 std deviation above the mean.

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Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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Option A is the correct answer. Ellora wants to accumulate 150,000 in an RRSP by making annual contributions of 5,000 at the beginning of each year. If interest is 5.5% compounded quarterly, calculate how long she has to make contributions.

First, we have to find the interest rate per quarter, which will be
\(5.5% / 4\)= 1.375%.
The formula for the future value of an annuity is: 
\(FV = (C * [(1 + r)^n - 1] / r)\),

For Ellora, \(FV = $150,000, C = $5,000, and r = 1.375%.\)
Substituting these values into the formula gives:
\(150,000 = 5,000 * [(1 + 0.01375)^n - 1] / 0.01375\)
Simplifying this equation gives:
\(30 = [(1.01375)^n - 1]\)

We can solve this using logarithms:
\(ln 30 = ln [(1.01375)^n - 1]\)
\(ln 30 = n * ln 1.01375 - ln 1.01375e^(ln 30) / e^(-ln 1.01375) = n18.202125 = n\)

Therefore, it will take Ellora 18.202125 years to accumulate 150,000 in her RRSP through \($5,000\)annual contributions made at the beginning of each year with interest of \(5.5%\) compounded quarterly.

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The expected number of defective items and the probability of at least 4 are defective is equal to 3.6 and 0.370 or 37.0%.

Total number of items 'n' = 18

Probability of an item being defective 'p' =20%

                                                                    = 0.2  

Expected number of defective items,

Use the formula for the expected value of a binomial distribution,

E(X) = np

where X is the number of defective items.

Plug in the values we have,

E(X) = 18 x 0.2

      = 3.6

Expect average items out of 18 to be defective = 3.6  .

Probability that at least 4 items are defective,

Calculate the probability of 4, 5, 6, ..., 18 defective items

Use the complement rule to simplify it,

P(at least 4 defective)

= 1 - P(less than 4 defective)

Using the CDF function,

'binomcdf' is the binomial cumulative distribution function.

18 is the number of trials,

0.2 is the probability of success,

And 3 is the maximum number of successes

P(less than 4 defective)

= binomcdf (18, 0.2, 3)

= P(X <= 3)

=\(\sum_{x=0}^{3}\) ¹⁸Cₓ × (0.2)^x × (0.8)^(18-x)

= ¹⁸C₀× (0.2)^0 × (0.8)^(18-0) + ¹⁸C₁× (0.2)^1 × (0.8)^(18-1) + ¹⁸C₂× (0.2)^2 × (0.8)^(18-2) + ¹⁸C₃× (0.2)^3 × (0.8)^(18-3)

= (0.8)^(18) + 18× (0.2) × (0.8)^(17) + 153 × (0.04) × (0.8)^(16) + 1632× (0.008) × (0.8)^(15)

= 0.630

Plug in the values,

P(at least 4 defective)

= 1 - 0.630

= 0.370

Therefore, the expected items to be defective and probability that at least 4 items out of 18 are defective is equal to 3.6 and 0.370 or 37.0%.

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The radius of convergence of the series \(\sum\limits^{\infty}_{n=0}\frac{x^{n+4}}{4n!}\) is ∝

From the question, we have the following parameters that can be used in our computation:

\(\sum\limits^{\infty}_{n=0}\frac{x^{n+4}}{4n!}\)

Given that a series takes the form

\(\sum\limits_{n=0}^{\infty} a_nx^n\)

The radius of convergence is:

\(r = \lim_{n\to\infty} \left|\frac{a_n}{a_{n+1}}\right|.\)

Here, we have

\(\sum\limits^{\infty}_{n=0}\frac{x^{n+4}}{4n!}\)

Rewrite as

\(\sum\limits_{n=0}^{\infty} \frac{x^4}{4n!} \cdot x^n.\)

This means that

\(a_n = \frac{x^4}{4n!}\)

And, we have the ratio to be

\(r = \frac{a_n}{a_{n+1}}\)

This gives

\(r = \frac{\frac{x^4}{4n!}}{\frac{x^4}{4(n+1)!}}\)

So, we have

\(r = \frac{x^4(n+1)!}{x^4n!}\)

Evaluate

\(r = \frac{(n+1)!}{n!}\)

r  = n + 1

Take the limits to infinity

So, we have

\(\lim_{n\to\infty} \left|\frac{a_n}{a_{n+1}}\right| = \lim_{n\to\infty} |n + 1|.\)

Evaluate

r = ∝

Hence, the radius of convergence is ∝

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Complete question

Find the radius of convergence, r, of the series

\(\sum\limits^{\infty}_{n=0}\frac{x^{n+4}}{4n!}\)

Answer:

I hope it help..........

To determine whether the number of customers, which is expected to be 15 each day, follows a uniform distribution, a chi-square test for goodness of fit should be performed with a specified significance level (alpha).

The chi-square test for goodness of fit is used to determine if observed data follows an expected distribution. In this case, we want to test whether the number of customers each day, which is expected to be 15, follows a uniform distribution.

To perform the test, we need to collect data on the number of customers over a period of time and compare it to the expected uniform distribution. The observed frequencies for each category (e.g., the number of days with 0 customers, 1 customer, 2 customers, etc.) would be obtained.

Then, the chi-square test statistic can be calculated based on the observed and expected frequencies. The test statistic measures the discrepancy between the observed and expected distributions.

To interpret the test results, we compare the calculated chi-square value to the critical chi-square value at the chosen significance level (alpha). If the calculated chi-square value exceeds the critical value, we reject the null hypothesis and conclude that the number of customers does not follow a uniform distribution. Conversely, if the calculated chi-square value does not exceed the critical value, we fail to reject the null hypothesis, indicating that the number of customers can be considered to follow a uniform distribution.

Please note that the specific calculations and decision-making process require additional data and the use of statistical software or tables to obtain the critical chi-square value.

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Answer:

see explanation

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

(- 1, - 2 ) → (- 2, - 1 )

(1, 1 ) → (1, 1 )

(4, - 3 ) → (- 3, 4 )

The following is an assembly program that calculates the value of the given polynomial, assuming signed integers x and y are stored in register r2 and r3, respectively.

\(```.LIST.ALIGN 4    .GLOBAL _start_start:    PUSH {R4, R5, LR}\)
   \(MOV R4, R2        // R4 < - x    MOV R5, #2        // R5 < - 2\)\(MUL R4, R4, R4    // R4 < - x^2    MUL R4, R4, R5    // R4 < - 2x^2    MOV R5, #3        // R5 < - 3\)
  \(ADD R4, R4, R5, LSL #16    // R4 < - 2x^2 + 3x^2    MOV R5, #5        // R5 < - 5    MUL R5, R5, R2    // R5 < - 5x\)
  \(SUB R4, R4, R5, LSL #16    // R4 < - 2x^2 + 3x^2 - 5x    MOV R5, #11       // R5 < - 11    SUB R4, R4, R5, LSL #16    // R4 < - 2x^2 + 3x^2 - 5x - 11\)
  \(MOV R3, R4        // R3 < - y    POP {R4, R5, PC}.END```\)

Explanation: The polynomial is given as

\(`y = 2x^4 + 3x^2 - 5x - 11`.\)

To calculate this polynomial in assembly language, we need to perform the following steps:

Load the value of `x` into a register. We assume that `x` is stored in register `r2`.

Calculate \(`2x^2`\) and add \(`3x^2`\) to it. We first square the value of `x` by multiplying it with itself and then multiply it with `2`. We then add \(`3x^2`\) to this result. We store this result in register `r4`.

Calculate `5x` and subtract it from the result of step 2. We first multiply the value of `x` with `5` and then subtract it from the result of step 2. We store this result in register `r4`.

Subtract `11` from the result of step 3. We subtract `11` from the result of step 3 and store this result in register `r4`.

Load the value of `y` into a register. We assume that `y` is stored in register `r3`.

Return from the subroutine. We pop the registers from the stack and return from the subroutine.

The assembly program that is used to calculate the value of a given polynomial assuming signed integers x and y are stored in registers r2 and r3, respectively. The polynomial given is\(y = 2x4 + 3x² - 5x - 11\). In this assembly program, we load the value of x into a register, calculate 2x^2, add 3x^2 to it, subtract 5x from the result, and subtract 11 from the final result. The value of y is then stored in a register, and we return from the subroutine.

This assembly program is designed for 32-bit ARM architecture, and it can be run on any ARM processor. The program is written in ARM assembly language, which is a low-level programming language used to write programs that run on ARM processors. It is a complex language that requires a deep understanding of the processor architecture and instruction set.

In conclusion, the assembly program presented here can be used to calculate the value of a given polynomial using signed integers x and y stored in registers r2 and r3, respectively. This program can be adapted to calculate other polynomials or perform other arithmetic operations on ARM processors. It is a powerful tool for low-level programming and optimization, but it requires a significant amount of expertise to write and debug.

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Answer:

y = 6

may help you i think so