Please solve this problem... I will mark you brainliest

Answer:

\(\boxed{\textsf{ The factorised form is \textbf{(4x+1)(3x+1)}.}}\)

Step-by-step explanation:

A quadratic polynomial is given to us and we need to find its factorised form . The given quadratic polynomial is ,

\(\sf\implies p(x)= 12x^2+7x+1\)

And this equation is similar to the equation in ax² + bx + c form . So in order to factorise it .

Step 1: Multiply the coefficient of x² with the constant term .

Here the coefficient of x² is 12 and the constant term is 1 . So on multiplying them we get 12*1= 12 .

Step 2: Look out for the possible factors of the number .

Here the obtained number is 12 . So the possible factors of 12 is

Step3: Choose the factor whose sum is equal to the coefficient of the middle term .

Here we can see that the middle term is 7 . And the sum of 4 and 3 is equal to 7 . Hence here we will break 7x as 4x + 3x .

Step 4: After proper arrangements take out the common term and then factorise.

After suitable rearrangment we get ,

\(\sf\implies p(x)= 12x^2+4x+3x+1 \\\\\sf\implies p(x)= 4x(3x+1)+1(3x+1) \\\\\implies\boxed{\red{\sf p(x)= (4x+1)(3x+1)}}\)

We can infer and logically deduce that the arc intersected by these chords are not congruent.

A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

In Geometry, a circle is generally considered to be a conic section which is formed by a plane intersecting a double-napped cone that is perpendicular to a fixed point (central axis) because it forms an angle of 90° with the central axis.

In Geometry, an arc can be defined as a trajectory that is generally formed when the distance from a given point has a fixed numerical value.

Let the radii of the two (2) different circles with center O and O' be r₁ and r₂ respectively. Also, two (2) isosceles triangles AOB and COD would be formed and as such we have:

AO = OB = r₁.

CO = O'D = r₂.

By critically observing the diagram (see attachment) of these circles, we can logically deduce that the arc intersected by chord AB is greater than the arc intersected by the chord CD.

This ultimately implies that, the arcs intersected by these chords are not congruent.

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Complete Question:

Two circles with different radii have chords AB and CD, such that AB is congruent to CD. Are the arcs intersected by these chords also congruent? Explain.

Hint: It would be helpful to draw two circles and label them according to the given information, then evaluate possible arc measures.

Consider the type of triangle that may be drawn by connecting the endpoints of a chord to the center of a circle. Compare the triangles made by two circles with different radii.

The proportion of students who can roll their tongues will be estimated and the margin of error for a 95 percent confidence interval for the true proportion of tongue rollers among students will be determined. There were 317 tongue rollers out of a sample of 400 students.

      As a result, the sample proportion is 317/400 = 0.7925.

      We'll compute the margin of error next. The margin of error (E) for a 95 percent confidence interval is:

                E = zα/2 * sqrt[p(1 - p) / n]

                              where zα/2 is the z-score that corresponds to the level of confidence α/2, p is the sample proportion, and n is the sample size.

               E = 1.96 * sqrt[0.7925 * (1 - 0.7925) / 400]E

                  = 1.96 * sqrt[0.7925 * 0.2075 / 400]E

                  = 1.96 * sqrt(0.00040875)E

                  = 1.96 * 0.0202E

                  = 0.0395

    The margin of error is approximately 0.04 or 4 percent. Hence, the correct option is 0.04.

The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to 0.04

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Answer:

208

Step-by-step explanation:

the formula is:

2*(width*lenght+height*lenght+height*width)

2*(6*8+4*8+4*6)

208

Answer:

\( \: \)

Step-by-step explanation:

In the given figure, it is given a net of cuboid where, the length is 8m, the breadth is 6m and the height is 4m and we have to find the surface area of the cuboid.

So, the formula for finding the surface area is ;

\(\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: Surface\: area_{(cuboid)}=2(lb + bh + lh )}}}}}} \: \: \bigstar \\ \\\)

Now, we'll substitute the values in the formula :

\(\\{ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(8.6 + 6.4 + 8.4 }}}}}}) \: \: \\ \\\)

\({ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(48 + 24 + 32 }}}}}}) \: \: \\ \\\)

\({ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(104 }}}}}}) \: \: \\ \\\)

\({ \longrightarrow \qquad{ { \pmb{ \frak{ { \: Surface\: area_{(cuboid)}=208 }}}}}}\: \: \\ \\\)

Therefore,

The gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:

\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)

To find the gradient of the function \(\( f(x, y) = e^{3x} \sin(4y) \)\) at the point \(\((-1, -3)\)\), we need to compute the partial derivatives with respect to \(\(x\) and \(y\)\) and evaluate them at that point.

The gradient of a function is given by:

\(\[\nabla f(x, y) = \left(\frac{{\partial f}}{{\partial x}}, \frac{{\partial f}}{{\partial y}}\right)\]\)

Let's calculate the partial derivatives:

\(\[\frac{{\partial f}}{{\partial x}} = \frac{{\partial}}{{\partial x}}\left(e^{3x} \sin(4y)\right) = 3e^{3x} \sin(4y)\]\)

\(\[\frac{{\partial f}}{{\partial y}} = \frac{{\partial}}{{\partial y}}\left(e^{3x} \sin(4y)\right) = 4e^{3x} \cos(4y)\]\)

Now, we can evaluate these derivatives at the point \(\((-1, -3)\):\)

\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{3(-1)} \sin(4(-3)) = 3e^{-3} \sin(-12)\]\)

\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{3(-1)} \cos(4(-3)) = 4e^{-3} \cos(-12)\]\)

Simplifying further:

\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{-3} \sin(-12) = -3e^{-3} \sin(12)\]\)

\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{-3} \cos(-12) = 4e^{-3} \cos(12)\]\)

Therefore, the gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:

\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)

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Answer:

The specific values mentioned in the content (e.g., λ = 1, μ = 0.5) are needed to perform the calculations accurately.

Step-by-step explanation:

To find the pdf (probability density function) of Z, let's start by understanding the variables involved:

X and Y are independent random variables with exponential pdfs (probability density functions). The pdf for X is given by

fX(x) =\(\lambda e^_(-\lambda x)\),

where λ = 1 for X.

Similarly, the pdf for Y is

fY(y) = \(\mu e^_(-\mu y)\),

where μ = 0.5 for Y.

(a) Finding the pdf of Z = X + Y:

To find the pdf of Z, we need to determine the distribution of the sum of two random variables. Since X and Y are independent, the sum Z = X + Y will follow the convolution of their individual pdfs.

Let's denote the pdf of Z as fZ(z). To find fZ(z), we convolve fX(x) and fY(y) using the convolution integral:

fZ(z) = ∫[fX(x) * fY(z - x)] dx

Plugging in the pdfs of X and Y, we have:

fZ(z) = \(\int[e^{(-\lambda x)} * \mu e^{(-\mu(z - x))}] dx\)

Simplifying the expression and integrating, we obtain the pdf of Z.

(b) Finding the pdf of Z = |X - Y|:

To find the pdf of Z, we need to determine the distribution of the absolute difference between X and Y. Since X and Y are independent, we can consider the cases where X > Y and Y > X separately.

For X > Y:

Z = X - Y, so the pdf can be obtained by finding the distribution of X - Y and taking its absolute value.

For Y > X:

Z = Y - X, so the pdf can be obtained by finding the distribution of Y - X and taking its absolute value.

In both cases, we need to perform the convolution of the individual pdfs, similar to part (a), but with a slight modification for taking the absolute value.

By evaluating the convolutions and considering both cases (X > Y and Y > X), we can derive the pdf of Z - |X - Y|.

The specific values mentioned in the content (e.g., λ = 1, μ = 0.5) are needed to perform the calculations accurately.

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The formula Arya stark will use to find the 95% confidence interval is normal approximation of the distribution.

For the given question, the data is-

The formula for finding the 95% confidence interval is normal approximation of the distribution.

z = (x - μ)/s

Where, s = σ/√n

The corresponding value of z for 96% is taken from the z score table.

Thus,  formula Arya stark will use to find the 95% confidence interval is normal approximation of the distribution.

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The answer of the equation is:

500000 x 0.5% = 2500

Step 1: The output value is 500000.

Step 2: Represent unknown value as x .

Step 3: 500000 = 100 .

Step 4: Likewise $x=0.5\%$.

Step 5: Two simple equations:

500000 = 100%.

⇒ x = 0.5%.

Step 6: Divide Equation 1 by Equation 2 and notice that both right sides of Equation have the same units (%).

500000 = 100%(1).

Step 7: Round-trip both sides again

    500000 / x = 100%/0.5%

⇒ x / 500000 = 0.5/100

⇒ x = 2500

Therefore, 0.5% of 500000 is 2500.

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The age of Barbra is 22 years.

The algebraic method for solving simultaneous linear equations is the substitution method. A quantity of one variable through one expression is replaced in the second equation, as the name implies.

Now, according to the question.

Let 'a' be the age of Alice.

Let 'b' be the age of Barbra

Let 'c' be the age of Carol.

The sum of age of all three sisters is 68 years.

Thus,  a + b + c = 68

Now, as Alice is three years younger than Barbra.

a = b - 3

and, Barbra is 5 years younger than Carol.

b = c - 5

c = b + 5

By substitution of values of a and c in total age.

(b - 3) + b + (b + 5) = 68

3b - 3 + 5 = 68

On solving the expression.

b = 22

Therefore, the age of Barbra is 22 years.

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The value of the expression 200% of of $25,000 is $50,000

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

200% of $25,000

The above expression is a percentage expression and mathematically, can be expressed as

Value = 200% of $25,000

Express "of" as products

So, we have

Value = 200% of $25,000

Evaluate the products in the expression

So, we have the following

Value = $50,000

Hence, the solution of the expression 200% of of $25,000 is $50,000

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Answer:

D

Step-by-step explanation:

Answer:

C or D

Step-by-step explanation:

I think I am not sure

The total amount you earn minus payroll deductions is your taxable income

What is taxable income?

Taxable income means the total amount an employee earns for work done minus payroll deductions, bearing in mind that payroll deductions means those amounts out of the gross income which are not taxable or serve as tax-free benefits for the employee

Gross income is the total earned before payroll deductions, where net income applies to a business not an employee

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Here are the major balance sheet classifications and their proper balance sheet classification.Current assets (CA)Long-term investments (LTI)Property, plant, and equipment (PPE) Intangible assets (IA) Stockholders’ equity (SE) Current liabilities (CL) Long-term liabilities (LTL).

Matching of balance sheet items to its proper balance sheet classification: Salaries and wages payable - Current Liabilities (CL) Equipment - Property, plant, and equipment (PPE) Service revenue - Current assets (CA)Depreciation expense - NA Interest payable - Current liabilities (CL) .

Goodwill - Intangible assets (IA)Debt investments (short-term) - Current assets (CA)Retained earnings - Stockholders’ equity (SE)Mortgage payable (due in 3 years) - Long-term liabilities (LTL)Unearned service revenue - Current liabilities (CL)Investment in real estate - Long-term investments (LTI)Accumulated depreciation—equipment - Property, plant, and equipment (PPE)

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Answer:

52.

Step-by-step explanation:

Answer: 52

Step-by-step explanation:

Answer:

0.0031

Step-by-step explanation:

31/10000=0.0031

you divided by 10000 and it has four zeroes so you should have four numbers after 0

Answer:

.0031

Step-by-step explanation:

The 10,000ths place is the fourth place to the right of the decimal. This is where you place the 1 in 31, as it is out of 10,000, and the 3 goes to the left of it, so it is .0031.

Step-by-step explanation:

3x4=12

÷2=6

First triangle =6

3x4=12

÷2=6

2nd triangle =6

6+6= 12

The answer should be d(12 Square feet)

The error made by the student is in simplifying the expression inside the square root.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The student made an error in simplifying the expression inside the square root.

The expression should be simplified as follows:

25 + 4(2)(-12) = 25 - 96 = -71

So the correct expression inside the square root is -71, not 121.

Therefore, the correct solution using the Quadratic Formula is:

x = (-(-5) ± √((-5)² - 4(2)(-12)))/(2(2))

x = (5 ± √(25 + 96))/4

x = (5 ± √121)/4

x = (5 ± 11)/4

Hence, the solutions are x = -3 and x = 4/2, which simplifies to x = 2.

Therefore, the error made by the student is in simplifying the expression inside the square root.

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Answer:

B. Intersection of the lines drawn from each vertex of the triangle and perpendicular to its opposite side

Step-by-step explanation:

The orthocenter of a triangle is the point of concurrency of the three altitudes or extensions of the the altitudes of a triangle, each of which are perpendicular lines drawn from a vertex of the triangle to the side opposite the vertex

The type of concurrent construction needed to find the orthocenter of a triangle is the point of intersection of the perpendicular lines drawn from each vertex of the triangle, to the side opposite the vertex

Therefore, the correct option is option B. intersection of the lines drawn from each vertex of the triangle and perpendicular to its opposite side.

Answer:

Choice 3 and 5

Step-by-step explanation:

Answer: A,B,E

Step-by-step explanation:

Just trust me

1. The function for this problem is given as follows: f(x) = x - 3.

2. The numeric value of the function at x = 2 is of f(2) = -1.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

We define the function in this problem as follows:

f(x) = x - 3.

The numeric value at x = 2 is found replacing the lone instance of 2 by 2, hence:

f(2) = 2 - 3

f(2) = -1.

We attribute the function in this problem as f(x) = x - 3.

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The conclusion that is correct in a two-tailed test at α = .05 is There appears to be no difference in the mean occupancy rates.

From the given values:

Thus, the P-value = 0.1791

Interpret results. Since the P-value (0.1791) is greater than the significance level (0.05), we failed to reject the null hypothesis.

From the above test, we do not have sufficient evidence in favor of the claim that there is a difference in the mean occupancy rates.

Thus, option A is correct.

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The sum of the first three terms in the series is -557.921 and a bound for the error is approximately 865.474.

What is series?

In mathematics, a series is the sum of the terms of a sequence. It is represented by the sigma notation (∑), which indicates that a sequence of terms is being added together.

To calculate the sum of the series and find the bounds for the error, let's break down the problem step by step.

The series can be represented as:

\(\sum_{n=1}^{\infty} [(-1)^n * 400*n^{0.6}]\)

To find the sum of the first three terms, S3, we need to calculate the values for n = 1, 2, and 3 and then sum them up.

For n = 1:

\((-1)^1 * 400 * 1^{0.6\) = -400

For n = 2:

\((-1)^2 * 400 * 2^{0.6\) = 564.189...

For n = 3:

\((-1)^3 * 400 * 3^{0.6\) = -721.110...

Now, let's calculate the sum of the first three terms, S3:

S3 = -400 + 564.189 + (-721.110) = -557.921

The sum of the first three terms, S3, is approximately -557.921.

To find a bound for the error, we can use the Alternating Series Estimation Theorem. The theorem states that the error in approximating an alternating series is less than or equal to the absolute value of the next term.

In this case, the next term of the series would be for n = 4:

\((-1)^4 * 400 * 4^{0.6\) = 865.474...

The bound for the error is given by the absolute value of this term:

|Next Term| = |865.474...| ≈ 865.474

Therefore, a bound for the error is approximately 865.474.

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The number of it take if a customer buys 5 coffees is 7 minutes

What is the equation for the number of minutes(time) it takes to make coffee?

The number of minutes it takes one to make coffee at Starbucks is given below where t is the unknown number of minutes and the n is the number of coffees bought

t = 2n − 3

n=5= number of coffees

t=(2*5)-3

t=7

In essence, it takes seven minutes to purchase 5 coffees at the Starbucks

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Answer:

x=-7

Step-by-step explanation:

-2(x+3)=8

-2x-6=8

-2x=8+6

-2x=14 -2x/-2=14/-2

x= -7

if you want to be sure do the following

-2(-7+3)=8

-2(-4)=8

8=8

Therefore, based on the given information, the estimated age of the tomb is approximately 3,970 years.

To estimate the age of the tomb based on the radioactive carbon-14 (C-14) content in the cypress beam, we can use the decay equation:

A = A₀ * e*(kt)

Where:

A = Final amount of radioactive substance (55% of the original C-14 content)

A₀ = Initial amount of radioactive substance (100% of the original C-14 content)

k = Decay constant (ln(2) / half-life of C-14)

t = Time (age of the tomb)

Given that the half-life of C-14 is approximately 5600 years, we can calculate the decay constant:

k = ln(2) / 5600 years

Now we can plug in the values:

0.55A₀ = A₀ * e*((ln(2) / 5600 years) * t)

Dividing both sides by A₀:

0.55 = e*((ln(2) / 5600 years) * t)

Taking the natural logarithm of both sides:

ln(0.55) = (ln(2) / 5600 years) * t

Now we can solve for t, the age of the tomb:

t = (ln(0.55) * 5600 years) / ln(2)

Evaluating the expression:

t ≈ 3,970 years

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Answer:

£34.05

Step-by-step explanation:

36/4=9

36/12=3

36/6=6

9x0.75=6.75

3x0.42=1.26

6x1.10=6.6

36x0.54=18.44

6.75+1.26+6.6+19.44= £34.05

The formula in getting possible zeros in rational root theorem is given as ± p / q.

According to rational root theorem if a polynomial expression which is written in descending order of the exponents and has integer coefficients, then any rational zero must be of the form ± p / q

Here, p is a factor of the constant term or the numerator and q is a factor of the leading coefficient or the denominator.

As the name implies, the rational root theorem is used to find the rational solutions to a polynomial equation . Polynomial roots or zeros are the solutions we get when we solve a  polynomial equation. A polynomial does not need required rational zeros only.

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Answer:

The area of the unpainted region on the four inch board = 160·√3 in.²

Step-by-step explanation:

Here we have that the boards are crossing each other on their flat sides Therefore, when the boards are separated, the area of the unpainted region is the area of a parallelogram

The dimensions of the formed parallelogram are;

Interior angles = 60° and 120° (adjacent angles of a parallelogram)

Height, h of parallelogram formed = 4 inches

From the angle of crossing of the parallelogram, we have;

Angle between the width or perpendicular cross section of the 6 inches board and the angle of crossing of the two boards = 90° - 60° = 30°

Therefore, length of base, b of the parallelogram formed by the unpainted region is given as follows;

\(b = \frac{60}{cos(30)} = 40\cdot \sqrt{3} \ inches\)

Therefore, the area of the parallelogram = b × h = 4 × 40·√3 = 160·√3 in.²

Hence, the area of the unpainted region on the four inch board = 160·√3 in.².