A side of the triangle below has been extended to form an exterior angle of 147°. Find
the value of x

Answer:

y= -1/2x + 4

Step-by-step explanation:

Answer:

2x2+108x+75 =187 is answer

Answer:

1/12 and 1/3

Step-by-step explanation:

There are 2 choices for flipping a coin (heads or tails) and 6 choices for rolling the die (1 - 6) so the total possible outcomes are 2 * 6 = 12. Of these, there's only one possibility where we get a tail and a 5 so the answer to b is 1/12. For c, there's only one head but there are 4 numbers less than 5 (1 - 4) so the total number of outcomes that satisfy our condition is 1 * 4 = 4 which makes the probability 4/12 = 1/3.

Answer:

Step-by-step explanation:

The probable results are:

Head + 1/2/3/4/5/6

Tail + 1/2/3/4/5/6.

B. This gives 12 results and tail + 5 is one of them, so the probability of getting that is 1/12.

C. A result with a head and a number less than 5 is available 4 times, making the fraction 4/12 or 3/4

Hope this helps

The value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.

According to the question,

We have the following expressions:

f(x) = -5x+9/2

Now, we will find the all the values of f(x) by replacing x with the given digits:

f(4) = -5*4+4.5

f(4) = -20+4.5

f(4) = -15.5

The value of f(1/4):

f(1/4) = -5/4+4.5

f(1/4) = -1.25+4.5

f(1/4) = 1.375

The value of x when f(x) = 2:

-5x+4.5 = 2

-5x = 2-4.5

-5x = -2.5

x = 2.5/5

x = 0.5

g(x) = 1.5\(x^{2}\)-8

Now, we will find all the values of g(x) by replacing x with the given digits.

The value of g(-2):

g(-2) = 1.5(-2)(-2)-8

g(-2) = 6-8

g(-2) = -2

The value of g(2.5):

g(2.5) = 1.5*2.5*2.5-8

g(2.5) = 9.375-8

g(2.5) = 1.375

The value of x when g(x) = 16:

1.5\(x^{2}\)-8 = 16

1.5\(x^{2}\) = 16+8

1.5\(x^{2}\) = 24

\(x^{2}\) = 24/1.5

\(x^{2}\) = 16

x = +4 and -4

Hence, the value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.

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When we describe relationships between variables, a correlation nearer to 1.00 (plus or minus) indicates the relationship between variables is strong.

The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

When correlation is known, predictions can be made using it. Knowing a score on one measure helps us predict another that is closely related to it more accurately. The forecast will be more accurate the stronger the correlation between/among the variables.

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The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.

Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:

1/4(4 + x) = 4/3

4 * 1/4(4 + x) = 4 * 4/3

Simplifying:

4 + x = 16/3

Subtract 4 from both sides of the equation:

4 + x - 4 = 16/3 - 4

Simplifying:

x = 16/3 - 12/3

x = 4/3

A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.

Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.

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Answer:

\(x=2\frac{1}{12}\)

Step-by-step explanation:

1. The first step is to get 14.8 on the other side. It is a positive number which means that you have to subtract 14.8 on both sides:

\(32.3=14.8+8.4x\)

-14.8   -14.8

\(17.5 = 8.4x\)

2. The second step is to get x by itself. Right now it is being multiplied by x so to get it by itself you have to do the opposite of multiplication which is division, so you will divide 8.4 by both sides:

\(\frac{17.5}{8.4} = \frac{8.4x}{8.4}\)

\(x=2\frac{1}{12}\)

Answer:

x=2.083333333

Step-by-step explanation:

Hope this helps!

Brainliest pls

Have a great day!

Answer: 8

Step-by-step explanation:

\(15 + 3(\frac{6}{2} )-4^2\)

Using order of operations, solve parenthesis first

\(15 + 3(3 )-4^2\\15 + 9-4^2\)

Next, solve exponents. Note that only the '4' is getting raised to the '2' power, not '-2'

\(15 + 9-(4^2)\\15 + 9-16\)

Simplify

\(15+9-16\\=8\)

Answer:

just apply d formular 4 each

lykfor the mean=£fx/£f...which x is the inches and f is the frequency...multiply both from 63 to 75 inches e.g 63×2=126, 65×1=65...then add the scores together.... then divide it by the summation of the frequency which is 2+1+4+3+1+2+2+2+1+3+2+2=23. note am applying this method based on the formular

for median=£f/2 since it's odd number add +1

=£f+1/2

=23+1/2

=24/2

=12 .the 12 would fall on 69 inches using the cumulative method

mode is 66 since it's the number with the highest frequency

Answer: A.

Step-by-step explanation:

yeet

Answer:

A.

Step-by-step explanation:

Because if you multiply out the top of the fraction to simplify it, it will equal zero. And zero divided by any number is equal to zero because no number fits into zero. So A. would be the best answer since you are multiplying an expression by zero on the top, and you can't get any number other then zero for the answer of the fraction. And 0 + 9.4 = 9.4.

Answer: the second sequence.

25- 20= 20-15=15-10=10-5.

From this we can see that the common difference is 5

Step-by-step explanation:

Step-by-step explanation:

The two numbers having a sum of 19 and difference of 9 is

14 and 5

14 + 5 = 19

14 - 5 = 9

Hope it will help :)

Answer:

14 and 5

Step-by-step explanation:

-#--#--2-#--$--#6*363282873737282

Answer:

a times 48

Step-by-step explanation:

a times 2 times p(6) times r(4)

2 times 6 is 12

multiply 12 by 4 to get 48

that is how you get a times 48

Answer:

1. correct (conversion = x1000)

2. correct (conversion = [divided by] 1000)

3. wrong (conversion should be x100)

4. wrong (conversion should be x1000)

5. correct (conversion = x10)

Answer:

option 1, 2 and 5 are correct

Step-by-step explanation:

1 Km = 1000 m

1) 1.25 km = 1.25 * 1000 = 1250 m

2) 0.345 km = 0.345 *1000 = 345 m

5)   1.7m cm = 1.7 * 10 = 17 mm

Answer:

x= 4.3125

Step-by-step explanation:

Answer:

x=4+7i and x=4-7i

Step-by-step explanation:

Rewrite the given quadratic equation by completing the square.

x^2-8x=-65

x^2-8x+16=-65+16

x^2-8x+16=-49

(x-4)^2=-49

Now, solve the equation by applying the square root property and isolating x.

(x-4)^2=-49

√(x-4)^2 = √-49

x-4=+7i

x=4+7i

So, the solutions to the given quadratic equation are x+4+7i and x=4-7i.

After 5 years of compounding interest at a rate of 4% per year, your balance will be approximately $349.65.

To calculate the balance after 5 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount (balance)

P = the principal amount (initial investment)

r = the annual interest rate (expressed as a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, the principal amount (P) is $300, the annual interest rate (r) is 4% (or 0.04 as a decimal), and the time period (t) is 5 years. The interest is compounded annually, so the number of times interest is compounded per year (n) is 1.

Plugging these values into the formula, we have:

A = 300(1 + 0.04/1)^(1*5)

A = 300(1 + 0.04)^5

A = 300(1.04)^5

A ≈ 349.65

Therefore, after 5 years of compounding interest at a rate of 4% per year, your balance would be approximately $349.65.

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(a) Using Simpson's rule, the approximation of the integral is obtained, and the absolute error can be calculated.

(b) To achieve a more accurate approximation than Simpson's rule, the step size h for the composite trapezoidal rule needs to be smaller than approximately 3.47.

a) To approximate the integral I = ∫²₀ x⁵/² dx using Simpson's rule, we divide the interval [0, 2] into subintervals and use a quadratic polynomial to approximate the function within each subinterval. The Simpson's rule formula is given by:

I ≈ (h/3) [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + 2f(x₄) + ... + 4f(xₙ₋₁) + f(xₙ)]

where h is the step size and n is the number of subintervals.

In this case, let's choose a step size of h = 1, which gives us two subintervals: [0, 1] and [1, 2]. We can evaluate the function at the endpoints and the midpoint of each subinterval:

f(0) = (0^5/2) = 0

f(1) = (1^5/2) = 1

f(2) = (2^5/2) = 8

Now we can apply the Simpson's rule formula:

I ≈ (1/3) [0 + 4(1) + 2(0) + 4(8) + 2(0)]

Simplifying this expression gives us:

I ≈ (1/3) [0 + 4 + 0 + 32 + 0] = (1/3) * 36 = 12

So, the approximate value of the integral I using Simpson's rule is 12.

To calculate the absolute error of this approximation, we need the exact value of the integral. Integrating the function x^5/2 over the interval [0, 2], we have:

∫²₀ x⁵/² dx = [(2^7/2) / 7] - [(0^7/2) / 7] = (128/7) - 0 = 128/7 ≈ 18.29

The absolute error is the absolute difference between the exact value and the approximation:

|18.29 - 12| ≈ 6.29

Therefore, the absolute error of the Simpson's rule approximation is approximately 6.29.

b) To determine the step size h that would ensure a more accurate approximation than Simpson's rule, we can analyze the error formula of the composite trapezoidal rule and compare it with the error formula of Simpson's rule.

The error formula for the composite trapezoidal rule is given by:

Rₙᶜᵀ[f] = f''(ξ)/12 * h² * (b - a)

where f''(ξ) represents the second derivative of the function f(x) evaluated at some point ξ in the interval [a, b].

In order to have a more accurate approximation than Simpson's rule, we need the error term of the composite trapezoidal rule to be smaller than the absolute error we obtained from Simpson's rule.

To determine the step size h, we need to find the maximum value of the second derivative of the function f(x) on the interval [0, 2]. Let's compute the second derivative:

f''(x) = (5/2) * (5/2 - 1) * x^(5/2 - 2) = 25/4 * x^(1/2)

The maximum value of f''(x) on the interval [0, 2] occurs at x = 2. Therefore, f''(ξ) ≤ 25/4 for all ξ ∈ [0, 2].

Substituting this value into the error formula of the composite trapezoidal rule:

Rₙᶜᵀ[f] = (25/4) / 12 * h² * (2 - 0)

         = (25/48) * h²

We want this error term to be smaller than the absolute error obtained from Simpson's rule, which was approximately 6.29. Therefore, we can set up the inequality:

(25/48) * h² < 6.29

Solving for h²:

h² < (6.29 * 48) / 25

h² < 12.0448

Taking the square root of both sides:

h < √12.0448

h < 3.47

Therefore, to ensure a more accurate approximation than Simpson's rule, we need to choose a step size h smaller than approximately 3.47.

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Answer:

120 history textbooks

360 physics textbooks

Step-by-step explanation:

Physics textbooks = 3 times the amount of history textbooks

History textbooks = x

Physics textbooks = 3x

480 = x + 3x

= 4x

480/4 = x

x = 120

120 history books sold

480-120 = 360

360 physics textbooks sold

btw sorry if I didn't give enough working or help you understand it I'm not great at this kind of thing

a) 4x + 2x = 6x - 4

= 6x = 6x - 4

cannot be solved further.

b) 3(2x + 4) = 2(2x - 4)

= 6x + 12 = 4x - 4

(bring the numbers and variables on one side)

= 6x + 4x = 12 - 4

10x = 8

x = 8/10 = 4/5

can be solved.

c) 5(x - 3) = 5x - 3

= 5x - 15 = 5x - 3

= (bring the variables and numbers on one side)

5x + 5x = -15 - 3

= 10x = -18

x = -18/10 = 9/5

can be solved

d) 2x = 2x + 4

= 2x + 2x = 4

= 4x = 4

x = 4/4 OR 1.

Answer:

x=6

Step-by-step explanation:

To solve, we'll reverse the terms in order to find x.

Reverse Terms:

-7 + 13 = x

Solve:

x=6.

Answer:

x=-7+13

x=6

Explanation

-13 after the equal sign becomes positive.you take -13 and put it after the equal sign,then add

  Among the given options (A, B, C, D), the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

In a population regression model, we are interested in modeling the relationship between a dependent variable (Y) and one or more independent variables (X1, X2, etc.). The model equation consists of the regression coefficients (β0, β1, β2, etc.) that represent the effect of each independent variable on the dependent variable, and the error term (e) that captures the unexplained variation in the data.
Among the given options, only option D includes all the necessary components of a population regression model with two independent variables (k = 2). It includes the dependent variable Y, the regression coefficients β0, β1, and β2 for the independent variables X1 and X2, respectively, and the error term e.
Options A, B, and C are incorrect because they either omit the error term or have an incomplete equation. The error term is crucial in accounting for the unobserved factors and random variation in the relationship between the variables.
Therefore, the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

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Answer:

c=6

Step-by-step explanation:

6c±7=13±7c

6c-7c=-1c

7-13=-6

-1c=-6

-1c=-6÷-1c   to get the value of

Answer: $87

Step-by-step explanation:

Answer: x = 34

Step-by-step explanation:

2x+3+3x+7=180

5x+10=180

5x=170

x = 34

$10

Because 20% of 50 is 10

Answer:  

42 dollars

Step-by-step explanation:

Answer:
20% of 30 is 6 which would leave 24 dollars left to pay

Step-by-step explanation:

30 x 0.2= 6

30-6=24

Answer:

b 2

Step-by-step explanation:

x is an integer that is greater than 3 and less than or equal to 6.

x can be 4, 5, 6.

Answer: b 2

According to the NIOSH guidelines, a lifting index (LI) value below 1 is considered acceptable, indicating a low risk of developing work-related musculoskeletal disorders.

In the given scenario, the LI values for the two lifts are calculated as follows:

For the first lift:

LI = 20/12.52 = 1.60

For the second lift:

LI = 20/29.56 = 0.68

Based on these calculations, the second lift with an LI value of 0.68 is acceptable according to the NIOSH guidelines since it is below the threshold of 1.

To reduce the LI value below 1, several changes can be made to the layout and lifting procedure:

Reduce the weight of the castings: If it is possible to use lighter castings, it would decrease the load weight, resulting in a lower LI value.

Modify the work area height: Adjusting the work area height to a lower level, closer to the inspector's body, would decrease the vertical distance of the lift and consequently lower the LI value.

Optimize the horizontal distance: If feasible, reposition the work area closer to the inspector's body to reduce the horizontal distance of the lift, which would contribute to a lower LI value.

By implementing these changes, the new LI values can be calculated using the provided formulas to ensure compliance with the company policy of maintaining an LI value below 1.

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The given series \(\sigma_n=1^\infty 5/n^3\) is convergent.

The series given is:

Σₙ= \(1^\infty\) 5/n³

The nth partial sum of this series is given by:

\(S_n = \sigma_k=1^n 5/k^3\)

To calculate the first eight terms of the sequence of partial sums, we substitute n = 1, 2, 3, ..., 8 in the expression for Sₙ:

Rounding each partial sum to four decimal places, we get:

Based on these partial sums, it appears that the series is convergent. As we compute more and more terms of the sequence of partial sums, we observe that the sums increase, but at a decreasing rate, which suggests convergence.

To show that the series is convergent, we need to show that the sequence of partial sums approaches a finite limit as n approaches infinity.

We can use the Integral Test to show that the series converges. According to the Integral Test, if the series \(\sigma_n=1^\infty a_n\)  is a series of non-negative terms and the integral from 1 to infinity of a continuous, positive, decreasing function f(x) is finite, then the series converges.

In this case, we can use f(x) = 5/x³ as the function and integrate from 1 to infinity:

Integral from 1 to infinity of 5/x³ dx = [5/(-2x²)] from 1 to infinity

= \(-5/2 \lim (x- > \infty)[1/x^2 - 1/1]\)

= 5/2

Since the integral of f(x) is finite, the series \(\sigma_n=1^\infty 5/n^3\) converges by the Integral Test.

Therefore, the given series is convergent, as observed from the partial sums, and the sum of the series can be found by taking the limit of the sequence of partial sums as n approaches infinity.

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To find the sum of the polynomials (-x^2 + 9) and (-3x^2 - 11x + 4), we need to add the corresponding terms together:

(-x^2 + 9) + (-3x^2 - 11x + 4)

Combining like terms, we have:

(-x^2 - 3x^2) + (9 - 11x) + 4

This simplifies to:

-4x^2 - 11x + 13

Therefore, the sum of the polynomials (-x^2 + 9) and (-3x^2 - 11x + 4) is -4x^2 - 11x + 13.

If we consider the additional polynomials (-4x^2 - 2x + 4) and (2x^2 + 20x + 4), we can add them to the previous sum:

(-4x^2 - 11x + 13) + (-4x^2 - 2x + 4) + (2x^2 + 20x + 4)

Combining like terms again, we get:

(-4x^2 - 4x^2 + 2x^2) + (-11x - 2x + 20x) + (13 + 4 + 4)

This simplifies to:

-6x^2 + 7x + 21

Therefore, the sum of the polynomials (-x^2 + 9), (-3x^2 - 11x + 4), (-4x^2 - 2x + 4), and (2x^2 + 20x + 4) is -6x^2 + 7x + 21.

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