Find the slope of the line through the points (7,8) and (-13, -13).

The value of the sum of the arithmetic sequence from a₃ to a₆ is 38

An arithmetic sequence is a sequence in which the difference between two consecutive terms is a constant.

The first term of the sequence is 20, the common difference is 17 - 20 = 14 - 17 = 11 - 14 = 8 - 11 = 5 - 8 = 2 - 5 = -3

The sum from n = 3 to n = 6 of aₙ is found as follows;

The sequence is an arithmetic progression of the form aₙ = a + (n - 1)·d

Where;

aₙ is the value of the nth term

a = The first term

d = The common difference

From the sequence, we have;

a = 20, d = -3, from which we have;

aₙ = 20 + (n - 1) × (-3) = 20 - 3·(n - 1)

aₙ = 20 - 3·(n - 1)

From which we have;

a₃ = 20 - 3×(3 - 1) = 14

a₄ = 20 - 3×(4 - 1) = 11

a₅ = 20 - 3×(5 - 1) = 8

a₆ = 20 - 3×(6 - 1) = 5

a₃ + a₄ + a₅ + a₆ = 5 + 8 + 11 + 14 = 38

Learn more about arithmetic sequence or progression here:

https://brainly.com/question/6561461

#SPJ1

(a) The mean free path (mfp) of 0.0253eV neutrons in Zr can be calculated using the formula mfp = 1/(σ * N), where σ is the neutron cross-section and N is the number density of Zr atoms.

(b) To estimate the probability of interaction as the neutron goes through a 2-mm thick Zr wall, we can use the exponential attenuation law. The probability can be calculated using the formula P = 1 - exp(-μx), where μ is the macroscopic cross-section and x is the thickness of the material.

Given the information about Zr, including its atomic mass (A), density (p), and atomic number (Z), we can calculate the mfp.

(a) The mean free path (mfp) of 0.0253eV neutrons in Zr can be calculated using the formula:

mfp = 1/(σ * N)

To calculate the mfp, we need the neutron cross-section (σ) and the number density of Zr atoms (N).

The neutron cross-section depends on the specific energy of the neutrons and can be obtained from experimental data or theoretical calculations. Once we have the neutron cross-section, we can determine the mfp using the given values for Zr.

(b) To estimate the probability that a neutron will interact as it goes through a 2-mm thick Zr wall, we can use the exponential attenuation law. The probability of interaction (P) can be calculated using the formula:

P = 1 - exp(-μx)

In this formula, μ is the macroscopic cross-section and x is the thickness of the material. The macroscopic cross-section is related to the neutron cross-section and the number density of Zr atoms. By substituting the appropriate values, including the given thickness of the Zr wall, we can calculate the probability of interaction.

(c) The probability that the neutron will be absorbed can be estimated using the same exponential attenuation law. The probability of absorption is given by:

P_absorption = exp(-μx)

By substituting the values for the macroscopic cross-section (μ) and the thickness of the Zr wall (x), we can calculate the probability of absorption.

Please note that the actual values for the neutron cross-section, macroscopic cross-section, and number density of Zr atoms need to be determined from appropriate sources or experiments to obtain precise calculations for parts (a), (b), and (c).

To learn more about probability visit:

brainly.com/question/31828911

#SPJ11

Piecewise Function of the given question is

\(g(t)=72-3t\), 0≤t≤24;

\(g(t)=0\), 24≤t≤46;

\(g(t)=2(t-36)\), 36≤t≤60.

A function with many parts of curves in its graph is said to be piecewise. It implies that based on the value of the input, it has many definitions. In other words, a piecewise function responds differently to various inputs.

A piecewise function, or f(x), is a function with various definitions at various intervals of x. A piecewise function's graph is divided into sections that each correspond to one of its definitions. A very good illustration of a piecewise function is the absolute value function. Let's examine the origin of the name. We are aware that the definition of an absolute value function is:

\(f(x)=x,\) x≥0

\(f(x)=-x,\) x≤0

This piecewise function should be understood as

When x is more than or equal to 0, f(x) is equal to x, and when x is less than 0, f(x) is equal to -x.

Given:

Initial water in pool=72 gallons;

Rate of draining= 3 gallons per minute;

So, water in pool will be empty in ,\(\frac{72}{3}=24\);

Cleaning takes 12 minutes

Rate of refilling=3 gallons per minute;

Time taken to refill=\(\frac{72}{3}=24\)

Total time is \(24+12+24=60 minutes\);

Number of  gallons in pool from 0 to 24minutes(time to empty) is,

\(72-3t\);

Number of  gallons in pool from 24 to 36minutes is 0 gallons

Number of  gallons in pool from 36 to 60minutes(time to empty) is,

\(3(t-36)\);

Domain= (0,60);

Range=(0,72);

g(15),as 15 is between 0 and 24;

\(g(15)=72-3(15)=72-45=27\);

Piecewise Function of the given question is

\(g(t)=72-3t\), 0≤t≤24;

\(g(t)=0\), 24≤t≤46;

\(g(t)=2(t-36)\), 36≤t≤60.

To refer more about Piecewise functions, visit:

brainly.com/question/27262465

#SPJ1

Answer:

yvhj gycvnuvngfyggjcgybkivuv

Answer:

Quadrant 1

Step-by-step explanation:

The measure of angle ABC is given as follows:

m < ABC = 145º.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

In a parallelogram, we have that the opposite angles are supplementary.

The opposite angles for this problem are given as follows:

Hence the measure of angle ABC is given as follows:

m < ABC + 35º = 180º.

m < ABC = 145º.

More can be learned about supplementary angles at brainly.com/question/2046046

#SPJ1

Answer:

It should be D

Step-by-step explanation:

Answer:

The answer is 6.25

Step-by-step explanation:

Root 38 is exactly 6.16441400297. That number estimated would be 6.20 since 6.16 is close to 6.20. The closest number to 6.20 is 6.25.

Answer

What grade are u in because I never seen that before!

The line segment and the parametric equations of a, b, c, and d are:
a = 0
b = -1
c = -7
d = 17

To find the values of a, b, c, and d, we need to use the given information about the line segment and the parametric equations:

At t=0, the parametric curve starts at (0,-7), which means:

x = a + bt = 0 when t = 0
y = c + dt = -7 when t = 0

This gives us two equations:

a = 0
c = -7

At t=1, the parametric curve ends at (-1,10), which means:

x = a + bt = -1 when t = 1
y = c + dt = 10 when t = 1

This gives us two more equations:

a + b = -1
c + d = 10

We now have four equations in four unknowns, which we can solve simultaneously to find the values of a, b, c, and d:

a = 0 (from the first equation)
c = -7 (from the second equation)
a + b = -1 (from the third equation)
c + d = 10 (from the fourth equation)

Solving for b and d, we get:

b = -1
d = 17

Therefore, the parametric equations for the line segment are:

x = bt = -t
y = -7 + 17t
To learn more about : parametric

https://brainly.com/question/30451972
#SPJ11

\(5(x - 5) = 2(2x - 4)\)

\(5x - 25 = 4x - 8\)

Subtract both sides 4x

\(5x - 4x - 25 = 4x - 4x - 8\)

\(x - 25 = - 8\)

Add both sides 25

\(x - 25 + 25 = - 8 + 25\)

\(x = + 17\)

There u go...

Have a great day ❤

This theorem states that:

\(a^2+b^2=c^2\)

In this diagram, notice how there are two smaller triangles that create the large triangle.

To find a and b, we can look at the two small triangles instead of seeing everything as a whole.

Let the top triangle be Triangle A and the bottom triangle be Triangle B.

Solve for a using the Pythagorean theorem:

\(a^2+b^2=c^2\\12^2+6^2=a^2\\a=\sqrt{12^2+6^2}\\a=13.42\)

Solve for b using the Pythagorean theorem:

\(a^2+b^2=c^2\\6^2+3^2=b^2\\b=\sqrt{6^2+3^2}\\b=6.71\)

a = 13.42

b = 6.71

Answer:

I feel like it would be B

Step-by-step explanation:

I  dont like to divide so i basically multiply all the answer choices for questions like these! I choose B becuase A is 3 pigeons short. while B would have room or more pigeons the others are unreasonable cause there would be Way too many cages

Answer:

Not a function

Step-by-step explanation:

For an equation to be a function, there should be only one y-coordinate per x-coordinate. Since this relation has both (-1,9) and (-1,4), this is not a function.

Answer:not a function

Step-by-step explanation:

because when you put the points on the coordinate plane your shape will come out as a v shaped object. In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers

Evaluating Georgianna's claim using a hypothesis test.The claim is that the average child takes less than 5 years of piano lessons. Therefore, we use a one-tailed hypothesis test with a null hypothesis asH0: µ ≥ 5 versus the alternative hypothesis Ha: µ < 5.

Level of significance is not given, hence we can assume it to be 0.05. Calculating the test statistic as follows:$$t=\frac{\overline{x}-\mu }{s/\sqrt{n}}$$Substituting the given values in the above equation, we get$$t=\frac{4.6-5}{2.2/\sqrt{20}}$$So, t = -1.69, for a one-tailed test (left-tailed) and the degrees of freedom are n-1 = 19. Using the t-distribution table with α = 0.05 and 19 degrees of freedom, the critical value is -1.73, hence, -1.69 falls within the non-rejection region. Therefore, we cannot reject the null hypothesis. There is not enough evidence to support Georgianna's claim.b. Constructing a 95% confidence interval for the number of years students in this city take piano lessons, and interpret it in the context of the data.

The formula for confidence interval for a population mean is Interpretation: We can be 95% confident that the average number of years students in this city take piano lessons falls between 4.01 and 5.19 years.c. Explaining if the results from the hypothesis test and the confidence interval agreeYes, the results from the hypothesis test and the confidence interval agree because we cannot reject the null hypothesis in the hypothesis test. This means that the null hypothesis, H0: µ ≥ 5 is plausible. Further, the 95% confidence interval for the mean number of years students take piano lessons lies completely above the value of 5 years, which is Georgianna's claim. This is in line with the hypothesis test result. Thus, we can conclude that there is no sufficient evidence to support Georgianna's claim.

To know more about hypothesis visit :

https://brainly.com/question/31319397

#SPJ11

For the given equation 6+(x/2)=1/4(x-4)-1 the solution is x= -32. So, option D is correct.

A solution is a process of giving the unknown variables values that make the equation's equality true. A value or group of values (one for each unknown) that, when substituted for the unknowns, cause the equation to produce an equality is known as a solution.

In order to build an equation, the equal sign is placed between two numerical or variable expressions, as in 3x+5=11. The solution to an equation is a number that may be used as the variable to generate a true number statement. 6+5=11 is true, as stated by the formula 3(2)+5=11. The solution is consequently 2,

6+(x/2)=1/4(x-4)-1

(12+x)/2=(x-4-4)/4

24+2x=x-8

x= -32

Therefore, option D is correct.

For the given equation 6+(x/2)=1/4(x-4)-1 the solution is x= -32. So, option D is correct.

To know more about solutions, visit:

https://brainly.com/question/24816340

#SPJ1

Answer:

Step-by-step explanation:

A rectangular pyramid has five sides. It consists of a rectangular base and four triangular faces that meet at a common vertex or apex.

≧◉◡◉≦

Answer:

The scale factor is not 2

Step-by-step explanation:

Given

See attachment for the dilated triangles

Triangle ABC is dilated through center point O to form triangle A'B'C'.

From the attachment, we have:

\(OC = 2\) i.e. the distance from the center point to C

and

\(OC' = 6\) i.e. the distance from the center point to C'

The length of OC' is calculated using:

\(OC' = OC + CC'\)

\(OC' = 2 + 4\)

\(OC' = 6\)

The scale factor (k) is then calculated by dividing OC' by OC

\(k = \frac{OC'}{OC}\)

\(k = \frac{6}{2}\)

\(k = 3\)

Hence, Tiffany's claim is incorrect.

Answer:

(1) f(x)=(x-2)(x-3)

(2) f(x)=x²-5x+6

Step-by-step explanation:

(1) f(x)=(x-p)(x-q)

   f(x)=(x-2)(x-3)

(2) f(x)=x²-3x-2x+6

    f(x)=x²-5x+6

Answer:

Try the first one I think and I remember when I did this one but I forgot the answer to this

3/8 as a decimal is 0.375. To change a fraction to a decimal, you can divide the numerator (the top number) by the denominator (the bottom number).

To change 3/8 into a decimal without a calculator, you can use long division or mental math. Here's how to do it using long division:

1. Write 3 as the dividend and 8 as the divisor.

2. Divide 8 into 3. The quotient is 0, so write 0 above the division line.

3. Add a decimal point to the dividend and add a zero to the end. The new dividend is 30.

4. Divide 8 into 30. The quotient is 3, so write 3 above the division line.

5. Subtract 24 from 30 to get 6.

6. Add another zero to the end of 6 to get 60.

7. Divide 8 into 60. The quotient is 7 with a remainder of 4.

8. Add another zero to the end of 4 to get 40.

9. Divide 8 into 40. The quotient is 5 with no remainder.

It's also useful to remember that 3/8 is approximately equal to 0.375, which can be helpful for estimation and mental math.

To learn more about decimal click on,

https://brainly.com/question/20819492

#SPJ4

Answer:

In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the standard error of the estimate b. 0​

Step-by-step explanation:

If the plots on a scatter diagram lie on a straight line in a simple linear regression model, it indicates a perfect fit between the predictor variable and the response variable. In this case, the standard error of the estimate would be 0.

The standard error of the estimate represents the average distance between the observed values and the predicted values by the regression model. When the scatter diagram forms a perfect straight line, it means that the regression model can precisely predict the response variable using the predictor variable without any error.

Consequently, the residuals, which are the differences between the observed and predicted values, become zero for all data points, resulting in a standard error of 0. It is important to note that this scenario of a perfect fit on a scatter diagram is rare in real-world data, as there are typically variations and uncertainties in the relationship between variables.

Learn more about scatter diagram here,

https://brainly.com/question/6592115

#SPJ11

Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

Therefore , the solution of the given problem of prime factor comes out to be 30 is the smallest integer for the three different prime number.

A prime factor is any non-zero natural integer that has just itself and 1 as its divisors. The first real numbers include 1,2,5,3,7  among others. a quantity that has been repeated to yield a different quantity. For example, we obtain (3) 5 = 15 when we divide 15 by Three and 5. primary components All elements that seem to be prime but aren't composite are referred to be prime factors. 2, 3, and 5 are some prime factors of 30.

Here,

Given :

The lowest three prime numbers can be calculated by

adding them together.

The answer is

=> 2 x 3 x 5 = 30,

since the first 3 prime numbers being 2, 3, and 5.

Thus , 30 is the smallest integer for the three different prime number

Therefore , the solution of the given problem of prime factor comes out to be 30 is the smallest integer for the three different prime number.

To know more about prime factor visit:

https://brainly.com/question/29775157

#SPJ1

We know that : The Sum of the angles in a triangle should be equal to 180°

Given : The Triangle is a Right angled Triangle

It means : One of the Angle in the triangle is 90°

It means : The sum of the other two angles should be equal to 90°

Given : One acute angle is 8x + 5 and the other one is 4x + 9

⇒   8x + 5 + 4x + 9 = 90°

⇒   12x + 14 = 90°

⇒   12x = 76°

⇒   x = 6.333°

The larger angle among the acute angles is 8x + 5

⇒   8(6.333) + 5

⇒   50.67 + 5

⇒   55.67

\(\huge\bold{Given :}\)

Angle 1 = ( 8x + 5 ) ...(i)

Angle 2 = ( 4x + 9 ) ...(ii)

Angle 3 = 90° ( ∵ it is a right-angled triangle )

\(\huge\bold{To\:find :}\)

The value of the larger angle of the two acute angles.

\(\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}\)

\({\boxed{\mathcal{\red{ A. \:55.67° .\:}}}}\). ✅

\(\large\mathfrak{{\pmb{\underline{\blue{Step-by-step\:explanation}}{\blue{:}}}}}\)

We know that,

\(\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}\)

➪ ∠ 1 + ∠ 2 + ∠ 3 = 180°

➪ 8x + 5 + 4x + 9 + 90° = 180°

➪ 12x + 104° = 180°

➪ 12x = 180° - 104°

➪ 12x = 76°

➪ x = \( \frac{76° }{12} \)

➪ x = 6.333°

The value of x is 6.333°.

Now,

Substituting the value of x in eq. (i) & (ii), we have

Angle 1 = 8x + 5

= 8 x 6.333 + 5

= 50.666 + 5

= 55.67°

Angle 2 = 4x + 9

= 4 x 6.333 + 9

= 25.332 + 9

= 34.332°

Clearly, angle 1 is greater than angle 2.

Therefore, the value of the larger angle of the two acute angles is 55.67°.

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}\)

Answer:

I deleted my answer bc i accidentally answered the wrong question

The surface area of the given shape above would be = 47.2

To determine the surface area of the solid shape above,the surface area of a cone and a cylinder is first determined and then added together.

The formula for the surface area (SA) of cone = πrs + πr²

where;

r = 1

s = 6

S.A = 3.14×1×6 + 3.14×1×1²

= 18.84+3.14

= 21.98

Formula for Surface area of cylinder = 2πr(r+h)

where;

r = 1

h = 3

SA = 2×3.14×1 (1+3)

= 25.12

Therefore, the surface area of the solid shape = 21.98+25.22 = 47.2

Learn more about area here:

https://brainly.com/question/28470545

#SPJ1

b =(17,6x 8,9):19,7=7,95

Answer:

-6x - 6

Step-by-step explanation:

-6 x x = -6x

-6 x 1 = -6

put them together to get:

-6x - 6

Answer:

−6x−6

Step-by-step explanation: