Use Heron's formula to find the area of the triangle with side lengths 6, 9, and 12, as shown below.

No, the pairs of vectors 3i - 8j, 8i - 3j are not orthogonal.

The dot product will help us to determine if the pair of vectors are orthogonal or not.

If the dot product is equal to zero, then the pair of vectors are orthogonal.

The dot product of the vectors is calculated as follows;

(3i - 8j).(8i - 3j)

= (3i x 8i) - (3i x 3j) - (8j x 8i) + (8j x 3j)

= (24) - (0) - (0) + (24)

= 24 + 24

= 48

So the pairs of vectors are not orthogonal.

Learn more about orthogonal vectors here: https://brainly.com/question/17278431

#SPJ1

The angle that is marked as Q has a value of 30°

The cosine rule, also known as the law of cosines, is a mathematical formula used to calculate the length of a side or the measure of an angle of a triangle.

Cosine rule  useful in solving triangles when you know the lengths of two sides and the measure of the angle between them, or when you know the lengths of three sides.

By the use of the cosine rule, we have that;

7^2 = 12^2 + 14^2 - 2(12 * 14)Cos Q

49 = 144 + 196 -336CosQ

49- 340 =  -336CosQ

-291=  -336CosQ

Q = Cos-1 (-291/-336)

Q = 30

Learn more about cosine rule:https://brainly.com/question/26952873

#SPJ1

Answer:

C you are so welcome I hope it helped you

The requried lottery commission should make a single deposit of Kenya Shillings 8.7475 million (rounded to 4 decimal places) to fund Peter's annuity.

To calculate the present value of Peter's annuity,

[tex]PV = PMT * (1 - (1 + r)^{-n}) / r[/tex]

where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.

In this case, PMT = 87325, r = 0.107/12 = 0.008917, and n = 21*12 = 252.

Substitute the value in the formula given above:

[tex]PV = 87325 * (1 - (1 + 0.008917)^{-252} / 0.008917[/tex]

PV = 8747531.78

Thus, the lottery commission should make a single deposit of Kenya Shillings 8.7475 million (rounded to 4 decimal places) to fund Peter's annuity.

Learn more about PMT here:

https://brainly.com/question/31325062

#SPJ1

Answer:

We can use the formula for compound interest:

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

where A is the ending amount, P is the principal (starting amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

We know P = $5700, A = $6100, n = 1 (since the interest is compounded annually), and t = 12. We can solve for r:

$6100 = $5700(1 + r/1)^(1*12)

$6100/$5700 = (1 + r)^12

1.0702 = (1 + r)^12

log(1.0702) = log[(1 + r)^12]

0.0291 = 12log(1 + r)

0.00243 = log(1 + r)

10^(0.00243) = 1 + r

r = 0.0059 or 0.59%

Therefore, the interest rate of the savings account is 0.59%.

The most accurate for a Zero-Based Budget is You put every dollar of your take-home pay into a budget category each month. Option A

Zero-based budgeting (ZBB) is simply defined as a method of budgeting having that all expenses must be checked for each new period.

The process of zero-based budgeting is one that begins from a zero account

Note that the budgets are carried out when it is needed for the upcoming period, regardless of whether the budget is less or greater than the previous one.

It is important to note the following;

Learn more about zero-based budget at: https://brainly.com/question/26195666

#SPJ1

The function that represents the fox population is P(t) = 6100 x [tex]1.06^{t}[/tex]

The fox population in 2008 is 9722.

The equation that would represent the population of the foxes is an exponential equation.

The form of the exponential equation would be

Future population = present population x [tex](1 + r)^{t}[/tex]

Where:

P(t) = 6100 x [tex](1 + 0.06)^{t}[/tex]

P(t) = 6100 x [tex]1.06^{t}[/tex]

Fox population in 2008 = 6100 x [tex]1.06^{8}[/tex] = 9722

To learn more about exponential functions, please check: https://brainly.com/question/26331578

#SPJ1

There is not enough evidence to support the claim that more than 20% of users develop nausea at a 0.01 significance level.

We have,

Based on a sample of 217 subjects, 53 of them developed nausea.

To test this claim, a hypothesis test is conducted using a significance level of 0.01.

The null hypothesis, denoted as H0, assumes that the true proportion of users who develop nausea is less than or equal to 20%, while the alternative hypothesis, denoted as Ha, assumes that the true proportion is greater than 20%.

If the test statistic, calculated from the sample data, falls in the rejection region, which is determined based on the significance level and the degrees of freedom, then the null hypothesis is rejected, and it can be concluded that there is sufficient evidence to support the alternative hypothesis.

In this case,

If the test statistic falls in the rejection region, it means that the evidence suggests that more than 20% of users of the pain drug develop nausea, and the claim that less than or equal to 20% of users develop nausea is not supported by the data.

Thus,

There is not enough evidence to support the claim that more than 20% of users develop nausea at a 0.01 significance level.

Learn more about hypothesis testing here:

https://brainly.com/question/30588452

#SPJ1

The type of relationship that is indicated by the residual plot is given as follows:

Non-linear relationship.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

For this problem, we have an alternative pattern, where the function neither multiplied nor added/subtracted by a constant value when the input is increased by one, hence we merely classify the relationship as a non-linear relationship.

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Answer:

a) Utilizando la fórmula para el tamaño de muestra, tenemos:

n = (Z * σ / E)^2

donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 95% (Z = 1.96), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 2).

Sustituyendo los valores, obtenemos:

n = (1.96 * 9 / 2)^2 ≈ 77

Por lo tanto, se debe tomar una muestra de al menos 77 familias.

b) De manera similar, tenemos:

n = (Z * σ / E)^2

donde Z es el valor crítico de la distribución normal estándar para un nivel de confianza del 99% (Z = 2.58), σ es la desviación estándar poblacional (σ = 9), y E es el error máximo que se desea cometer en la estimación (E = 1.5).

Sustituyendo los valores, obtenemos:

n = (2.58 * 9 / 1.5)^2 ≈ 261

Por lo tanto, se debe tomar una muestra de al menos 261 familias.

Step-by-step explanation:

The linear regression equation is y = 22.6x + 52.33

The profit would reach 234 thousand dollars during the calendar year of 2020.

Replacing the means, the intercept a is given by:

108.8 = 22.6(2.5) + a.

a = 108.8 - 22.6(2.5)

a = 52.33

Therefore, the linear regression equation is y = 22.6x + 52.33

The profit would reach 234 thousand dollars during the calendar year of 2020.

Learn more about regression on

https://brainly.com/question/21826199

#SPJ1

Answer:

Step-by-step explanation:

Answer:

The correlation coefficient of a data set can be significantly altered by removing an influential point from the data set.

Step-by-step explanation:

Please give the brainliest, really appreciated. Thank you

The function of g(x) is 3 ([tex]2^x[/tex]) + 3.

We have,

f(x) = 3 ([tex]2^x[/tex]) -3

Now, the function f(x) have shifted by -3 unit to move 6 unit up.

This means that we have the shifting of

= -3 + 6

= +3 unit

Also, g(x) crosses the y-axis at about 5 or 6 when x=0.

Then, the function of g(x) is

= 3 ([tex]2^x[/tex]) + 3

Learn more about Transformation here:

https://brainly.com/question/11963169

#SPJ1

The radius of the sphere that has a volume of 33.51032164 cubic meters is approximately 2 meters.

The radius of a sphere is the distance from the center of the sphere to any point around the circumference. The radius is half of the length of the diameter of a sphere.

The volume of  a sphere = 4/3 * π * r³

Given that:

Volume ≈ 33.5 cubic meters

Use the formula to find the radius of the sphere:

33.5 = 4/3 * π * r³

33.5 = 4π/3 * r³

3 * 33.5 = 4π * r³

100.5/4π = r³

r³ = 7.998

r = ∛7.998

r ≈ 2 meters.

Learn more about volume of sphere on:

https://brainly.com/question/30522100

#SPJ1

The volume of the given figure is 1176 cubic cm.

The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).

The volume of the figure is calculated as,

Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )

Volume = 1176 Cubic cm

Hence, the volume of the figure will be equal to 1176 Cubic cm.

To know more about volume follow

https://brainly.com/question/29568631

#SPJ1

The graph is a function: yes

The domain of this function is: x ≥ -3.

The range of this function: all real numbers.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.

Range = {-∞, ∞} or all real numbers.

Read more on domain here: brainly.com/question/17440903

#SPJ1

Some solutions for the given system of inequalities are:

(5, 12)

(6, 12)

(7, 13)

And so on.

Here we have the following system of inequalities:

x > 4

y  ≥ 12

We want to see which ordered pair, of the form (x, y), is a solution for the system.

A solution is a pair that makes both inequalities true.

So, x must be larger than 4.

y can be equal to 12, or larger than 12.

Then some solutions are:

(5, 12)

(6, 12)

(7, 13)

And so on.

Learn more about systems of inequalities:

https://brainly.com/question/9774970

#SPJ1

The approximate height of the pole in centimeters is 17,500 centimeters.

We have,

Let's start by calculating the total length of the pole, which is buried plus the part that protrudes from the ground.

We know that the part that protrudes is 25 meters and that it represents one-seventh of the total length.

25 = L/7

where L is the total length of the pole.

We can solve for L by multiplying both sides of the equation by 7:

L = 7 x 25

  = 175 meters

Now we need to convert this length to centimeters.

Since 1 meter is equal to 100 centimeters,

175 meters x 100

= 17,500 centimeters

Therefore,

The approximate height of the pole in centimeters is 17,500 centimeters.

Learn more about unit conversion here:

https://brainly.com/question/13899873

#SPJ1

The complete question.

The Clarisse company, dedicated to the telephone business, is expanding its coverage, due to this, it is placing poles, where the seventh part of a pole is buried, and protrudes 25 meters from the ground. Calculate the approximate height of the pole in centimeters.

Answer: Discover how a 3D solid shape can be made up from a 2D net. Understand how nets are formed with examples of common 3D polygons and prisms.

Step-by-step explanation:

Note that the estimated population mean is 2.2

The mean absolute deviation is 1

The average distance each data value is from the mean is 1 hours per night

The distribution has _Low_ variability

Where the data graphed is:

Hours Per Night       Students

0.5                                       0

1                                            2

1.5                                           3

2                                              4

2.5                                        2

3                                             2

3.5                                          1

4                                             1

The estimate of the population mean is

0.5 (0 ) + 1 ( 2) +  1.5( 3) + 2(4) + 2.5(2) + 3( 2 ) + 3.5( 1) + 4( 1) =3 3

⇒ 33 / 15

population Mean = 2.2



To find the Mean Absolute Deviation:

0.5 - 2.2 = - 1.7

1 -  2.2 = -1 .2

1.5 - 2.2   = - 0.7

2 -  2.2  = - 0.2

2.5   - 2.2  =0.3

3  -  2.2 = 0.8

3.5 - 2.2 = 1.3

4 - 2.2 =   1.8

The absolute deviations from the sample mean are

1.7 ,  1.2, 0.7, 0.2 , 0.3, 0.8 , 1.3,1.8

Thus

(1.7 + 1.2 + 0.7 + 0.2+0.3 + 0.8 + 1.3 +1.8) / 8 = 8/8 = 1

Therefore, the M.A. D is 1 hours per nigh


For average distance each data value is from the mean...

|(-1.7)| + |( -1.2) | + | ( -0.7)| + |( -0.2 | + | 0.3| + |  0.8| + | 1.3 | + | 1.8 | = 8

8/ 8 = 1


So average distance of each data value form the mean is 1 hours per night.


We discovered that the M.A. D in this scenario is 1hr/ night. We may claim that the distribution has low variability because this number is quite tiny.

Learn more about Mean Absolute Deviation:
https://brainly.com/question/10528201
#SPJ1

Answer:

Step-by-step explanation:

35.26    rounded to  35.3

8.32   rounded to        8.3

6.78    rounded to       6.8

35.3 + 8.3 = 43.6

43.6 + 6.8 = 50.4

The answer is 50.4.

39.26 rounds to 35.3

8.32 rounds to 8.3

6.78 rounds to 6.8

When you add them together, you get 50.4.

Selena can serve the pizza at around 6:40 P.M.

The regression line should have the equation y = -1.7x + 300, where y is the temperature, x is the time in minutes since the pizza was taken out of the oven, -1.7 is the slope of the line, and 300 is the y-intercept.

Set y (the temperature) to 130°F, and solve for x (the time).

130 = -1.7x + 300

-170 = -1.7x

x ≈ 100

According to the regression model, the pizza will reach 130°F after about 100 minutes after it was taken out of the oven. Therefore, Selena can serve the pizza at around:

= 5 + 1:40

= 6:40 P.M.

Learn more about regression on

https://brainly.com/question/25987747

#SPJ1

Alma need to use 6 cups of blue paint and 4 cups of red paint with the 2 cups of white paint.

Here, Alma makes 5 cups of her favorite shade of purple paint by mixing

3 cups of blue paint,

1 1/2 cups of red paint,

and 1/2 a cup of white paint.

Alma has 2 cups of white paint.

The ratio of blue to the white paint is:

3 : (1/2)

so, for 2 cups of white paint,

3 : (1/2) = x : 2

x = 6 cups of blue paint

The ratio of red to the white paint is,

3: (1 1/2)

3 : (3/2)

So, for 2 cups of white paint,

3 : (3/2) = y : 2

y = 4 cups of red paint

Learn more about the ratio here:

https://brainly.com/question/29774220

#SPJ1

The domain of the function g(x) is given as follows:

B. All values of x such that x ≥ 0.

The domain of a function is the set of all the possible input values that can be assumed by the function.

The function for this problem is defined as follows:

[tex]g(x) = \sqrt{8x}[/tex]

The square root function assumes values that are greater than or equals to zero, hence the domain of the function is obtained as follows:

8x ≥ 0.

x ≥ 0.

More can be learned about the domain of a function at https://brainly.com/question/10687170

#SPJ1

Answer: In decimal form, 14.85

Answer in fraction form: 297/20

Step-by-step explanation:

The resultant between the two vectors is 21.17 lb

Parallelogram law of vectors says that if two vectors acts on a point, the resultant of this vectors can be represented by the diagonal from the point of intersection.

R² = x²+y2+2xycos (tetha)

where x and y are the vectors

When x = 20.6 and y = 17.4

R² = 20.6²+17.4²+2(20.6)(17.4)cos 112.9

R² = 727.12+716.88cos 112.9

R² = 727.12 -278.95

R² = 448.17

R = √448.17

R = 21.17 lb

Therefore the resultant is 21.17lb

learn more about parallelogram law of vectors from

https://brainly.com/question/23867486

#SPJ1

The key number, ac, is -104.

Key number is the product of the coefficients of the first and last terms. The right binomial factors for a quadratic expression can be determined with its assistance.

We must multiply the coefficient of the quadratic term by the constant term to obtain the key value, ac, which results in:

ac = 13(-8) = -104

Therefore, The key number, ac, is -104.

Learn more about key number here : brainly.com/question/29574610

#SPJ1

A conversion of 300 degrees to radians is equal to 5.24 radians.

In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.

Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):

Arc length = rθ

Where:

Next, we would convert degrees to radians;

300 = rads × 180/π

Radians = 300π/180 = 5.24 radians.

Read more on arc length here: brainly.com/question/28108430

#SPJ1