Which of the following points is not coplanar with points C, D and E?

Answer:

A. 72°

D. 144°

E. 216°

Step-by-step explanation:

are you tempted to calculate the internal angles ?

that is, I guess, the trap set by your teacher here, and it would be the wrong approach.

nevertheless, quickly just as a reminder :

the sum of all internal angles in a polygon is

(n - 2)×180°

n being the number of sides.

in our case that is

(5 - 2)×180 = 3×180 = 540°

so, each internal angle is 540/5 = 108°.

but we are not turning at an edge or vertex. no, we are turning the pentagon around is central point.

we are running each vertex along a circle arc. the center of that circle being P.

after every 1/5 of the circle arc there is a vertex of the pentagon.

and whenever we rotate one vertex on top of the next one, we carry the pentagon visually onto itself.

so, instead of a full circle rotation we need only 1/5 of that :

360 / 5 = 72°

and with every additional 1/5 of the circle arc (or 72°) we get it again.

that means at

72°

144°

216°

288°

360°

the pentagon carries onto itself.

therefore, A, D and E are correct.

Answer:

t = 480

Step-by-step explanation:

When we have equations with variables, we always want to isolate the variable, so lets get rid of 4 first.

Add 4 to both sides :

-96 = -t/5

Multiply both sides by the denominator :

-480 = -t

Divide both sides by negative 1 :

t = 480

Answer:

Step-by-step explanation:

-t/5 - 4 = -100

-t/5 = -96

t/5 = 96

t = 480

Answer:

$30.40

Step-by-step explanation:

to find out how much 20 candy bars would cost, first, we have to find out how much 1 candy bar costs. we do this by dividing $19.76 by 13.

$19.76 ÷ 13 = $1.52

so now we know that one candy bar costs $1.52. now, we multiply this value to 20, to know how much 20 candy bars cost. therefore, we get:

20 × $1.52 = $30.40

well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years

\(~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}\)

\(A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}\)

\(A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}\)

Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

To determine the number of pounds of raw materials that should be purchased in July, we need to calculate the raw materials production needs for August and then consider the inventory policies given in the information provided.

Each unit of finished goods requires 5 pounds of raw materials. The budgeted unit sales for August are 19,000 units. Therefore, the raw materials production needs for August would be 19,000 units multiplied by 5 pounds per unit, which equals 95,000 pounds.

The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Therefore, the desired ending raw materials inventory for July would be 10% of 95,000 pounds, which is 9,500 pounds.

To calculate the raw materials purchases for July, we need to consider the payment terms provided. Thirty-five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.

Let's assume the raw materials purchases for July are X pounds. Then the payment for 35% of X pounds will be made in July, and the payment for 65% of X pounds will be made in August.

The payment for raw materials purchases in July (35% of X pounds) will be:

0.35 * X pounds

The payment for raw materials purchases in August (65% of X pounds) will be:

0.65 * X pounds

Since the raw materials purchases for July should cover the desired ending raw materials inventory for July (9,500 pounds), we can set up the following equation:

Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

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Answer:

<a=138°

<b=42°

<c=138°

<d=138°

<e=42°

<f=42°

Step-by-step explanation:

<a is supplementary with the 42° angle:

<a=180°-42°=138°

<b and the 42° are vertical angles, so:

<b=42°

<c and <a are also vertical angles so:

<c=<a=138°

<d and <a are corresponding angles, so:

<d=<a=138°

<e and <b are corresponding angles, so:

<e=<b=42°

<f and the 42° angle are corresponding angles, so:

<f=42°

<g and <c are corresponding angles, so:

<g=<c=138°

The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.

Speed is simply referred to as distance traveled per unit time.

It is expressed as;

Speed = Distance ÷ time.

Given that the car is traveling at a rate of 30 meters per second.

First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.

1 kilometer = 1000 meters

1 hour = 3600 seconds

Hence;

Speed = 30m/s = ( 30 × 3600/1000 )kmh

Speed = 108 kmh

Next, the distance covered in 5 hours will be:

Speed = Distance / time

Distance = speed × time

Distance = 108 kmh × 5 h

Distance = 540 km

Therefore, the disatnce covered is 540 kilometers.

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Plane ADF is another way to label Plane J.

In order to determine which of the given options is another way to label Plane J, we need to first identify the key characteristics of Plane J.

These characteristics are its points, lines, and planes that it contains. We can then use these characteristics to compare and match them with the given options.

Here are the key characteristics of Plane J: Points: J, A, D Lines: JA, JD, AD Planes: Plane J Now let's examine each option to see which one matches the characteristics of Plane J: Option A: Plane h This option is not a match since Plane h is not one of the planes that contain the points J, A, and D.

Option B: Plane ABD This option is not a match since Plane ABD contains points A, B, and D but not point J.

Option C: Plane EFG This option is not a match since Plane EFG contains points E, F, and G but not point J.

Option D: Plane ADF This option is a match since Plane ADF contains points A, D, and F which are all points that are contained in Plane J.

Therefore, Plane ADF is another way to label Plane J.

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Answer:

I think this is helpful .

Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

The number of ways which he can choose 4 courses if more than 2 must be science is; 224 ways.

Combination of outcomes;

He can choose from 4 humanities courses and 8 science courses.

If the condition requires that he chooses more than 2 science courses, it follows that;

He can only choose three science courses and only 1 humanities courses.

8C3 x 4C1 = 56x 4 = 224

On this note, the number of ways he can choose the required 4 courses is; 224 ways.

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Answer:

$210

Step-by-step explanation:

do 84/4 to find out money per day which is 21. 21 x 10 = 210

therefore 210 is the answer

The cross sectional area of the cylinder is 176.6cm² and the volume is 4768.2 cm³.

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

The cross sectional area of a cylinder is expressed as the area of a circle.

A = πr²

where r is the radius

radius = diameter/2

= 15/2 = 7.5 cm

Area = 3.14 × 7.5²

= 176.6 cm²

The volume of cylinder is expressed as;

V = πr²h

V = 3.14 × 7.5² × 27

V = 176.6 × 27

V = 4768.2 cm³

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Step-by-step explanation:

If x=10

\(\tt{ x^2-2(x+5) }\) ⠀

\(\tt{ (10)^2-2×(10+5) }\) ⠀

\(\tt{100-2×15 }\) ⠀

\(\tt{ 100-30 }\) ⠀

\(\bold{ 70 }\) ⠀

Answer:

f(t)= (9.6/2)cosBt

= 4.8cosBt

where B=2pi/period

use cosine to avoid a phase shift

Answer:

The number of books sold were:

Math textbooks: 426
Sociology textbooks = 46

Step-by-step explanation:

Let us use the variable \(m\)  to represent the number of math books sold

Let us use the variable \(s\)  to represent the number of math books sold

Combined total of 426 math and sociology books were sold is represented by the equation:
\(m + s = 426\quad\quad\quad(1)\)

Number of math books sold was 46 more than the number  of sociology textbooks sold is given by
\(m - s = 46\quad\quad\quad(2)\)

Adding the equations (1) + (2):
\((m + s) + (m - s) = 426 + 46\\\\2m = 472\\\\m = \dfrac{472}{2}\\\\m = 236\\\\\)

Using Equation (1): \(m + s = 426\)  we get

\(236 + s = 426\\\\s = 426 - 236\\\\s = 190\)

Answer:

$28 per hour

Step-by-step explanation:

Let's first find out how much extra Victoria was paid during the week she worked overtime.

Without overtime, Victoria's weekly paycheck would be $550. However, she received $690 that week. The difference between the two amounts is the extra pay for overtime:

Extra pay = Total pay - Regular pay = $690 - $550 = $140

Now, we know that Victoria worked 5 hours of overtime. To find her overtime pay per hour, we can divide the total overtime pay by the number of overtime hours:

Overtime pay per hour = Total overtime pay / Overtime hours = $140 / 5 = $28

Victoria's overtime pay is $28 per hour.

Hope this helps!

Answer:

Victoria is paid $28 per hour of overtime.

Step-by-step explanation:

Get the difference of Victoria's paycheck with and without overtime.

Difference = $690 - $550

Difference = $140

The difference is the amount that she was paid for the overtime.

Since she worked for 5 hours then we can just divide the amount over the time.

Rate = $140/5hours

Rate = $28/hr

Answer:

The calculated value Z = 1.5950 < 1.96 at 0.05 level of significance

The null hypothesis is accepted at a 0.05 level of significance

The proportion of cell phone owners in that country who have a smartphone has not increased over time

Step-by-step explanation:

Step(i):-

Given that the random sample size 'n' = 934

Given that the population proportion P = 0.51

                                                            Q= 1-P

                                                           Q = 1- 0.51 = 0.49

The sample proportion

                                   \(p = \frac{x}{n} = \frac{501}{934} = 0.5364\)

Level of significance = 0.05

Critical value Z₀.₀₅ = 1.96

Step(ii):-

Null hypothesis:  P < 0.51

Alternative Hypothesis : P > 0.51

  Test statistic

                    \(Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }\)

                   \(Z = \frac{0.536-0.51}{\sqrt{\frac{0.51 x 0.49}{934} } }\)

                  Z =  1.5950

Final answer:-

Given that P-value 0. 0532

P-value > 0.05

Rejected Alternative Hypothesis and accepted null hypothesis

               ( OR)

The calculated value Z = 1.5950 < 1.96 at 0.05 level of significance

The null hypothesis is accepted at a 0.05 level of significance

The proportion of cell phone owners in that country who have a smartphone has not increased over time

The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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Answer:

n = 9

Step-by-step explanation:

Using index laws, multiply 3 into 3 to get 9

(x3)^3 = x^n

x^9 = x^n

9 = n

Answer:

n = 9

Step-by-step explanation:

hey mate make my answer brainiest

(x*3)*3=x*n

3×3=n. (reason when bases are same powers are also same)

9=n

n=9

I hope this helps

Answer:

1133.4312 US$

Step-by-step explanation:

Just use a calculator or write it down

Answer:

Your answer is 154.55 as the reduction price.

Your answer is 1,133.44 as the complete price after the discount.

Step-by-step explanation:

12% = 0.12

1287.88 x 0.12 = 154.5588

Round to 154.55$.

1287.99 - 154.55 = 1,133.44

Answer:

because it just is

Step-by-step explanation:

Therefore, the perimeter of the tablecloth is 24 feet.

A is the area, L is the length, W is the width, and * is the multiplicand. A denotes area, s denotes side length, and is the multiplication sign. Let's have a look at a few examples of how to calculate the area of rectangles. Example 1: Determine the dimensions of a square with 2-inch sides.

The area of a square is given by the formula A = s^2, where A is the area and s is the length of one of the sides of the square. In this case, we know that the area of the tablecloth is 36 square feet, so we can write:

36 = s²

Taking the square root of both sides, we get:

s = 6

So the length of one side of the square tablecloth is 6 feet. Since all four sides of a square are equal in length, the perimeter of the tablecloth is:

4s = 4(6) = 24 feet

Therefore, the perimeter of the tablecloth is 24 feet.

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Answer: \(\boxed{y=\frac{4}{5}x-2}\)

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so as the slope of the given line is -5/4, the slope of the perpendicular line is 4/5.

Substituting into point-slope form,

\(y-6=\frac{4}{5}(x-10)\\\\y-6=\frac{4}{5}x-8\\\\\boxed{y=\frac{4}{5}x-2}\)

The vertex of the graph is a maximum at (-2, 4)

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

The graph

The graph is a quadratic function

From the graph, we can see that the graph has a maximum value

This maximum value represents the vertex of the graph

And it is located at (-2, 4)

So, we have

Maximum = (-2, 4)

Hence, the maximum value of the function is (-2, 4)

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Answer:

1/2

Step-by-step explanation: