Translate and solve the following: Five less than z is 4.

Answer:

see explanation

Step-by-step explanation:

using the tangent ratio in the right triangle

tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then

∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then

∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )

AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )

Answer:

a) Var (x) is larger

b)E(x)= 10 and E(y)=  2.5

Step-by-step explanation:

a) Var (x) is larger because the number of students selected can be greater than 1 but Var(y) will always be less because the numbers of drivers chosen can be only one at a time.

b) The expected value of X and y can be computed by multiplying the numbers with their probabilities

x         10    20    30      40

P(x)    0.1    0.2    0.3    0.4

P (x= 10) = 10/ 10+20+30+40= 10/ 100= 0.1

E(x) = 10(0.1) +20(0.2) +30(0.3)+40(0.4)

E(x)= 1=2+3+4= 10

Now the expected value of y

y         1                2         3           4

P(y)    0.25     0.25      0.25       0.25

E(y)=  1(0.25) +2(0.25) +3(0.25)+4(0.25)

E(y)= 0.25 +0.5 +0.75 +1 = 2.5

Step-by-step explanation:

radius=6cm.

π=22 over 7

circumference=2πr

circumference=2×22 over7×6

circumference=51.04cm

Answer:

37.68

Step-by-step explanation:

i had this one

The person that is correct among the students is Frank who said the pencils are an example of parallel lines.

Parallel lines are lines that can never meet. These are lines that run a direction that is quite opposite to each other as we can see from the image. It is clear that the lines as shown are not able to meet at any point even if they are extended.

Thus, the person that is correct among the students is Frank who said the pencils are an example of parallel lines.

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Answer:

you should try searching it up

Step-by-step explanation:

Answer:

C. 7°F

Step-by-step explanation:

Answer: \(7.39466666\)

Step-by-step explanation:

Setting \(x=2.2\) and \(n=3\),

\(e^{2.2} \approx \sum^{3}_{k=0} \frac{2.2^{k}}{k!}=\frac{2.2^0}{0!}+\frac{2.2^1}{1!}+\frac{2.2^2}{2!}+\frac{2.2^3}{3!} \approx 7.39466666\)

Answer:

7.39466667 (8 d.p.)

Step-by-step explanation:

We can approximate the value of eˣ for any x using the following sum formula:

\(\boxed{e^{x} \approx \displaystyle \sum^n_{k=0}\dfrac{x^k}{k!}}\)

To approximate \(e^{2.2}\) with n = 3, substitute x = 2.2 and n = 3 into the given sum formula:

\(e^{2.2} \approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}\)

To calculate the sum, substitute k with each value from 0 to 3 and add the results together:

\(\begin{aligned}e^{2.2} &\approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}\\\\&= \dfrac{2.2^0}{0!}+\dfrac{2.2^1}{1!}+\dfrac{2.2^2}{2!}+\dfrac{2.2^3}{3!}\\\\&= \dfrac{1}{1}+\dfrac{2.2}{1}+\dfrac{4.84}{2}+\dfrac{10.648}{6}\\\\&= 1+2.2+2.42+1.774666666...\\\\&=7.39466667\; \sf (8\;d.p.)\end{aligned}\)

Therefore, the approximate value of \(e^{2.2}\) is:

\(\large \textsf{$e^{2.2}$}=\boxed{7.39466667}\; \sf (8\;d.p.)}\)

Note: To obtain a more accurate approximate value, increase the value of n.

To find the slope we need to apply:

We have two points and we have:

Now we find m,

After that, we apply the general equation of the line:

and from that, the intercept will be:

Answer:

d)

\( {i}^{740} \)

Step-by-step explanation:

i¹= i

i²= -1

i³= -i

i⁴= 1

i¹²⁴= i^(124 +0)

i^124 . i^0

i^(4×31) . i^0 = 1³¹. i^0

1.i^0= i^0

= 1

a) i^179= i^(176+3)

i^176 . i³ = i^(4×44) . i³

1⁴⁴. i³ = 1. i³

= -i

b) i^582 = i^(580 + 2)

i^580 . i²= i^(4×145) . i²

1^145 . i²= 1.i²

= -1

c) i^165= i^(164+1)

i^164 . i¹ = i^(4×41) . i¹

1⁴¹ . i¹ = 1.i

= i

d) i^740= i^(740+0)

i^740 . i^0 = i^(4×185) . i^0

1^185 . i^0 = 1. i^0

= 1

i¹²⁴= i^740 = 1

Answer:

The approximate user base of the social media site 10 months from now would be approximately 52,374.

Step-by-step explanation:

To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:

1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04

2. Apply the growth factor to the current user base for each month:

  Month 1: 35,930 * 1.04 = 37,387.2 (approx.)

  Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)

  ...

  Month 10: Previous Month * 1.04

By repeating this calculation for each month, we can determine the approximate user base 10 months from now.

Month 1: 37,387.2

Month 2: 38,868.49

Month 3: 40,391.33

Month 4: 41,957.61

Month 5: 43,569.34

Month 6: 45,228.24

Month 7: 46,936.32

Month 8: 48,695.44

Month 9: 50,507.45

Month 10: 52,374.40 (approx.)

Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.

Answer:

20\(c^{6}\)

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

given

(- 4c³)(- 5c³) ← remove parenthesis

= - 4 × c³ × - 5 × c³

= - 4 × - 5 × c³ × c³

= 20 × \(c^{(3+3)}\)

= 20\(c^{6}\)

1. The congruent angles are: ∠7 and ∠2; ∠1 and ∠8; ∠3 and ∠6; ∠5 and ∠4; and ∠3 and ∠7

2. The supplementary angles are: ∠6 and ∠4; ∠3 and ∠5; and ∠2 and ∠8

3. x = 26

4. x = 4

5. x = 14

6. x = 12

Congruent angles have equal angle measure. They include:

If they lie on two lines that are intersected by a transversal, then the lines are parallel.

Supplementary angles that are formed on two lines that are intersected by a transversal and proves that the lines are parallel include:

1. The congruent angles that proves that the two lines are parallel are:

2. The supplementary angles that proves that the two lines are parallel are:

3. m∠3 + m∠5 = 180 [same-side interior angles]

Substitute

4x + 10 + 3x - 12 = 180

7x - 2 = 180

7x = 182

x = 26

4. m∠1 = m∠8 [alternate exterior angles]

Substitute

12x + 2 = 4x + 34

12x - 4x = -2 + 34

8x = 32

x = 4

5. m∠7 = m∠2

Substitute

6x + 42 = 10x - 14

6x - 10x = -42 - 14

-4x = -56

x = 14

6. m∠2 + m∠5 = 180

Substitute

10x - 3 + 3x + 27 = 180

13x + 24 = 180

13x = 156

x = 12

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Answer:

I need Help on this one too.

Step-by-step explanation:

PLease Help

Answer:

Part A: it is linear because it is not curving and it consists of straight lines.

Part B: in side A it is increasing because it has a positive slope. In side b it is constant because the slope is 0 since it is straight. Finally, side C is decreasing because the slope is negative.

Part C: during side A the ant is crawling out of the hole in 2 seconds. After that, the ant stops for 2 more seconds as shown in side B. Then, he crawls back into the hole as shown by the decrease in distance due to the slope.

Step-by-step explanation:

Answer:

7 3/4

Step-by-step explanation:

4 1/8 + 3 5/8

Add the whole numbers, 4 + 3 = 7.

Add the fractions, 1/8 + 5/8 = 6/8.

You get 7 6/8. Simplify 6/8 to get 3/4.

Your answer is 7 3/4.

The number of people that nare expected to vote in the election is 260,000. people.

Simply put, a fraction is a portion of a whole. Mathematically, the number is represented as a quotient with split numerator and denominator. The numerator and denominator of a simple fraction are both integers. On the other hand, a complex fraction has a fraction in either the numerator or the denominator.

In this situation, the pre-election survey showed that two out of every three eligible voters would cast ballots in the county election and there are 390,000 eligible voters in the county.

The number of people expected to vote will be:

= Fraction of expected voters × Total number of people

= 2/3 × 390000

= 2 × 130000

= 260000

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ANSWER:

Yes

STEP-BY-STEP EXPLANATION:

For two quantities with inverse variation, just as one quantity increases, the other quantity decreases. Thus, the quantities are inversely proportional.

In this case we can observe that while the x-axis increases, the y-axis decreases, therefore, if there is an inverse relationship.

The equation starts from the following form:

And k is a constant value that represents in this case the decrease, and this value in the graph is observed when the value of y is close to 1, therefore, the value of k is 11.

The equation would be:

To calculate the exact minimum taxable income, we need the missing information regarding the standby charge and the stock options exercise.

To calculate Tanja's 2022 minimum taxable income, we need to consider her various income sources and deductions. Let's break it down:

Salary: $93,500

Year-end bonus: $12,000

Defined benefit RPP contributions: Tanja's and her employer's contributions are not taxable income.

Employment Insurance (EI) contributions withheld: $953

Canada Pension Plan (CPP) contributions withheld: $3,500

Tuition fee for Chinese course paid by employer: $3,600 (not taxable)

Disability insurance benefits: $6,500 (taxable as it is a replacement for employment income)

Employer-provided automobile: We need to calculate the standby charge and operating cost benefit.

Standby charge: The standby charge is calculated based on the original cost of the car and the number of personal use kilometers. Since the car was left in the employer's garage for one month, the standby charge is reduced. We need additional information to calculate this.

Operating cost benefit: $7,240 (taxable as it is a personal use benefit)

Financial counseling services provided by the employer: $450 (not taxable)

Value of the Las Vegas trip: $5,620 (taxable as a non-cash prize)

Stock options exercise: We need additional information to calculate the taxable benefit.

To calculate the exact minimum taxable income, we need the missing information regarding the standby charge and the stock options exercise. Once we have those details, we can calculate Tanja's 2022 minimum taxable income by adding up the taxable components mentioned above and subtracting any applicable deductions or credits.

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Answer:

To simulate one trial of this situation using a random number table, we can follow these steps:Step 1: Assign the digits 00-04 to represent packages not delivered on time and 05-99 to represent packages delivered on time.Step 2: Generate a two-digit random number from the random number table.Step 3: If the generated number falls between 00 and 04, count it as a package not delivered on time. If the generated number falls between 05 and 99, count it as a package delivered on time.Step 4: Repeat steps 2 and 3 until we get a package not delivered on time.The correct option is: Read two-digit numbers. Count the number of packages that are needed in order to find one that was not delivered on time.

Step-by-step explanation:

1. Revised Net Operating Income = $66,760

2. Revised Net Operating Income  =$64,640

3. Revised Net Operating Income  =$52,

1. If the sales volume increases by 40 units:

So, New Sales = 8,700 units + 40 units = 8,740 units

and, New Contribution Margin =

= $14.00 x 8,740 units

= 122, 360

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 122360 - 55600

= 66,760.

2. If the sales volume decreases by 40 units:

New Sales = 8,700 units - 40 units = 8,660 units

New Contribution Margin

= 14 x 8660

= 121,240

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 65,640

3. If the sales volume is 7,700 units:

New Sales = 7,700 units

New Contribution Margin

= 14 x 7700

= 107,800

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 52, 200

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Answer:

\( x = 23 \)

Step-by-step explanation:

Given, \( \frac{x - 5}{2} = 9 \), solve for x.

Multiply both sides by 2

\( \frac{x - 5}{2} \times 2 = 9 \times 2 \)

\( x - 5 = 18 \)

Add x to both sides

\( x - 5 + 5 = 18 + 5 \)

\( x = 23 \)

The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.

The solution of the matrix equation is calculated by applying Cramer's rule as shown below;

[ 1     1     -1 ]  [ 7 ]

[ 2    3     0 ] [ 18 ]

[ -5   -7    -1 ] [ -43 ]

The determinant of the matrix is calculated as follows;

[ 1     1     -1 ]  

[ 2    3     0 ]

[ -5   -7    -1 ]

Δ = 1 (-3 - 0) - 1(-2 - 0 )  - 1(-14 + 15)

Δ = -2

The x determinant of the matrix is calculated as follows;

[ 7     1     -1 ]  

[ 18    3     0 ]

[ -43   -7    -1 ]

Δx = 7 (-3 - 0) - 1 (-18 - 0 )  - 1(-126 + 129)

Δx = -6

The y determinant of the matrix is calculated as follows;

[ 1     7     -1 ]  

[ 2    18     0 ]

[ -5   -43   -1 ]

Δy = 1 (-18 - 0 )   - 7(-2 - 0 )  -1(-86 + 90)

Δy = -8

The z determinant of the matrix is calculated as follows;

[ 1     1     7 ]  

[ 2    3    18 ]

[ -5   -7   -43]

Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)

Δz = 0

The values of x, y , and z is calculated as;

x = Δx/Δ = -6/-2 = 3

y = Δy/Δ = -8/-2 = 4

z = Δz/Δ = 0/-2 = 0

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Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

In hyperbolic geometry, the angle sum of a triangle is always less than 180 degrees.

A lune is a wedge of a sphere with angle θ, represented by L(θ) in the proof.

α, β, and γ are the three angles of the triangle.

4πr²+4area[αβγ]=2L(α)+2L(β)+2L(γ)

2(2πr²+2area[αβγ])=2(L(α)+L(β)+L(γ))

2πr²+2area[αβγ]=L(α)+L(β)+L(γ)

At this point, we need to use a theorem that states that a lune whose corner angle is θ radians has an area of 2θr².

2πr²+2area[αβγ]=2αr²+2βr²+2γr²

2πr²+2area[αβγ]=2r²(α+β+γ)

π+area[αβγ]r²=α+β+γ

At this point, it is clear that the sum of the angles is equal to π plus the area[αβγ]r² (which cannot be zero).

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By multiplying the time of rowing by the speed we get the distance, like this:

d = S×t

Where d is the distance, S is the speed and t is the time.

When the team is going in the direction of the current their actual speed is the speed of the current plus their still speed, then we can rewrite the above expression to get:

100 = (s + 6)t

Where 100 was the distance the team rowed in miles and 6 is the current rate in miles per hour.

Similarly, when the team goes against the current their actual speed is the still speed minus the speed of the current, then we can rewrite the expression to get:

20 = (s - 6)t

By dividing the first equation by the second one, we get:

From this expression, we can solve for s to get:

Then, the still speed of the rowing team is 9 miles per hour

The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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