f(x) = | 5x + 1 | - 3
g(x) = 4

Find (f - g) (x)

Answer:

_Area top_= √1/4(a+b+c)(b+c−a)(c+a−b)(a+b−c) + _Area bottom_ √1/4(a+b+c)(b+c−a)(c+a−b)(a+b−c)+ Area lateral =h(a+b+c)

1) Surface Area: 76,017.691

√V=1/4h(a+b+c)(b+c−a)(c+a−b)(a+b−c)

2) Volume: 631,332.519

Volume - given empty space

3) 631,332.519 - 335,954.96= 295,377.559

Percentage of 335,954.96 in 631,332.519=

Bonus Question) 53.21%

Step-by-step explanation:

Answer:

2^0

Step-by-step explanation:

When you are dividing 2 exponents with the same base (in this case, 2) you subtract them. 2^5 ➗ 2^5 => 2^(5-5) = 2^0 => which is equal to 1, but the answer here would be 2^0.

There are two ways to go about this problem.

The first way, the generic way, is to know that,

\(\frac{a^n}{a^m}=a^{n-m},a\neq0\).

So,

\(\frac{2^5}{2^5}=2^{5-5}=\boxed{2^0}\).

The second way is to realise that both numerator and denominator are equal and when diving two equal numbers you obtain 1. (except when diving zeros) aka,

\(\frac{a}{a}=1, a\neq0\)

And 1 equals to any number raised to the power of zero,

\(a^0=1,a\neq0\)

So we just have to say that the 1 we got is rewritten as some base to the power of zero.

Since our base needs to be 2, we just simply say,

\(2^0\).

Et Viola.

Hope this helps.

The rate of discount on the music system during the sale is 13.58%.

The rate of discount is the percentage reduction in the original price of a product during a sale.

The regular cost of the music system is $80,999 and it was sold during the sale for $69,999.

The rate of discount, we first need to find the amount of discount.

We can do this by subtracting the sale price from the regular price:

Discount = Regular price - Sale price

Discount = $80,999 - $69,999

Discount = $11,000

So the discount on the music system during the sale is $11,000.

Next, we can calculate the rate of discount as a percentage of the regular price.

We can use the formula:

Discount rate = (Discount / Regular price) x 100%

Plugging in the values we have:

Discount rate = ($11,000 / $80,999) x 100%

Discount rate = 0.1358 x 100%

Discount rate = 13.58%

The music system was discounted by 13.58% during the sale, resulting in a sale price of $69,999.

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Answer:

20 ringgits.

Step-by-step explanation:

Ratio of $1:4 ringgits

5 * 4=20

The required arc length of sector VW is 8\(\pi\).

Given that, in a circle U, radius  UV = 9 and  central angle of sector m∠VUW = 160°.

To find the arc length of sector VW, we can use the formula:

Arc length = (central angle / 360) x circumference of the circle.

First,  find the circumference of the circle by the  formula for the circumference of a circle is given by:

Circumference = 2 x \(\pi\) x radius.

Circumference = 2 x \(\pi\) x 9 = 18π.

Now, let's find the arc length of sector VW using the central angle of 160 degrees:

Arc length = (160/360) x 18π

Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).

Therefore, the arc length of sector VW is 8\(\pi\).

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The return on portfolio is 4.11%.

The initial investment

Investment in Merck = Number of shares of Merck × Price per share Investment in Merck = 120 shares × $40 per share

Investment in Merck = $4,800

Investment in Yahoo = Number of shares of Yahoo × Price per share Investment in Yahoo = 100 shares × $25 per share

Investment in Yahoo = $2,500

Now, let's calculate the current value of the portfolio

Current value of Merck = Number of shares of Merck × Current price per share

Current value of Merck = 120 shares × $45 per share

Current value of Merck = $5,400

Current value of Yahoo = Number of shares of Yahoo × Current price per share

Current value of Yahoo = 100 shares × $22 per share Current value of Yahoo = $2,200

Current value of the portfolio = Current value of Merck + Current value of Yahoo

Current value of the portfolio = $5,400 + $2,200 Current value of the portfolio = $7,600

To calculate the return on the portfolio, we need to subtract the initial investment from the current value of the portfolio and divide it by the initial investment

Return on portfolio = (Current value of the portfolio - Initial investment) / Initial investment

Return on portfolio = ($7,600 - ($4,800 + $2,500)) / ($4,800 + $2,500)

Return on portfolio = ($7,600 - $7,300) / $7,300

Return on portfolio = $300 / $7,300

Return on portfolio ≈ 0.0411 or 4.11%

Therefore, the return on your portfolio is approximately 4.11%.

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The question is incomplete the complete question is :

Answer:

A) (-4,-3), B) (-1,1.5), D) (0,3)

Step-by-step explanation:

First turn 4y - 6x = 12 to slope intercept form

(y = mx + b), by adding 6x on both sides in order to move it to the other side. So now you have

4y = 6x +12, next divide both sides by 4 in order to get y by its self. Now you have y = 6/4x + 3, since 6 can't be divided by 4 yet 12 can.

Lastly you graph it, here it is graphed for you above⤴⤴⤴

Hope this helped :)

Answer:

2*10²

Reduce the expression, if possible, by cancelling the common factors.

Scientific Notation:

Hi!

Lets go through this together.

Using the operation, PEMDAS, we start from left, then go to right.

since there are two pairs of parenthesis, we start with the one on the left.

(6x10^2)

so now, we do the exponent, 10^2

10x10= 100

So our answer for this part is 100.

Now we have (6x100)

6x100=600

So now, the equation is 600÷(3x10^-3)

Now, we do the parenthesis on the right.

(3x10^-3)

First, we do the exponent, 10^-3

10x-10x-10= 1,000

so now, the equation is (3x1,000)

Now, we multiply.

3x1,000=3,000

So now, the equation is 600 ÷ 3,000

600 ÷ 3,000 = 0.2

So, your answer is 0.2.

__________________________________________________________

(6 x 10^2) ÷ (3 x 10^-3)

=(6 x 100) ÷ (3 x 10^-3)

= 600 ÷ (3 x 10^-3)

= 600 ÷ (3 x 1,000)

= 600 ÷ 3,000

= 0.2

(also, the scientific notation is 2x10^2)

__________________________________________________________

Hope this helps!

Let me know if you need anymore help!

Yours truly,

The definition and explanation of an equation are given below with an example.

in mathematics, an equation is defined as an expression that expresses equality between 2 quantities or expressions. We use equations quite a lot in our daily lives whenever we have to equate two quantities and find out how they are equal. These are used in all branches of science because of the huge purpose they serve.

in simple words it tells what we have on the Left-Hand Side of the "=" sign is the same as what we have on the right-hand side of the statement. Some examples of equations are-

E²=m²c⁴+p²c²

x²+3x-1=0

70 oranges= 7 oranges × 10 oranges

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Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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Answer:

Step-by-step explanation:

2x+15+x+10+3x+5=180 degree(sum of interior angles of a triangle)

6x+30=180

6x=180-30

x=150/6

x=25

therefore the value of x is 25 degree.

Answer:

I think the answer is odd. I am not sure because I don't know this topic really well.

Step-by-step explanation:

The area of the spill is increasing at a rate of 90π square inches per minute when the radius is 18 inches.

The formula for the area of a circle is A = πr², where A is the area and r is the radius.

We are given that the radius of the spill is increasing at a constant rate of 2.5 inches per minute, which means dr/dt = 2.5 inches/minute.

We want to find dA/dt, the rate of change of the area with respect to time.

We differentiate the area formula with respect to time:

dA/dt = d/dt (πr²)

To differentiate the equation, we can use the chain rule:

dA/dt = d(πr²)/dr × dr/dt

Now let's substitute the given values.

We are asked to find dA/dt when the radius of the spill is 18 inches

so r = 18 inches. Also, dr/dt = 2.5 inches/minute.

dA/dt = d(π(18)²)/dr × 2.5

Simplifying the equation:

dA/dt = 2π(18) × 2.5

dA/dt = 90π

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Answer:

Step-by-step explanation:

To find the normal plane and osculating plane, we first need to find the required derivatives.

x = 5t, y = t^2, z = t^3

dx/dt = 5, dy/dt = 2t, dz/dt = 3t^2

So, the velocity vector v and acceleration vector a are:

v = <5, 2t, 3t^2>

a = <0, 2, 6t>

Now, let's evaluate them at t = 1 since the point (5, 1, 1) is given.

v(1) = <5, 2, 3>

a(1) = <0, 2, 6>

The normal vector N is the unit vector in the direction of a:

N = a/|a| = <0, 1/√10, 3/√10>

Using the point-normal form of the equation for a plane:

normal plane equation = 0(x-5) + 1/√10(y-1) + 3/√10(z-1) = 0

Simplifying this equation we get:

5x + 2y + 3z = 30

The osculating plane can be found using the formula:

osculating plane equation = r(t) · [(r(t) x r''(t))] = 0

where r(t) is the position vector, and x is the cross product.

At t = 1, the position vector r(1) is <5, 1, 1>, v(1) is <5, 2, 3>, and a(1) is <0, 2, 6>.

r(1) x v(1) = <-1, 22, -5>

r(1) x a(1) = <12, -6, -10>

v(1) x a(1) = <-12, 0, 10>

Substituting these values into the formula, we get:

osculating plane equation = (x-5, y-1, z-1) · <12, -6, -10> = 0

Simplifying this equation we get:

3x - 15y + 5z = 5

Therefore, the equations for the normal plane and osculating plane at (5, 1, 1) are:

(a) 5x + 2y + 3z = 30

(b) 3x - 15y + 5z = 5

Answer:

x = y = 20

Step-by-step explanation:

The two triangles shown are similar because one is simply an extension of othe other.

From this, we can use a similar side lengths formula specifically for triangles.

\(\frac{y + 5}{y} = \frac{15}{12}\\\)

Notice that this represents the ratio of the whole side to the smaller side and says that this proportion is equal to the proportion for its adjacent side lengths. Cross mutiply the above equation to solve for y.

12(y+5) = 15y

12y + 60 = 15y

y = 20

Now we need to find the value of x. We have a side and hypotenuse's length of this large triangle, so we can use the pythagorean theorem to calculate the unknown side length.

(12 + 3)² + x² = (20 + 5)²

15² + x² = 25²

225 + x² = 625

x² = 400

x = ±20

The negative 20 doesn't make sense for this application so use the positive 20.

Therefore x = 20, y = 20.

Answer:

\( \pi\)

Step-by-step explanation:

\( Lim_{x \to\pi} f(x) \)

\( =Lim_{x \to\pi} \pi \)

(\( \because for\: x =\pi, \: f(x) = \pi\))

\( = \pi \) (Applying limit)

The given equation is dR/R = k dt, where dR represents the change in R and dt represents the change in time t. To solve this differential equation, we can separate the variables and integrate both sides.

Starting with the equation dR/R = k dt, we can rewrite it as dR = kR dt. Then, dividing both sides by R gives dR/R = k dt.

Next, we integrate both sides. On the left side, we have ∫dR/R, which evaluates to ln|R|. On the right side, we have ∫k dt, which evaluates to kt.

Therefore, the equation becomes ln|R| = kt + C, where C is the constant of integration.

To find the general solution, we can exponentiate both sides to eliminate the natural logarithm: |R| = e^(kt + C). Since e^C is a positive constant, we can rewrite this as |R| = Ce^kt. Finally, we can consider two cases: when R is positive, we have R = Ce^kt, and when R is negative, we have R = -Ce^kt. So, the general solution is R = Ce^kt or R = -Ce^kt, where C is an arbitrary constant.

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If you want to find out if differences exist between thirty car brands on their average miles per gallon. You should perform ANOVA test. The correct answer is B.

To compare the average miles per gallon across thirty car brands, the appropriate test to perform would be ANOVA (Analysis of Variance). ANOVA is used when comparing the means of three or more groups to determine if there are significant differences between them. In this case, you have thirty car brands, which qualify for an ANOVA analysis.

ANOVA (Analysis of Variance) is a statistical test used to compare the means of three or more groups or treatments to determine if there are significant differences between them. It analyzes the variation between the group means and compares it to the variation within the groups.

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Given:

The inequality is:

\(6x+\dfrac{1}{4}(4x+3)>12\)

To find:

The values for x.

Solution:

We have,

\(6x+\dfrac{1}{4}(4x+3)>12\)

Using distributive property, we get

\(6x+\dfrac{1}{4}(4x)+\dfrac{1}{4}(3)>12\)

\(6x+x+\dfrac{3}{4}>12\)

\(7x>12-\dfrac{3}{4}\)

\(7x>\dfrac{48-3}{4}\)

On further simplification, we get

\(7x>\dfrac{45}{4}\)

Divide both sides by 7.

\(x>\dfrac{45}{7\times 4}\)

\(x>\dfrac{45}{28}\)

Therefore, the required solution is \(x>\dfrac{45}{28}\).

Note: All options are incorrect.

Answer:

-5

Step-by-step explanation:

-5x+6 = 2(-3x + 1) + x - 16

-5x+6 = -6x + 2 + x - 16

-5x+6 = -5x -14

+6≠-14⇒x∈Ф

The probability that a committee of four people randomly selected from the group of 5 married couples does not include a husband and his wife is approximately 2.976%.

To calculate the probability that a committee of four people randomly selected from a group of 5 married couples does not include a husband and his wife, we need to consider the total number of possible committees and the number of committees that do not include a husband and his wife.

Total number of possible committees:

To select a committee of four people, we need to choose four individuals from a total of 10 individuals (5 couples). This can be calculated using combinations:

Number of ways to choose 4 individuals out of 10 = C(10, 4) = 10! / (4! * (10-4)!) = 210

Number of committees that do not include a husband and his wife:

To form a committee without a husband and his wife, we can select one individual from each of the 5 couples, which gives us 5 possibilities for each couple. Since we need to select four individuals, the total number of committees without a husband and his wife can be calculated as:

Number of ways to choose 1 individual from each of the 5 couples = 5^4 = 625

Now, we can calculate the probability:

Probability = Number of committees without a husband and his wife / Total number of possible committees

= 625 / 210

≈ 2.976

Therefore, the probability that a committee of four people randomly selected from the group of 5 married couples does not include a husband and his wife is approximately 2.976%.

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Answer:

x=1, y=-6. (1, -6).

Step-by-step explanation:

y=-6x

-2x-7y=40

------------------

-2x-7(-6x)=40

-2x+42x=40

40x=40

x=40/40

x=1

y=-6(1)=-6

By using subtraction, Brenda needs an additional amount of $ 182.75 for the school trip.

In this question we notice that Brenda is aware of how much money she needs to make her school trip and besides we find a table with all the money saved during a 4-month period. Lastly, we must determine if the amount of money saved by Brenda is sufficient or not.

The money needed for the school trip is:

y = $ 197 + $ 230 + $ 85

y = $ 512

And the money saved by Brenda is:

x = $ 67 + $ 30.50 + $ 160 + $ 71.75

x = $ 329.25

Then, the additional money needed for Brenda is found by subtacting the second result from the first result:

z = y - x

z = $ 512 - $ 329.25

z = $ 182.75

Brenda needs an additional amount of $ 182.75 for the school trip.

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Answer:

\(the \: answer \: is \: b \\ 4x = y \\ 2 {x}^{2} - y = 0 \\ 2 {x}^{2} - 4x = 0 \\ 2x(x - 2) = 0 \\ x = 0 \: and \: x = 2 \\ y = 0 \: and \: y = 8\)

b.

Bedroom area

Lenght = 5 squares

= 5 × 1/4 inchi

= 5/4 inchi

Width = 4 squares

= 4 × 1/4 inchi

= 1 inchi

Large area = 5/4 × 1 inchi

= 5/4 inchi

Living room

Lenght = 7 squares

= 7 × 1/4 inchi

= 7/4 inchi

Width = 4 squares

= 4 × 1/4 inchi

= 1 inchi

Large area = 7/4 × 1 inchi

= 7/4 inchi

Total Area

Bedroom area + Living room area

= 5/4 + 7/4

= (5+7)/4 inchi

= 12/4 inchi

= 3 inchi

1 square yard = 1296 square inches

so 1 square inches = 1/1296 square yard

3 inchi = 3×1/1296

= 3/1296

= 1/432

Cost = 1/432 × $18

= $1/24

It would cost $1/24 to carpet the bedroom and living room.

The highest common factor (H.C.F.) of 'a' and 'b' can be determined by finding the greatest common divisor of 14 and 1 since 'a' is a multiple of 'b' and 'b' is a factor of 'a'. Therefore, the H.C.F. of 'a' and 'b' is 1.

Given that 'a' and 'b' are two positive integers and a = 14b, we can see that 'a' is a multiple of 'b'. In other words, 'b' is a factor of 'a'. To find the H.C.F. of 'a' and 'b', we need to determine the greatest common divisor (G.C.D.) of 'a' and 'b'.

In this case, the number 14 is a multiple of 1 (14 = 1 * 14) and 1 is a factor of any positive integer, including 'b'. Therefore, the G.C.D. of 14 and 1 is 1.

Since 'b' is a factor of 'a' and 1 is the highest common divisor of 'b' and 14, it follows that 1 is the H.C.F. of 'a' and 'b'.

In conclusion, the H.C.F. of 'a' and 'b' is 1, indicating that 'a' and 'b' have no common factors other than 1.

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Answer:

2.015 is already in decimals. In words it is two and fifteen thousandths.

The probability of success on trial 9 is  0.072.

A binomial experiment consists of 12 trials, and the probability of success on trial 5 is 0.3. To find the probability of success on trial 9, we need to calculate the probability of not having a success in the first 8 trials and then having a success on trial 9.

Since the probability of success on trial 5 is 0.3, the probability of failure on trial 5 is 1 - 0.3 = 0.7.

Similarly, the probability of not having a success on trial 6, 7, and 8 is also 0.7.

Therefore, the probability of not having a success in the first 8 trials is (0.7)^4 = 0.2401.

To find the probability of success on trial 9, we need to multiply the probability of not having a success in the first 8 trials by the probability of success on trial 9.

So, the probability of success on trial 9 is 0.2401 * 0.3 = 0.072.

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The probability of success on trial 9 in a binomial experiment can be calculated using the binomial probability formula. The formula is given by P(X = k) = C(n, k) * p^k * q^(n-k), p is the probability of success on a single trial, and q is the probability of failure on a single trial (1 - p). To calculate C(12, 9), we can use the formula for combinations: C(n, k) = n! / (k! * (n-k)!). In this case, C(12, 9) = 12! / (9! * (12-9)!).

In this case, we know that there are 12 trials and the probability of success on trial 5 is 0.3. To find the probability of success on trial 9, we need to determine the values of n, k, p, and q.

Here's the step-by-step calculation:

1. n = 12 (number of trials)
2. k = 9 (number of successes on trial 9)
3. p = 0.3 (probability of success on a single trial)
4. q = 1 - p = 1 - 0.3 = 0.7 (probability of failure on a single trial)

Now, we can substitute these values into the binomial probability formula:

P(X = 9) = C(12, 9) * 0.3^9 * 0.7^(12-9)

To calculate C(12, 9), we can use the formula for combinations: C(n, k) = n! / (k! * (n-k)!). In this case, C(12, 9) = 12! / (9! * (12-9)!).

After substituting all the values into the formula, we can simplify and calculate the probability of success on trial 9.

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Based on the coordinates of the vertices of the parallelogram ORST, the coordinates of S can be found to be (a + b, d).

As this is a parallelogram, the horizontal distance between O and R would be the same as the horizontal distance between S and T.

The horizontal distance between O and R is represented by "b".

The horizontal distance between T and S would therefore be:

= a + b

The fact that R and S are on the same plane would mean that the y-value of S is the same as that of R which is d.

The coordinates of S is:

( a + b, d).

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