If 90% of a drink is real fruit juice, what per cent is not fruit juice?

The identity \(\frac{d}{dz}\log z = \frac{1}{z}\) is proven by expressing \(\log z\) in terms of its real and imaginary components and applying the chain rule.

To prove the identity \(\frac{d}{dz}\log z = \frac{1}{z}\), we can start by expressing \(\log z\) in terms of its real and imaginary components: \(\log z = \log |z| + i\arg(z)\). Then, we differentiate both sides using the chain rule. The derivative of \(\log |z|\) with respect to \(z\) is zero since it depends only on the magnitude of \(z\). For the second term, \(\frac{d}{dz}(i\arg(z)) = i\frac{d}{dz}\arg(z) = i\frac{1}{|z|}\), which simplifies to \(\frac{1}{z}\) after expressing \(z\) in polar form. Thus, \(\frac{d}{dz}\log z = \frac{1}{z}\) is proven.

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Answer:

The answer is 6

Step-by-step explanation:

⅔(18 - 9)

2/3 (9) = 2 × 3 = 6

Thus, The answer is 6

-TheUnknownScientist 72

Answer:

Step-by-step explanation:

\(\dfrac{2}{3}(18 - 9) = \dfrac{2}{3}*9 = 2 *3 = 6\)

Answer:

The 43rd day of spending $45.

Step-by-step explanation:

Let the number of days = x.

If she spends $45 per day, then in x days she spends 45x.

She starts with $2400, so 45x is subtracted from 2400.

2400 - 45x < 500

Subtract 2400 from both sides.

-45x < -1900

Divide both sides by -45. Remember to change the direction of the inequality sign when multiplying or dividing by a negative number.

x > 42.2

Answer: The first day is the 43rd day of spending $45.

Answer:

her mistake was at 12-6+4

instead of adding 4 to negative six she subtracted it really should by 10-2 ad her answer should be 8

Step-by-step explanation:

Answer:

f(x)=(5+a)/(a-1)

Step-by-step explanation:

input a+2 for x

f(x)=(a+5)/(a-1)

and no ur not dumb u just need practice :D

Answer:

-4 and 1/7 is your answer.

Step-by-step explanation:

\(f(x)=\frac{3}{19+2} -\sqrt{19-3}\)

The magnitude of the resultant velocity of the soccer ball is 25.06 m/s .

Let the horizontal component of velocity be \(V_{x}\) and the vertical component  of velocity be \(V_{y}\).

The magnitude of the resultant velocity will be represented by V.

So, we can write

The horizontal component of velocity = \(V_{x}\) = 22 m/s

The vertical component  of velocity = \(V_{y}\) = 12 m/s

The relation between horizontal component, vertical component and resultant velocity is,

\(V^{2} = V_{x} ^{2} + V_{y} ^{2}\)

On substituting value of horizontal component and vertical component, we get

\(V^{2}\) = \((22)^{2} + (12)^{2}\)

\(V^{2}\) = 484 + 144

\(V^{2}\) = 628

V = \(\sqrt{628}\)

V = 25.06 m/s

The magnitude of the resultant velocity of the soccer ball is 25.06 m/s .

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Answers:

RS = 13

ST = 8

==================================================

Explanation:

S is between R and T. I'm assuming also that S is on line RT.

If that's the case, then by the segment addition postulate, we can say  RS+ST = RT.

In other words, the longest segment RT is broken into two smaller pieces RS and ST (not necessarily equal but they may be). Gluing the pieces back together should get us the original longest segment.

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

Apply substitution and solve for x.

RS+ST = RT

(2x+5)+(3x-4) = 21

(2x+3x)+(5-4) = 21

5x+1 = 21

5x = 21-1

5x = 20

x = 20/5

x = 4

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

If x = 4, then,

Then notice how RS+ST = 13+8 = 21, which is is the length of RT

This confirms that RS+ST = RT is true and it confirms our answers.

The correct answer is b. Each block should consist of volunteers who live in similar environments when it comes to mosquitoes.

Explanation:

In a randomized block design, blocks are formed to control for potential confounding factors or sources of variation that may affect the outcome of the experiment. By forming blocks based on similar environments when it comes to mosquitoes, the researchers ensure that any differences in the effectiveness of the bracelet and bug spray are not solely due to variations in mosquito exposure.

If the researchers were to choose option a (both the volunteers and researchers should be kept blind as to which block the volunteers are in), it would be related to blinding the participants and researchers to the treatment assignment, not forming blocks. This method does not address the need for controlling potential confounding factors.

Option c (each block should consist of volunteers who live in different environments when it comes to mosquitoes) would not be suitable because it would introduce additional variability and make it difficult to compare the effectiveness of the bracelet and bug spray.

Option d (each volunteer should be randomly assigned to a block) is not recommended in this case because it does not take into account potential confounding factors related to mosquito exposure.

Option e (volunteers in one block should use the bracelet, while volunteers in the other block should use bug spray) does not control for potential confounding factors, as individuals in different blocks may have different levels of mosquito exposure.

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The equation of the line that passes through the point (14,3) and is perpendicular to the given equation is y = x - 11.

To solve the equation 5(y+x)-6(x-y)=-8, we need to use the distributive property and combine like terms.

5(y+x)-6(x-y)=-8

Distribute the 5 and -6:

5y + 5x - 6x + 6y = -8

Combine like terms:

11y - x = -8

Now, we need to find the slope of the line that passes through the point (14,3) and is perpendicular to the given equation.

The slope of the given equation is -1, so the slope of the perpendicular line is the negative reciprocal, which is 1.

Using the point-slope form, we can write the equation of the perpendicular line:

y - 3 = 1(x - 14)

Distribute the 1:

y - 3 = x - 14

Add 3 to both sides:

y = x - 11

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If total income is $55,000, his exemptions total $8,700, and his deductions are $8,540 and $1,500, Roger's taxable income is $36,260.

To determine Roger's taxable income, we need to subtract his exemptions and deductions from his total income.

First, we add up his exemptions:

$8,700

Next, we add up his deductions:

$8,540 + $1,500 = $10,040

We then subtract the total exemptions and deductions from his total income:

$55,000 - $8,700 - $10,040 = $36,260

Therefore, Roger's taxable income is $36,260. This is the amount of income he will be taxed on according to the tax laws in his country or region.

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Answer:

13m

Step-by-step explanation:

Use Pythagoras's theorem to find the hypotenuse length (line PQ)

1. 34- 29= 5m

2. hypotenuse= \(\sqrt{a^{2} +b^{2} }\)

--> a= 5m

--> b=12m

3. hypotenuse= \(\sqrt{25+144}\)

4. hypotenuse= \(\sqrt{169}\)

5. hypotenuse= 13m

a) The limit as x approaches 0 of (sin(x) - cos(x) + 1) / (x^2 + 1) is equal to 1.

b) The limit as x approaches -1 is undefined.

a. As x approaches 0, both sin(x) and cos(x) approach 0. Thus, the numerator approaches 0 + 1 = 1. The denominator, x^2 + 1, approaches 0^2 + 1 = 1. Therefore, the overall limit is 1.

b. In the given question, it seems like the symbol "#" is used instead of "x." Regardless, let's assume the variable is x. The limit as x approaches -1 involves finding the behavior of the function as x gets arbitrarily close to -1.

If there is no additional information provided about the function or expression, we cannot determine its limit as x approaches -1. The limit might exist or not depending on the specific function or expression involved. It is essential to have more context or specific instructions to evaluate the limit accurately.

In summary, without further information, the limit as x approaches -1 is indeterminate or undefined.

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Yes, the given statement is true if the variance of the population 'a' is smaller than the variance of population 'b' it represents that population 'b' is more variable than 'a'.

Therefore, the given statement is true for the variance of population 'a' and 'b'.

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If the columns of matrix B are linearly dependent, then the columns of AB are also linearly dependent.

Suppose the columns of matrix B are linearly dependent, which means there exist constants c₁, c₂, ..., cₙ (not all zero) such that c₁b₁ + c₂b₂ + ... + cₙbₙ = 0, where b₁, b₂, ..., bₙ are the columns of B.

Now, let's consider the product AB. Suppose A is an m × n matrix.

The jth column of AB is given by the product AB(:, j) = A(b₁j) + A(b₂j) + ... + A(bₙj), where b₁j, b₂j, ..., bₙj are the jth columns of B.

Substituting the linear dependence relation for the columns of B into the expression for AB(:, j), we get:

AB(:, j) = A(c₁b₁ + c₂b₂ + ... + cₙbₙ)

         = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

Since matrix multiplication distributes over column vectors, we have:

AB(:, j) = c₁A(b₁) + c₂A(b₂) + ... + cₙA(bₙ)

This shows that the jth column of AB can be expressed as a linear combination of the columns of A, multiplied by the corresponding coefficients c₁, c₂, ..., cₙ. Therefore, if the columns of B are linearly dependent, the columns of AB are also linearly dependent.

In conclusion, if the columns of matrix B are linearly dependent, then so are the columns of the product AB.

Complete Question:

Show that if the columns of B are linearly dependent, then so are the columns of AB.

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The registrants would be able to see the 6 sightseeing tours in 18 ways.

Here it is given that the convention has organized the 6 sightseeing tours on 3 days each.

This implies that the 6 sightseeing tours are available on all three days.

Hence, the registrants would be able to book the tour on any of the one days.

Hence, on day 1

the registrants will be able to tour in  ways

On day 2

the registrants would again be able to tour in 6 ways,

Similarly on day 3, they will again be able to tour in 6 ways.

Since they need to choose either of the days given, the total number of ways to tour will be

no.of ways for day 1  +  no. of ways for day 2  +  no. of d6ays for day 3

= 6  +  6  +  6

= 18 ways

Hence, they can go on a sightseeing tour in 18 ways.

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Answer:

The probability that a randomly selected camper likes to have a cookout will be 0.93.

Step-by-step explanation:

did it already.

Answer:   To solve this problem, we need to find the probability that a randomly selected camper likes swimming or having a cookout, but not both. We can do this by using the formula:

P(S or C, but not both) = P(S) + P(C) - 2P(S and C)

We are given the following probabilities from the Venn diagram:

P(S) = 0.06 (the proportion of the circle labeled S)

P(C) = 0.04 (the proportion of the circle labeled C)

P(S and C) = 0.89 (the proportion of the shared area)

Substituting these values into the formula, we get:

P(S or C, but not both) = 0.06 + 0.04 - 2(0.89)

= 0.10 - 1.78

= -1.68

This is not a valid probability, as probabilities cannot be negative. Therefore, there must be an error in the problem statement or the Venn diagram. Please check the values again and ensure they are correct.

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

in math, dilate means changing the size of an object without changing its shape

Have a good day, sorry if I'm wrong:)

(if I am wrong, plz tell me<3)

Answer:

\( \pm \sqrt{13} \)

Step-by-step explanation:

\( \bigg(a + \frac{1}{a} \bigg)^{2} = {a}^{2} + \frac{1}{ {a}^{2} } + 2 \times a \times \frac{1}{a} \\ \\ \bigg(a + \frac{1}{a} \bigg)^{2} = 11 + 2 \\ \\ \bigg(a + \frac{1}{a} \bigg)^{2} = 13 \\ \\ \bigg(a + \frac{1}{a} \bigg) = \pm \sqrt{13} \)

The approximate energy requirement for the car when driven at 95 km/h is 789.47 kcal/km.

We have,

If a car averages 38 km/gal when driven at 95 km/h, we can calculate the fuel consumption in gallons per kilometer (gal/km).

Fuel consumption (gal/km) = 1 / (average fuel efficiency in km/gal)

Fuel consumption (gal/km) = 1 / 38

Now, to determine the energy requirement in kcal per kilometer (kcal/km), we multiply the fuel consumption by the energy released per gallon of gasoline:

Energy requirement (kcal/km) = Fuel consumption (gal/km) * Energy released per gallon (kcal/gal)

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

Now,

Fuel consumption (gal/km) = 1 / 38

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

≈ 789.47 kcal/km

Therefore,

The approximate energy requirement for the car when driven at 95 km/h is 789.47 kcal/km.

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The complete question:

"Burning gasoline in a car releases approximately 3 x 10^4 kcal/gal. If a car averages 38 km/gal when driven at 95 km/h, what is the energy requirement in kcal per kilometer (kcal/km) for the car?"

the total amount of money that jayden made when both paychecks were the same is $99.45

To determine the number of hours Jayden worked the week his paycheck was the same for both jobs, we can solve an equation. The equation we'll use is 14.86h + 17.10 = 99.45. We can subtract 17.10 from both sides, leaving 14.86h = 82.35. Then we cane b divide both sides of the equation by 14.86, which will give us the result of h = 5.55 hours. The total amount of money that Jayden made when both paychecks were the same is 99.45. This can be confirmed by combining his earnings for both jobs, which would be 9.64h + 82.35 + 14.86h + 17.10 = 99.45.

Jayden worked 5.55 hours in the week his paycheck was the same for both jobs, and he earned a total of $99.45.

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The algebraic expression which would not have the same meaning if the number and variable were reversed is; m-k.

It follows from the associative property of real numbers that changing the grouping of adding or multiplying real numbers does not change the result.

Hence, only the expression with the subtraction sign will change as a result of reversing the number and variable.

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Answer:

There are three more square chocolates left

Step-by-step explanation:

We know that Irena breaks off 2 complete strips and eats 12 meaning each strip had 6 squares. Jack breaks off 9. So if we add all the squares into rows of 6, we get four strips of chocolate from the beginning. Since Jack and Irena obtained 21 chocolate squares altogether, we have 3 chocolate squares that are remaining. I hope this helps ;)

The number of Squares of chocolate left in the bar is; 15 squares

A square has 4 equal sides and since one row contains 6 squares because irena ate 2 complete rows that had 12 squares.

It means that each of the vertical height must also contain 6 squares as well.

Now, two rows are gone and so we now have 4 rows with vertical height of 4 squares. That is 24 squares left.

Now, Jack ate 9 squares and so;

Amount of squares left = 25 - 9 = 15

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The graph of the exponential function y = (3/4)^x is given by the following option:

Option A.

The general format of an exponential function is defined as follows:

\(y = ab^x\)

The meaning of the parameters a and b are given as follows:

In this problem, the function is given by:

y = (3/4)^x.

Hence the values of the parameters are:

a = 1, b = 3/4.

The parameter a = 1 means that the function crosses the y-axis at y = 1, hence options B and C are removed.

From the table given in the problem, at x = -2 the function is very close to 2, while it decreases to a value close to 0.5 at x = 2, hence option A is the correct option for the graph of the exponential function.

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Answer:

x = notebooks

y = indexboks

3x+4y=32 ( here is spent all money so I add 32 here )

5x+5y=50

by elemination method

3x+4y=32×5

5x+5y=50×4 ( here I'm going to eliminate y )

15 x+20y= 160

20x+20y= 200

- - = -

____________

-5x = -40

x = - 40 / -5

x = 8

here - × - = + so iam taking positive 8

now substitute the value of x in any equation

3×8+4y = 32

24 + 4y = 32

4y = 32-24

y = 8 / 4

y = 2

CHECKING

SUBSTITUTE BOTH VALUES IN ANY EQUATION

5×8+5×2 = 50

40 + 10 = 50

50 = 50

I SUBSTITUTE IN 2ND EQUATION

Answer:

(8,2)

Step-by-step explanation:

Given that:

3x + 4y = 32  --------- eq1

5x + 5y = 50 --------- eq2

From taking 5 common from eq2:

x + y = 10

Or it can also be written as:

x = 10 - y ----------eq3

Now put this value of x in eq1

3(10 - y) + 4y = 32

By simplifying:

30 - 3y +4y= 32

30 +y = 32

Subtracting 30 from both sides:

y = 32 - 30

y = 2

Putting value of y in eq 3

x = 10 - 2

x = 8

Answer:

Step-by-step explanation:

according to the question expression can be written as

=3(2+4)

Answer:

I thinkkk Roses -11 feet per min and Lucy is 10 feet per min

Step-by-step explanation:

Answer:

k = 5

Step-by-step explanation:

\((x + 2)(x + 3) = {x}^{2} + 5x + 6\)

Now comparing left hand side & right hand side ,

\( {x}^{2} + kx + 6 = {x}^{2} + 5x + 6\)

Cancelling x^2 & 6 from both left hand side & right hand side ,

kx = 5x

=> k = 5

Answer:

a) \(2\frac{3}{8}\)

b) \(28\frac{1}{2}\)

Step-by-step explanation:

\(1\frac{3}{8} +1=2\frac{3}{8}\)

\(2\frac{3}{8}\) × 12 = \(28\frac{1}{2}\)

Answer:

x² - 4x + 3 = 0

Step-by-step explanation:

given roots x = a and x = b then the corresponding factors are

(x - a) and (x - b)

the equation is then the product of these factors , that is

(x - a)(x - b) = 0

given

roots x = 3 and x = 1 , then factors are (x - 3) and (x - 1) , then

(x - 3)(x - 1) = 0 ← expand factors using FOIL

x² - 4x + 3 = 0