Solve log (3x + 4) = log (x – 2) + 3 log 2

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[tex]\qquad \sf  \dashrightarrow \: volume = length \sdot width \sdot height[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = (24) \sdot(15) \sdot(2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: v = 720 \: \: ft {}^{3} [/tex]

now, we know :

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: yard {}^{3} = 27 \: \: ft {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 1 \: \: ft {}^{3} = \cfrac{1}{27} \: \: yard {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 720 \: \: ft {}^{3} = \cfrac{1}{27} \times 720 \: \: yard {}^{3} [/tex]

[tex]\qquad \sf  \approx\: 26.67 \: \: yard {}^{3} [/tex]

now, total cost of ingredients used is :

[tex]\qquad \sf  \dashrightarrow \: 26.67 \times 12.75[/tex]

[tex]\qquad \sf  \dashrightarrow \: 340.04[/tex]

so, total cost is $ 340.04

The pre-image of the triangle has the following vertices: A'(x, y) = (4, 4/3), B'(x, y) = (- 2, 0) and C'(x, y) = (1, 3).

In this problem we must use a transformation rule known as dilation, a kind of rigid transformation, to derive the preimage of the triangle, whose formula is:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]     (1)

Now we proceed to find the preimage of the triangle: O(x, y) = (0, 0), k = 2/3

Point A'

A'(x, y) = (0, 0) + (2/3) · [(6, 2) - (0, 0)]

A'(x, y) = (4, 4/3)

Point B'

B'(x, y) = (0, 0) + (2/3) · [(- 3, 0) - (0, 0)]

B'(x, y) = (- 2, 0)

Point C'

C'(x, y) = (0, 0) + (2/3) · [(1.5, 4.5) - (0, 0)]

C'(x, y) = (1, 3)

The pre-image of the triangle has the following vertices: A'(x, y) = (4, 4/3), B'(x, y) = (- 2, 0) and C'(x, y) = (1, 3).

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The sum of the geometric series is 1328600

The given parameters are:

a1 = 5

r = 3

n = 12

The sum of the terms is:

[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]

This gives

[tex]S_n = \frac{5 * (1 - 3^{12})}{1 - 3}[/tex]

Evaluate the difference

[tex]S_n = \frac{5 * (1 - 531441)}{-2}[/tex]

This gives

[tex]S_n = \frac{5 * - 531440}{-2}[/tex]

Evaluate

[tex]S_n = 1328600[/tex]

Hence, the sum of the geometric series is 1328600

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$1045 was invested at the interest rate 6% whereas $1,995 was invested at 14%

How is interest computed?

Interest is determined as the amount invested multiplied by the interest rate.

Let Y be the amount invested at 6%

Interest=Y*6%

Interest=0.06Y

The amount invested at 14%, which is $950 more , is Y+950

Interest=(Y+950)*14%

Interest=0.14Y+133

Total interest =0.06Y+0.14Y+133

Note that total interest is 342

342=0.06Y+0.14Y+133

342=0.20Y+133

342-133=0.20Y

209=0.20Y

Y=209/0.20

Y=$1,045(amount invested at 6%)

Amount invested at 14%=$1,045+$950

Amount invested at 14%=$1,995

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The height of the leafy part will be 6m.

Other part of the question:

At the same time, a vertical pole 3m high vast s shadow 4m long.

Based on the information given, the height will be:

h/8 = 3/4

h = (3 × 8)/4

h = 6

Therefore, the height is 6m.

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Answer:

8,9,5

Step-by-step explanation:

Cultural identity component of an individual which makes him identifiable with a given group. For example, British Asian is a cultural identity.

Cultural identity can be described as a component of an individual which makes him identifiable with a given group that share the same characteristics.

Examples of cultural identities may include the following:

I can state that I am a British Asian. British Asian is my cultural identity.

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The numerical values of the mean and standard deviation are 4 and 1.55, respectively

The given parameters are:

n = 10

π = 0.4

The probability is then calculated as:

[tex]P(x) = ^nC_x * \pi^x *(1-\pi)^{n-x}[/tex]

So, we have:

[tex]P(6) = ^{10}C_6 * 0.4^6 *(1-0.4)^4[/tex]

Apply the combination formula

[tex]P(6) = \frac{10!}{6!4!} * 0.4^6 *0.6^4[/tex]

So, we have:

[tex]P(6) = 210 * 0.4^6 *0.6^4[/tex]

Evaluate

P(6) = 0.1115

Hence, the numerical value of the probability that x = 6 is 0.1115

The mean value is:

[tex]\bar x = n\pi[/tex]

This gives

[tex]\bar x = 10 * 0.4[/tex]

[tex]\bar x = 4[/tex]

The standard deviation value is:

[tex]\sigma = \sqrt{\bar x(1-\pi)[/tex]

This gives

[tex]\sigma = \sqrt{4(1-0.4)[/tex]

[tex]\sigma = 1.55[/tex]

Hence, the numerical values of the mean and standard deviation are 4 and 1.55, respectively

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Step-by-step explanation:

when you mark such points on a coordinate grid, and mark also the coordinate differences in x and y direction as soft lines, you notice that these coordinate difference lines and the direct connection between the 2 points create a right-angled triangle.

so, Pythagoras applies :

c² = a² + b²

with c being the Hypotenuse (the baseline opposite of the 90° angle, which is the direct connection between the 2 points). a and b are the legs (coordinate differences).

so,

distance² = (8 - 6)² + (2 - 10)² = 2² + (-8)² = 4 + 64 = 68

distance = sqrt(68) = 8.246211251... ≈ 8.2

Using the angle of intersecting tangents theorem, the measure of angle A is: C. 70°

Based on the angle of intersecting tangents theorem, measure of angle A = 1/2(the positive difference of the intercepted arcs).

Measure of one of the intercepted arcs = 250°

The second intercepted arc = 360 - 250 = 110°

Positive difference of the intercepted arcs = 250 - 110 = 140°

Measure of angle A = 1/2(140)

Measure of angle A = 70°

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Answer:

the answer is 70. hope this helps <3

Step-by-step explanation:

Answer:

(x - 5) ^2 + (y -2)^2 = 1

Step-by-step explanation:

This is for a circle.

We need to complete the square

(x^2 -10x      ) + ( y^2 -4y       )  = -28

(x^2 - 10x +25) + (y^2 - 4y 2y) = -28 + 25 + 4

(x-5)^2 + (y-2)^2 = 1

The center of this circle would be (5,2)  with a radius of 1.

Using the probability concept, the odds that the ticket is worth at least $25 are of 1:3.67.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering the probability, the odd is given by:

o = probability:(1 - probability)

From the given table, the probability that the ticket is worth at least $25 is:

p = 0.2 + 0.01 + 0.004 = 0.214.

Hence the odd is:

o = 0.214/(1 - 0.214) = 0.214/0.786 = 1:3.67.

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Answer:

Step-by-step explanation:

no idea tbh

x is 40 degrees

y is 40 degrees

Hope this helps!

Probability someone chosen at random will not have brown hair = 1/6

The number of girls = 15

The number of boys = 15

The total number of children = 15 + 15 = 30

Probability that someone chosen at random will have a brown hair, P(Brown hair) = 5/6

P(Brown hair) + P(Not Brown hair) = 1

5/6  +  P(Not brown hair) = 1

P(not brown hair) = 1 - 5/6

P(not brown hair) = 1/6

Therefore, if someone is chosen at random, probability that they will not have brown hair = 1/6

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I assume [tex]f(x)=0[/tex] otherwise. If [tex]f(x)[/tex] is indeed a proper PDF, then its integral over the support of [tex]X[/tex] is 1.

[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = k \int_0^2 (2x + 3x^2) \, dx = 1[/tex]

Compute the integral.

[tex]\displaystyle \int_0^2 (2x + 3x^2) \, dx = (x^2 + x^3)\bigg|_{x=0}^{x=2} = (2^2 + 2^3) - (0^2 + 0^3) = 12[/tex]

Then

[tex]12k = 1 \implies \boxed{k=\dfrac1{12}}[/tex]

Answer:

I wish I could I didnt do good with this in math

Answer:

[tex]r=\sqrt{\frac{V}{\pi h}}[/tex]

Step-by-step explanation:

[tex]V = \pi r^{2} h \\ \\ r^{2} =\frac{V}{\pi h} \\ \\ r=\sqrt{\frac{V}{\pi h}}[/tex]

LHS = (1-sin² cos²)/(cos²)

= (sin² + cos² - sin² cos²)/(cos²)

= (sin/cos)² + 1 - sin²

= tan² + cos²

= RHS

La relación dada es una función si x = 4 y y = - 1. La representación de la función es f= {(2, 8), (4, 5), (- 2, 9), (3, 9), (5, 4)}.

Las relaciones están formadas por dos conjuntos relacionados entre sí, un conjunto de entrada denominado dominio y uno de salida denominado rango. Una función es una relación cuyos elementos del dominio solo están asociados a un solo valor del rango.

Bajo estas consideraciones, tenemos que (2, 8) = (2, x² - 2 · x) y (3, 9) = (3, y + 4), cuyas ecuaciones algebraicas se resuelven a continuación:

x² - 2 · x = 8     (1)

y + 4 = 9     (2)

By (1):

x² - 2 · x - 8 = 0

(x - 4) · (x + 2) = 0

x = 4 ∨ x = - 2

By (2):

y = 5

Si sabemos que x = 4 y y = - 1, entonces la representación de la función es:

f= {(2, 8), (4, 5), (- 2, 9), (3, 9), (5, 4)}

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Using proportions, it is found that 40 ml of water have to be added to make the ratio of oil to water of 1:3.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The jar contains 100 ml of oil and water in the ratio 1:4, hence:

Oil was added to make the ratio 1/2, hence:

[tex]\frac{20 + x}{100 + x} = \frac{1}[3}[/tex]

3(20 + x) = 100 + x

60 + 3x = 100 + x

x = 20.

Then there are 40 ml of oil and 80 ml of water, for a total of 120 ml. Now we want a ratio of 1:3, that is, 3/4 of the mixture being water, hence:

[tex]\frac{80 + x}{120 + x} = \frac{3}{4}[/tex]

4(80 + x) = 3(120 + x)

320 + 4x = 360 + 3x

x = 40

40 ml of water have to be added to make the ratio of oil to water of 1:3.

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Answer:

Divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

Step-by-step explanation:

Answer:

The value of the slope b/n these two pts. will be 1.

Step-by-step explanation:

Greetings !

For finding slope from two points of a line (x₁, y₁) and (x₂, y₂), we use the formula (y₂ - y₁) / (x₂ - x₁).

Thus, m=(y₂ - y₁) / (x₂ - x₁)

The value of 1376 * 13 is 17888

The expression is given as:

1376 * 13

Express 1376 as 1300 + 76

(1300 + 76) * 13

Expand

1300 * 13 + 76 * 13

Evaluate the product

16900 + 988

Evaluate the sum

17888

Hence, the value of 1376 * 13 is 17888

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Answer:

5:8

Step-by-step explanation:

Nichole sold 15 while Andrew sold 24, so the ratio is 15:24. Simplify the ratio by dividing both sides by 3, and we’ll get 5:8.

Answer:

2

Step-by-step explanation:

Select two points that the red line goes through like (0,-10) and (2,-6).  If I start at the bottom left of the red line, I can see that I am moving to the right and up.  That means that the slope will be positive.  As my x is increasing so is my y.  Starting at point (0,-10) 2 space, but each space counts as 2, so I really move up 4.  Then I check to see how much I moved right.  It is only one space, but again, I am counting by 2s, so I really moved 2 units to the right.  

The fraction would be 4/2 which just equals 2/1  or 2.  

The sequence pattern for 3¹/₃, 3¹/₄, 3¹/₅, ...... is; f(n) = 3 + 1/(2 + n)

We are given the sequence;

3¹/₃, 3¹/₄, 3¹/₅, ......

Now, we can see that;

First term is 3¹/₃.

However, for the second term, 1 has been added to the denominator.

Thus, we can suggest that the sequence pattern here is;

f(n) = 3 + 1/(2 + n)

where n is the nth term.

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The possible zeros of f(x) = 3x^6 + 4x^3 -2x^2 + 4 are [tex]\mathbf{\pm\{1,2,4,\frac 13, \frac 23,\frac{4}{3}}\}[/tex]

The function is given as:

f(x) = 3x^6 + 4x^3 -2x^2 + 4

The leading coefficient of the function is:

p = 3

The constant term is

q = 4

Take the factors of the above terms

p = 1 and 3

q = 1, 2 and 4

The possible zeros are then calculated as:

[tex]\mathbf{Zeros = \pm\frac{Factors\ of\ q}{Factors\ of\ p}}[/tex]

So, we have:

[tex]\mathbf{Zeros = \pm\frac{1,2,4}{1,3}}[/tex]

Expand

[tex]\mathbf{Zeros = \pm\frac{1,2,4}{1},\pm\frac{1,2,4}{3}}[/tex]

Solve

[tex]\mathbf{Zeros = \pm\{1,2,4,\frac 13, \frac 23,\frac{4}{3}}\}[/tex]

Hence, the possible zeros of f(x) = 3x^6 + 4x^3 -2x^2 + 4 are [tex]\mathbf{\pm\{1,2,4,\frac 13, \frac 23,\frac{4}{3}}\}[/tex]

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Climate is the long-term weather pattern that can be seen in an area over a period of years.

Earth’s climate changing as the Earth's atmosphere heats up, it collects, retains, and drops more water, thereby changing weather patterns and making wet areas wetter and dry areas drier.

The factors that affect climate includ deforestation, desertification, urbanization, etc.

Scientists know that recent climate change is largely caused by human activities from an understanding of basic physics by comparing observations with models, and then fingerprinting the detailed patterns of climate change caused by different human and natural influences

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Answer:

At 15 hours of work they will be equal.

Step-by-step explanation:

James: y = 10x + 20

Kelly: y = 8X + 50

Set them equal to each other and solve

10x + 20 = 8x + 50  Subtract 8x from both sides of the equation

2x + 20 = 50  Subtract 20 from both sides of the equation

2x = 30  Divide both sides by 2

x =15

The answers to the question are

b. (l + 2f) (w + 2f)

c. f + 4, f + 6

d.  52.25

a. The diagram is an attachment.

The equation says

(l + 2f) (w + 2f)

We have the lengths of w and l as 8 and 12 respectively. Hence we have

(8 + 2f) (12 + 2f) as the area

c. (8 + 2f) (12 + 2f)

= 96 + 16f + 24f + 4f²

= 4f² + 40 f + 96

We have to factorize this using the quadratic equation calculator

f + 4, f + 6

= f = -4 and f = -6

d. If it is 1.25 thick we would have

1.25 x 2 = 2.5

12 - 2.5 = 9.5

8 - 2.5 = 5.5

Area = l * w

= 5.5 * 9.5

= 52.25

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Answer:

So the questions isn't clear enough, but I could tell u that the nearest answer is the last answer, but without the multiplied 2

It's _15x_35xsquared

Answer:

5x(–3 – 7x)

(5x)(–3) + (5x)(–7x)

–15x – 35x2

Step-by-step explanation:

D