Determine the smallest integer value of x in the solution of the following inequality.
5x7-1

To divide complex numbers, you multiply by the conjugate of the denominator:

    [tex]\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i}[/tex]

We do this to turn the denominator into a real number.

[tex]\begin{aligned}\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i} &= \dfrac{-9+6i-18i+12i^2}{9-4i^2}\\[0.5em] &= \dfrac{-9-12i-12}{9+4}\\[0.5em] &= \dfrac{-21-12i}{13}\\[0.5em] &= -\dfrac{21}{13}-\dfrac{12}{13}i\end{aligned}[/tex]

Answer:

[tex]-\dfrac{21}{13}-\dfrac{12}{13}i[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{-3-6i}{3+2i}[/tex]

Multiply the numerator and denominator by the complex conjugate of the denominator:

[tex]\implies \dfrac{-3-6i}{3+2i} \cdot \dfrac{3-2i}{3-2i}[/tex]

Simplify:

[tex]\implies \dfrac{(-3-6i)(3-2i)}{(3+2i)(3-2i)}[/tex]

[tex]\implies \dfrac{-9+6i-18i+12i^2}{9-4i^2}[/tex]

[tex]\implies \dfrac{-9-12i+12i^2}{9-4i^2}[/tex]

Apply the imaginary number rule [tex]i^2=-1[/tex] :

[tex]\implies \dfrac{-9-12i+12(-1)}{9-4(-1)}[/tex]

[tex]\implies \dfrac{-9-12i-12}{9+4}[/tex]

[tex]\implies \dfrac{-21-12i}{13}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a-b}{c}=\dfrac{a}{c}-\dfrac{b}{c}:[/tex]

[tex]\implies -\dfrac{21}{13}-\dfrac{12}{13}i[/tex]

Answer:

There are 80 coins in her collection.

Step-by-step explanation:

We can find out how many coins are in her coin collection by first converting 5% into a fraction by moving the decimal place to the left twice. Which then we get 0.05. Then, we can set up this equation:

4 ÷ 0.05 = 80

Now, let's check our answer:

0.05 x 80 = 4.

Yep! It checks out!

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The values of x and y are x = 80° and y = 130°.

What is conservative interior angles?

When a line, referred to as the transversal line, crosses two other lines, two angles are created that are known as consecutive interior angles. Consecutive interior angles, or co-interior angles for short, are the angles formed on the inside of the two lines and on the same side of the transversal line.

Consecutive interior angle CONVERSE is another name for the same side interior angle CONVERSE.

Line line n || m

if (x - 30) + (x + 50) = 180.

x -  30 + x + 50 = 180

2x + 20 = 180

subtract 20 from both sides

2x = 160

divide both sides by 2

x = 80

IF (x - 30) + y = 180, then k || j.

(80 - 30) + y = 180

50 + y = 180

subtract 50 from both sides

y = 130

Hence, the values of x and y are x = 80° and y = 130°.

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Complete question:

Complete question is attached below,

The numerical value of the statistic ^p or sample proportion (p-hat) is 0.2.

^p = X/N where X denotes the number of successes and N denotes the size of the sample. Here, X=55 and N=11.

Sample Proportion (p-hat) of the data:

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Outside temperature over a day can be modeled as a sinusoidal function. suppose you know the temperature is 65 degrees at midnight and the high and low temperature during the day are 76 and 54 degrees, respectively. assuming t is the number of hours since midnight, the temperature, d, in terms of t. The Equation is :

                                    D = - 11 sin(π/12) + 65

The range is 76 - 54 = 22

so, a = 11

we know that the period is 24 hours

So, 2π/k=24

  ⇒ 24k = 2π

⇒ k = π/12

So far we have:

D = 11 sin(π/12)(t) + 65

Giving us a range from 76 to 54

But obviously the temp after midnight would decrease, whereas our function has it increasing to 76 when t = 6 (6:00 am)

We could do a phase shift, or more simply, just flip the function to

D = -11sin(π/12)t + 76

Checking some values

t = 0 , D = -11sin0 + 65 = 65

t=6 , (6:00 am) D = -11 sin (π/2) + 65 = 54

t = 12 (noon), D = -11 sin π + 65 = 65

t = 18 , (6:00 pm) , D = -11sin 3π/2 + 65 = 76

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Answer:

gradient = 2

Step-by-step explanation:

calculate the gradient m using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 5) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line

m = [tex]\frac{-1-(-5)}{2-0}[/tex] = [tex]\frac{-1+5}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer:

t >28= the temp is warmer than 28

t >29= the table is heavier than 29 kilos

t <29= tony is you get than 29 yrs old

t <28= tia ran the race in under 28 secs

Step-by-step explanation:

hope this helps

From the given statement the mean mcr rt tomatometer score is significantly above fresh.  

What is tomatometer score?

The Tomatometer score represents the percentage of professional critic reviews that are positive for a given film or television show.

To find answer we need to perform hypothesis.

The mean MCU Rotten Tomatoes score is equal to or less than 75%, which is the null hypothesis.

The mean MCU Rotten Tomatoes score is more than 75%, which is the alternative hypothesis. To test this theory, we can use a one-tailed t-test.

The null hypothesis can be rejected if the p-value is less than the significance level, which is typically 0.05, at which point it can be determined that the mean MCU Rotten Tomatoes score significantly exceeds fresh.

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As per the question the required hypothesis are

Null Hypothesis, H0: p=0.72

Alternate Hypothesis, H1 : p ≠ 0.72

The null hypothesis reflects that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H0.

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample.

Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses.

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The experimental probability of an odd number other than 9 being generated is 38%.

For the stated question-

Other odd numbers outside nine are as follows: 72 - 15 = 57

Probability =  (number of odd numbers except nine)]/(total number)

Probability = 57/150

Probability = 0.38.

Thus, the experimental probability of an odd number other than 9 being generated is 38%.

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Short Answer:

The given equation has one solution; [tex]n=0[/tex].

______________________________________________________

"How Can You Determine Whether An Equation Has One Solution, Infinite Solutions, or No Solution?"

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This being said, lets now go back to the given scenario and determine the amount of solutions it has, if any.

1. We are given the following to solve:

2. First, subtract 1 from both sides.

3. Simplify.

4. Move 4n to the left side, leaving us with our final solution.

____________________________________________________

Hope this helps!

Answer:

Step-by-step explanation:

A health researcher conducted a survey and recorded the percentage of body fat of 20 randomly selected men from two different towns.

Answer: 7 hrs and 15 minutes

Step-by-step explanation: because 15 - 8 = 7 45 - 30 = 15

98% of the quarters can be expected to see a profit of at least $0.5 million.

What is a standard deviation?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Z score = 0.7-0.5 = 0.2

σ = 0.1

P-value from Z-Table:

P(x<0.5) = 0.97725

             ≈ 98%

Hence, 98% of the quarters can be expected to see a profit of at least $0.5 million.

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The difference between these distances on the Earth is 3.32 × 10⁴.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression that shows the multiplication for the same number. Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor. Exponents are used to show repeated multiplication of a number by itself

Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.

The difference will be:

= 4.00x10^4 km - 6.8x10^3 km.

= 3.32 × 10⁴

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The probability that the first ball drawn is a red is 8/14

the probability that the first ball drawn is a yellow is 6/13

Let A = getting a red ball

B= getting a yellow ball given that first was red ball

P( A ) = 8/14

P( B  ) = 6/ 13 (since 1 red ball is out)

A(A ∩ B)= 6/13 x 8/14 =

48/182

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

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The frequentist probability is objective, based on observed data, need large sample or long term frequency, and doesn't have prior knowledge.

Frequentist probability is a definition of probability that defines the probability of an event as the probability of an event being observed in a long-term or infinite experiment.

Frequentist probability is different from Bayesian probability in following points,

Thus, the statement are true for frequentist definition for the probability is doesn't have prior knowledge, need large sample, based on observed data, and objective.

Your question is incomplete, but it is general information about the frequentist definition of probability.

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Answer: [tex]512x^3+960x^2+600x+125[/tex]

Step-by-step explanation: Start by spreading the expression out so it turns into (8x + 5)*(8x + 5)*(8x + 5). (* means multiply). Then, foil (multiply the first numbers, outside numbers, inside numbers, and last numbers to form a new expression) the first two expressions to get 64x^2+80x+25*(8x + 5). Foil that again, going through and multiplying each number from both expressions by every number in the other expression to get 512x^3+960x^2+600x+125. Hope that helps.

Answer:

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Perfect Cube Formula}\\\\$\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3$\\\end{minipage}}[/tex]

To find the product of the given expression, use the perfect cube formula.

Given expression:

[tex](8x + 5)^3[/tex]

Therefore:

Apply the perfect cube method:

[tex]\begin{aligned}(8x+5)^3&=(8x)^3+3(8x)^2(5)+3(8x)(5)^2+5^3\\&=8^3 \cdot x^3+3 \cdot 64x^2\cdot5+3\cdot 8x\cdot 25+125\\&=512x^3+960x^2+600x+125\end{aligned}[/tex]

Answer: rate of change is 2

Step-by-step explanation:

The variance of the number of occasions a 6 appears when a fair die is thrown 12 times is 0.156.

It determines the likelihood of achieving a specific number of successes over a specific number of trials with a consistent success rate using the binomial distribution.

With a 1/6 likelihood of success for each trial, the number of successes in this example is equal to the number of 6s that occur.

The probability of each conceivable value of the quantity of 6s that appear may be calculated using the binomial formula. The likelihood of receiving exactly 0 number of 6s is (12 choose 0) ×[tex](\frac{1}{6})^0[/tex] × [tex](\frac{5}{6}) ^{12}[/tex] = 0.1680. The probability of getting exactly 1 number of 6 is (12 choose 1) × [tex](\frac{1}{6})^1[/tex] × [tex](\frac{5}{6})^{11}[/tex] = 0.4401. The probability of getting exactly 2 numbers of 6s is (12 choose 2) × [tex](\frac{1}{6})^2[/tex] × [tex](\frac{5}{6})^{10}[/tex] = 0.3744. And so on.

The likelihood of receiving 0 6s, for instance, multiplied by the square of the 0's divergence from 2 is 0.1680 × (0 - 2)² = 0.7056. The likelihood of receiving 1 6 when multiplied by the square of the difference between 1 and 2 is 0.4401 × (1 - 2)² = 0.4401. And so on.

To get the anticipated value of the squared departure of the number of 6s that occur from 2, we may finally total up all of these probabilities.

This predicted value is equal to 1.8801 by adding 0.7056, 0.4401, 0.3744, 0.1596, 0.0368, and 0.0036.

The range in the number of 6s that appear after tossing a fair die 12 times is thus 1.8801.

To express the variation in decimal notation, divide the difference by the total number of rolls (12), then round the output to the closest three decimals.

As a consequence, we obtain a variance of 0.1567. The variance in the number of occasions a 6 appears when a fair dice is rolled 12 times is thus 0.1567.

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Answer:

22x

Step-by-step explanation:

2x 2(6x+3)

2x 12x+6x

22x

Answer:

the first one at the top . but can you put up a better picture ?

Step-by-step explanation:

If David wants to withdraw $32,635.15 every year from his account at the end if each year for 30 years, he has to have $783243.6 in the bank account .

We would use the equation for calculating present annuity.

It is written as

PV = R[1 - (1 + r)^- n]

In which.

Considering the data provided,

r = 1.5/100 = 0.015

n = 30 years

R = $32,635.15

Put the values in the formula,

PV = 32635.15[1 - (1 + 0.015)⁻³⁰]/0.015

PV = 32635.15[1 - (1.015)⁻³⁰]/0.015

PV = 32635.15(1 - 0.64)/0.015

PV = 32635.15 × 24

PV = $783243.6

Thus, amount David must have in the bank presently is  $783243.6.

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Answer:

Ok this is easy you got this!

Step-by-step explanation:

Ok so, we know their over total is 98.00, we also know that the boots cost $34 each

lets start with 34+34= 68

now we are going to take that from 98

98-68=30

now because they bought two canteens we will divide 30 by 2

30 divided by 2 is 15

the cost of each canteen is $15

Answer:

Step-by-step explanation:

The price decreases by $288,000*(0.19)=$54,720

The current value is then $233,280.

Answer:

i found something that might help you

Step-by-step explanation:

The general antiderivative is; (x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C

Given,

f (x) = x/8 + 1/8x + (1/8)ˣ

We have to find the antiderivative;

Antiderivative;-

In calculus, a differentiable perform F whose spinoff is sufficient to the initial perform f could be an antiderivative, inverse derivative, primitive perform, primitive integral, or integral of a perform f. Symbolically, this could be expressed as F' = f.

Here,

To find antiderivative, we have to integrate the function first;

Then,

∫ f(x) + g(x) dx = ∫ f(x) dx + g(x) dx

∫ f(x/8) dx = x² / 16

∫ f(1/8 x) dx = 1/8 ln |x|

∫ f(1/8ˣ) dx = -1/ (3 ln × 2 × 8ˣ)

That is,

∫ x/8 + 1/8x + 1/8ˣ dx = (x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C

Therefore,

(x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C will  be the antiderivative.

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Answer:

Step-by-step explanation:

You want the domain, range, intercepts, asymptotes, and holes of the rational function f(x) = (2x³ +10x² +8x)/(x³ +7x² +12).

The given function can be simplified by cancelling common factors from numerator and denominator. These cancelled factors show where the holes are in the graph.

  [tex]f(x)=\dfrac{2x^3+10x^2+8x}{x^3+7x^2+12}=\dfrac{2x(x+4)(x+1)}{(x(x+4)(x+3)}=2\left(\dfrac{x+1}{x+3}\right)\quad x\notin\{-4,-3,0\}[/tex]

The function is defined for all real numbers except those where the denominator is zero: {-4, -3, 0}.

The function can produce every output value except the value of the horizontal asymptote: y = 2. The range is all real numbers except 2.

The x-intercept is found where the numerator of the simplified function is zero: x = -1

The y-intercept is the function value at x=0. The function is undefined there, so the y-intercept does not exist. (The limit as x approaches zero is y = 2/3.)

The function has a horizontal asymptote at the y-value corresponding to the ratio of the highest-degree terms of the numerator and denominator: y = 2.

The vertical asymptote is at the uncanceled denominator zero, x = -3.

The holes are where a numerator and denominator factor cancel. The y-value at the hole is the limit of the function value as x approaches the hole location. This is the value of the simplified function.

The holes are (-4, 6) and (0, 2/3).

The box's dimensions that reduce the overall cost of the materials are as follows:

L = W = 16 cm

H = 32 cm

Given,

What is the dimensions of the rectangle?

A rectangle has two dimensions: a length and a width that are both perpendicular to it. The interior of an oval or a triangle also has two dimensions.

Here,

We've got

Volume = 512 cm3 L* W * H

Sides of the box cost = 1 cent/cm²

Top and bottom cost 2 cent/cm²

Then,

Box dimensions that reduce the overall cost of materials used

We are aware of

L× W × H = 512 cm³

Where,

L stands for length, W for width, and H for height.

So, when we reduce the cost function

C(L, W, H) = (1) 1 H + (2) 1 (L + W)

Thus insert H.

Replacing H with 512/LW yields,

C(L, W) = 512(1/L, 1/W), plus 2LW

So

When both partial derivatives are 0, there will be a minimum cost.

512/L2 - 2W = dC/dL = 0

So

512/W2 - 2L = 0 for dC/dW.

L = 256/W²

Now

The answer to the aforementioned equation is

L = W = (256)⁻³ = 16cm

And

H = 512/16 = 32

H = 32 cm

Consequently, the box's measurements that reduce the overall cost of the materials utilized are:

L = W = 16 cm

H = 32 cm

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No, there cannot be a horizontal tangent at the point where the curve intersects the x-axis.

A smooth-drawn figure or line with a bend or turn is referred to as a curve.

A circle is an illustration of a curved shape.

The path, also known as the topological arc, is the name of the curve (or just arc).

If a curve is the continuous injective image of an interval or a circle, it is considered simple.

If a curve is determined by a continuous function, in other words.

So, it possible for the curve to have a horizontal tangent:

On the curve, horizontal tangents appear where:

x = -1 and y ≠ -1

y = 0 where the curve crosses the x-axis.

-1² + 2(-1) + 0⁴ + 4.0 ≠ 5

No, the point where the curve crosses the x-axis cannot have a horizontal tangent.

Therefore, no, there cannot be a horizontal tangent at the point where the curve intersects the x-axis.

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Complete question:

Consider the closed curve in the xy-plane given by : x²+2x+y⁴=4y = 5

Is it possible for this curve to have a horizontal tangent at points where it intersects the x-axis? explain your reasoning.

The increase in the salary for Charolette will be $251.65.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Since Charolette earns 3,595 per month at her job. She will receive a 7% raise. The amount of raise will be calculated by simply multiplying the percentage that she was given for the raise in the salary by the initial salary that she was earning.

This will be illustrated thus:

= Percentage × Salary

= 7% × $3595

= $251.65

The value of $251.65 will the increase in the salary.

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