-3, 6, -12, 24, -48, what are the next two numbers in the set?

Answer:

it's 70°

Step-by-step explanation:

the opposite sides are equal, so it's 70°

The number of bacteria in 25g sample is 1.225*10^8

Data;

To find the number of bacteria in 25g, we just need to multiply the number of bacteria in 1g by 25. This implies that the bacteria increase in a multitude of 25.

\(1g = 4.9*10^6\\25g = x\)

Let's cross multiply both sides and solve for x

\(1g =4.9*10^6\\25g = x\\x = 25 * 4.9*10^6\\x = 122,500,000\\\\x = 1.225*10^8\)

The number of bacteria in 25g sample is 1.225*10^8

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Given:

To solve for x:

Taking square root on both sides we get,

Hence, the correct option is, B.

Answer:

(x+11)(x-1)

Step-by-step explanation:

Answer:

x = 11, and x = -1

Step-by-step explanation:

X^2 - 10x -11 =0

(x - 11) (x +1 ) = 0

x = 11, -1

Answer:

Arc=26\(\pi\)/9 yds

Step-by-step explanation:

In previous problems, I recited that the arc formula is this:

Arc= degree x \(\pi\)/180 x radius

Let's plug in the numbers shall we?

Arc=130 x  \(\pi\)/180 x 4

Arc=13\(\pi\)/18 x 4

Arc=26\(\pi\)/9 yds

Answer:

-8(x+2.5)^2

This is the same function as if you were to graph h(g(f(x)))

I hope this helps

Answer:

8

Step-by-step explanation:

24 divided by 3 = 8

Answer:

32

Step-by-step explanation:

Given that:

Number of granola bars = 96

Number of popcorn balls = 64

Greatest number of party favors that can be made from granola bars and popcorn balls ;

Obtain the greatest common factor of both 96 and 64

Factors of :

96 : 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

64 : 2, 4, 8, 16,32

greatest common factor is 32,

Hence, greatest number of party favors that can be made is 32

Answer:

Step-by-step explanation:

¡Hola! Lo siento, pero no hablo español. ¡qué tengas un lindo día!

Answer:d

Step-by-step explanation:

The answer is d. None of the above is true.

To calculate velocity, we need to use the equation:

Velocity = M * P / Y

Given:

M = 1,000

P = 2.25

Y = 2,000

Plugging in the values:

Velocity = 1,000 * 2.25 / 2,000

Simplifying:

Velocity = 2.25 / 2

The result is:

Velocity = 1.125

Therefore, the correct answer is: d. None of the above is true.

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Answer:

13

Step-by-step explanation:

❤️❤️❤️❤️❤️

Aid in the elimination of metabolic byproducts, excess electrolytes (for example, salt and potassium), and urea, a waste product generated during the digestion of ingested protein. Sweating helps to regulate body temperature.

Maintain a regular body temperature. Joints should be lubricated and cushioned. Safeguard your spinal cord and other delicate structures. Wastes can be eliminated by urine, sweat, and bowel motions. Dehydration can also cause a decrease in strength and stamina. It is the most common cause of heat exhaustion. At this point, you should be able to reverse dehydration by consuming extra fluids. Chronic dehydration might impair your kidney function and raise your risk of kidney stones. Water also helps with normal bowel function, muscular performance, and clean, young skin. Failure to drink enough water, on the other hand, can result in dehydration and negative symptoms such as weariness, headache, reduced immunity, and dry skin.

Here,

Assist in the elimination of metabolic byproducts, excess electrolytes (for example, salt and potassium), and urea, a waste product generated during the digestion of ingested protein. Sweating regulates body temperature.

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The value of the composite function (f o f)(x) is 8x⁴

The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)). It means here function g is applied to the function of x. So, basically, a function is applied to the result of another function.

In the given problem, the function given is;

f(x) = 2x²

The value of (f o f)(x) can be calculated as;

(f o f)(x) = (f(x) * f(x)

(f o f)(x) = 2x² * 2x²

(f o f)(x) = 8x⁴

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The soap used by the machine last year is 5399.76 gallons.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage." This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."

Let the soap used last year = x.

Then, according to the given condition:

4,508.8 = x (1 - 16.5%)

4,508.8 = x (83.5/100)

x = 4,508.8(100) / 83.5

x = 5399.76

Hence, the soap used by the machine last year is 5399.76 gallons.

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Answer:

B. 1.828 meters

Step-by-step explanation:

Since we have covered both cases and shown that in each case, a^2 is divisible by 4 or is 1 more than an integer divisible by 4, we can conclude that for any natural number a, a^2 satisfies the given condition.

To prove that for any natural number a, a^2 is divisible by 4 or is 1 more than an integer divisible by 4, we can consider two cases:

Case 1: a is an even number

If a is an even number, then it can be expressed as a = 2k, where k is also a natural number. In this case, we have:

a^2 = (2k)^2 = 4k^2

Since 4k^2 is divisible by 4, the statement holds true.

Case 2: a is an odd number

If a is an odd number, then it can be expressed as a = 2k + 1, where k is a natural number. In this case, we have:

a^2 = (2k + 1)^2 = 4k^2 + 4k + 1 = 4k(k + 1) + 1

Here, we observe that 4k(k + 1) is divisible by 4, and adding 1 does not change its divisibility. Therefore, a^2 is 1 more than an integer divisible by 4.

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Answer:

solution,

hypotenuse (h)=10 cm

base(b)=5 cm

perpendicular (p)=?

Now,

Using Pythagoras theorem,

\( {h}^{2} = {p}^{2} + {b}^{2} \\ {p }^{2} = {h}^{2} - {b}^{2} \\ or \: {p}^{2} = {(10)}^{2} - {(5)}^{2} \\ or \: {p}^{2} = 100 - 25 \\ or \: {p}^{2} = 75 \\ or \: p = \sqrt{75} \\ p = 5 \sqrt{3} \: cm\)

Hope this helps...

Good luck on your assignment...

Answer:

she is smart.

Step-by-step explanation:

she

used

her

brain.

Cedric could conduct further random samplings to get a better estimate of the number of marbles in each bag.

To make a better estimate of the number of marbles in each bag, Cedric could perform additional random samplings and use the results to refine his estimates.

The larger the sample size, the more accurate the estimates are likely to be.

For example, Cedric could pull out another 10 marbles from the bag and record the number of orange and green marbles.

If he gets similar results as his initial sampling (i.e., mostly orange marbles), then his estimate of 4000 orange and 1000 green marbles may be more reliable.

However, if he gets a different distribution of colors in the second sampling, he may need to adjust his estimates accordingly.

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Answer:

Step-by-step explanation:

So I'm assuming you meant to type f(t) = 1000(1.03)^t

and assuming t is in years, we let t = 0.25, therefore 1000(1.03)^0.25

= 1.00741707178, then subtracting 1000 (assuming that is the original money), we get approx = 0.007 of whatever currency

a)The 95% to 5% split for 160 coin tosses is approximately 44.34% to 55.66%.

b)The probability of detecting a 60% coin is approximately 0.0436 or 4.36%.

c)The probability of detecting a 70% coin is approximately 0.0527 or 5.27%.

a) The 95% to 5% split refers to the range of outcomes that would be considered statistically significant. In the case of a coin toss, we can determine this split using binomial distribution. The formula to calculate the range is as follows:

p ± z\(\times \sqrt((p \times (1 - p)) / n)\)

Where:

p = probability of success (0.5 for a fair coin)

z = z-score corresponding to the desired confidence level (1.96 for a 95% confidence level)

n = number of trials (160 coin tosses)

Calculating the split:

Lower bound = 0.5 - 1.96 * sqrt((0.5 * (1 - 0.5)) / 160)

Upper bound = 0.5 + 1.96 * sqrt((0.5 * (1 - 0.5)) / 160)

Lower bound ≈ 0.4434

Upper bound ≈ 0.5566

Therefore, the 95% to 5% split for 160 coin tosses is approximately 44.34% to 55.66%.

b) To determine the probability of detecting a 60% coin, we can use the binomial distribution formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) = probability of getting exactly k successes

C(n, k) = number of combinations of n items taken k at a time

p = probability of success (0.6 in this case)

n = number of trials (160 coin tosses)

k = number of successful outcomes (96 for 60% of 160)

Calculating the probability:

P(X = 96) = C(160, 96) * 0.6^96 * (1 - 0.6)^(160 - 96)

The calculation involves a large number of terms and may be better suited for a statistical software or calculator. Using software, the probability is approximately 0.0436.

Therefore, the probability of detecting a 60% coin is approximately 0.0436 or 4.36%.

c) Similarly, to determine the probability of detecting a 70% coin, we can use the same binomial distribution formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) = probability of getting exactly k successes

C(n, k) = number of combinations of n items taken k at a time

p = probability of success (0.7 in this case)

n = number of trials (160 coin tosses)

k = number of successful outcomes (112 for 70% of 160)

Calculating the probability:

P(X = 112) = C(160, 112) * 0.7^112 * (1 - 0.7)^(160 - 112)

Again, the calculation involves a large number of terms. Using software, the probability is approximately 0.0527.

Therefore, the probability of detecting a 70% coin is approximately 0.0527 or 5.27%.

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Domain of f(x) = (−∞, -4)∪(-4, ∞) when rational function is f(x)=x²+6x+8/x+4 which is function f of x.

Given that,

We have to find what are the domain and range of the function f of x is equal to the quantity x squared plus 6x plus 8 end quantity ÷ by the quantity x + 4 end quantity.

We know that,

If a rational function is defined as R(x)=p(x)/q(x), then the domain of the rational function is the intersection of domains of p(x) and q(x) except those values for which q(x)=0.

The given rational function is

f(x)=x²+6x+8/x+4

We need find the domain of the given function.

Here, both the numerator and the denominator are polynomial functions, and the range of a polynomial function is the entire real number range.

So, domain of the given function is all real number except those values of x for which x+4=0.

x+4=0

x=-4

Domain of f(x) = All real numbers except -4.

Domain of f(x) = (−∞, -4)∪(-4, ∞)

Therefore, Domain of f(x) = (−∞, -4)∪(-4, ∞) when rational function is f(x)=x²+6x+8/x+4.

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If 64 is a perfect cube the length of each edge of the block can be found. The edge length of a cube is: 4cm.

Given:

Volume of cube=64cm³

Hence:

Volume of the cube = a³

Volume of the cube, a³= 64 cm³

Using this formula

Cube edge length =∛(side)³

Let plug in the formula

Cube edge length =∛(64cm³)

Cube edge length=4cm

Therefore if 64 is a perfect cube the length of each edge of the block can be found. The edge length of a cube is: 4cm.

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Probability of both = 6/8 * 2/8 = 12/64 which reduces to 3/16.

acc  to our question-

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The required equation is ~

\( \boxed{ \sf{y = \frac{x}{2} + 2 }}\)

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

Let's find the slope of given line ~

comparing it with general slope - intercept form of line (y = mx + c) we get, m = -2 (that is slope of the line)

let the slope of the required line be n

And, now since the required line Is perpendicular to the given line. the product of their slopes is -1

that is ~

slope of required line is ~ 1/2

now, let's use the point - slope form of line to find the equation of required (perpendicular) line (using point (0 , 2) ~

that is ~

here, m = slope ~

I hope it helps ~

Answer: 6/5 and -3/4

Step-by-step explanation:

(2x-3)/9=(3x-4)/6

18*(2x-3)/9=18*(3x-4)/6

2(2x-3)=3*(3x-4)

4x-6=9x-12

-5x=-6

x=6/5

(8x+2)/4=4x/3

12*(8x+2)/4=12*4x/3

3(8x+2)=4*4x

24x+6=16x

8x=-6

x=-3/4

Answer:250

Step-by-step explanation:

We have proved that f o g is uniformly continuous on R, as desired.

F(g(x)) or (f g)(x) denotes the combination of the functions f(x) and g(x), where g(x) acts first. It brings together two or more functions to produce a new function.

To prove that the composite function f o g is uniformly continuous on R, we need to show that for any ε > 0, there exists a δ > 0 such that for any x, y ∈ R,

| x - y | < δ implies | (f o g)(x) - (f o g)(y) | < ε

We can start by using the uniform continuity of g to choose a δ1 > 0 such that for any x, y ∈ R,

| x - y | < δ1 implies | g(x) - g(y) | < ε

Now, we can use the uniform continuity of f with ε replaced by δ₁ to choose a δ₂ > 0 such that for any u, v ∈ R,

| u - v | < δ₂ implies | f(u) - f(v) | < δ₁

Finally, we can choose δ = δ₂ to show that for any x, y ∈ R,

| x - y | < δ implies | (f o g)(x) - (f o g)(y) | < ε

To see why this is true, let's assume that | x - y | < δ. Then, by the definition of the composite function,

(f o g)(x) - (f o g)(y) = f(g(x)) - f(g(y))

Now, since | g(x) - g(y) | < δ₁, we know that | f(g(x)) - f(g(y)) | < ε, by the choice of δ₁. And since | x - y | < δ₂ implies | g(x) - g(y) | < δ₁, we have shown that

| x - y | < δ₂ implies | (f o g)(x) - (f o g)(y) | < ε

Therefore, we have proved that f o g is uniformly continuous on R, as desired.

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Management has decided to inspect a sample of 20 phones from the day's production, which consists of 1,000 iPhones.

To ensure the quality of the iPhones' display screens, the management of the factory, where 1,000 iPhones were produced, has decided to inspect a sample of 20 phones from the day's production. This decision allows them to evaluate the quality of the screens efficiently.

Inspecting a sample of 20 phones from the day's production is a practical approach to quality control. It would be impractical and time-consuming to inspect each individual phone's display screen out of the 1,000 produced. By selecting a representative sample, the management can make reasonable inferences about the overall quality of the entire batch.

Sampling provides a cost-effective way to assess quality while minimizing the time and resources required. Since it takes about 10 minutes to inspect an individual phone's display screen, inspecting all 1,000 phones would take approximately 10,000 minutes or over 166 hours. By inspecting a sample of 20 phones, the total inspection time reduces to only 200 minutes or around 3.3 hours. This significantly reduces the inspection time without compromising the assessment of quality.

The chosen sample size of 20 phones is a balance between statistical reliability and practicality. It is large enough to provide a representative snapshot of the batch's quality, ensuring that any potential issues with the display screens can be identified. However, it is also small enough to be manageable within a reasonable timeframe.

During the inspection process, the chosen sample of 20 phones will undergo a thorough examination of their display screens. This evaluation aims to identify any deviations or defects from the desired quality standards set by the management. If issues are found within the sample, appropriate actions can be taken, such as improving the manufacturing process, addressing quality control measures, or conducting further inspections.

By inspecting a sample of 20 phones, the management can make informed decisions regarding the quality of the iPhones' display screens before shipping them to retail stores. This sampling approach balances efficiency, practicality, and reliable quality assessment, ensuring that the end-users receive products that meet the desired standards.

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