What is the solution set for the exponential inequality (1/2)^2x+1 <4?

From this proportion of days he does the activities, sometimes they will meet in one day.

He will do both in the same day when the day is a common factor of 3 and 4.

Since today he did both, the next time he will do so will be in the least common factor of 3 and 4.

To get the least common factor of these, we can identify the divisors of each and makes the divisions until both get to 1. If one of the divisiors is divisior for both, we don't repeat it.

So, from 3 and 4, we can start by the divisior of 2. 2 Is a divisior of 4, but not of 3, so we divide only the number for:

3, 4 | 2

3, 2 |

Now, we have 3 and 2, so we can divide for 2 again:

3, 4 | 2

3, 2 | 2

3, 1 |

Now, we have 3 and 1, so we can only divide by 3 now:

3, 4 | 2

3, 2 | 2

3, 1 | 3

1 , 1 |

So, in the end we have 2, 2 and 3, so the least common factor is 2*2*3 = 12.

Since the common factor of 3 and 4 is 12, Tyler will lift and jog on the same day 12 days after today.

It is difficult to determine which sample will be the most representative without more information.

There are a few factors to consider when evaluating the representativeness of a sample:

Sample size: Larger sample sizes are generally more representative because they include more individuals, which makes it less likely that the results will be biased.

Sampling method: Random sampling methods, such as Ruth's method of calling randomly selected registered voters, are generally more representative than other methods because they aim to include a representative sample of the population.

Population: The population being surveyed will also impact the representativeness of the sample. For example, if Levonia's friends are not representative of the general population, her sample may not be representative.

Overall, it is important to consider all of these factors when evaluating the representativeness of a sample.

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To evaluate (f+g)(-4) and (g*f)(2), we substitute the given values of x into the functions f(x) and g(x), perform the respective operations, and compute the results.

First, let's evaluate (f+g)(-4). We substitute x = -4 into the functions f(x) and g(x). For f(x), we have f(-4) = -3((-4)-2)² - 1 = -3(-6)² - 1 = -3(36) - 1 = -108 - 1 = -109. For g(x), we have g(-4) = (2(-4) + 3) / (-4 + 5) = (-8 + 3) / 1 = -5.

To find (f+g)(-4), we add the results of f(-4) and g(-4): (-109) + (-5) = -114.

Next, let's evaluate (g*f)(2). We substitute x = 2 into the functions f(x) and g(x). For f(x), we have f(2) = -3((2)-2)² - 1 = -3(0)² - 1 = -3(0) - 1 = -1. For g(x), we have g(2) = (2(2) + 3) / (2 + 5) = (4 + 3) / 7 = 7/7 = 1.

To find (g*f)(2), we multiply the results of g(2) and f(2): (1) * (-1) = -1.

In conclusion, (f+g)(-4) = -114 and (g*f)(2) = -1, according to the given functions f(x) and g(x). By substituting the values of x into the functions, performing the respective operations, and computing the results, we obtain these values.

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Step-by-step explanation:

Given

\( = 27^{ \frac{1}{3} } \times 16^{ \frac{ - 1}{4} } \\ = {3}^{3 \times \frac{1}{3} } \times 2 {}^\frac{ - 1 \times 4}{4} \\ = 3 \times - 2 \\ = - 6\)

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Answer:

A: 16

Step-by-step explanation:

its in between

A two-tailed test seeks evidence that the population parameter for sample (1) is either greater than or less than the population parameter for sample (2).

For a two-sample hypothesis which tests for differences in population parameters (1) and (2), a two-tailed test seeks evidence that there is a significant difference between the means of the two populations, regardless of the direction of the difference.

In other words, the null hypothesis is that there is no difference between the two population means, and the alternative hypothesis is that there is a difference between them, either in the positive or negative direction.

The two-tailed test is used when we do not have any prior knowledge about the direction of the difference and want to be able to detect any significant difference, whether it is positive or negative.

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Answer:

x = √39

Step-by-step explanation:

both triangles have one same side, which can be called y

so y^2 = 10^2 - 6^2

and y^2 = x^2 + 5^2

then x^2 + 5^2 = 10^2 - 6^2

x^2 = 100 - 36 - 25 = 39

x = √39

(a) The graph of the uniform density function for the given range is a rectangle with a base of 10 units and a height of 0.1. The area under the curve represents the probability, and in this case, it should be equal to 1 since the entire range of values is covered.

(b) To find the probability that x falls between 12 and 15, we calculate the area under the curve between these two points. The width of the rectangle in this range is 3 units, and the height remains at 0.1. Multiplying the width and height gives us the probability of this event.

(c) To find the probability that x falls between 13 and 18, we again calculate the area under the curve between these two points. The width of the rectangle in this range is 5 units, and the height remains at 0.1. Multiplying the width and height gives us the probability of this event.

(a) The graph of the uniform density function is a rectangle with a base of 10 units (from x = 10 to x = 20) and a height of 0.1. The area of a rectangle is calculated by multiplying the base by the height, so in this case, the area under the curve is 10 * 0.1 = 1. This means that the total probability is equal to 1, as expected for a probability density function.

(b) To find the probability that x falls between 12 and 15, we calculate the area under the curve between these two points. The width of the rectangle in this range is 3 units (from x = 12 to x = 15), and the height remains at 0.1. Therefore, the probability is given by the area of the rectangle, which is 3 * 0.1 = 0.3.

(c) To find the probability that x falls between 13 and 18, we calculate the area under the curve between these two points. The width of the rectangle in this range is 5 units (from x = 13 to x = 18), and the height remains at 0.1. Therefore, the probability is given by the area of the rectangle, which is 5 * 0.1 = 0.5.

In summary, the area under the curve of the uniform density function is 1, indicating that the total probability is 1. The probability that x falls between 12 and 15 is 0.3, and the probability that x falls between 13 and 18 is 0.5. These probabilities are obtained by calculating the areas of the corresponding rectangles under the curve.

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Answer:

2 in 43, 3 in 45, 1 in both 46 and 42, and then a 2 in 44

Step-by-step explanation:

just count how many there is for each thingy for example if you look on the chart there is 3 45s so you'd put 3 in the 45 column

Answer:

3

Step-by-step explana

sorry if its wrong

Answer: 38.35%

Step-by-step explanation:

59%=59/100=0.59

0.59-0.35(0.59)=

0.59-0.2065=

0.5900-0.2065=

0.3835=38.35%

Answer:

area = PI x r^2

area = 3.14 x 13^2

area = 3.14 x 169

area = 530.66

Step-by-step explanation:

Plz Mark as brainliest hope this helps

Answer: A

Step-by-step explanation:

The total area would have to be 1, so (1/2)(5)(height)=1

2.5height = 1

height = 1/2.5 = 2/10 = 1/5

The height for the density curve will be 1/5. The correct option is A.

The area under the curve represents 100% of all probabilities. Because we normally use decimals in probabilities, we can also say that the area is equal to 1 (because 100% is a decimal). The density curve shown above depicts how body weights are distributed.

The image of the triangle is showing the base 5 units. For the density curve, the area under the curve must be 1. The height of the curve will be calculated as,

Area = 1

1/2 x B x H = 1

1/2 x 5 x H = 1

2.5 x H = 1

H = 1 / 2.5

H = 1 / 5

Therefore, the height will be 1 / 5.

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Answer:

n = 84

Step-by-step explanation:

18 + 3 = 21, so that means the quotient of the number and 4 is 21.

21 * 4 = 84

CHECK:

84 / 4 = 21

21 - 3 = 18

Answer: \(1\dfrac{29}{60}\text{ minutes}\)

Step-by-step explanation:

Given: A total eclipse solar eclipse in 2003 lasted \(5\dfrac{3}{20}\) minutes

\(=\dfrac{5(20)+3}{20}=\dfrac{103}{20}\text{ minutes}\)

& a total eclipse solar eclipse in 2005 lasted \(3\dfrac{2}{3}\)minutes

\(=\dfrac{3(3)+2}{3}=\dfrac{11}{3}\text{ minutes}\)

Difference= \(\dfrac{103}{20}-\dfrac{11}{3}=\dfrac{103\times3-11\times20}{60}\)

\(=\dfrac{309-220}{60}\\\\=\dfrac{89}{60}\text{ minutes}\\\\=1\dfrac{29}{60}\text{ minutes}\)

So, 2003 solar eclipse was \(1\dfrac{29}{60}\text{ minutes}\) longer than solar eclipse in 2005.

exterior angle is equal to sum of two opposite interior angle

141= 32 + x

141-32= x= 109° ANS.

The direction of vector R with respect to the positive x-axis is approximately −16.70i − 20.00j. The magnitude and direction of vector R are option (d) 16.7,309.0.

To find the magnitude of the vector R=B⋅A, we first need to calculate the dot product of vectors A and B:
B⋅A = (4.50i − 5.00j)⋅(−6.00i + 8.00j)
    = 4.50(−6.00) + (−5.00)(8.00)
    = −27.00
The magnitude of vector R is equal to the absolute value of the dot product of A and B:
|R| = |B⋅A| = 27.00
To find the direction of vector R with respect to the positive x-axis, we need to calculate the angle between vector R and the positive x-axis. We can do this by finding the angle between vector R and the positive x-axis using the arctangent function:
θ = tan⁻¹(Ry/Rx)
where Rx and Ry are the x and y components of vector R, respectively. To find Rx and Ry, we first need to calculate the components of vector R:
R = B⋅A = −27.00
Rx = R cos(θ) = R cos(tan⁻¹(Ry/Rx)) = −27.00 cos(51.10∘) ≈ −16.70
Ry = R sin(θ) = R sin(tan⁻¹(Ry/Rx)) = −27.00 sin(51.10∘) ≈ −20.00
Therefore, the direction of vector R with respect to the positive x-axis is approximately −16.70i − 20.00j. The magnitude and direction of vector R are option (d) 16.7,309.0.

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Answer:

(3x-4)(x + 1)

Step-by-step explanation:

first, split the middle term,

3x^2-x-4

= 3x^2 + 3x - 4x - 4

= 3x( x+ 1) - 4( x + 1)

= (3x-4)(x + 1)

plz mark as brainliest

Answer:

(3x − 4)(x + 1)

Step-by-step explanation

Answer:

Step-by-step explanation:

10.8

Answer:

Janet's dog weighs 10.8 pounds more

Step-by-step explanation:

The possible solution set for the system is (- 1, 4) and (4, - 1).

Given are the equations as -

x + y = 3

x² + y² = 17

Refer to the graph of the function attached. The points of intersection represents the possible solution set.

Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).

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Answer:

\(\large \boxed{\sf \bf \ \ a^2+b^2=20 \ \ }\)

Step-by-step explanation:

Hello, please consider the following.

\(a^b=b^a\\\\\text{ We can replace a by 2b.}\\\\(2b)^b=2^b\cdot b^b=b^{2a}=b^2\cdot b^b\\\\\text{ Let's assume that b is different from 0 and we can divide by }b^b \\ \\ \text{ both sides of the equation, and it come.}\\\\2^b=b^2\\\\\text{ We find b = 2 and then a = 4, So}\\\\a^2+b^2=4^2+2^2=16+4=20\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: θ≈48,81°.

Step-by-step explanation:

\(sin\theta=\frac{8}{\sqrt{113}}\\sin\theta } =\frac{8*\sqrt{113} }{\sqrt{113}*\sqrt{113} } \\sin\theta=\frac{8*\sqrt{113} }{113} \\sin\theta\approx0,75258\\\theta\approx48,81^0.\)

Good luck an' have a nice day!

The two angle of the right triangle are found as 30 degrees and 60 degrees.

Less than 90 degrees is considered an acute angle. Right angles have a 90 degree angle. More than 90 degrees is found in obtuse angles.

By using angle sum property of right angle triangle:

x + 2x + 90 = 180

3x = 90

x = 30 (one angle)

2x = 60 (Other angle)

Thus, the two acute angle of the right triangle are found as 30 degrees and 60 degrees.

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Answer:

The correct option is;

There are no solutions

Step-by-step explanation:

From the graph of the inequality, with the y-intercept = 1 and slope = 3 for the blue shaded inequality

The equation is y > 3x + 1

While that of the other red shaded inequality, the slope is 3 and the y-intercept = -3

The equation is y < 3x - 3

Given that the two inequalities are parallel line that their domains do not overlap, we have that there are no solutions as the y-coordinate values of  y > 3x + 1 are always larger for a given x-coordinate value than the y-coordinate value of y < 3x - 3.

Answer:

No solution is correct.

Step-by-step explanation:

I took the test

Answer:

See below.

Step-by-step explanation:

13/24 + 7/12:    LCD is 24

7/6 + (-5/12):     LCD is 12

-3/4 - 2/3:    LCD is 12

5 - 7/10:    LCD is 10

1/8 - 5/3:    LCD is 24

3/2 - 4/5:    LCD is 10

Answer:

16^6

Step-by-step explanation:

a. At values of x=1 and x =3 the local maximum and minimum values of g occur

b. The absolute maximum value of g(x) is approximately 0.76 and occurs at x = 4.

c. On the intervals [0, 1) and (3, 4] g concave downward

Since g(x) is defined as the definite integral of f(t) from 0 to x, we can use the First Fundamental Theorem of Calculus to find g'(x) in terms of f(x):

g'(x) = f(x)

Similarly, we can use the Second Fundamental Theorem of Calculus to find g''(x) in terms of f'(x):

g''(x) = f'(x)

(a) The local maximum and minimum values of g occur at critical points of g(x), which are values of x where g'(x) = f(x) = 0 or is undefined. From the graph of f(x), we see that f(x) = 0 at x = 1 and x = 3, so these are possible candidates for critical points of g(x). We also see that f(x) is undefined at x = 2, so this is another possible critical point. Evaluating g'(x) and g''(x) at each of these values, we have:

g'(1) = f(1) = 0, g''(1) = f'(1) < 0, so g(x) has a local maximum at x = 1.

g'(2) is undefined, so x = 2 is not a critical point of g(x).

g'(3) = f(3) = 0, g''(3) = f'(3) > 0, so g(x) has a local minimum at x = 3.

Therefore, the local maximum of g(x) occurs at x = 1, and the local minimum of g(x) occurs at x = 3.

(b) To find the absolute maximum value of g(x), we need to examine the values of g(x) at the endpoints of the interval [0, 4]. We have:

g(0) = 0

g(4) = R 4 0 f(t)dt = the area under the curve of f(x) from x=0 to x=4.

From the graph, we can see that the absolute maximum value of g(x) occurs when x is in the interval [1, 3], so we can evaluate g(x) at the critical points found in part (a) and the endpoints of the interval to find the absolute maximum value of g(x):

g(1) = R 1 0 f(t)dt ≈ 0.72

g(3) = R 3 0 f(t)dt ≈ 0.65

g(4) = R 4 0 f(t)dt ≈ 0.76

Therefore, the absolute maximum value of g(x) is approximately 0.76 and occurs at x = 4.

(c) The function g(x) is concave downward on an interval if its second derivative, g''(x), is negative on that interval. From part (a), we know that g''(x) = f'(x), so we need to find where f'(x) is negative. From the graph of f(x), we can see that f'(x) is negative on the intervals [0, 1) and (3, 4]. Therefore, g(x) is concave downward on the intervals [0, 1) and (3, 4].

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The correct option is that C. Player A is the most consistent, with an IQR of 2.5.

The IQR is a spread metric that is less influenced by extreme values. It is the difference between the third (Q3) and first (Q1) quartiles. The quartiles for Player A are as follows:

Q1 = 2

Q3 = 4

IQR = Q3 - Q1 = 4 - 2 = 2

The quartiles for Player B are as follows:

Q1 = 2

Q3 = 5.5

IQR = Q3 - Q1 = 5.5 - 2 = 3.5

The IQR is regarded a better indicator of variability than the range since it is less impacted by extreme results. As a result, we may infer that the interquartile range is the best measure of variability for this data.

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