Please Hurry! What is the solution to log2_(9x)-log2_3=3?

In a contingency table, we describe the relationship between two variables measured at the ordinal or nominal level (option a).

A contingency table is a statistical table that displays the frequency distribution of two categorical variables and helps identify any associations or dependencies between them. The table organizes the data into rows and columns, with each cell representing the frequency count or proportion of observations falling into a particular combination of categories.

By examining the distribution of frequencies across the table, patterns and relationships between the variables can be discerned. This information can be useful in various fields, such as social sciences, market research, and epidemiology, for analyzing survey responses, understanding consumer preferences, or investigating the relationship between risk factors and diseases, among other applications.

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The solutions for the equation sinx = √1 - cosx in the interval [0, 2π) are x = 0, π/2, and 3π/2.

To solve this equation, we first need to square both sides:
sin^2x = 1 - cosx
Next, we can use the identity sin^2x + cos^2x = 1 to substitute sin^2x with 1 - cos^2x:
1 - cos^2x = 1 - cosx
Now we can simplify by moving all the terms to one side:
cos^2x - cosx = 0
Factorizing, we get:
cosx(cosx - 1) = 0
So the solutions are when cosx = 0 or cosx = 1. In the interval [0, 2π), the solutions for cosx = 0 are x = π/2 and 3π/2. The solution for cosx = 1 is x = 0. Therefore, the solutions for the equation sinx = √1 - cosx in the interval [0, 2π) are x = 0, π/2, and 3π/2. We express these solutions in radians in terms of π.

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Answer:

80%p=d

Step-by-step explanation:

20% discount is 80% of original.

An equation for the relationship between the discount price of an item, d, and it's original price, p is p = 0.8d.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

A store is offering a 20% discount on all items.

Let the discount price of an item, d, and it's original price, p.

The original price = (100 - 20%)discount price

p = 80%d

p = 0.8d

Therefore, p = 0.8d is the required equation.

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Answer:

  4.4 m

Step-by-step explanation:

The scale shows you the width of the bedroom is ...

  1.2 + 2.1 + 1.1 = 4.4 . . . meters

Answer:

2/3 and 3/5 is same, then 5/6

Step-by-step explanation:

you can convert the fractions to decimals to find their value and then arrange them from least to the greatest.

Answer:

3/5, 2/3, 5/6 [From Least to Greatest]

Step-by-step explanation:

First you're going to want to know which one is "the bigger piece of pie".

I made a few drawing and look at the pictures (Just in case you have a different opinion from my answer)

Answer:

\(51-m=n\)

Step-by-step explanation:

M - Number of cookies his family ate

N - The remaining number of cookies left

Answer:

add like terms the simplified answer is 2m+5p-3

Step-by-step explanation:

lmk if it is not supposed to be simplified

Answer:

Step-by-step explanation:

Answer: The area is 6.5

Answer:

x ≤ -6

Step-by-step explanation:

The line is moving towards the left, which means that the numbers are getting smaller. X is going to be less than something.

The dot on -6 is colored in. This means that -6 is included in our inequality. [X could equal -6]

So, we could write the equation x ≤ -6

Answer:

12.5 miles

Step-by-step explanation:

1 mile= 4 min.

x miles= 50 min.

1/4 = x/50

*cross multiply

4x= 50

divide by 4

x= 12.5 miles

4/5 × 2/3

= (4×2)/(5×3)

=8/15

Let

a------------> first number

b------------> second number

we know that

a+b=-7--------> a=-7-b----------> equation 1

a-b=14--------> equation 2

I substitute 1  in 2

(-7-b)-b=14-------------> -7-b-b=14----------> -7-2b=14-------> 2b=-7-14

2b=-21---------> b=-10.5

a=-7-b-------> a=-7-(-10.5)-----> a=-7+10.5------> a=3.5

the answer is

the two numbers are

a=3.5

and

b=-10.5

now gimme brainliest

The confidence interval of 99% for μ₂ - μ₁ for the given mean and standard deviation is equal to (23.7377, 49.7713).

Confidence interval = 99%  

Confidence interval for μ₂ - μ₁, we need to follow these steps,

Calculate the sample mean difference and the standard error of the mean difference.

Sample mean difference

= ¯x₂ - ¯x₁

= 162.75 - 126

= 36.75

Standard error of the mean difference

= √[(s₁^2/n₁) + (s₂^2/n₂)]

= √[(8.062^2/5) + (3.5^2/4)]

= 4.0065 (rounded to four decimal places)

The t-value for a 99% confidence level with degrees of freedom

= n₁ + n₂ - 2

= 5 + 4 - 2

= 7.

Using a t-distribution table attached ,

The t-value for a 99% confidence level with 7 degrees of freedom is 3.250.

Margin of error

= t-value x standard error of the mean difference

= 3.250 x 4.0065

= 13.0213 (rounded to four decimal places)

Confidence interval

= Sample mean difference ± Margin of error

= 36.75 ± 13.0213

= (23.7377, 49.7713)

Therefore, the 99% confidence interval for μ₂ - μ₁ is (23.7377, 49.7713).

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9514 1404 393

Answer:

  8 seconds

Step-by-step explanation:

Your answer is the time interval at which the projectile is at or above ground level.

The way I read the question, it is asking for the value of t when the projectile hits the ground. It is 8 (seconds). My answer to this question would be 8, or 8 seconds.

__

Comment

We cannot tell whether the answer is intended to include units, or not. The usual clues are missing here.

a. We have shown that lim sn = s when an ≤ sn ≤ bn for all n and lim an = lim bn = s, using the squeeze lemma.

b. We have shown that lim sn = 0 when sn ≤ tn for all n and lim tn = 0, using the squeeze lemma.

In mathematical analysis, the squeeze theorem—also referred to as the sandwich theorem, sandwich rule, police theorem, pinching theorem, and occasionally the squeeze lemma—is used to determine a function's limit when two other functions with known limits are also present.

(a) To prove that lim sn = s when an ≤ sn ≤ bn for all n and lim an = lim bn = s, we can use the squeeze lemma.

Since an ≤ sn ≤ bn for all n, we have 0 ≤ |sn - s| ≤ max{|an - s|, |bn - s|} for all n. Then, for any ε > 0, we can choose N such that |an - s| < ε and |bn - s| < ε for all n ≥ N. This implies that |sn - s| < ε for all n ≥ N, since |sn - s| ≤ max{|an - s|, |bn - s|} < ε. Therefore, by the definition of the limit, we have lim sn = s.

Thus, we have shown that lim sn = s when an ≤ sn ≤ bn for all n and lim an = lim bn = s, using the squeeze lemma.

(b) We have already proved in part (a) that lim sn = 0 when |sn| ≤ tn for all n and lim tn = 0, using the squeeze lemma. Therefore, to prove that lim sn = 0 when sn ≤ tn for all n and lim tn = 0, we can use the same argument.

Since sn ≤ tn for all n, we have -tn ≤ sn ≤ tn for all n. Then, taking the limit as n approaches infinity, we have:

lim (-tn) ≤ lim sn ≤ lim tn

Since lim tn = 0, we have lim (-tn) = -lim tn = 0. Therefore:

0 ≤ lim sn ≤ 0

By the squeeze lemma, we conclude that lim sn = 0.

Thus, we have shown that lim sn = 0 when sn ≤ tn for all n and lim tn = 0, using the squeeze lemma.

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given that for all numbers of p and q,

q = 5/3p + 46

lets find p when q is 21

so lets substitute the value of q into the given equation

q = 5/3p + 46

21 = 5/3p + 46

lets collect like terms

21 - 46 = 5/3p

-25 = 5/3p

lets cross multiply

3 X -25 = 5p

-75 = 5p

5p = -75

divide both sides by 5

5p/5 = -75/5

p = -15

therefore for all values of p and q, q = 5/3p + 46,

the value of p is -15 when q is 21

Answer:

P = 72 ft

Step-by-step explanation:

the perimeter P is the sum of the 3 sides.

Tangents to a circle from an external point are congruent , then

side 24 = 15 + 9

side 21 = 9 + 12

Third side = 12 + 15 = 27 ft

P = 24 + 21 + 27 = 72 ft

The difference between the mean of the sample and the mean of the population is A. 0.55

Given the population data is:

0 3 3 1 3 2 2 2 5 4 3 3 3 0 1 2 0 2 3 3

The sample data is:

5 3 0 2 4

The mean of the population data is:
45/20= 2.25

The mean of the sample data is:

14/5= 2.8

Therefore, the difference between the mean of the sample and the population is:

2.8-2.25= 0.55

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Explanation

Step 1

we have a expression in the form.

we need two a and b numbers such as

now, we can factorize

I hope this helps you

The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

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

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

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

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

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

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

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

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

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

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

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

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

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

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

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

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

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

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

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

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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The annual interest rate that $500 would have to be invested at to grow to $1,934.77 in 15 years is 6.6%.

The formula for compound interest is:

\(\begin{equation}A = P(1 + r)^t\end{equation}\)

Where:

A is the future value

P is the present value

r is the interest rate

t is the number of years

In this case, the future value is $1,934.77, the present value is $500, and the number of years is 15. Plugging these values into the formula, we get:

1934.77 = 500(1 + r)¹⁵

(1 + r)¹⁵ = 3.86954

1 + r = 1.066

r = 0.066

Therefore, the annual interest rate is 6.6%.

It is important to note that this is just an estimate. The actual interest rate that $500 would earn would depend on a number of factors, including the type of investment and the market conditions.

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Based on this exhibit, a high school student is required to determine whether the proportion of the population in favor of candidate A is significantly option (b) or (c) greater than 80% or 75% at a 0.05 level of significance.

In statistical analysis, determining the proportion of a population in favor of a candidate or an idea is crucial in predicting election outcomes or measuring public opinion. Exhibit 9-6 presents statistical data on the proportion of the population in favor of candidate A

To answer this question, we need to conduct a hypothesis test and calculate the p-value. The null hypothesis (H0) states that the proportion of the population in favor of candidate A is equal to or less than the given proportion, while the alternative hypothesis (Ha) states that the proportion is greater than the given proportion. Therefore, the hypotheses can be stated as follows:

H0 => p ≤ 0.80 or p ≤ 0.75

H1 => p > 0.80 or p > 0.75

We then calculate the test statistic, which is the z-score. This can be done using the formula:

z = (p - p₀) / √(p₀(1-p₀)/n)

where p is the sample proportion, p₀ is the given proportion, and n is the sample size.

Next, we calculate the p-value, which is the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true. Since this is a one-tailed test, we use the standard normal distribution table and look up the area to the right of the calculated z-score. The p-value is the probability of getting a z-score as extreme or more extreme than the calculated one. If the p-value is less than the level of significance, we reject the null hypothesis and conclude that the alternative hypothesis is true.

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The running rate is 5 miles per hour.Let's denote the running rate as "r" and the driving rate as "9r" (since the driving rate is nine times the running rate).

To find the running rate, we need to determine the time spent driving and running separately and then add them together to equal 3 hours.

The time spent running can be calculated as the distance divided by the running rate:

Time running = Distance / Running rate = 5 / r

The time spent driving can be calculated similarly:

Time driving = Distance / Driving rate = 90 / (9r) = 10 / r

The total time spent driving and running is given as 3 hours:

Time running + Time driving = 3

5 / r + 10 / r = 3

To solve this equation, we can combine the fractions on the left side:

(5 + 10) / r = 3

15 / r = 3

Next, we can cross-multiply to isolate the variable:

15 = 3r

Dividing both sides by 3, we find:

r = 5

Therefore, the running rate is 5 miles per hour.

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f ( x ) = x² + 144

=> x² + 144 = 0

=> ( x + 12 ) ( x - 12 ) = 0

=> x + 12 = 0 and x - 12 = 0

=> x = -12 and x = 12

So,the zeroes of f are -12 and 12 .

angle B = ( arc ADB ) ÷ 2

46 = ( arc ADB ) / 2

Multiply both sides by 2

46 × 2 = 2 × ( arc ADB ) / 2

92 = arc ADB

arc AB = arc ADB

arc AB = 92

The measure of arc AB is 92°. Therefore, option B is the correct answer.

Given that, ∠B = 46°.

We need to find the measure of arc AB.

The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.

Now, ∠B = ( arc ADB ) ÷ 2

46° = ( arc ADB ) / 2

Multiply both sides by 2

46° × 2 = 2 × ( arc ADB ) / 2

92° = arc ADB

arc AB = arc ADB

arc AB = 92°

The measure of arc AB is 92°. Therefore, option B is the correct answer.

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Answer:

Step-by-step explanation:

A rational number is a number that can be expressed as a ratio of two integers, or as a fraction. A rational number is any number that can be written in the form a/b, where a and b are integers and b is not equal to zero.

In this case, the correct answer is d. 5.3333333.... This number can be written as a fraction in the form 5 3/9, which is a ratio of two integers and thus a rational number.

The other three choices are not rational numbers because they are repeating decimals, or irrational numbers. An irrational number is a number that cannot be written as a ratio of two integers. Irrational numbers are numbers that are not rational.

The linear equation that gives the rule for this table is y = -5x + 15

The table of values is given as:

x y

1 10

2 5

3 0

4 –5

On the above table, we can see that:

As x increases by 1, the value of y decreases by 5

This means that the slope is

Slope = -5

Also, the above table can be modified as follows (using the slope of -5)

x y

0 15

1 10

2 5

3 0

4 –5

This means that the y-intercept is

y-intercept = 15

A linear equation is represented as

y = slope * x + y-intercept

So, we have

y = -5x + 15

So, the equarion is y = -5x + 15

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1.

c² = n²

√c² = √n²

c = n

2.

if

c = 3 + 6 = 9

and

n = 5 + 4 = 9

Answer:

c = ±n

Step-by-step explanation:

Taking the square root of both sides yields

√c² = √n² or c = ±n

c² = n² is a quadratic equation, so we expect that there will be two roots:  one positive and one negative.