Luke's retirement party will cost $30 if he invites 6 guests. What is the maximum number of
guests there can be if Luke can afford to spend a total of $35 on his retirement party? Solve
using unit rates.
guests
Submit

Answer:

13

Step-by-step explanation:

If a = 4 and m = –3, evaluate a – 3m.

= Solution,

= a - 3m

= 4 - 3 ( - 3 )

= 4 + 9

= 13

Answer:

13 is the answer :)

Step-by-step explanation:

If,

a = 4 and m = -3

Then a - 3m ,

4 - 3(-3)

4+9

= 13

Answer:

I think this is the answer

Step-by-step explanation:

1511664158726899051326

The upper limit of the confidence interval for the proportion of millennials that care about immigration is 0.20.

In order to find the upper limit of the confidence interval for the proportion of millennials that care about immigration,

we first need to calculate the confidence interval using the margin of error (MOE) and sample proportion.

The formula to find the confidence interval is given by:

Confidence Interval = Sample Proportion ± Margin of Error (MOE)

Where Sample Proportion = Poll Result / 100

Let's first find the Sample Proportion of millennials that care about immigration.

Sample Proportion = Poll Result / 100= 17 / 100= 0.17

Now let's calculate the confidence interval using the MOE.

Confidence Interval = Sample Proportion ± Margin of Error (MOE)

Upper Limit of Confidence Interval = Sample Proportion + MOE= 0.17 + 0.03= 0.20

Therefore, the upper limit of the confidence interval for the proportion of millennials that care about immigration is

0.20.

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Answer:

0.5

Step-by-step explanation:

-1+3(10-12)^3/-16

-1+3(-2)^3/-16

-1+(-24)/-16

.5

A) When φ≈0, we can approximate sin(φ) by φ and cos(φ) by 1.

B)  The approximate solutions for φ are given by:φ ≈ -b + sqrt(\(b^2\) - b)

We used derivatives and linear approximation to estimate the values of sin(φ) and cos(φ) when φ≈0. In part (B), we substituted these approximations into the given equation to obtain an approximate equation. In part (C), we solved this approximate equation to find the approximate solutions for φ.

(A) To estimate the values of sin(φ) and cos(φ) when φ≈0, we can use derivatives and linear approximation. First, we find the derivatives of sin(φ) and cos(φ) with respect to φ:

d(sin(φ))/dφ = cos(φ)

d(cos(φ))/dφ = -sin(φ)

Next, we can use the linear approximation of a function f(φ) at a point φ=a, which is given by:

f(φ) ≈ f(a) + f'(a) (φ-a)

In this case, we can choose a=0 and use the derivatives we just found to get:

sin(φ) ≈ sin(0) + cos(0) φ = φ

cos(φ) ≈ cos(0) - sin(0) φ = 1

Therefore, when φ≈0, we can approximate sin(φ) by φ and cos(φ) by 1.

(B) To approximate the given equation by substituting the approximations for sin(φ) and cos(φ), we can use the identities:

\(sin^2\)(φ) + \(cos^2\)(φ) = 1

\(cos^2\)(φ) = 1 - sin^2(φ)

Substituting sin(φ) ≈ φ and cos(φ) ≈ 1, we get:

φ^2 + b(2 + φ) ≈ 0

(C) To solve this approximate equation for φ, we can use the quadratic formula:

φ ≈ (-2b ± sqrt(4\(b^2\) - 4b))/2 = -b ± sqrt(\(b^2\) - b)

Therefore, the approximate solutions for φ are given by:φ ≈ -b + sqrt(\(b^2\) - b)

φ ≈ -b - sqrt\((b^2\) - b)

These are the approximate values of the angle φ that satisfy the given equation.

To summarize, in part (A), we used derivatives and linear approximation to estimate the values of sin(φ) and cos(φ) when φ≈0. In part (B), we substituted these approximations into the given equation to obtain an approximate equation. In part (C), we solved this approximate equation to find the approximate solutions for φ.

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Images that are reflected are mirror images of each other. The coordinate D reflected over the y-axis will give (0, 1).

Images that are reflected are mirror images of each other.

The reflection rule of a coordinate (x, y) over the y-axis is given as:

(x, y) - > (-x, y)

Given the coordinate CD expressed as C(-5, -5) and D(0,1), the coordinate D reflected over the y-axis will give (0, 1).

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Answer:

(0, 1)

Step-by-step explanation:

Answer:

p-6

Step-by-step explanation:

You just balance the equation by putting the variable equations on the first side, and the equation on the other side. Simple!

Answer:

p-6

Step-by-step explanation:

You just balance the equation by putting the variable equations on the first side, and the equation on the other side. Simple!

Answer:

16

Step-by-step explanation:

the answer is 16 because the full shape is a square and it is evenly divided into 4 pieces so if CZ is 16 that means ZE would be the same.

80........................

Answer:

9(x+3)

Step-by-step explanation:

9x + 27

Taking 9 as the common factor in the 2 terms

=> 9(x) + 9(3)

=> 9(x+3)

Given the following question:

The graph of the two plans intersect at a point, the point is called the "point of intersection". This is when two lines intersect and create opposite angles. Knowing these two lines intersect at a certain point, tells us that these two lines have a common point and at one point they both cost the same as each other. If the lines did not intersect then the lines would be parallel.

a) The sample proportion of students who took the tram is 0.52 (52%). b) The 90% confidence interval for the population proportion of tram users is 47.9% to 56.1%. We are 90% confident that the true proportion falls within this range.


a) To determine the sample proportion of students who took the tram, we divide the number of students who stated they took the tram (208) by the total number of students in the sample (400):
Sample proportion = Number of students who took the tram / Total number of students
Sample proportion = 208 / 400 = 0.52
Therefore, the sample proportion of students who took the tram is 0.52, or 52%.

b) To construct a 90% confidence interval for the population proportion, we can use the formula:
Confidence interval = Sample proportion ± Margin of error
The margin of error is determined by the level of confidence and the standard error, which is calculated using the sample proportion.
The standard error can be found using the formula:
Standard error = sqrt((Sample proportion * (1 – Sample proportion)) / Sample size)
For a 90% confidence interval, the level of confidence is 90%, which corresponds to a z-value of 1.645 (assuming a large sample size).
Using the provided information, we can calculate the standard error:
Standard error = sqrt((0.52 * (1 – 0.52)) / 400) = 0.025
Now we can calculate the margin of error:
Margin of error = z-value * Standard error
Margin of error = 1.645 * 0.025 = 0.041
Finally, we can construct the confidence interval:
Confidence interval = Sample proportion ± Margin of error
Confidence interval = 0.52 ± 0.041
Confidence interval = (0.479, 0.561)
Practical interpretation: The 90% confidence interval for the population proportion of students who take the tram to university is from 47.9% to 56.1%. This means that if we were to conduct multiple surveys and construct 90% confidence intervals using the same methodology, approximately 90% of those intervals would contain the true proportion of students who take the tram. In the context of this question, it implies that we are 90% confident that the true proportion of students who take the tram falls within this range.

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1) The wavelength of A is equal to 6.98 × \(10^{-8}\)meters

2) The wavelength of B is equal to 3.45 × \(10^{-11}\) meters

Since we know that the wavelength = speed of light / frequency

The speed of light is 3.00 × \(10^8\) meters per second.

For light sample A with a frequency of 4.30 × 10^15 Hz can be calculated as;

wavelength of A = (3.00 ×  \(10^8\)  m/s) / (4.30 × 10^15 Hz)

wavelength of A = 6.98 ×  \(10^{-8}\) meters

For light sample B with a frequency of 8.70 × \(10^18\) Hz can be calculated as;

wavelength of B = (3.00 ×  \(10^8\) m/s) / (8.70 ×\(10^18\) Hz)

wavelength of B = 3.45 ×  \(10^{-11}\)  meters

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Answer:

107

Step-by-step explanation:

Since the p - value is less than significance level . So, we will accept the null hypothesis.

​(a) State the appropriate null and alternative hypotheses to assess whether women are taller today.

Definition of null hypothesis : The null hypothesis attempts to show that no variation exists between variables or that a single variable is no different than its mean. it is denoted

Alternative Hypothesis : In statistical hypothesis testing, the alternative hypothesis is a position that states something is happening, a new theory is true instead of an old one (null hypothesis).

We are given that The mean height of women 20 years of age or older was 63.7 inches.

So, null hypothesis :  H₀ : μ = 63.7

Alternative Hypothesis :  H₁ : μ > 63.7

b)The​ P-value for this test is 0.06.

The p-value represents the probability of getting a sample mean height of 20 years old women is  64.1 inches.

c) Write a conclusion for this hypothesis test assuming an alpha equals 0.10 level of significance.

p- value = 0.06

Since the p - value is less .

So, we will accept the null hypothesis

So,  

Hence The mean height is 63.7 inches

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Answer:

x=8

Step-by-step explanation:

start by simplifying both sides.

Answer:

A) 3 cents difference

Step-by-step explanation:

Fresh fruity mints costs 20 cents per piece:

$2.40 / 12 = 20 cents

Circle mints costs 17 cents per piece:

$5.00 / 30 = 16.6666 cents which rounds to 17

20 - 17 = 3

Answer is A

In this task, you are asked to drag the tiles to the correct boxes to complete pairs. Not all tiles will be used. The vector matrix [-3 -5] is rotated at different angles.

To complete this task, you will need to understand how vector rotation works.

1. Start by understanding what a vector matrix is. A vector matrix is a rectangular array of numbers, arranged in rows and columns. In this case, the vector matrix is [-3 -5].

2. The vector matrix represents a 2-dimensional vector with components -3 and -5. These components represent the length and direction of the vector in the x and y axes, respectively.

3. To rotate the vector matrix at different angles, you need to apply a rotation matrix. The rotation matrix is a 2x2 matrix that describes the transformation of the vector.

4. The general formula for rotating a vector by an angle θ is:
  - new_x = old_x * cos(θ) - old_y * sin(θ)
  - new_y = old_x * sin(θ) + old_y * cos(θ)

5. To apply the rotation matrix to the vector matrix [-3 -5], you need to substitute the old_x and old_y values into the formula from step 4. For example, if you want to rotate the vector by 45 degrees, θ would be equal to 45 degrees.

6. Calculate the new_x and new_y values using the formula from step 4. For the vector matrix [-3 -5], and a rotation angle of 45 degrees, the calculations would be as follows:
  - new_x = -3 * cos(45) - (-5) * sin(45)
  - new_y = -3 * sin(45) + (-5) * cos(45)

7. Calculate the values for new_x and new_y using a scientific calculator or by hand. In this example, new_x would be approximately -4.95 and new_y would be approximately -2.12.

8. Repeat steps 6 and 7 for different rotation angles to find the new_x and new_y values for each angle.

By following these steps, you can calculate the new coordinates of the vector matrix [-3 -5] when it is rotated at different angles.

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The number of players the team can bring to the tournament would be = 24 players

The softball game is the type of game that involves two teams which is made up of 9. - 10 players.

The total amount of money raised by a softball team=

$2089.50

The amount of money spent on rented bus = $1087.50

The amount left after rent deductions= 2,089.50 - 1,087.50 = 1,002

The amount budgeted for meals for each player= $41.75

The number of players that would be brought for tournament= 1,002/41.75

= 24 players.

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Answer:

(x+9)(x+9)

Step-by-step explanation:

To factor this expression, we first need to put into standard form, that is, \(ax^2 + bx + c\).

So it becomes \(x^2 + 18x + 81\)

Now we need to find two numbers that:

A. When multiplied get us c (81)

B. When added get us b (18)

9 and 9 match those requirements, so out product of two binomials for this becomes (x+9)(x+9).

Hope this helped!

The value of the function f(x)-g(x)-h(x) is -5x^2+6x+6. Option D

It is important that we know functions are expressions showing the relationship between two variables.

These variables are called;

From the information given, we have the functions as;

f(x)=3x+5 g(x)=4x^2-2 h(x)=x^2-3x+1

Now, to determine the function, f(x)-g(x)-h(x). substitute the expressions, we get;

f(x)-g(x)-h(x) =3x + 5 - 4x² + 2 - x² + 3x - 1

Now, collect the like terms, we get;

f(x)-g(x)-h(x) = -4x² - x² + 3x+ 3x + 5 + 2 - 1

Add or subtract the like terms, we get;

f(x)-g(x)-h(x) = -5x² + 6x + 6

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Answer:

Step-by-step explanation:

decrease 7%

100 - 7% = 93

increase 12%

93 + 12% = 104.16

104.16 - 100 = 4.16%

Answer:

Step-by-step explanation:

The ratio of boys to girls:

If there are a total of 132 boys, then number of girls is:

Total number of students:

a.  the probability that in any particular cookie being inspected, fewer than five chip parts will be found is approximately 0.1881. b. the probability that in any particular cookie being inspected, fewer than five chip parts will be found is approximately 0.1881. c. the probability that in any particular cookie being inspected, five or more chip parts will be found is approximately 0.8119.

To calculate the probabilities related to the number of chip parts per cookie in the batch of chocolate-chip cookies, we need to use the Poisson distribution. Given that the mean number of chip parts per cookie is 6.5, we can solve for the probabilities as follows:

a) The probability that in any particular cookie being inspected, fewer than five chip parts will be found:

We can calculate this probability using the Poisson distribution formula and summing the probabilities for 0, 1, 2, 3, and 4 chip parts.

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

Using the Poisson distribution formula with λ (mean) = 6.5:

P(X = k) = (e^(-λ) * λ^k) / k!

Calculating the probabilities for each value:

P(X = 0) ≈ 0.0016

P(X = 1) ≈ 0.0081

P(X = 2) ≈ 0.0265

P(X = 3) ≈ 0.0580

P(X = 4) ≈ 0.0949

Summing the probabilities:

P(X < 5) ≈ 0.0016 + 0.0081 + 0.0265 + 0.0580 + 0.0949 ≈ 0.1881

Therefore, the probability that in any particular cookie being inspected, fewer than five chip parts will be found is approximately 0.1881.

b) The probability that in any particular cookie being inspected, exactly five chip parts will be found:

Using the Poisson distribution formula with λ (mean) = 6.5:

P(X = 5) = (e^(-λ) * λ^5) / 5!

P(X = 5) ≈ (e^(-6.5) * 6.5^5) / 5! ≈ 0.1454

Therefore, the probability that in any particular cookie being inspected, exactly five chip parts will be found is approximately 0.1454.

c) The probability that in any particular cookie being inspected, five or more chip parts will be found:

To calculate this probability, we can subtract the probability of finding fewer than five chip parts from 1 (since it's the complement event).

P(X ≥ 5) = 1 - P(X < 5) = 1 - 0.1881 ≈ 0.8119

Therefore, the probability that in any particular cookie being inspected, five or more chip parts will be found is approximately 0.8119.

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Therefore, The grading function is not a one-to-one correspondence since two numerical ranges, [70, 73) and [67, 70), have the same grade assigned to them.

Explanation:
A one-to-one correspondence means that each input has a unique output and vice versa. In this case, the grading function assigns a grade to a numerical range.
To determine if it is a one-to-one correspondence, we need to check if any two numerical ranges have the same grade assigned to them.
Looking at the given ranges, we can see that there is an overlap between [70, 73) and [67, 70) since they share the grade. Therefore, this grading function is not a one-to-one correspondence.

Therefore, The grading function is not a one-to-one correspondence since two numerical ranges, [70, 73) and [67, 70), have the same grade assigned to them.

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After 1 year, the estimated number of trout in the lake would be approximately 209.

To calculate the number of trout after 1 year using the logistic growth model, we need to apply the formula:

\(N(t) = K / (1 + ( (K - N_0) / N_0 ) * e^{(-r * t)} )\)

Where:

N(t) is the population size at time t,

K is the carrying capacity (maximum population size),

N₀ is the initial population size,

r is the growth rate, and

t is the time period.

Given:

K = 2000 (maximum population size),

N₀ = 100 (initial population size),

r = 0.8 (growth rate),

t = 1 year.

Plugging in the values into the logistic growth formula, we get:

\(N(1) = 2000 / (1 + ((2000 - 100) / 100) * e^{(-0.8 * 1) })\)

Simplifying further:

\(N(1) = 2000 / (1 + (1900 / 100) * e^{(-0.8)} )\)

\(= 2000 / (1 + 19 * e^{(-0.8)} )\)

Calculating the exponential term:

\(e^{(-0.8)} = 0.4493\)

Plugging it back into the formula:

N(1) = 2000 / (1 + 19 * 0.4493 )

= 2000 / (1 + 8.5347)

= 2000 / 9.5347

≈ 209.67

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