i suck at this topic :(

Answer:

12t - 1

Step-by-step explanation:

Hey there!

-5(5 - 30) = -10

-5(5) - 5(-30) = -10

-25 + 150 = -10

125 = -10

125 ≠ -10

Therefore, your answer should be:

125 ≠ -10

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

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Given the following quadratic expression:

Let's check if the given equation can be solved by factoring.

a.) Let's determine the original equation.

From the original equation, we observed that the constant 155/9 is not a perfect square. For the original quadratic equation to be factorable, we must apply the method of completing the square.

Therefore, we can say that the original quadratic equation can't be solved by factoring.

Answer:

19.95t - $10

Step-by-step explanation:

I think this is the answer but i could be absolutely wrong

Answer: No its not a right angled triangle. Please mark as brainliest!

Answer:

Yes

Step-by-step explanation:4 mm and 5 mm are the A and B part of the triangle while the 8 mm is the hypotenuse

Answer:

15.  y = 3x + 23

16.  y = -2x + 11

17.  y = (1/4)x + 6

18.  y = x

19.  y = (-8/5)x - 4

20.  y = (-7/5)x - 5

Step-by-step explanation:

Point-slope form:  y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line

15.  y - 2 = 3(x + 7)

⇒ y = 3x + 23

16. y - 5 = -2(x - 3)

⇒ y = -2x + 11

17. y - 7 = (1/4)(x - 4)

⇒ y = (1/4)x + 6

Slope formula: m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line

Point-slope form:  y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line

18. let (x1, y1) = (-2, -2)

    let (x2, y2) = (-5, -5)

⇒ m = (-5 + 2) / (-5 + 2) = 1

⇒ y + 2 = 1(x + 2)

⇒ y = x

19. let (x1, y1) = (0, -4)

    let (x2, y2) = (-5, 4)

⇒ m = (4 + 4) / (-5 - 0) = -8/5

⇒ y + 4 = (-8/5)(x - 0)

⇒ y = (-8/5)x - 4

20. let (x1, y1) = (-5, 2)

    let (x2, y2) = (0, -5)

⇒ m = (-5 - 2) / (0 + 5) = -7/5

⇒ y - 2 = (-7/5)(x + 5)

⇒ y = (-7/5)x - 5

Answer:

10

Step-by-step explanation:

a 4 side polygon has 360° interior angle

120 +120=240

360-240=120

120÷2=60

60÷6=10

A plasmid used in both yeast and bacteria requires two different selection markers because the same selection may not work for both hosts and bacteria and yeast recognize different promoters.

When using a plasmid in both yeast and bacteria, it is important to have two different selection markers for several reasons. First, the same selection, such as the presence of an antibiotic, may not be effective in both hosts. Different organisms have varying sensitivities to antibiotics, so a marker that works in bacteria may not work in yeast or vice versa. Therefore, two different selection markers are needed to ensure successful selection in both hosts.

Additionally, bacteria and yeast recognize different promoters, which are DNA sequences that control the initiation of gene expression. Promoters are specific to each organism and play a crucial role in regulating gene expression. By incorporating two different selection markers into the plasmid, each marker can be driven by a promoter recognized specifically by the corresponding host. This ensures that the selection marker is effectively expressed in the appropriate host organism, enabling accurate selection and maintenance of the plasmid.

In summary, using two different selection markers in a plasmid intended for both yeast and bacteria is necessary because the same selection may not be effective in both hosts, and different promoters are recognized by bacteria and yeast. This approach allows for successful selection and maintenance of the plasmid in both organisms.

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The number of quarters is 16

Given d = {dn: n ∈ N} where dn = (−n, 1/n) for n ∈ N.Find the union and intersection of the given family of d sets.

The given family of sets is {d1, d2, d3, ...} where di = (−i, 1/i) for all i ∈ N.1. To find the union of the given family of sets d, take the union of all sets in the given family of sets.i.e. d1 = (−1, 1), d2 = (−2, 1/2), d3 = (−3, 1/3), ...

Thus, the union of the given family of sets d is{d1, d2, d3, ...} = (-1, 1].Therefore, the union of the given family of sets d is (-1, 1].2. To find the intersection of the given family of sets d, take the intersection of all sets in the given family of sets .i.e. d1 = (−1, 1), d2 = (−2, 1/2), d3 = (−3, 1/3), ...Thus, the intersection of the given family of sets d is{d1, d2, d3, ...} = Ø. Therefore, the intersection of the given family of sets d is empty.

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Answer:

Step-by-step explanation:

y + 5 = x - 0

y = x - 5

1. The height of the cone is equal to

2. You can solve for the slant height, s by applying Pythagorean's theorem.

3. To get from the base of the cone to the top of the hill, an ant has to crawl 29 mm.

In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:

Volume of cone, V = 1/3 × πr²h

Where:

By substituting the given parameters into the formula for the volume of a cone, we have the following;

8792 =  1/3 × 3.14 × 20² × h

26,376 =  3.14 × 400 × h

Height, h = 26,376/1,256

Height, h = 21 mm.

Question 2.

In order to solve for the slant height, s, we would have to apply Pythagorean's theorem since the height of the cone has been calculated above.

Question 3.

By applying Pythagorean's theorem, we have the following:

r² + h² = s²

20² + 21² = s²

400 + 441 = s²

s² = 841

Slant height, s = √841

Slant height, s = 29 mm.

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Answer:

equation we have to do addition or divide

The problem asks to find the approximate change in the value of z when the variables x and y change from (2, -1) to (2.04, -0.95), given the function z = x^2 - xy/(6y^2). Therefore, the approximate change in z is about 0.1933.

To find the rate of change of z with respect to x and y, we first need to take the partial derivatives of z with respect to each variable:

∂z/∂x = 2x - y/6y^2

∂z/∂y = -x/(3y^3) + 1/(2y)

Then, at the point (2, -1), we can evaluate these partial derivatives to find:

∂z/∂x = 2(2) - (-1)/(6(-1)^2) = 4 + 1/6

∂z/∂y = -2/(3(-1)^3) + 1/(2(-1)) = 2/3 - 1/2

Using the formula for total differential, we can approximate the change in z as:

Δz ≈ ∂z/∂x Δx + ∂z/∂y Δy

where Δx and Δy are the changes in x and y, respectively. In this case, Δx = 2.04 - 2 = 0.04 and Δy = -0.95 - (-1) = 0.05. Substituting the partial derivatives and the values for Δx and Δy, we get:

Δz ≈ (4 + 1/6)(0.04) + (2/3 - 1/2)(0.05) = 0.1933...

Therefore, the approximate change in z is about 0.1933.

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The solution to this system is a1 = 2, a2 = -1, and a3 = 0. Therefore, the coordinate vector of p(x) relative to the basis B is [2, -1, 0].

(a) To show that B is a basis for P2, we need to show that B is linearly independent and spans P2.

Linear Independence:
Suppose that a1(1 + x + x2) + a2(1 + 2x − x2) + a3(1 − 2x − x2) = 0 for some scalars a1, a2, and a3. Then we have:

a1 + a2 + a3 = 0    (coefficients of x^0)
a1 + 2a2 - 2a3 = 0  (coefficients of x^1)
a1 - a2 - a3 = 0    (coefficients of x^2)

We can solve this system of equations to get a1 = 1, a2 = 1, and a3 = -1. Since the only solution is the trivial one, B is linearly independent.

Spanning:
Let p(x) be an arbitrary polynomial of degree at most 2. We need to show that we can write p(x) as a linear combination of the polynomials in B. We can do this by solving the system of equations:

a1 + a2 + a3 = p(0)      (coefficients of x^0)
a1 + 2a2 - 2a3 = p(1)    (coefficients of x^1)
a1 - a2 - a3 = p(-1)     (coefficients of x^2)

This is a system of linear equations with unknowns a1, a2, and a3. It can be solved using standard techniques, and the solution will always exist since the system is consistent. Therefore, B spans P2.

Since B is linearly independent and spans P2, it is a basis for P2.

(b) To find the coordinate vector of p(x) = 1 + 2x + 3x^2 relative to the basis B, we need to find scalars a1, a2, and a3 such that:

1 + 2x + 3x^2 = a1(1 + x + x^2) + a2(1 + 2x - x^2) + a3(1 - 2x - x^2)

This is equivalent to solving the system of equations:

a1 + a2 + a3 = 1
a1 + 2a2 - 2a3 = 2
a1 - a2 - a3 = 3

The solution to this system is a1 = 2, a2 = -1, and a3 = 0. Therefore, the coordinate vector of p(x) relative to the basis B is [2, -1, 0].

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Answer:

x = 30, -30

Step-by-step explanation:

The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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Answer:

its the way it goes from minus 4

Answer:

10 cm is the answer because 30÷3 angles

       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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The value of X in the diagram provided is

We can use the trigonometric function of sine to find the angle θ, where θ is the angle between the opposite side and the hypotenuse.

sin(θ) = opposite / hypotenuse

sin(θ) = 12 / 13

To find θ, we can take the inverse sine of both sides:

θ = sin⁻¹(12/13)

θ = sin⁻¹(0.9231)

θ = 67.38°

Note that we use calculator to find the θ

Therefore, the angle in the right-angled triangle with opposite side 12, adjacent side 5, and hypotenuse 13 is approximately 67.38 degrees.

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let's firstly convert the mixed fraction to improper fraction and let's convert the decimal amount to a fraction, and how much she spent is just their product.

\(\stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}}~\hfill 1.\underline{75}\implies \cfrac{175}{1\underline{00}}\implies \cfrac{7}{4} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{11}{3}\cdot \cfrac{7}{4}\implies \cfrac{77}{12}\implies 6.41\overline{6}\qquad \impliedby \textit{about 6 bucks and 42 cents}\)

Answer:

.15¢

Step-by-step explanation:

1.20$ total divided by 8 and its .15¢

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

The margin of error for the poll, at the 90% confidence level, is approximately ± 0.0252.

To find the margin of error for a poll, we need to consider the sample size and the confidence level. In this case, the poll had a sample size of 380 people, and we want to calculate the margin of error at the 90% confidence level.

The margin of error is determined using the formula:

Margin of Error = Critical Value * Standard Error

The critical value corresponds to the desired confidence level and can be found using a standard normal distribution table or a statistical calculator. For a 90% confidence level, the critical value is approximately 1.645.

The standard error is calculated as follows:

Standard Error = sqrt[(p * (1 - p)) / n]

where p is the proportion of respondents who answered positively (in this case, 68% or 0.68), and n is the sample size (380).

Substituting the values into the formula, we have:

Standard Error = sqrt[(0.68 * (1 - 0.68)) / 380]

Calculating the standard error:

Standard Error = sqrt[(0.2176) / 380]

Standard Error ≈ 0.0153

Now we can calculate the margin of error:

Margin of Error = 1.645 * 0.0153

Margin of Error ≈ 0.0252

Therefore, at the 90% confidence level, the margin of error for this poll is approximately ± 0.0252.

This means that if we were to repeat the poll multiple times and calculate the confidence interval each time, approximately 90% of the intervals would contain the true proportion of people who like dogs in the population. The margin of error indicates the range around the estimated proportion (68%) within which the true proportion is likely to fall.

In summary, the margin of error for the poll, at the 90% confidence level, is approximately ± 0.0252. This value represents the uncertainty associated with estimating the proportion of people who like dogs based on the sample data.

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Answer:

0.67

Step-by-step explanation:

The total number of spins is

7 + 13 + 20 + 14 + 9 = 63

The numbers of spins that landed on blue, green, and purple are:

13, 20, 9

Total blue, green, purple: 13 + 20 + 9 = 42

Based on the spins that are tabulated, the probability the spinner will land on blue, green, or purple is

42/63 = 2/3 = 0.67

Answer

f(n)=4•(0.5)^n-1