Tiyana is saving for a vacation. She wants to have at least $75 for each of the 12 days of her trip. If she saves $ 85 each month for 10 months, will she save enough money?

Use mental math to find the total amount she will save. Then write a division equation to see if she will save enough.

Kevin says he can solve this problem a different way. He says that he can compare 85 x 10 and 75 x 12. Do you agree? Explain your thinking.

The power of (√3 −i)⁶ using De Moivre's Theorem is:

(√3 − i)⁶ = (2 cis (-π/6))⁶ = 2⁶ cis (-6π/6) = 64 cis (-π) = -64

To simplify the expression, we first convert (√3 −i) into polar form. Let r be the magnitude of (√3 −i) and let θ be the argument of (√3 −i). Then, we have:

r = |√3 −i| = √((√3)² + (-1)²) = 2

θ = arg(√3 −i) = -tan⁻¹(-1/√3) = -π/6

Thus, (√3 −i) = 2 cis (-π/6)

Using De Moivre's Theorem, we can raise this complex number to the power of 6:

(√3 −i)⁶ = (2 cis (-π/6))⁶ = 2⁶ cis (-6π/6) = 64 cis (-π)

Finally, we can convert this back to rectangular form:

(√3 −i)⁶ = -64(cos π + i sin π) = -64(-1 + 0i) = 64

Therefore, the fully simplified answer in the form a + bi is -64.

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To calculate the sample size needed to provide a margin of error of 3 or less with a 0.95 probability, we can use the formula:

n = (Z * σ / E)^2

Where:
n = sample size
Z = z-score corresponding to the desired confidence level (in this case, 0.95)
σ = population standard deviation
E = margin of error

Given that the population standard deviation (σ) equals 17 and the margin of error (E) is 3, we can substitute these values into the formula:

n = (Z * σ / E)^2
n = (1.96 * 17 / 3)^2
n = (33.32 / 3)^2
n = 11.107^2
n ≈ 123.29

Since the sample size cannot be a decimal, we need to round it up to the nearest whole number. Therefore, the sample size needed to provide a margin of error of 3 or less with a 0.95 probability when the population standard deviation equals 17 is 124.

In conclusion, a sample size of at least 124 is needed to achieve a margin of error of 3 or less with a 0.95 probability, assuming a population standard deviation of 17.

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Answer:

A and E

Step-by-step explanation:

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\) ← distance formula

it is important that the x and y coordinates are placed correctly, that is not mixed together.

First version

let (x₁, y₁ ) = X (- 5,  4 ) and (x₂, y₂ ) = Y (7, 15 ) , then

XY = \(\sqrt{(7-(-5)^2+(15-4)^2}\) → A

or

Second version

let (x₁, y₁ ) = Y (7, 15 ) and (x₂, y₂ ) = X (- 5, 4 ) , then

XY = \(\sqrt{(-5-7)^2+(4-15)^2}\) → E

Answer:

Graph Below:

Answer:

The correct answer would be A.

Step-by-step explanation:

You're right because the translation would make it so the circles have the same center. Because they have the same center it would be easier to see the correlation between them.

I hope this helps!!

Answer:

60

Step-by-step explanation:

LCM of 12 and 15

First Method: Listing the multiples

First, write the common multiples of all three numbers.

Common Multiples of 12: 12,24,36,48,60,72,….

Common Multiples of 15: 15, 30, 45, 60, 75,…

Hence, the Least common multiple of 12 and 15 is 60.

Second method: By prime factorisation

Let us write the prime factors of the two numbers individually.

12 = 2 x 2 x 3

15= 3 x 5

Multiply each factor the maximum number of times it occurs in either number

= 2 X 2 X 3 X 5

= 60

LCM of 12 and 15= 60

Answer

LCM of 12 and 15= 60

Hope this helps :)

Answer:

60

Step-by-step explanation:

we have to use prime factorisation method to obtain the answer.

12 and 15 have LCM 60.

Answer:

A

Step-by-step explanation:

The unit rate would be stitches per minute.

Divide total stitches by total time:

3600 / 3 = 1200

Unit rate = 1200 stitches per minute.

The most appropriate procedure from the given options that would improve the reliability and validity of grading short essay tests, thus addressing the complaint of sensitivity to bias and variability in grading, is: D) Using a scoring rubric.

A scoring rubric is a predefined set of criteria or guidelines that outlines the specific expectations and standards for evaluating student responses. By using a scoring rubric, the grading process becomes more objective, consistent, and transparent, thereby reducing bias and variability in grading.

A scoring rubric provides a structured framework that allows graders to assess and assign scores based on predetermined criteria, such as content knowledge, organization, clarity, coherence, and grammar. It ensures that all essays are evaluated using the same standards and eliminates subjective judgment as much as possible.

Administering more pretests (option A) may provide additional practice or feedback to students but does not directly address the issue of bias and variability in grading.

Grading on the curve (option B) adjusts grades based on the performance of other students in the class, which does not directly address bias or variability in grading. It can introduce its own set of issues and may not reflect the true quality of each individual student's work.

Implementing a contract system (option C) refers to a negotiated agreement between students and instructors regarding grading criteria, which may help clarify expectations but does not inherently address bias or variability.

Therefore, using a scoring rubric (option D) is the most appropriate procedure to improve the reliability and validity of grading short essay tests while minimizing sensitivity to bias and variability in grading.

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The first term and common difference of the arithmetic series are -11 and 3.

In the arithmetic series, S₄₀ = 1900 and U₄₀ = 106

Hence,

Sₙ = n / 2 (2a + (n - 1)d)

S₄₀ = 20(2a + 39d)

S₄₀ = 40a + 780d

1900 =  40a + 780d

Uₙ = a + (n - 1)d

U₄₀ = a + 39d

106 = a + 39d

Combine the equation

a + 39d = 106

40a + 780d = 1900

20a + 780d = 2120

40a + 780d = 1900

20a = - 220

a = -220 / 20

a = -11

Hence,

106 = a + 39d

106 = -11 + 39d

106 + 11 = 39d

117 = 39d

divide both sides by 39d

d = 117 / 39

d = 3

Therefore, the first term and common difference of the arithmetic series are -11 and 3.

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T3(x) = x - x^2/2 + x^3/6.

The Taylor polynomial of degree 3 for the function f(x) = x + e^-x centered at a = 0 is given by:

T3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3

= 1 + (-1 + 1)x + (e^-0 - (-1)(-1)e^-0)x^2/2! + (0 + (-1)(-1)(-1)e^-0)x^3/3!

= x - x^2/2 + x^3/6

So T3(x) = x - x^2/2 + x^3/6.

An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics.

The nth Taylor polynomial of the function is a polynomial of degree n that is created by the partial sum of the first n + 1 terms of a Taylor series. Approximations of a function made by Taylor polynomials get generally better as n rises. Quantitative estimates of the mistake brought about by the use of such approximations are provided by Taylor's theorem. If a function's Taylor series is converging, its total is the upper bound of the Taylor polynomials' infinite sequence. A function's Taylor series sum may not match.

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The measure of angle EBF is  80° .

In the question ,

it is given that ,

point A, B and C lie on a straight line .

and G , B and F lie on a different straight line .

angle GBA = 24° so ,

GBA + GBC = 180°   ...because linear pair

So , GBC = 180 - 24 = 156°

angle CBF = 24°          ......because vertically opposite angles are equal .

from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,

156° = ABE + EBF         .....(1)

Since the line AC and DF are parallel and BE is the transversal

So  , angle DEB + angle ABE = 180°

104° + ABE = 180°

ABE = 180-104

ABE = 76°

Substituting ABE = 76° in the equation (1) ,

we get ,

156 = 76+ EBF

EBF = 156 - 76

EBF = 80°

Therefore , The measure of angle EBF is  80° .

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If 0.4 Customers arrives after 1 minute-

0.4*5 = 2.0 cm

From 1947 to 1987, Willowbrook State School served Staten Island's Willowbrook neighborhood as a state-funded facility for youngsters with intellectual disabilities. The school had 6,000 students enrolled by 1965 despite being intended for 4,000.

Aerts entered through the doors of Willowbrook State School in 1971 with former Staten Island Advance writer Jane Kurtin, and took disturbing photos of children and adults with special problems who were confined in cages, hungry, and used as research experiments.

Geraldo Rivera, who was working as an investigative reporter for WABC-TV in New York at the time, began an investigation into Willowbrook soon after and found a number of appalling circumstances there, including overcrowding and subpar sanitary facilities.

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Answer:

As I answered in the other one the answer is 1/3

Step-by-step explanation:

To get minimum profit Jin needs to sell 130 bicycles.

Assume the number of bicycles with a variable and calculate the cost to make 'x' bicycles and the revenue that can be produced.

Using the above cost and revenue forms an inequality and solve the inequality for the value of 'x'.

Here we have

Jim owns a business that produces bicycles. He must bring in more in revenue than he pays out in costs in order to turn a profit.

It costs $50 in labor and materials to make each of his bicycles.

His rent each month for his factory is $9,100.

He sells each bicycle for $120.  

Let's assume that at 'x' bicycles Jim will get a minimum profit

The total cost to make bicycles = 50x + 9100

Total revenues by selling 'x' bicycles = 120x

Since Jim will get a minimum profit

Here 50x + 9100 ≤ 120x

=> 120x ≥ 50x + 9100

Subtract - 50x from both sides

=> 120x - 50x ≥ 50x - 50x + 9100  

=> 70x ≥ 9100  

=> 7x ≥ 910  

Divide by 7 into both sides

=> 7x/7 ≥ 910/7

=> x ≥ 130  

Therefore,

To get minimum profit Jin needs to sell 130 bicycles.

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There is only one way 345 can be written as the sum of an increasing sequence of two or more consecutive positive integers. The correct answer is A) 1.

To find the number of ways 345 can be written as the sum of an increasing sequence of two or more consecutive positive integers, we need to consider the factors of 345.

First, let's find the prime factorization of 345: 345 = 3 * 5 * 23.

Now, let's focus on factor 23. Since the sequence needs to have at least two consecutive positive integers, the smallest possible sequence would be 23 and 24. We can see that any larger sequence would have a sum greater than 345.

Therefore, the only possible way to write 345 as the sum of an increasing sequence of two or more consecutive positive integers is 23 + 24.

Hence, the answer is option (a) 1.

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We have a segment RT, and S is a point between R and T.

The length of RT is 4x-4.

The length of RS is 2x+6.

The length of ST is 16.

As S is between R and T, we can write:

Then:

With the value of x, we can calculte RS:

The length of RS is 32.

Answer:

B

Step-by-step explanation:

I think

Answer:

-1/2

Step-by-step explanation:

step 1: Using Bodmas we have below

-6/35--1/14--9/35

step 2: Take L. C. M of 35 and 14 i.e 490

-84--35--126/490 = -245/490 = -1/2 or -0.5

Abby's MAD is 45 and her IQR is 51.5. Caleb's MAD is 28 and his IQR is 16. The coach should choose Caleb.

MAD

Simply calculate the mean (average) of all the data and find the maximum deviation. Make sure you look at data both larger and smaller than the mean. e.g. Abby:

(146+147+178+231+195+209+207+219+187)/9 = 191

The data with the largest deviation from the mean is 146, so 191-146=45

IQR

To compute the quartiles, the data must be put into ascending order of value. I will use Caleb's data set as an example; please see the photo for details.

Therefore, because both Caleb's MAD and his IQR are lower than those of Abby, the coach should choose him.

Answer:

  a)  y = 2x +4

  b)  y = 1/2x +4

  c)  y = -2x +11

Step-by-step explanation:

The given equations are in slope-intercept for, so we can read the slope directly from the equation. It is the x-coefficient.

We can then write an equation of a parallel line using the point-slope form of the equation of a line:

  y -k = m(x -h) . . . . for a line with slope m through point (h, k)

If you like, you can rearrange this to "slope-intercept" form. Add k and simplify.

  y = mx +(k -mh)

__

a) m = 2, (h, k) = (3, 10)

  y = 2x +(10 -2·3)

  y = 2x +4

__

b) m = 1/2, (h, k) = (0, 4)

  y = 1/2x +(4 -(1/2)·0)

  y = 1/2x +4

__

c) m = -2, (h, k) = (4, 3)

  y = -2x +(3 -(-2)(4))

  y = -2x +11

Answers:

=====================================================

Work Shown:

x = some positive real number

2x = amount Ally gets

3x = amount Barry gets

5x = amount Cat gets

Note that the ratio 2x:3x:5x reduces to 2:3:5 after dividing all parts by x.

Add up the parts and you should get a sum of 500 pounds. Solve for x.

2x+3x+5x = 500

10x = 500

x = 500/10

x = 50

Based on that x value, we then can say:

As a check, 100+150+250 = 500.

Also, note that the ratio 100:150:250 fully reduces to 2:3:5 after dividing all parts by the GCF 50.

Those two facts help confirm our answers.

Answer:

n = 4/8 or 1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Move all terms not containing n

to the right side of the equation.

Exact Form:

n=12

Decimal Form:

n=0.5

Answer:

€18 is the answer

If you’ve been given an estimate, use that to determine how much £13.50 would be by cross multiplying

Step-by-step explanation:

x² - 9

1. There is no common factor other than 1.

2. √x² = x; √9 = 3

3. a = x; b = 3

4. x² - 9 = (x - 3)(x + 3)

(4) The series diverges by the Comparison Test. Each term is greater than that of a divergent geometric series.

To determine whether the series converges or diverges, we can use the Comparison Test.
First, we can simplify the series by dividing both the numerator and denominator by n:
[Infinity] (4 + 1/n) / (3 - 5/n)

As n approaches infinity, both the numerator and denominator approach 4/3, so we can write:
[Infinity] (4 + 1/n) / (3 - 5/n) = [Infinity] 4/3

Since the harmonic series [Infinity] 1/n diverges, we can conclude that the original series diverges as well.
Therefore, the correct answer is:
4. The series diverges by the Comparison Test. Each term is greater than that of a divergent geometric series.

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Therefore, In the figure, a∥b  angle m∠7 = 34° .

An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. Angles of two rays lie in the plane containing the rays. Angles can also result from the intersection of two planes. Dihedral angles are the name given to them.

Here,

Given that a and b are parallel lines,

∠3 and ∠7  are corresponding angles and congruent

m∠3 = 34°

thus ,m∠7 =m∠3 = 34°

so, m∠7 = 34°

Therefore, In the figure, a∥b  m∠7 = 34° .

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Answer:

-15(4) or -4(15) or 15(-4)

Step-by-step explanation:

As long as you stick with the same variables, you can change their position in the equation or change both of their signs. This should give you the same answer.

Let's say your equation was -2(6). This means you must multiply -2 and 6. This should give you -12. You could also phrase it as 2(-6) or -6(2) or 6(-2). They all give you -12 as a result.

Answer:

(-1)(15+15+15+15)

(-15)+ (-15)+ (-15)+ (-15)

Step-by-step explanation: