Abigail plans to save 2/5 of her earnings each week for 12 weeks. She earns approximately 180 per week about how much will Abigail have saved from earnings at the end 12 weeks

(a) There exists a student in your school who has visited North Dakota.

(b) Every student in your school has visited North Dakota.

(c) There exists a student in your school who has not visited North Dakota.

(d) No student in your school has visited North Dakota.

In (a), the existential quantifier (∃) indicates that there is at least one student in your school who has visited North Dakota. The statement N(x) is true for at least one student.

In (b), the universal quantifier (∀) indicates that the statement N(x) is true for every student in your school. In other words, every student in your school has visited North Dakota.

In (c), the existential quantifier (∃) indicates that there is at least one student in your school who has not visited North Dakota. The negation of N(x), denoted by ¬N(x), is true for at least one student.

In (d), the universal quantifier (∀) indicates that the negation of N(x) is true for every student in your school. In other words, no student in your school has visited North Dakota.

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\(\boxed{ \sf{Answer}}\)

⏩ Substitute the value of 'f' in the equation.

\(4 - 2f \\ = 4 - 2(1) \\ = 4 - 2 \\ = 2\)

⏩ The answer will be 2.

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Answer:

2

Step-by-step explanation:

If you multiply 2 by 1, you get 2. Then subtract 2 from 4 to get 2.

Hope that this helps!

Answer:

\(-\frac{22}{91} = x\)

Step-by-step explanation:

To solve the equation \(3x - 23 = 94x - 1\), we'll follow these steps:

Start by simplifying the equation by combining like terms. In this case, we have terms with x on both sides, as well as constants:

\(3x - 23 = 94x - 1\)

To isolate the x terms, we can subtract 3x from both sides of the equation:

\(3x - 3x - 23 = 94x - 3x - 1\)

Simplifying further, we get:

\(-23 = 91x - 1\)

Next, we want to isolate the constant term on one side of the equation. We can do this by adding 1 to both sides:

\(-23 + 1 = 91x - 1 + 1\)

Simplifying further:

\(-22 = 91x\)

Finally, we can solve for x by dividing both sides of the equation by 91:

\(-\frac{22}{91}=\frac{91x}{91}\)

Simplifying further:

\(-\frac{22}{91} = x\)

Therefore, the solution to the equation \(3x - 23 = 94x - 1\) is \(-\frac{22}{91} = x\)

Answer:

The range is -7 ≤ y ≤ 8

Step-by-step explanation:

The range is the full measurement of a graph on the y-axis.

I know this can be confusing at times as I had struggles with this in the past

Hopefully, this helps!

Answer:

2

Step-by-step explanation:

The base of a shape can be found by measuring the width of the cross section. In the example you provided, the base of the plank is 2 feet.

The slope of the line from the equation is 2/3.

The line:

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.

The formula of a line:

y = mx + c

m = slope

c = y-intercept

Here we are provided with the equation:

8x - 12y = 108

12y = 8x - 108

y = 2/3x - 9

So by equating we get the slope:

m = 2/3

Therefore the slope is 2/3.

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Yes, the accuracy of the central limit theorem (CLT) improves when the trial success proportion (p) is closer to 50%.

The central limit theorem states that for a sufficiently large sample size, the distribution of sample means (or sums) will approach a normal distribution regardless of the shape of the population distribution. This means that even if the original population is not normally distributed, the sampling distribution of the mean will be approximately normal.

When the trial success proportion (p) is closer to 50%, it means that the probability of success and failure in each trial is relatively balanced. In this scenario, the binomial distribution approaches a symmetrical shape, which is similar to the normal distribution.

As p approaches 50%, the standard deviation of the binomial distribution becomes larger, and the shape of the distribution becomes more bell-shaped and symmetric. This makes the approximation to a normal distribution more accurate.

On the other hand, when p is close to 0 or 1 (i.e., heavily skewed towards one outcome), the binomial distribution becomes more skewed, and the approximation to a normal distribution becomes less accurate. In such cases, the sample size needs to be larger for the CLT to hold.

Therefore, when the trial success proportion (p) is closer to 50%, the accuracy of the central limit theorem improves, and the normal approximation to the sampling distribution of the mean becomes more reliable.

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1. The most likely color for the taxi = green

2. The probability that the taxi is blue = 0.25

Let us assume that tg represents the taxi was green and tb represents the taxi was blue;

Also yg represents the taxi appeared green and yb  represents the taxi appeared blue.

9 out of 10 athenian taxis are green

So, P(tg) = 0.90

And, P(tb) = 1 - P(tg)

                = 1 - 0.90

                = 0.10

As under the dim lighting conditions, discrimination between blue and

green is 75% reliable,

P(yb | tb) = 0.75.

So, P(yg | tb) = 1 - P(yb | tb)

                     = 0.25

Similarly P(yg | tg) = 0.75

Thus, P(yb | tg) = 1 - P(yg | tg)

                         = 0.25

P(tb | yb) = P(tb, yb) / P(yb)

               = [P(yb | tb) P(tb)] / [P(yb, tg)P(tg) + P(yb | tb) P(xb)]

               = 0.25

Thus the probability that the taxi is blue = 0.25

P(tg | yb) = 1 - P(tb | yb)

              = 0.75

We can observe that P(tb | yb) > P(tb) but the posterior P(tb | yb) is smaller than 0.5, since the prior P(tb) is very small. Thus, the taxi was most likely green.

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The complete question is:

Suppose you are a witness to a nighttime hit-and-run accident involving a taxi in Athens.All taxi cars in Athens are blue or green. You swear under oath that the taxi was blue.Extensive testing shows that, under the dim lighting conditions, discrimination between blue and green is 75% reliable.

1. is it possible to calculate the most likely color for the taxi? (*hint:* distinguish carefully between the proposition that the taxi *is* blue and the proposition that it *appears* blue.)

2. what is the probability of the taxi being blue, if you know that 9 out of 10 athenian taxis are green?

According to the question we have the first four terms of the Maclaurin series of f(x) are: 1, 7x, 2x^2/3, 5x^3/36

The Maclaurin series of a function f(x) is a power series expansion that approximates the function around x=0. The first four terms of the Maclaurin series of f(x) can be found using the formula:

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

Substituting the given values, we get:

f(x) = 1 + 7x + (4/2!)x^2 + (5/3!)x^3 + ...

Simplifying the second and third terms, we get:

f(x) = 1 + 7x + 2x^2/3 + 5x^3/36 + ...

Therefore, the first four terms of the Maclaurin series of f(x) are:

1, 7x, 2x^2/3, 5x^3/36

Note that we can use this series to approximate the value of f(x) for small values of x. The more terms we include, the better the approximation.

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The null hypothesis is \(H_{0} : x=0.60\) and alternative hypothesis is \(H_{1} :x\neq 0.60\).

What is null and alternative hypothesis?

The null hypothesis is that the statement that researchers usually aim to disprove by performing tests of significance on the dataset. the most purpose of the null hypothesis is to help disprove a hypothesis or nullify it in favor of the alternate hypothesis that the researchers want to prove.

Let the percentage of readers who own a laptop be \(x.\)

As newsletter publisher believes that \(60\)`% of their readers own a laptop.

Therefore the null hypothesis is \(H_{0} : x=0.60\) and alternative hypothesis is \(H_{1} :x\neq 0.60\).

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Given:

Amanda sold 13 rolls of plain wrapping paper and 12 rolls of holiday wrapping paper for a total of $208.

And,

Mofor sold 4 rolls of plain wrapping paper and 3 rolls of holiday wrapping paper for a total of $55.

Let, x be the cost of one roll of plain wrapping paper and y be the cost of one roll of holiday wrapping paper.

The equations are,

Solve the equations,

Put the value of y in equation (2),

Answer:

The cost of one roll of plain wrapping paper is x = $4.

The cost of one roll of holiday wrapping paper is y = $13.

Answer:

the answer is: 8(x)= 4 -5

Step-by-step explanation:

The graph of parent function and translated function are given below. Therefore, the transformation is shifted down 5 units.

The given function is g(x)=x-5.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Here, parent function is g(x) = x

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Shifted down: 5 units

The graph of parent function and translated function are given below. Therefore, the transformation is shifted down 5 units.

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Given:

The function f is continuous on the interval [3, 11].

Required:

to find the approximate value f'(9).

Explanation:

The function f(x) is continuous on [3,11].

So

Final Answer:

The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given triangle has coordinates,

A(2, -2), B(5, -3) and C(2, -4).

First the triangle is translated by the rule (x, y) → (x - 1, y + 6)

A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).

B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)

C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)

Then the translated triangle is reflected across the Y axis.

When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.

A'(1, 4) becomes A''(-1, 4)

B'(4, 3) becomes B''(-4, 3)

C'(1, 2) becomes C''(-1, 2)

Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).

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The correct answer is 0.75x + 0.15y = 90 is the equation that describes the quantity of pens and pencils the glee club can purchase.

The maximum number of pens the club can purchase is 120.

The maximum number of pencils the club can purchase is 600.

Each pen costs $0.75.

Total number of pens = x

Each pencil costs $0.15

y = number of pencils

(Cost of each pen) x (Number of pens) + (Cost of each pencil) x (Number of pencils) = $90 which equals the total cost for pens and pencils.

The formula for the quantity of club pens and pencils is 0.75x + 0.15y = 90.

When 0.75x = 90

x = 90/0.75

x = 120, the club purchases the most pens.

The maximum number of pens the club can purchase is 120.

When the club purchases the most pens, 0.15x = 90

x = 90/0.15

x = 600

Hence, the maximum number of pencils the club can purchase is 600 and the formula for the quantity of club pens and pencils is 0.75x + 0.15y = 90.

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Answer:

v = 200 m/s

Step-by-step explanation:

The formula for the speed of a tsunami in deep water is given by :

\(v=\sqrt{gh}\)

Here,

g is acceleration due to gravity

h is the depth of the ocean in meters.

We need to find the speed at which the tsunami that started with an earthquake in Sumatra struck Sri Lanka about 1550 km away. The Bay of Bengal is 4 km (4000 m) deep.

It means we need to find v if h = 4000 m

So,

\(v=\sqrt{10\times 4000}\\\\v=200\ m/s\)

So, the speed of the tsunami is 200 m/s.

Answer: y=-3m+13

Step-by-step explanation:

y=mx+c

m is the gradient

y=-3x+c

We know one point

-2=3(-5)+c

Solve for c

-2=-15+c

13=c

y=-3m+13

The calculated chi-squared value is [calculated value]. Since the calculated chi-squared value is [greater than/less than/equal to] the tabled chi-squared value of 9.488, we can [reject/fail to reject] the null hypothesis.

To determine whether the number of customers varies by day of the week, we can conduct a chi-squared test. The null hypothesis states that the number of customers coming into the shop is equal for each weekday, while the alternate hypothesis suggests that the number of customers differs by day. To perform the test, we need to calculate the chi-squared value.

First, we calculate the expected frequency for each day by taking the average of the total number of customers over the entire week. For this given week, the expected frequency would be the sum of all the customers (50 + 60 + 40 + 47 + 53) divided by 5, resulting in 50 customers per day. Next, we calculate the chi-squared value by summing up the squared differences between the observed and expected frequencies, divided by the expected frequency for each day. Once we have the calculated chi-squared value, we compare it with the tabled chi-squared value at a given significance level (5%) and degrees of freedom (4). If the calculated chi-squared value is greater than the tabled value (9.488), we can reject the null hypothesis. Conversely, if the calculated chi-squared value is less than or equal to the tabled value, we fail to reject the null hypothesis. By applying the appropriate calculations and comparing the calculated chi-squared value with the tabled chi-squared value, we can determine whether the number of customers actually varies by day of the week.

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Answer:

The associative property of multiplication

 8 . ( 5. b ) = ( 8. 5) . b

Step-by-step explanation:

Explanation

The associative property of multiplication

 a . ( b. c ) = ( a. b) . c

Given numbers are  8, 5 and b

The associative property of multiplication

 8 . ( 5. b ) = ( 8. 5) . b

 8 . ( 5. b ) = ( 8. 5) . b = 40 b

The calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.



To determine the number of significant figures in a calculation, we follow the rules for significant figures:

1. Addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
2. Multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

Let's break down the calculation step by step:
\(9.04-8.23+21.954+81.0\) yields \(104.764\).

Now, multiplying this result by \(3.1416\) gives \(329.5719744\).

The measurement with the fewest significant figures in the calculation is \(3.1416\), which has 5 significant figures.

According to the rule for multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures. Hence, the result, \(329.5719744\), will be rounded to 4 significant figures.

Therefore, the calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.

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Answer:

B 4 is the correct answer

Step-by-step explanation:

b - 12 = - 8

b = 12 - 8

b = 4

Answer:

i)  25130 Liters

ii) 16 cm

Step-by-step explanation:

The volume of the tank is in cubic meters, not liters.  So the answer to question i) would be 25.13 cubic meters, which equals 25130 Liters.

ii) Now we find the depth.  2000 is 7.959% of 25130.  7.959% of the 2 meter height is 15.917 cm.  Rounded to the nearest cm, it would be 16 cm.

The parabola g(x) is reasonable because it can be derived of parabola f(x) by rigid transformations.

Parabolas are represented by second order polynomials in vertex form, whose definition is shown below:

y - k = C · (h - k)²

Where:

In this problem we must create the expression for the image of the parabola by means of rigid transformations, that is, transformations that change the parabola without changing Euclidean distances. Most common rigid transformations are listed below:

The procedure is summarized below:

Now we proceed to apply the rigid transformations in that order:

Step 1

y = f(x) → y = f(x - 3)

y = x² → y = (x - 3)²

Step 2

y = f(x - 3) → y - 2 = f(x - 3)

y = (x - 3)² → y - 2 = (x - 3)²

Step 3

y - 2 = f(x - 3) → y - 2 = - f(x - 3)

y - 2 = (x - 3)² → y - 2 = - (x - 3)²

Step 4

y - 2 = - f(x - 3) → y - 2 = - f[0.5 · (x - 3)]

y - 2 = - [0.5 · (x - 3)]²

Finally, we proceed to plot both parabolae by help of a graphing tool.

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The rectangle maximum area will be A=9 square units with the length=3 and the width=3.

Area is defined as the space occupied by a plane or rectangle having length and width in two dimensional plane.

It is given that the perimeter of rectangle is P=12

So from the formula of perimeter of rectangle

2(L+W)=12

L+W=6

L=6-W

Now the area of rectangle will be

A=LxW

A=(6-W)W

Now for maximum area we will find the derivative and equate to zero.

\(A=(6W-W^2})\)

\(A'=6-2W=0\)

\(W=3\)

\(L=6-W=6-3=3\)

So the area will be

\(A=3\times 3=9 \ square \ units\)

Hence the rectangle maximum area will be A=9 square units with the length=3 and the width=3.

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The variable assigned to strgrade when intscore equals 90 would likely be 'A'.

When the variable intscore equals 90, the corresponding value assigned to the variable strgrade would typically be 'A'. This suggests that a score of 90 is associated with the highest grade achievable in the given context. The specific mapping between integer scores and letter grades may vary depending on the grading system or criteria in place. It is important to note that without further information about the grading scale or specific rules defined within the system, it is difficult to determine the exact value of strgrade assigned to intscore of 90.

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Answer:81.85 km/hr is the average speed

Step-by-step explanation:

Answer: ≈ 84,3 km/h.

Step-by-step explanation:

\(\displaystyle\\V{average}=\frac{\Delta S}{\Delta t}=\frac{S_1+S_2+S_3}{t_1+t_1+t_3} .\\1.\ S_1=50\ km\\ t_1=\frac{S_1}{V_1}\\ V_1=25*\frac{3600}{1000} \\V_1=90\ \frac{km}{h} .\\t_1=\frac{50}{90}\\ t_1=\frac{5}{9} \ h.\\2.\ S_2=120\ km\ \ \ \ V_2=80\ \frac{km}{h} \\t_2=\frac{S_2}{V_2} \\t_2=\frac{120}{80} \\t_2=\frac{3}{2}\ h.\\\)

\(3.\ V_3=90\ \frac{km}{h} \\t_3=35\ minutes\\t_3=\frac{35}{60} \\t_3=\frac{7}{12}\ h.\\ S_3=V_3*t_3\\S_3=90*\frac{7}{12} \\S_3=52,5\ km.\\Hence,\\V{average}=\frac{50+120+52,5}{\frac{5}{9}+\frac{3}{2} +\frac{7}{12} } \\V{average}=\frac{222,5}{\frac{95}{36} } \\Vaverege\approx84,3\ \frac{km}{h} .\)

Answer:

c.

Step-by-step explanation:

In table one , the rate of change is by adding 7 to each number

in table 2, the rate of change is by adding 6 to each number

in table 4, the rate of change is by adding 8 to each number

but in table 3, there is no precuse addition of numbers

The approximate value for the probability that at least 80 flips are necessary is 0.3897.

Given:

a fair coin is flipped repeatedly until 50 heads are observed

using the central limit theorem, calculate an approximate value for the probability that at least 80 flips are necessary.

P (h>25)=p(h>=26)= 1-p(h<=26)

Assume the situation is approximately normal

u= np =50(1/2)=25 , s=√(npq) = √( 50)(.5)(.5) =√12.5

z=(x-u)/s = ( 26–25)/√12.5 = 0.283

P(z=0.283) =0.1103

Edit p(z>0.283)=0.1103

P(h <= 80)= 0.5+ 0.1103= 0.6103

P(h>=80) 1 - 0.6103 = 0.3897

Hence we get the required answer.

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Answer:

34

Step-by-step explanation:

They gave us -3+5i.

The conjugate of -3+5i is

-3 - 5i

You use the same numbers -3 and 5i, but with a minus sign instead of a plus.

Then multiply them together.

(-3 + 5i)(-3 - 5i)

-3•-3 + 15i - 15i - 25i^2

= 9 - 25i^2

Remember i^2 is -1.

= 9 - 25(-1)

= 9 + 25

= 34

Shortcut version:

When you multiply a complex number and its conjugate, square both numbers and add them together.

3^2 + 5^2

= 9 + 25

= 34