(Chapter 12) If u and v are in V3, then |u * v| ⤠|u||v|

Using concepts of Mean, we got Paired samples test for the difference between two means is the type of test researcher is using.

The test procedure, called the two-sample t-test, is correct when the following conditions are met:

If the sample findings are not in favour, given the null hypothesis, the researcher rejects the null hypothesis. Typically, this will involves comparing the P-value to the significance level, and rejecting null hypothesis when the P-value is smaller than the significance level.

Hence, the test type which researcher is using Paired samples test for the difference between two means.

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Answer:

1:6ab  

2: c^6x

3: 10y^7x

4:3g^4 h^5 x^4

The interquartile range for Tom's data is 5

Tom and Susan park at different lots.

Tom's IQR :

IQR = Q3 - Q1

Q3 = third quartile (value at the endpoint of the box)

Q1 = 1st quartile (value at the beginning of the box)

IQR = 9 - 4

IQR = 5

SUSAN :

QR = Q3 - Q1

Q3 = third quartile (value at the endpoint of the box)

Q1 = 1st quartile (value at the beginning of the box)

IQR = 8 - 5

IQR = 3

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1. The total amount (future value) Marcus had at the end of the second year of investing $5,000 at 2.5% compounded annually was $5,253.13.

2. The minimum number of years Marcus must leave the $5,253.13 to be more than $10,000 is 11.3 years.

The future value is the compounded present value at an interest rate.

The future value can be derived from an online finance calculator as follows:

With the future value so determined, we can then compute the minimum time in years required for it to reach more than $10,000 at the simple interest rate.

Initial investment = $5,000

Interest rate = 2.5% compounded annually

Investment period = 2 years

N (# of periods) = 2

I/Y (Interest per year) = 2.5%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

FV = $5,253.13

Total Interest = $253.13

Principal = $5,253.13

Interest rate = 8% per annum

Future amount = $10,000

Time to reach the future amount = (Future Value/Principal - 1) ÷ Interest rate

= ($10,000/$5,253.13 - 1) ÷ 0.08

= 11.3 years

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To find the Maclaurin series of f(x) given the derivatives at 0, we can use the general formula for the Maclaurin series expansion:

f(x) = f(0) + f'(0)x + (1/2!)f''(0)x^2 + (1/3!)f'''(0)x^3 + ...

Given the derivatives f(0) = 9, f'(0) = -8, f''(0) = 15, and f'''(0) = -8, we can substitute these values into the formula to find the first four terms of the series:

f(x) = 9 - 8x + (1/2!)(15)x^2 + (1/3!)(-8)x^3

Simplifying this expression, we have:

f(x) = 9 - 8x + (15/2)x^2 - (4/3)x^3

Therefore, the first four terms of the Maclaurin series of f(x) are: 9, -8x, (15/2)x^2, and -(4/3)x^3.

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Answer:

5x

Step-by-step explanation:

NOte: it is an expression and not an equation as originally asked.

"Product" means the answer to a multiplication of two numbers.

You are asked to write the answer to 5 and a number being multiplied together.

Let the unknown number be

x

The product is therefore

5x

x

=

5x

Answer:

Step-by-step explanation:

In the figure attached,

ΔABC is an equilateral triangle,

Sides AB = BC = AC and points P, Q, and R are the midpoints of these sides respectively.

If the coordinates of A(0, 0), B(2a, 0) and C(a, b)

AB = 2a

AC = \(\sqrt{a^2+b^2}\)

Since AB = AC

2a = \(\sqrt{a^2+b^2}\)

4a² = a² + b²

3a² = b²

Therefore, ordinate pairs representing midpoints of AB, BC and AC will be

P = \((\frac{2a+0}{2},\frac{0}{2})\) =(a, 0)

Q = \((\frac{a+2a}{2},\frac{b}{2})\) = \((\frac{3a}{2},\frac{b}{2})\)

R = \((\frac{a+0}{2},\frac{b+0}{2})\) = \((\frac{a}{2},\frac{b}{2})\)

Now we will find the lengths of medians with the help of formula of distance between two points (x, y) and (x', y')

d = \(\sqrt{(x-x')^2+(y-y')^2}\)

AQ = \(\sqrt{(0-\frac{b}{2})^2+(0-\frac{3a}{2})^2}\)

     = \(\sqrt{\frac{b^2}{4}+\frac{9a^2}{4}}\)

     = \(\frac{1}{2}(\sqrt{b^2+9a^2})\)

     = \(\frac{1}{2}\sqrt{12a^2}\)  [Since b² = 3a²]

     = \(a\sqrt{3}\)

BR = \(\sqrt{(2a-\frac{a}{2})^{2}+(0-\frac{b}{2})^2}\)

     = \(\sqrt{(\frac{3a}{2})^2+(-\frac{b}{2})^2}\)

     = \(\frac{1}{2}\sqrt{b^2+9a^2}\)

     = \(\frac{1}{2}(\sqrt{12a^2})\)

     = \(a\sqrt{3}\)

CP = b = \(a\sqrt{3}\)

Therefore, AQ = BR = CP = \(a\sqrt{3}\)

Hence, medians of an equilateral triangle are equal.

Answer:

Hi! Please refer to the image attached. I promise this is a real answer, I got this question right on mine. :D

Good luck!

Answer:

31 and 37

Step-by-step explanation:

Those are the only two numbers

Answer:

The two numbers between 30 and 40 which have only 2 factors are -

31 and 37

Hope it helps you.

Answer:

a = -3

Step-by-step explanation:

Step 1:  Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:

5^a = 1/125

Step 2:  Take the log of both sides

log(5^a) = log(1/125)

Step 3:  According to the power rule of logs, we can bring a down and multiply it by log(5):

a * log(5) = log (1/125)

Step 4:  Divide both sides by log(5) to solve for a:

(a * log(5) = log(1/125)) / log(5)

a = -3

Optional 5:  We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:

5^-3 = 1/125

1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator

1/125 = 1/125

Answer:

48 = 98x   (where x is the width)

Step-by-step explanation:

Area of a rectangle = length × width

Let x = width

Given:

⇒ 48 = 98x

Answer:

x=0.4897599184

Step-by-step explanation:

→Solution,

Area(A)=48 in²

Lenght(l)=98in

Breadth(b)=?

Let the breadth be x.

As we have,

Area of rectangle=l×b

48 in²=98 in × x

48 in²/98 in = x

x=0.4897599184

CosA is negative for the largest angle in an obtuse triangle. Using the law of cosines, a²>b²+c², a>b, and a>c are derived.

Step 1: As the obtuse triangle has the largest angle A (more than 90 degrees), the cosine function's value is negative.

Step 2: By applying the Law of Cosines in the triangle, a²>b²+c², which is derived from a²=b²+c²-2bccosA, and hence a>b and a>c can be derived.

Step 3: From the previously derived inequality a²>b²+c², we can conclude that a>b and a>c as a²-b²>c². The value of a² is greater than both b² and c² when a>b and a>c.

Therefore, the largest angle of an obtuse triangle is opposite the longest side.

Step 4: In triangle ABC, A=103°, a=25, and c=30.

a² = b² + c² - 2bccos(A),

a² = b² + 900 - 900 cos(103),

a² = b² + 900 + 900 cos(77),

a² > b² + 900, so a > b.

Similarly, a² > c² + 900, so a > c.

Therefore, triangle ABC satisfies a>b and a>c.

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Answer:

x=0, y=3. (0, 3)

Step-by-step explanation:

5x+2y=6

3y=2x+9

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

y=2/3x+9/3

y=2/3x+3

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

5x+2(2/3x+3)=6

5x+4/3x+6=6

15/3x+4/3x=6-6

19/3x=0

x=0/(19/3)=0

5(0)+2y=6

0+2y=6

2y=6

y=6/2=3

Answer:The result obtained by differentiating the result of an integral.

The derivative of an integral is given by the fundamental theorem of calculus. More specifically, if f(x) is a continuous function on the interval [a, b], then the derivative of the integral of f(x) from a to x is given by f(x).

In other words, if F(x) is an antiderivative of f(x), then the derivative of the integral of f(x) from a to x is F'(x) = f(x).

Symbolically, we can write:

d/dx ∫[a,x] f(t) dt = f(x)

where the integral sign ∫ represents the integral operation and d/dx represents the derivative operation.

This result is very useful in calculus, as it allows us to easily compute derivatives of functions that are defined as integrals.

Answer:

Step-by-step explanation:

The total number of seventh-grade students who play an instrument is 9 + 9 + 11 + 9 = 38. The number of seventh-grade students who play an instrument other than guitar is 9 + 11 + 9 = 29. Therefore, the probability that a seventh grader chosen at random will play an instrument other than guitar is 29/38 ≈ 0.76 (rounded to the nearest hundredth).

The two types of control charts for variables are the X-bar chart and the R-chart.

Control charts are widely used in statistical process control to monitor and analyze the variability and stability of processes over time. They are used for variables data, which are measurements or observations that can be quantified.

1. X-bar Chart: The X-bar chart is used to monitor the central tendency or average of a process. It tracks the sample means over time to detect any shifts or trends. It helps in assessing whether the process is in control or if there are any systematic variations from the target value.

2. R-chart (Range chart): The R-chart is used to monitor the variability or dispersion within a process. It tracks the ranges (the difference between the highest and lowest values) of samples over time. By analyzing the range values, it helps in understanding whether the process is stable and consistent or if there are any unusual variations or outliers.

Together, the X-bar chart and the R-chart provide valuable insights into process performance and allow for early detection of any deviations or abnormalities, helping organizations maintain quality standards and take appropriate corrective actions when necessary.

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Solving the given data from topics including statistics, linear equations, geometry, and probability, we get, (a) a Graph showing earnings relation. (b) Same savings in 10 weeks. (c) Weak negative association. (d) 180° counterclockwise rotation. (e) P(No Heads) = 85%.(f)  FD ≈ 2.37. (g) Three halves. (h) Predict 40 occurrences.

a) The graph that shows the relationship between the amount of money the painter earns and the number of rooms he paints is the one with a coordinate grid, an x-axis labeled "Rooms Painted," a y-axis labeled "Amount of Money Earned," and a line going from the point (0, 60) through the point (3, 120).

b) To determine the number of weeks when sibling A and sibling B will have the same amount of money in their savings accounts, we need to solve the equation:

7x + 40 = 5x + 60.

7x + 40 = 5x + 60

2x = 20

x = 10 weeks

c) The scatter plot showing the cupcake pricing data exhibits a weak, negative linear association.

d) The polygon ABCD is rotated 180° counterclockwise to get polygon A'B'C'D'.

e) P(No Heads): To find the probability of getting no heads, we add the frequencies of the outcomes "Tails, Tails" and "Tails, Heads," which is 35 + 50 = 85. So the probability of getting no heads is 85%.

f) To determine the measurement of FD in triangle ABC ~ triangle DEF, we can use the ratios of corresponding sides. FD / DE = BC / AB. Plugging in the values, FD / 3.3 = 7.9 / 11. Solving for FD, we find FD ≈ 2.37.

g) The slope of the line that contains the points (-3, -1) and (3, 8) can be found using the formula:

slope = (y2 - y1) / (x2 - x1).

Plugging in the values, we get

(8 - (-1)) / (3 - (-3)) = 9 / 6 = three halves.

h) When rolling a fair, 6-sided die 60 times, the number of times it will land on a number greater than 2 can be estimated by considering that there are 4 out of 6 sides with numbers greater than 2. So the prediction would be 60 * (4/6) = 40 times.

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The inequality -x ≤ x cos ≤ x holds for all values of x ≥ 0. The value of x cos can be any real number between -1 and 1, inclusive, depending on the specific value of x.

To find the value of x cos in the inequality -x ≤ x cos ≤ x for all values of x ≥ 0, let's analyze each part separately.

First, we have -x ≤ x cos. Since x is non-negative (x ≥ 0), we can divide both sides of the inequality by x (assuming x ≠ 0) without changing the direction of the inequality:

-1 ≤ cos

The cosine function ranges from -1 to 1, so the inequality -1 ≤ cos is always true. Therefore, this inequality holds for all values of x ≥ 0.

Now, let's consider the second part, x cos ≤ x. Since x is non-negative (x ≥ 0), we can divide both sides of the inequality by x (assuming x ≠ 0) without changing the direction of the inequality:

cos ≤ 1

The cosine function's maximum value is 1, so the inequality cos ≤ 1 is always true. Therefore, this inequality also holds for all values of x ≥ 0.

Combining the two inequalities, we have -1 ≤ cos ≤ 1. In other words, the cosine function's values range from -1 to 1 for all values of x ≥ 0.

To find the value of x cos, we need a specific value of x. Let's choose x = 1 as an example. In this case, we have:

1 cos ≤ 1

Simplifying, we find that cos ≤ 1, which is always true. Therefore, for x = 1, the value of x cos (or 1 cos) is any value between -1 and 1, including -1 and 1 themselves.

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The grocer needs to mix 495 kg of almonds with the 180 kg of Brazil nuts to create a mixture that sells for $1.28/kg.

Let's assume that the grocer needs to mix x kilograms of almonds with the existing 180 kg of Brazil nuts to create a mixture that sells for $1.28/kg. To solve the problem, we can set up an equation that equates the cost of the nuts to the selling price of the mixture.

The cost of the almonds is $1.20/kg, and the cost of the Brazil nuts is $1.50/kg. The cost of the mixture is $1.28/kg. So, we can write:

1.20x + 1.50(180) = 1.28(x + 180)

Simplifying the equation, we get:

1.20x + 270 = 1.28x + 230.40

0.08x = 39.6

x = 495

In summary, the grocer can determine the amount of almonds needed by setting up an equation based on the cost of the nuts and the selling price of the mixture. By solving the equation, the grocer can determine that 495 kg of almonds are needed to create a mixture that sells for $1.28/kg.

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33333333333333333333333333333333333

Answer:

c⁶/d²

Step-by-step explanation:

a⁻ⁿ = 1/aⁿ

So :

c⁶d⁻² = c⁶/d²

Answer:

Step-by-step explanation:

2x +15 +2x +5 = 180

4x = 180 - 20

x = 160/4

x = 40

TVZ + 2x +5 =180

TVX +2(40) = 180 -5

TVX = 175 - 80

TVX = 95

Answer:

2.5

Step-by-step explanation:

The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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Answer:

A

Step-by-step explanation:

Slope is defined by \(\frac{y_2-y_1}{x_2-x_1} or \frac{rise}{run}\). Take 2 points from this table and plug into the formula to find the slope.

\(\frac{96-60}{-20--12} = \frac{36}{-8} = -9/2\)

From a logical standpoint, since when x increases and y decreases, the slope must be negative, eliminating answering B and D. Because the y value changed more than the x value, the slope must be more than 1, eliminating option C and leaving you with option A.

-8 = 6 - 14

use the number line:

go to 6 on the number line and count back until you reach -8; you should count 14

since it's a -8 that means the bigger number also has to be negative. between 6 and 14, 14 is bigger so it becomes a negative number

so your answer is -14

Answer:

(1/3) / (x+1) + (-1/3) / (x+4)

Step-by-step explanation:

1 / (x+1)(x+4) = (A/x+1) + (B/x+4)

1 =  ((A/x+1) + (B/x+4)) * (x+1)(x+4)

1 = A*(x+4) + B*(x+1)

* if x = -4

1 = A*(-4+4) + B*(-4+1)

1 = B*(-3)

B = -1/3

** if x = -1

1 = A*(-1+4) + B*(-1+1)

1 = A*(3)

A = 1/3

check: (1/3)/(x+1) + (-1/3)/(x+4) = ((1/3)*(x+4))/((x+1)(x+4)) + ((-1/3)*(x+1))/((x+1)(x+4))

==> ((1/3x + 4/3)+(-1/3x - 1/3)) / ((x+1)(x+4)) = 1 / (x+1)(x+4)

Answer:

VX=50

Step-by-step explanation:

VX=\(\frac{1}{2} *UT\) (The straight line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it.

\(z-41=\frac{1}{2} *z+9\)

\(z-41=z+9/2\)

do cross multiplication

2(z-41)=z+9

2z-82=z+9

2z-z=9+82

z=91

VX=z-41

=91-41

=50

Answer:

The duration is 135 minutes ie. 2 hours and 15 minutes