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If the inflation rate is positive, purchasing power
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This situation is reflected in the
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rate of return on an
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Answer: √5

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Step-by-step explanation:

Answer:

c

Step-by-step explanation:

all triangles equal 180°

Answer:

to get your answer you have to. Then after that, and finally

The convolution product of r(t) and s(t) is y(t) = 2(t+3)u(t+3) - 2(t-3)u(t-3) - 2(t+2)u(t+2) + 2(t-2)u(t-2) - 2(t+1)u(t+1) + 2(t-1)u(t-1) - 2tu(t) + 2(t-1)u(t-1) - 2(t-2)u(t-2) + 2(t-3)u(t-3).

To find the convolution product of r(t) and s(t), we need to evaluate the integral of the product of r(t) and s(t) over the appropriate range. In this case, r(t) = u(t) - u(t-1) and s(t) = 2u(t+3) - 2u(t-3).

To perform the convolution, we substitute the expression for r(t) and s(t) into the integral:

y(t) = ∫[u(τ) - u(τ-1)][2u(t+3-τ) - 2u(t-3-τ)] dτ.

Simplifying this expression, we obtain:

y(t) = 2∫[u(τ) - u(τ-1)][u(t+3-τ) - u(t-3-τ)] dτ.

The next step is to evaluate the integral over the appropriate range. Since the limits of integration depend on the variables involved, we need to consider different cases.

Case 1: t+3 ≥ τ ≥ t-3

In this case, both u(t+3-τ) and u(t-3-τ) are equal to 1, and the integral becomes:

y(t) = 2∫[u(τ) - u(τ-1)] dτ.

Case 2: t+3 ≥ τ > t

In this case, u(t+3-τ) = 1, and u(t-3-τ) = 0, so the integral becomes:

y(t) = 2∫[u(τ) - u(τ-1)] dτ + 2∫u(τ-3) dτ.

Case 3: t > τ ≥ t-3

In this case, u(t+3-τ) = 0, and u(t-3-τ) = 1, so the integral becomes:

y(t) = 2∫[u(τ) - u(τ-1)] dτ - 2∫u(τ-3) dτ.

By evaluating the integrals in each case, we can obtain the expression for y(t) as shown in the main answer.

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The 99% confidence interval for the population mean of all first-year teacher salaries is approximately $57,135 to $58,865.

To construct a 99% confidence interval for the population mean of all first-year teacher salaries, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

First, we need to find the critical value corresponding to a 99% confidence level.

Since the sample size is large (n > 30), we can assume the sampling distribution is approximately normal, and we can use a z-table. The critical value for a 99% confidence level is approximately 2.576.

Next, we need to calculate the standard error, which is the standard deviation divided by the square root of the sample size. The standard error is $2,500 / sqrt(43) = $381.71.

Now we can construct the confidence interval:

Lower bound = $58,000 - (2.576 * $381.71)

Upper bound = $58,000 + (2.576 * $381.71)

Therefore, the 99% confidence interval for the population mean of all first-year teacher salaries is approximately $57,135 to $58,865.

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Answer:

Answer is 9,49,169

Step-by-step explanation:

I hope it's helpful!

Have a nice day!

Answer:

a) Her reasoning is wrong because √50 does not simplify to 2√25, it simplifies to 5√2. With her thinking that √50 simplifies to 2√25, then this leads to her doing 2 * 5 which equals 10.

b) To estimate a square root, you have to find two square numbers that make the number lie in between the two squares. In this case we need to find two square numbers where one square number is smaller than 50 and the other one is bigger. You should have found the two square numbers to be 7 and 8 because 7² = 49 and 8² = 64. Now we divide 50 by either number, either 7 or 8. As we can't use a calculator it is easier to divide 50 by 8 than 7. 50/8 = 6.25 Now we find the average of 6.25 and 8 which is 14.25/2 = 7.125 7.125 rounded to the nearest tenth is 7.1 Therefore the answer for b is 7.1

Answer:

(a) √50 is not equal to 10.

√50 = √25√2 = 5√2

(b) √50 = 5√2 = 5(1.41) = 7.05 = 7.1

Answer:

a = 20°

b = 160°

c = 125°

u = 110°

v = 70°

w = 110°

x = 70°

y = 110°

z = 110°

Step-by-step explanation:

Theorems

Using the Vertical Angles Theorem:

⇒ a = 20°

Using the Angles on a straight line Theorem:

⇒ 20° + b = 180°

⇒ b = 180° - 20°

⇒ b = 160°

Using the Vertical Angles Theorem:

⇒ c + 35° = b

⇒ c + 35° = 160°

⇒ c = 160° - 35°

⇒ c = 125°

Using the Vertical Angles Theorem:

⇒ u = 110°

⇒ v = 70°

Using the Same-side Exterior Angles Theorem:

⇒ v + w = 180°

⇒ 70° + w = 180°

⇒ w = 180° - 70°

⇒ w = 110°

Using the Corresponding Angles Postulate:

⇒ y = 100°

Using the Vertical Angles Theorem:

⇒ y = z = 110°

Using the Angles on a straight line Theorem:

⇒ x + z = 180°

⇒ x + 110° = 180°

⇒ x = 180° - 110°

⇒ x = 70°

Answer:

$310

Step-by-step explanation:

starting backwards:

Answer:

$310

Step-by-step explanation:

To get the area of the shaded region, we must subtract the area of the bigger triangle on the outside and the area of the smaller triangle inside the bigger triangle.

Set up the equation:

  Area of big triangle - Area of small triangle = \(\frac{1}{2} *19*19 - \frac{1}{2} *13*13\)\(= \frac{1}{2} (19^{2} -13^{2} ) = \frac{1}{2}*192 = 96\)

So the area of the shaded region is 96.

Hope that helps!

As given by the question

There are given that the roll of die.

Now,

In the die, there are total outcomes is 6.

And,

The value in die which is odd number is:

1, 3, 5,

The number that an odd number or a number greater than 2

So, the succesfull outcomes is:

1, 3, 4, 5, 6.

Then,

The probability will be:

Hence, the correct option is B

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

The independent variable is the bill, and the dependent variable is the tip.

Step-by-step explanation:

The independent variable means it can stand alone on it's own.  The bill will always be $20 because that's how much the food costs.  The tip will be different depending on how much the bill is.

Both events A and B have probabilities of 1/12, and they are independent events since the outcome on one die does not affect the outcome on the other die.

The event A consists of all outcomes in which the number of spots showing on the red die is three or less.

Since the red die has six equally likely outcomes (1, 2, 3, 4, 5, and 6), the probability of A is:

P(A) = the number of outcomes in A / the total number of possible outcomes.

Out of the six possible outcomes on the red die, three of them are three or less: 1, 2, and 3.

Therefore, the number of outcomes in A is three.

Since there are six equally likely outcomes for the green die as well, the total number of possible outcomes is 6 x 6 = 36.

Therefore, we have:

P(A) = 3/36 = 1/12.

The event B consists of all outcomes in which the number of spots showing on the green die is more than three.

There are also three outcomes on the green die that satisfy this condition: 4, 5, and 6.

Thus, we have:

P(B) = 3/36 = 1/12.

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Answer:

35, 67 and 78

Step-by-step explanation:

the angles are:

n, 2n-3 and 2n+8

there are 180 degrees in a triangle, so adding those terms together will give us 180

5n + 5 = 180

180 - 5 = 175

5n = 175

175 / 5 = 35

n = 35

now we have n we can put it in to the formula we have for the angles at the start:

n = 35

2n - 3 = 67

2n + 8 = 78

so the angles are

35, 67 and 78

Answer:   3/2

Step-by-step explanation:    

The statements which are true regarding the students whose results on 9 tests are as shown are; The median of Nadia's data is equal to the median of Ben's data.

Nadia had the highest score on a test.

According to the task content, it follows that the results of the students in discuss are indicated by means of a box plot as in the attached image.

Consequently, it follows from observation that the median of Nadia and Ben as indicated in the attached box plot is 92 in both cases as indicated by the vertical line in both boxes.

Additionally, the highest score by Nadia is 100 while that for Ben is; 99.

Hence, Nadia had the highest score on a test.

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The quadratic function to model the values in the table will be,

y = 3x² + 3x - 3

Option 1 is true.

What is Quadratic equation?

An algebraic equation of the second degree in x is called Quadratic equation.

Given that;

The values of x and y are,

x = -1, 0, 3

y = -3, -3, 33

Let a quadratic function is,

y = ax² + bx + c     ... (i)

Then, It satisfy all the values given in table.

So, Substitute point (x, y) = (-1, -3) in equation (i) we get;

- 3 = a - b + c  ... (ii)

And, Substitute point (x, y) = (0, -3) in equation (i) we get;

-3 = c  .. (iii)

And, Substitute point (x, y) = (3, 33) in equation (i) we get;

33 = 9a + 3b + c ... (iv)

Now, Substitute c = -3 from (iii) in equations (ii) and (iv) we get;

From (ii);

- 3 = a - b - 3

a - b = 0      ... (v)

From (iv);

33 = 9a + 3b - 3

Divide by 3;

11 = 3a + b - 1

3a + b = 12   .... (vi)

Solve equations (v) nd (vi) we get;

a = 3 and b = 3

Thus, Substitute the values a = 3, b = 3 and c = -3 in quadratic equation we get;

y = ax² + bx + c

y = 3x² + 3x - 3

So, The quadratic function to model the values in the table will be,

y = 3x² + 3x - 3

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The solution of the equation 3z minus 2 is equal to 46 is 16.

The given equation '3z minus 2 is equal to 46' can be written as

    3z - 2  =   46

Now solving for z because the value of z will give the required solution of the given equation. So now finding the z from the equation:

   3z = 46  + 2

   3z =  48

   z = 48/3

   z = 16

The value of the z is 16 which represents the solution of the given equation i.e 3z minus 2 is equal to 46.

Therefore it is concluded that the solution of the equation 3z minus 2 is equal to 46 is 16.

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The expression 4 - (-5 - 0) is equivalent to the expression will be 4 - (-5) and 4 + 5. Then the correct options are A, B, and C.

The equivalent is the expression that is in different forms but is equal to the same value.

The numerical expression is given below.

⇒ 4 - (-5 - 0)

Simplify the expression, then we have

⇒ 4 - (-5 - 0)

⇒ 4 - (-5)

⇒ 4 + 5

⇒ 9

The expression 4 - (-5 - 0) is equivalent to the expression will be 4 - (-5) and 4 + 5. Then the correct options are A, B, and C.

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Step-by-step explanation:

Start by finding how many toys he builds in an hour

192÷8= 96÷4 = 24

Now divide 24 by 60 to find how many toys he builds per minute (60 because there are 60 minutes in an hour)

24÷60 = 12÷30 = 6÷15 = 2÷5= \(\frac{2}{5}\)

He builds \(\frac{2}{5}\) of a toy or 40% of a toy every minute

Multiply the amount of toy(s) he builds per minute times 5 to find out how many he would build in 5 minutes

\(\frac{2}{5}\) × 5= \(\frac{2}{5}\) × \(\frac{5}{1}\) = 2

He builds 2 toys every 5 minutes

I hope this helps!!!

The length of the curve  r(t) = (cos(2t), sin(2t), 2t) for -10 ≤ t ≤ 5 is approximately 10.61 units.(rounded to two decimal places)

To find the length of the curve given by the vector-valued function r(t) = (3 cos(t), 3 sin(t), 2t) for 0 ≤ t ≤ 8, we can use the arc length formula for curves in three-dimensional space:

L = ∫√(dx/dt)² + (dy/dt)²+ (dz/dt)²dt

Let's calculate the length using this formula:

dx/dt = -3 sin(t)

dy/dt = 3 cos(t)

dz/dt = 2

(dx/dt)² = (-3 sin(t))² = 9 sin²(t)

(dy/dt)² = (3 cos(t))² = 9 cos²(t)

(dz/dt)² = 2² = 4

Now, substitute these values into the arc length formula:

L = ∫√(9 sin²(t) + 9 cos²(t) + 4) dt

L = ∫√(9(sin²(t) + cos²(t)) + 4) dt

L = ∫√(9 + 4) dt

L = ∫√13 dt

Integrating √13 with respect to t gives:

L = √13 × t + C

where C is the constant of integration. Evaluating this expression from t = 0 to t = 8, we get:

L = (√13 × 8 + C) - (√13 × 0 + C)

L = √13 × 8 - √13 × 0

L = √13 × 8

L ≈ 11.36 (rounded to two decimal places)

Therefore, the length of the curve for 0 ≤ t ≤ 8 is approximately 11.36 units.

Now let's find the length of the curve given by r(t) = (cos(2t), sin(2t), 2t) for -10 ≤ t ≤ 5:

Using the same steps as before, we have:

dx/dt = -2 sin(2t)

dy/dt = 2 cos(2t)

dz/dt = 2

(dx/dt)² = (-2 sin(2t))² = 4 sin²(2t)

(dy/dt)² = (2 cos(2t))²= 4 cos²(2t)

(dz/dt)² = 2² = 4

Substituting these values into the arc length formula:

L = ∫√(4 sin²(2t) + 4 cos²(2t) + 4) dt

L = ∫√(4(sin²(2t) + cos²(2t)) + 4) dt

L = ∫√(4 + 4) dt

L = ∫√8 dt

L = √8 × t + C

Evaluating this expression from t = -10 to t = 5:

L = (√8 × 5 + C) - (√8 × (-10) + C)

L = √8 × 5 + √8 × 10

L = √8 × 15

L ≈ 10.61 (rounded to two decimal places)

Therefore, the length of the curve for -10 ≤ t ≤ 5 is approximately 10.61 units.

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The function is defined by m(x)=f(x)/2g(x) is m′(5))=\(\sqrt[3]{3/2}\) on graph.

A function is a relation that is "well-behaved," by which we mean that, given a starting point, we know the exact one ending spot to go to; given an x-value, we get only and precisely one corresponding y-value. As a result, even though all functions are relations [since they pair information], not all relations are functions. Family members who behave well are a subset of all your relations, just as well-behaved functions are a subset of all mathematical relations.)

f(x)=2x+3,XE[-1,2]

-2/3x+25/3, XE[2,8]

g(x)=√x^2−x+3 XE

m′(5))=\(\sqrt[3]{3/2}\)

The thing to notice here is that f(x) is expressed differentially in different domain.

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After solving, the factor of 32 is 1, 2, 4, 6, 8, 16, 32.

In the given question, we have to find the factors of 32.

We can employ a variety of techniques, including the division method and the multiplication method, to determine the factors of a given integer.

The qualities of a number's factors are as follows:

A number has a finite number of factors.

A number's factor will never be more than or equal to the provided number.

Every number contains at least two factors, 1 and the actual number, with the exception of 0 and 1.

Finding a number's factors requires utilizing division and multiplication operations.

So the factor of 32 is:

32 = 1, 2, 4, 6, 8, 16, 32

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Answer:

X=7

Step-by-step explanation:

Hope this helps, have a good day

y = 1.5x + 0.5 is the equation of the line passing through the coordinate points

The formula for finding the equation of a line in slope-intercept form is expressed as:

y =mx + b

where:

m is the slope

b is the intercept

Determine the slope

slope = 5-2/3-1

slope = 3/2

slope = 1.5

Determine the y-intercept

y = mx + b

5 = 1.5(3) + b

5 = 4.5 + b

b = 0.5

Hence the required equation of the line passing through ( 1,2) and (3,5) is

y = 1.5x + 0.5

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Complete question

What's the equation of a line that passes through (1,2) (3,5)?

Answer:

y=-5/3x

Step-by-step explanation:

y = -5/3x+b

-15 = -5/3(9)+b

-15=-15+b - Add 15 to both sides

0 = b

The surface area of the regular pyramid is equal to 1209 m² to the nearest whole number. The first option is correct.

Area of a regular polygon = 1/2 × apothem × perimeter

Area of the hexagon = (1/2 × 8.5√3 × 102) m²

Area of the hexagon = 750.8440 m²

Area of one triangle face = (1/2 × 17 × 9) m²

Area of one triangle face = 76.5 m²

Area of six triangle face = (76.5 × 6) m²

Area of six triangle face = 459 m²

Surface area of the regular pyramid = 750.8440 m² + 459 m²

Surface area of the regular pyramid = 1209.8440 m²

Therefore, the surface area of the regular pyramid is equal to 1209 m² to the nearest whole number. The first option is correct.

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