Find the value of each variable. Round your answers to the nearest tenth.

The domain of the vector function is : ( -6, -2) ∪ ( -2, 6)

The given vector function can be correctly expressed as:

r(t) = (t-2)i / (t+2) + sintj + ln(36-t²)k²

The domain of the given function can be determined by finding the domain of each respective component.

(t-2)i / (t+2)

Not defined, t = -2

Thus, the domain of the first component of the vector = (-∞, 2) ∪ (2, ∞)

The 2nd component = sin t

No restriction on t,

The 3rd component of the function is ㏑(36 - t²)

we know,

Natural number is defined for +ve numbers,

i.e.

36 - t² > 0

(6 + t) (6 - t) > 0

thus, it satisfies the inequality -6 < t < 6

The third domain = (-6,6)

Hence, the domain of the vector function is : ( -6, -2) ∪ ( -2, 6)

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Answer:

68

Step-by-step explanation:

We can use vector addition to solve this problem. Let's consider two vectors: the velocity of the plane relative to the ground, which we want to find, and the velocity of the wind relative to the ground, which we know is due south with a magnitude of 59 mph.

Let's call the ground speed of the plane "v" and the angle between the plane's velocity and the due east direction "θ". The bearing of 60.8 is the angle between the plane's velocity and due north, so the angle between the plane's velocity and due east is (90 - 60.8) = 29.2 degrees.

Now we can use trigonometry to find the components of the plane's velocity relative to the ground:

v(cosθ, sinθ) = (v cosθ, v sinθ)

The plane's velocity relative to the wind is due east, so its x-component is v cosθ = 59 mph. Therefore, we can solve for v:

v = 59 / cosθ

v = 59 / cos(29.2) ≈ 67.55 mph

So the ground speed of the plane is approximately 67.55 mph. Round it up to 68.

The area of the composite figure is 13 ft².

The figure is a composite figure. The are of the composite figure is the sum of the individual areas.

The composite figure can be divided into two shapes namely rectangle and triangle.

Therefore,

area of the composite figure = area of the rectangle + area of the triangle

Hence,

area of the rectangle = 4.5 × 2

area of the rectangle = 9 ft²

area of the triangle = 1 / 2 bh

where

Therefore,

area of the triangle = 1 / 2 × 4 × 2

area of the triangle = 8 / 2

area of the triangle = 4 ft²

Therefore,

area of the composite figure = 9 + 4

area of the composite figure = 13 ft²

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From the question that we have, the solution that we have gotten is that 4 cubic blocks with a side length of foot would be required to find the volume of the glass case

We have been given that a glass case is in shape of a rectangular prism.

The volume of a single cubic block is:

We have

Volume of block

= (1/5) * (1/5) * (1/5)

= 1/125 cubic feet

Next we will now have to divide the volume of the glass case by the volume of a single cubic block:

V olume of case / Volume of the block =

(4/125) / (1/125)

= 4

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A glass case is in the shape of a rectangular prism. The volume of the case is cubic 4/125 foot. How many cubic blocks with a side length of 1/5 foot would be required to find the volume of the glass case?

The graph is a function: yes.

The domain of this function is: all real numbers.

The range of this function: all real numbers.

In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞}, x|x ∈ R, or all real numbers.

Range = {-∞, ∞}, y|y ∈ R, or all real numbers.

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The slope of the line and its meaning in terms of the real-world scenario is; C. The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.

In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 24)/(6 - 0)

Slope (m) = -24/6

Slope (m) = -4.

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The first semi-annual interest payment with a credit to in the amount of $109.556.15

Given that, a company issues $50,000 of 8%, 10-year bonds dated January 1 that pay interest semiannually on June 30 and December 31 each year.

We need to find the amount,

[tex]A = P(1+r/2)^{2t}[/tex]

[tex]A = 50,000(1+0.08/2)^{2(10)[/tex]

[tex]A = 50,000(1.04)^{20[/tex]

[tex]A = 109,556.15[/tex]

Hence, the first semi-annual interest payment with a credit to in the amount of $109.556.15

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The annual premium for a Whole Life insurance policy, for the healthy male, would be A. $ 2, 881.61

From the given table, a 28 year old male would have to pay $ 17. 76 for each $ 1,000 of coverage of Whole Life Insurance.

For a policy that is worth $ 162, 253 therefore, the annual premium would therefore be:

= Amount per thousand / 1, 000 x  Policy coverage

= 17. 76 / 1, 000 x 162, 253

= 0.01776 x 162, 253

= $ 2, 881.61

In conclusion, the annual premium is $ 2, 881.61 .

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Answer:

The sample mean birth weight for the 195 boys is 3.04 kilograms and the sample standard deviation is 0.71 kilograms.

Step-by-step explanation:

The area of the rhombus is derived to be 70 square units

In calculating for the area of a rhombus, we multiply the length of its two diagonals and divide the result by two

For the given rhombus, we have diagonals:

5 + 5 = 10 and 7 + 7 = 14

thus;

Area of the rhombus = (10 × 14)/2

Area of the rhombus = 140/2

Area of the rhombus = 70 square units.

Therefore, the area of the rhombus is derived to be 70 square units.

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The volume of the small cylinder is 36π

Similar figures are two figures having the same shape. The two cylinders are similar but of different radius and height.

The height of the big cylinder is calculated as

V = πr²h

h = V/ πr²

h = 144π/π36

h = 144/36

h = 4 cm

Therefore the scale factor = 4/2

area factor =( 4/2)² = 16/4

therefore the volume of the cylinder is;

16/4 = 144π/ x

16x = 144π × 4

16x = 576

dividing both sides by 16

x = 576/16

x = 36π

therefore the volume of the small cylinder is 36π.

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Answer:

78.8888888889 or just round to 79

Step-by-step explanation:

Your welcome. Can you please mark me brainliest please? :)

Answer:

78.8888888889

Step-by-step explanation:

Answer:7

Step-by-step explanation:

use the Pythagoras theorem to find su (40^2-32^2) take the square root =24 use this to solve for ru. (25^2-24^2=49) square root of 49 is

The sample of hospitals would we need to be 99 percent confident that the sample mean is within 0.5 days of the population mean is A. 48

We want to find the sample size (n) that would give us a confidence interval of 0.5 days, so we can rearrange the formula to solve for n:

n = (z*σ/CI)^2

Plugging in the given values:

z = 2.576 (for 99% confidence level)

σ = 1.2 days

CI = 0.5 days

n = (2.576 × 1.2/0.5)²

n ≈ 48

Therefore, the correct option is A.

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According to the figure,

a. angle LCQ is 45 degrees

b. the major arc are KPR and QRPK

c. congruent minor arcs are LQ and QR

d. the three arcs that form a semicircle are RP,  LQ ,and QR

A major arc designates a segment of an arch with a measurement which surpasses 180 degrees.

Geometrically, the circle, a closed curve, exhibits all its points uniformly spaced from a central focal point named the center of the circle.

The arc is regarded as major when it comprises a superior portion of the circular geometry, extending beyond half of the total circumference.

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The polynomial can be written as a product of polynomials as (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)

option C.

To rewrite the polynomial as the product of its form, we will factor the polynomial as shown below;

9x²y⁶ − 25x⁴y⁸ = x²y⁶(9 − 25x²y²)

The function (9 − 25x²y²), can factored using difference of two squares;

(9 − 25x²y²) = 3² − (5xy)²

3² − (5xy)² = (3 - 5xy)(3 + 5xy)

The final equation as the product of its factors is calculated as;

9x²y⁶ − 25x⁴y⁸ =  x²y⁶(3 - 5xy)(3 + 5xy)

= (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)

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The critical value from the given data is 2.776.

Hypothesis Testing:

Step 1: State the null and alternative hypotheses.

Null Hypothesis (H0): The average number of units taken by students in PSY 190 is equal to the average number of units taken by Rio Hondo students.

Alternative Hypothesis (H1): The average number of units taken by students in PSY 190 is greater than the average number of units taken by Rio Hondo students.

Step 2: Calculate a test statistic.

To calculate a test statistic, we will use a one-sample t-test. The t-test will allow us to compare the average of the PSY 190 students to the average of all Rio Hondo students. The test statistic will be calculated as follows:

t = (x - μ) / (s/√n)

Where x is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

In this case, x = 10.6, μ = 9.1, s = 5.1, and n = 5.

Plugging these values into the equation, we get:

t = (10.6 - 9.1) / (5.1/√5) = 1.78

Step 3: Determine the critical value.

To determine the critical value, we need to determine the degrees of freedom, which is equal to n-1 = 4. We can then look up the critical value in a t-table with α = 0.05 and 4 degrees of freedom. The critical value is 2.776.

Step 4: Compare the test statistic to the critical value.

Since the test statistic (1.78) is less than the critical value (2.776), we fail to reject the null hypothesis.

Therefore, the critical value from the given data is 2.776.

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Answer:

415.67 = (1/3)(13.4)(11.7)h

415.67 = 52.26h

h = about 7.95 feet

Answer: the price of the item 8 years from today is approximately $1475.

Step-by-step explanation:

The given exponential function to model the future price of the item is:

P(t) = P(0) * (1.026)^t

Here, P(t) represents the price of the item t years from today, and P(0) is the current price of the item.

1. To find the current price, we need to find P(0):

P(0) = 1200 * (1.026)^0

Since any number raised to the power of 0 is 1:

P(0) = 1200 * 1

P(0) = $1200

So, the current price of the item is $1200.

2. To find the price 8 years from today, we need to find P(8):

P(8) = 1200 * (1.026)^8

Using a calculator:

P(8) ≈ 1200 * 1.229057

P(8) ≈ $1474.87

Rounded to the nearest dollar:

P(8) ≈ $1475

So, the price of the item 8 years from today is approximately $1475.

Answer: 6

Step-by-step explanation:

There are six possible ways that the three boys can initially choose shirts: ABC, ACB, BAC, BCA, CAB, CBA.

Answer: -4rootx+3root3x

Step-by-step explanation:

think of the expression under the radicals as like terms, you can only add those that are the exact same 1-5=-4(rootx) can't do anything with the middle

The company sales in year 14, given the rate of increase and the amount made in sales would be C $3,656,872.

In the first year, the sales of the company were $ 475, 000 and this sales is scheduled or predicted to grow at 17 %.

This means that the company sales in year 14 would be :

= Initial sales x ( 1 + rate ) ^ number of years

Initial sales = $ 475, 000

Rate = 17 %

Number of years = 14 years

The company sales in year 14 is:

= 475, 000 x ( 1 + 17 %) ¹⁴

= $3, 656, 872

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Answer:

I believe the answer is 30%

Answer:

2,600.

Step-by-step explanation:

Rounding 2,561 to the nearest hundred means rounding it to the nearest multiple of 100.

To do this, we need to look at the digit in the tens place, which is 6. Since 6 is greater than or equal to 5, we round up the digit in the hundreds place, which is 25, by 1.

Therefore, rounding 2,561 to the nearest hundred gives us 2,600.

AnswerAnswer:

55

60

57.27

Step-by-step explanation:

rearrange the values in order:

40, 45, 45, 50, 50, 55, 60, 60, 60, 95, 100

1. median is the middle number when we put all the numbers in order, and it is 55 for this list.

2. mode is the number that appears the most, and in this list, it's 45 and 60.

3. mean is the average of all the scores in the list, and it's 57.27 for this list.

chatgpt

The values for e, f, and g are -3, 4 and -2 respectively.

e × f = -12

e × g = 6

f × g = -8

From (1)

ef = -12

e = -12/f

From (3)

fg = -8

g = -8/f

Substitute e and g into (2)

e × g = 6

-12/f × -8/f = 6

96/f² = 6

cross product

96 = f² × 6

96 = 6f²

divide both sides by 6

f² = 96/6

f² = 16

find the square root of both sides

f = √16

f = 4

Hence,

e × f = -12

e × 4 = -12

4e = -12

e = -12/4

e = -3

e × g = 6

-3 × g = 6

-3g = 6

g = 6/-3

g = -2

f × g = -8

4 × -2 = -8

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Answer:

A: 6 as a fraction of 30 = 6/30 = 1/5

B: 30 centimetres as a fraction of 2 metres = 30/200 = 3/20

C: 16 pence as a fraction of £1 = 16/100 = 4/25

To compare these fractions, we need to express them with a common denominator. The smallest common multiple of 5, 20, and 25 is 100. So we can convert each fraction to have a denominator of 100:

A: 1/5 = 20/100

B: 3/20 = 15/100

C: 4/25 = 16/100

Now we can see that the largest fraction is C: 16 pence as a fraction of £1, which is 16/100 or 16%.

Step-by-step explanation:

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