Given the vector u equal to 2 (cos 325°, sin 325°) and vector v equal to
6 (cos 155°, sin 155°), find the sum u + v and write your answer in
magnitude and direction form with the magnitude rounded to the nearest
tenth and the direction rounded to the nearest degree, 0° ≤ 0 < 360°.

You have the derivative of a product:

first limit (7x+3)

second limit (4-3x)

The Rule for the derivative of a product is:

(first limit × derivative of second limit) + (second limit × derivative of first limit)

f(x) = (7x+3)(4-3x)

f'(x)=(7x+3)×-3 + (4-3x)×7 = -21x- 9 + 28-21x

f'(x) = -42x + 19

The side and angles of the right triangle are as follows:

1. 5 units

2. 5 units

3. tan ∅ = 4 / 5

The side of a right triangle can be found using Pythagoras's theorem and the angles of a right angle triangle can be found using trigonometric ratios as follows:

c² = a² + b²

where

Therefore,

1.

c² = 4² + 3²

c = √16 + 9

c = √25

c = 5 units

2.

a² = 13² - 12²

a = √169 - 144

a = √25

a = 5 units

3.

tan ∅ = opposite / adjacent

tan ∅ = 4 / 5

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The expanded logarithmic expression in the context of this problem is given as follows:

[tex]\log_7{(2 \times 11)^3} = 3\log_7{2} + 3\log_7{11}[/tex]

The logarithmic expression in the context of this problem is given as follows:

[tex]\log_7{(2 \times 11)^3}[/tex]

First we apply the power rule of logarithms, which states that the logarithm of a number applied to a power is equals to the power multiplying the logarithm of the number, hence:

[tex]\log_7{(2 \times 11)^3} = 3 \log_7{(2 \times 11)}[/tex]

Then we apply the product rule, which means that we can add the logarithms of base 7 of these two numbers, as follows:

[tex]\log_7{(2 \times 11)^3} = 3\log_7{2} + 3\log_7{11}[/tex]

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Answer: $4,998

Step-by-step explanation:

34000*1.147

38998-34000=4998

The 95% confidence interval for the total percentage of national park visitors who support supporting endangered species is approximately 33.3% to 52.7%.

To calculate the 95% confidence interval for the percentage of national park visitors who support supporting endangered species, we can use the formula:

Confidence Interval = Sample proportion ± (Critical value * Standard error)

Given that 43% of a sample of 100 visitors believe that additional funds should be used to preserve endangered species, the sample proportion is 0.43.

To calculate the standard error, we use the formula:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size. In this case, p = 0.43 and n = 100.

Standard Error = sqrt((0.43 * (1 - 0.43)) / 100) ≈ 0.0495

The critical value for a 95% confidence interval can be obtained from a standard normal distribution table. For a 95% confidence level, the critical value is approximately 1.96.

Now we can calculate the confidence interval:

Confidence Interval = 0.43 ± (1.96 * 0.0495)

Confidence Interval = 0.43 ± 0.097

The lower bound of the confidence interval is 0.43 - 0.097 = 0.333

The upper bound of the confidence interval is 0.43 + 0.097 = 0.527

Therefore, the 95% confidence interval for the total percentage of national park visitors who support supporting endangered species is approximately 33.3% to 52.7%.

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Answer:

100 cubic feet

Step-by-step explanation:

To find the volume of a rectangular prism, we need to multiply the area of the base by the height.

Given:

Area of the top face = 20 ft²

Height = 5 ft

The volume (V) can be calculated as follows:

V = Area of the top face * Height

V = 20 ft² * 5 ft

V = 100 ft³

Therefore, the volume of the rectangular prism is 100 cubic feet.

The angle opposite to side BC in triangle ABC is approximately 38.213 degrees.

We have,

To find the angle opposite to side BC in triangle ABC, we can use the Law of Cosines.

The Law of Cosines states that in a triangle with sides of lengths a, b, and c, and the angle opposite to side c being denoted as C, the following equation holds:

c² = a² + b² - 2ab x cos(C)

In this case,

Side a is BC with length 12, side b is AC with length 20, and side c is AB with length 11. We want to find the angle C, which is opposite to side BC.

Plugging the given values into the Law of Cosines equation:

11² = 12² + 20² - 2 x 12 x 20 x cos C

121 = 144 + 400 - 480 x cos C

121 = 544 - 480 x cos C

480 x cos C = 544 - 121

480 x cos C = 423

cos C = 423/480

Now, we can find the angle C by taking the inverse cosine (arccos) of (423/480):

C = arccos(423/480)

Using a calculator, we find that C is approximately 38.213 degrees.

Therefore,

The angle opposite to side BC in triangle ABC is approximately 38.213 degrees.

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[tex]|\Omega|=19+28+21+29=97\\|A|=19+28+21=68\\\\P(A)=\dfrac{68}{97}[/tex]

Hello!

4 times the sum of x and y

4 * (x + y)

it's a mutliplication

the sum of 4x and y

= 4x + y

it's a sum

Answer:one is multiplying other is some.

Step-by-step explanation:

4xy and =4xy

these two are

The volume of the extra space in the box is 9.0 cubic inches.

To estimate the volume of the extra space in the box, we shall find the difference between the volume of the box and the volume of the cracker tower.

First, volume of the box:

The volume can be calculated as the product of the height, length, and width (we assume the width is the same as the side length since it is a square prism):

Box volume = height * length * width

Given:

height = 8 inches

side length = 2 inches

Box volume = 8 * 2  * 2

= 32  in³

Next, the volume of the cracker tower:

The tower of the cracker is cylindrical, so we shall use the formula for the volume of a cylinder to estimate the volume:

Tower volume = π * (radius²) * height

Given:

height = 7.9 inches

diameter = 1.9 inches

radius = diameter / 2 = 1.9  / 2 = 0.95

Tower volume = π * (0.95)² * 7.9

≈ 22.994 in³ (rounded to three decimal places)

Then, the volume of the extra space in the box:

Volume of the extra space = Tower volume - Box volume:

= 32 in³ - 22.994 in³

≈ 9.006 in³ (rounded to three decimal places)

Therefore, the volume of the extra space in the box = 9.0 in³.

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All the slopes of tables are,

13) m = 2

14) m = - 1/1

15) m = 0

16) m = 3

17) m = infinite

18) m = - 1/3

We have to given that;

All the tables are shown.

And, To find the slope of all the table.

Since, We know that;

Slope passing through the points (x₁ , y₁) and (x₂, y₂) is defined as,

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, We get;

13) Two points are (- 2, - 3) and (- 1, - 1)

Hence, Slope is,

m = (- 1 + 3) / (- 1 + 2)

m = 2/1

m = 2

14) Two points are (- 4, 6) and (0, 4)

Hence, Slope is,

m = (4 - 6) / (0 + 4)

m = - 2/4

m = - 1/2

15) Two points are (6, 2) and (3, 2)

Hence, Slope is,

m = (2 - 2) / (3 - 6)

m = 0

16) Two points are (- 2, - 3) and (0, 3)

Hence, Slope is,

m = (3 + 3) / (0 + 2)

m = 6/2

m = 3

17) Two points are (3, 6) and (3, 4)

Hence, Slope is,

m = (4 - 6) / (3 - 3)

m = infinite

18) Two points are (- 4, 4) and (- 1, 3)

Hence, Slope is,

m = (3 - 4) / (- 1 + 4)

m = - 1/3

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The expression that we need to solve is 4*45 + 2*123 , and that is equal to 426.

Here we want to calculate the quadruple of the decimal part by adding twice the integer part of the following decimal number: 123.45​

The decimal part of this number is 45

The integer part of this number is 123.

Then the expression that we need to solve is:

4*45 + 2*123 = 426

That is the value of the mathematical sentence.

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The value of y is 10.8.

Here, we have,

given that,

The equation is: 5/3log_4(x)=9

or, 5 log₄x = 27

or, log₄x = 27/5

now, we have,

Using the property, x = loga, a = eˣ

we get,

x = 4²⁷/⁵

or, x = 4⁵°⁴

or, x = 2¹⁰°⁸

so, comparing with x=2^y , we get,

y = 10.8

Hence, The value of y is 10.8.

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Answer:

x = 17

Step-by-step explanation:

KL + LM = KM

x+8+12 = 3x-14

or, x+20 = 3x-14

or, 3x-x=20+14

or, 2x = 34

x = 17

Answer:

Step-by-step explanation:

3x-14=x+8+12

3x-x=8+12+14

2x=34

x=17

then

KL=(17)+8=25

Answer:

Step-by-step explanation:

all you have to do is replace the x in each equation with the x in the table for example for the first one y1 would be -8 and y2 would be 28/3

The value of x in the triangle is 28.3 degrees., y is 7.837 and z is 7.837.

We can find the value of x by using angle sum property.

It states that the sum of three angles in a triangle is 180 degrees.

61.7+90+x=180

151.7+x=180

Subtract 151.7 from both sides:

x=180-151.7

x=28.3 degrees.

Now let us find the value of y.

We know that tan function is a ratio of opposite side and adjacent side.

tanx=y/14.76

tan(28.3) = y/ 14.76

0.531 = y/14.76

Now apply cross multiplication:

y=0.531×14.76

y=7.837

Now let us find z:

sin 90=y/z

1=7.837/z

z=7.837

Hence, the value of x in the triangle is 28.3 degrees., y is 7.837 and z is 7.837.

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The expression that can be used to find the amount of oatmeal in the container, obtained from the formula for the volume of a cylinder is π · 2² · 8. The correct option is therefore, the option C.

C. π · 2² · 8

The volume of a cylinder is; V = π × Radius² × Height

The part of the question that appear missing, obtained from a similar question on the internet, includes;

The radius of the can = 2 inches

The height to which the can was filled = 8 inches

The volume of oatmeal in the can is therefore;

V = π·r²·h

Where;

r = The radius of the can = 2 inches

h = The height to which the oatmeal is filled = 9 - 1 = 8 inches

Therefore;

V = π × 2² × 8

The expression that can be used to find the amount of oatmeal in the can is therefore;

C. π · 2² · 8

The possible question options, obtained from the online question are;

A. (4·π·9) - 1

B. 2·π·8

C. π·2²·8

D. (4·π·9)/3

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Set B_V spans V and is linearly independent, satisfying the requirements for a basis.

The statement is true.

If W is a subspace of a vector space V and B_W is a basis for W, then it is true that there exists a unique subspace U such that V = W ⊕ U, where ⊕ represents the direct sum of subspaces.

This means that every vector in V can be uniquely expressed as the sum of a vector in W and a vector in U.

Additionally, there exists a basis B_U for U such that the union of B_W and B_U, denoted as B_V = B_W ∪ B_U, forms a basis for the entire vector space V.

This means that the set B_V spans V and is linearly independent, satisfying the requirements for a basis.

Hence, the statement is true.

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Correct answer is,

The mean is greater than the median, and the majority of the data points are to the left of the mean.

Since, The probability depicts the intended benefits of all possible values for just a specific data-generation procedure. This is a list of all of the possible values of random variables, along with the probability for each one of them.

We could see that the curve is tilted to the right by drawing a normal distribution bell curve.

This has a right tail, which implies it has a tail. This indicates that there are few points to the right of the mean.

A majority of the pieces of data are about the left of the mean, as stated.

The bulk of data are to the right, the median will be from the left of the mean, indicating that the median is less than the mean.

Hence, As just a result, the mean exceeds the median.

Therefore, the answer is "third choice".

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Answer:

b=76* (because different angles)

Answer:

76

Step-by-step explanation

*shows a flat angle (180 degrees)

180 - 104 = 76

Answer:

Here is an example of a dot plot (in text, did as best as I could to represent it) that matches the description you provided:

Number of Minutes Spent on Math Homework Problem

 |

10|    o

9| o

8|

7|       o

6|

5|          o

4|

3|             o

2|

1|                o

0|___________________

  1  2  3  4  5  6  7  8  9  10

  Students

This dot plot shows the number of minutes spent on a math homework problem by ten students. The mean amount of time is represented by the dot at the y-value of 9, and the MAD (Mean Absolute Deviation) is represented by the spread of the data around the mean.

Answer:

x=i[tex]\sqrt{2}[/tex], x=-i[tex]\sqrt{2}[/tex]

Step-by-step explanation:

This equation can be factored. In order to do so, we can split the expression into two parts: (x^3-3x^2) and (2x-6). The greatest common factor of the first group is x^2, factoring it out gives us x^2(x-3). The greatest common factor of the second group is 2, factoring it out gives us 2(x-3). Since both x^2 and 2 are being multiplied by x-3, we add them into a factored form of (x^2+2)(x-3)=0

x-3 provides us with one real root, so we can disregard it.
x^2+2=0 ---> x^2=-2--->x=±[tex]\sqrt{-2}[/tex]
Factoring out the imaginary number i (equals [tex]\sqrt{-1}[/tex]), we get x=±i[tex]\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

This number line says that  we can take all values of x that are less than or equal to 2. That is, the solution is

                                  [tex]x\leq 2[/tex]

NOTE: if the circle at 2 were not filled in then that would mean x<2 (2 would not be an accepted value of x)

The class has collected a total of 74 pounds of food so far.

The class collected 33 pounds on the first day and 41 pounds on the second day.

To find the total pounds of food collected, we add these two amounts together:

33 pounds + 41 pounds = 74 pounds

On the first day, the students gathered 33 pounds, and on the second day, they collected 41 pounds.

We combine these two figures together to get the total number of pounds of food collected:

33 lbs. plus 41 lbs. equals 74 lbs.

On the first day, the class brought in 33 pounds, and on the second, 41 pounds.

We combine these two figures to get the total weight in pounds of food collected:

44 pounds plus 33 pounds equals 74 pounds.

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Answer:

p=7.5 or 7 1/2

Step-by-step explanation:

To solve this equation you need to isolate the P

1) We can multiply P and the numerator (In this case 2) since it is the same thing. The rewritten equation is 2p/3=5.

2) Now we can multiply both sides by 3 to isolate 2p. The equation is now 2p=15

3) The next step is to divide both sides by 2 so we can isolate the p. We now have p=7.5 or 7 1/2

                                          Hope this helps :)

Answer:

6

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

To find the missing number in the given sequence, let's analyze the pattern:

2, 4, 3, 6, 6, 3, 8, 9, 7, 9, 8, ???

Looking at the sequence, we can identify a few patterns:

The sequence alternates between increasing and decreasing numbers.

The first two numbers, 2 and 4, are increasing.

The next two numbers, 4 and 3, are decreasing.

The following two numbers, 3 and 6, are increasing.

The subsequent two numbers, 6 and 3, are decreasing.

The next two numbers, 3 and 8, are increasing.

The subsequent two numbers, 8 and 9, are increasing.

Based on these observations, it appears that the sequence is following a pattern where it alternates between increasing and decreasing numbers, but the specific values being added or subtracted are not consistent.

Now let's determine the missing number:

From the pattern, the next two numbers should be decreasing. Following the pattern of alternating between increasing and decreasing numbers, the missing number after the last given number (8) should be less than 9.

Let's assume the missing number is x:

8 - x

Since the previous decreasing sequence was 6 - 3, we can assume that x is 1 less than the previous number (3):

8 - (3 - 1) = 8 - 2 = 6

Therefore, the missing number in the sequence is 6.

The complete sequence is:

2, 4, 3, 6, 6, 3, 8, 9, 7, 9, 8, 6