Find r. Use law of sine. Round to the nearest tenth.

The Pythagorean inequality is given below.

Statement of Pythagoras theorem:

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

                                        [tex]AC^{2}=AB^{2} +BC^{2}[/tex]

Let ABC be a triangle with the longest side opposite B

We can also write as follows:

If [tex]AC^{2} > AB^{2} +BC^{2} \\[/tex], then B is an obtuse angle.

If [tex]AC^{2} < AB^{2} +BC^{2} \\[/tex], then B is an acute angle.

If [tex]AC^{2}=AB^{2} +BC^{2}[/tex], then B is a right angle.

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Answer:

3 lunch specials are possible.

No, because each item does not have an equal chance of being selected. That is option D.

A simple random sample is defined as the type of random sampling where by a particular amount of data (subset) is being selected from the total population of data that is under study.

The simple random sampling method which is used by researchers has the following disadvantages such as:

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The margin of error for the confidence interval for a population is 0.71 ± 0.1.

The degree of error in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced likelihood of relying on a survey's or poll's findings, meaning that there will be less confidence in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.

The margin of error is given as:

MOE = U - L / 2

MOE = 0.81 - 0.61 / 2

MOE = 0.2 / 2

MOE = 0.1

The interval is:

Interval = P ± 0.1

Interval = (0.61 + 0.1) ± 0.1

Interval = 0.71 ± 0.1

Hence, the margin of error for the confidence interval for a population is 0.71 ± 0.1.

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Answer:

D

Step-by-step explanation:

using the rules of logarithms

• log a - log b = log ([tex]\frac{a}{b}[/tex] )

• log [tex]x^{n}[/tex] = nlog x

then

[tex]log_{4}[/tex] [tex]\frac{7}{x^3}[/tex]

= [tex]log_{4}[/tex] 7 - [tex]log_{4}[/tex] x³

= [tex]log_{4}[/tex] 7 - 3[tex]log_{4}[/tex] x

Answer:

2/35

Step-by-step explanation:

[tex](-\frac{1}{5})(-\frac{2}{7}) = \frac{2}{35}[/tex]

A beginning employee will produce 3 items per day

An experienced employee will produce 17 items per day

Beginning employee

From the question, we have the following parameters that can be used in our computation:

[tex]P\left(d\right)=3\ +\ 15\left(1-e^{-0.2d}\right)[/tex]

Next, we plot the graph (see attachment)

A beginner employee is represented as d = 0

From the graph, we have

P(0) = 3

An experienced employee

Using the graph as a guide, we have

The maximum number of production approximates to 17

This represents the number of items per day for an experienced employee

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The magnitude of the sum of these two vectors is 2.9486m

In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles.

The parameters that will help us to find the magnitude are

/OB/ = 3.14m

/OA/ = 2.71 m

Let /AB/= x

Sum of the angles is (-60+30)⁰ = 30⁰

Using cosine rule

x²= 3.14² +2.71² - 2*3.14*2.71 *cos30⁰

x² = 9.8596+7.3441 -8.5094

x²= 17.2037 -8.5094

x²= 8.6943

x = √8.6943

x = 2.9486

Therefore, the magnitude of the sum

of these two vectors is 2.9486m or 2.9m approximately

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The length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.

What is length?

The length of something measured from end to end or along its longest side, or the length of a specific section of something.

Convert the width from inches to feet:

Since there are 12 inches in a foot, the width in feet is:

9 / 12 = 0.75 ft

Calculate the length needed:

We know that the area of the gasket material is 19 sq ft, and the width is 0.75 ft. Let L be the length needed in feet. Then we have:

Area = Width x Length

19 sq ft = 0.75 ft x L

Solving for L, we get:

L = 19 sq ft / 0.75 ft

L = 25.33 ft (rounded to two decimal places)

Therefore, the length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.

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Answer: OD. 13

Step-by-step explanation:

Answer:

Step-by-step explanation:

Evaluate the expression 10 - 2x for the x-values given below.

a. x = 2 \quad b. x = \frac {1}{2}\quad c. x = -2

a.x=2b.x=

2

1

​

a.x=-2

The rate at which its unemployment changes  is, 54.6 %

Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.

So formula for the rate is,

m = change in one quantity/change in another quantity = Δy/Δx

Given that,

The initial number of unemployed workers was 3.4 million and the final number was 5.5 million.

The change in the number of unemployed workers is:

5.5 million - 3.4 million = 2.1 million

To find the initial number of employed workers, we need to subtract the initial number of unemployed workers from the total population:

76 million - 3.4 million = 72.6 million

Now, we can calculate the initial unemployment rate as:

3.4 million / 72.6 million = 0.0469 or 4.69%

Similarly, the final unemployment rate is:

5.5 million / 76 million = 0.0724 or 7.24%

The change in the unemployment rate is:

(0.0724 - 0.0469) / 0.0469 ≈ 0.546 or 54.6%

Therefore, the unemployment rate increased by about 54.6%, which is closest to answer choice A. It increased by about 27%.

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The procedure for angle measurement by the protractor is mentioned below:

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

To measure an angle using a protractor, follow these steps:

1. Place the protractor on the angle you want to measure, with the base of the protractor aligned with one side of the angle.

2. Make sure the protractor is centered and level, with the zero-degree mark on the protractor aligned with the vertex (corner) of the angle.

3. Read the measurement of the angle from the protractor, where the second side of the angle intersects with the protractor scale. The measurement is usually given in degrees.

If the angle is larger than 180 degrees, you may need to use a full-circle protractor or measure the angle in two parts and add the measurements together.

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Weight is 0.229 pounds after 4 weeks.

As a young channel catfish only weights 0.1 pounds,

It gains weight over the following 8 weeks at a rate of roughly 23% every week.

In this case, the exponential growth function is as follows:

Exponential formulas are provided by.

[tex]y=a(1+r)^{x}[/tex]

where an is the starting amount, r is the growth rate, x is the duration, and y is the weight at the end of "x" weeks.

Our values are a = 0.1, r = 0.23 (or 23%), and t = 4.

As a result,

[tex]y=0.1(1+0.23)^{4} \\[/tex]

y = 0.1(2.289)

y = 0.229

Consequently, the weight at 4 weeks is 0.229 pound.

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Complete question:

A young channel catfish weighs about 0.1 pound. During the next 8 weeks, its weight increases by about 23% each week. About how much will the catfish weigh after 4 weeks? Round your answer to the nearest thousandth of a pound.

Answer:

i think the answer is A and C, B and E

Answer:

D and F

A and C

B and E

Step-by-step explanation:

Answer:

[tex]x = -64\\\\y = -63\\\\z = -57[/tex]

Step-by-step explanation:

Diagonally opposite angles of a parallelogram are equal

Therefore

-y - 3 = 60

Add 3 to both sides; -3 terms on left side cancel out

- y = 60 + 3

- y = 63

Multiply both sides by -1

-1(-y) = -1(63)

y = - 63

Another property of a parallelogram is that the angles formed on either end by a side must equal 180°.

Rephrased,

The consecutive or adjacent angles are supplementary which means they add up to 180°

We see that -2z + 6 and 60° are adjacent angles
So

- 2z + 6 + 60 = 180

-2z + 66 = 180

-2z = 180 - 66

-2z = 114

z = 114/-2

z = -57

Similarly

-2x - 8 + 60 = 180

-2x + 52 = 180

-2x = 180 - 52

-2x = 128

x = 128/-2

x = -64

Answer:

Step-by-step explanation:

6x4=24

another way of writing it is using addition

add 4, six times

so

4+4+4+4+4+4

6 boxes each has four cakes

The perimeter of the triangle is 3x + 42.This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42.

The perimeter of a triangle is the sum of the lengths of its three sides. In this problem, the lengths of the three sides of the triangle are given as x + 15, 2x + 15, and x + 12, where x cannot equal zero. To calculate the perimeter of the triangle, we need  to add these three lengths together. This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42. Therefore, the perimeter of the triangle is 3x + 42.

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Answer: If the ratio of first-class, second-class, and third-class passengers who survived the shipwreck is 101:59:89, then for every 101 first-class passengers who survived, there were 59 second-class and 89 third-class passengers who survived.

If the total number of first-class passengers was 202, then there were 202 * 59/101 = 118 second-class passengers who survived, and 202 * 89/101 = 180 third-class passengers who survived.

Therefore, the total number of passengers who survived the shipwreck is 202 + 118 + 180 = 500 passengers.

Step-by-step explanation:

The volume of the cone shown can be described to be A. 513 π cubic units

The volume of a cone can be found by the formula :

= π x radius ² x height / 3

The radius of this cone is 9 units and the height is 19 units.

The volume of this cone then is :

= π x radius ² x height / 3

= π x 9 ² x 19/ 3

= π x 81 x 19/ 3

= π x 513

= 513 π cubic units

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Answer:

4 pounds

Step-by-step explanation:

2.36/4 = 0.59 cents a banana

1.83/3 = 0.61 cents a banana

It can  be estimated that there are 395 penguins in the area.

Proportion is a mathematical comparison between two numbers.  According to proportion, two sets of specified numbers are said to be directly proportional to each other if they increase or decrease in the same ratio. Symbols of proportions include "::" and "=".

We approach this problem by doing a simple proportion.We can presume that the same proportion of penguins were tagged during mating season if the biologists discovered 11 tagged individuals out of 82 penguins.

The proportion should therefore be [tex]x:53=82:11[/tex]  where x represents the total number of penguins. By solving this proportion, we may determine what x is worth:

[tex]11x=53*82\\\\11x=4346\\\\x=395.0909[/tex]

Since there is no such thing as half a penguin, we can round off the answer to the nearest unit.

395 penguins are in the area according to our estimation.

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The required measure of angle x in the triangle is 35°.

What are trigonometric equations?

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

From triangle,

Sin x = perpendicular/hypotenuse

Sin x = 4/7

Sin x = 0.57

X =sin⁻¹(0.57)

X = 34.9

x = 35°

Thus, the required measure of angle x in the triangle is 35°.

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Answer:

the last one

Step-by-step explanation:

first you have to distribute the 5 to all the variables.

when you do that you get

x---9x5=45

y---1x5=5

z---4x5=20

hope it helped

please mark brainliest

The total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 51 square units.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Divide the figure is into two rectangles and a triangle.

The points B, C, E, and F form a rectangle with base BC and height 7 units.

The points A, D, and G form a rectangle with base AG and height 5 units. The points C, D, and E form a triangle with base CE and height 4 units.

The length of BC is 4 - 4 = 0, so the area of the rectangle with base BC is 0.

The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.

Therefore, the total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6)  is 45 + 6 = 51 square units.

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A.) f(x-2)+f(2x)

To find this expression, we can substitute the definition of f(x) into the expression and simplify:

f(x-2)+f(2x) = [10(x-2)-4] + [10(2x)-4]

= 10x - 20 - 4 + 20x - 4

= 30x - 28

Therefore, f(x-2)+f(2x) = 30x - 28.

Given f(x) = 10x - 4, we need to find f(2a) - f(a).

f(2a) = 10(2a) - 4 = 20a - 4

f(a) = 10a - 4

Therefore,

f(2a) - f(a) = (20a - 4) - (10a - 4)

= 10a

Answer: f(2a) - f(a) = 10a. This means that the difference between the function evaluated at 2a and a is simply 10 times a.

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Answer:

The sum of the series is 260.

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

Each term of given series is expressed as:

This is an arithmetic progression with 13 terms and the first and last terms are:

Use the sum of the first terms of AP formula:

Answer:

The sum of the series is 260.

Step-by-step explanation:

[tex]\displaystyle \sum^{13}_{n=1}(3n-1)[/tex]

The given sigma notation means:

As (3n - 1) is linear, the series is arithmetic.

The first term (n = 1) is:

The second term (n = 2) is:

The third term (n = 3) is:

… and the last term (n = 13) is:

Therefore, we need to find 2 + 5 + 8 + ... + 38.

Since we know that the first term, a, is 2, the last term, l, is 38, and the common difference, d, is 3, we can use the sum of the first n terms formula to calculate the sum of the series of the first 13 terms.

[tex]\begin{aligned}\text{Using:} \quad S_{n}&=\dfrac{1}{2}n(a+l)\\\\\implies S_{13}&=\dfrac{1}{2}(13)(2+38)\\\\&=\dfrac{1}{2}(13)(40)\\\\ &=\dfrac{520}{2}\\\\&=260\end{aligned}[/tex]

Therefore, the sum of the series is 260.

Answer:

Step-by-step explanation:

S+8=D

S+D equals 94.

94/2= 45+2=47

47-8=39

Sydney is 39

Answer:

43

Step-by-step explanation:

94-8= 86

86/2= 43

43+8= 51

a:43

prove it :

51+43= 94

Answer:

$20,907

Step-by-step explanation:

To calculate the amount that needs to be placed in an account now to have $22,500 in 3 years, you can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount

P = principal (the initial amount placed in the account)

r = annual interest rate as a decimal

n = number of times the interest is compounded in a year

t = number of years

In this case, r = 0.048, n = 52 (since the interest is compounded weekly), and t = 3.

So, we have:

A = 22,500

P = ?

r = 0.048

n = 52

t = 3

Plugging these values into the formula:

22,500 = P * (1 + 0.048/52)^(52 * 3)

Solving for P, we get:

P = 22,500 / (1 + 0.048/52)^(52 * 3)

P = 22,500 / (1 + 0.048/52)^(156)

Rounding to the nearest dollar, we get:

P = $20,907

So, a person should place $20,907 in the account now, if the account pays 4.8% annual interest rate, compounded weekly, to have $22,500 in 3 years.