What is the slope of the line with points (3, 5) and (8, 2)?

The following tables include:

(1) The table appears to show two portfolios, Portfolio 1 and Portfolio 2, and the expected rate of return (ROR) for various investments within those portfolios. The investments listed are stock in a large, old company, stock in an emerging company, US Treasury bond, and certificate of deposit.

(2) The car insurance policy has a $1,000 deductible, meaning that the insurance will cover damages that exceed $1,000. In this case, the damages were $3,000, so the insurance will cover $2,000 ($3,000 - $1,000). Since the monthly premium is $120, the total cost of the insurance over the year would be $1,440.

(3) The table shows the 52-week high and low prices, as well as the current close price, for two stocks: Apple Inc (AAPL) and Amazon Inc (AMZN).

(4) The pie chart shows the distribution of some data into three categories where 60% represents one category, 30% represents another category, and 10% represents the remaining category.

(5) The formula shows how to calculate the annual gross wage required to save 80% of it annually for retirement. This amount divided by 0.04 gives the total amount needed for retirement.

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Using the parallelogram law to find m, the value of m is 50°.

The parallelogram law states that the sum of the squares for a parallelogram's four sides is equal to the sum of the squares for its two diagonals.

The parallelogram must have equal opposed sides in Euclidean geometry.

If ABCD is a parallelogram, then AB = DC and AD = BC, the parallelogram law is stated as:

2(AB)² + 2 (BC)² = (AC)² + (BD)²

If the parallelogram is a rectangle, the parallelogram law is stated as:

2(AB)² + 2 (BC)² = 2(AC)²

The value of the unknown angles in the parallelogram are as follows:

CED = 180 - (60 + 33 + 37)

CED = 50°

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Answer:

what is the expressio

Step-by-step explanation:

Error Analysis 1:(x-3)/(x+7)

Error Analysis 2:(x(x-7)(x+3))/2(x+1)(x+9)(x+5)

Error analysis is a procedure that is usually used to identify the cause of the issue when pupils continually make mistakes. The method entails going over a student's work and looking for patterns of misinterpretation. Mathematical errors can occur for a variety of reasons and can be factual, procedural, or conceptual. The study of the kind and quantity of mistake, or uncertainty, that might be present in the solution to a problem is known as error analysis in mathematics. This issue is particularly common in practical disciplines like statistics and numerical analysis. The teacher can examine a student's errors on a worksheet, test, or progress monitoring tool to do an error analysis for mathematics. In order to grade each problem, the teacher should mark each wrong digit in the student's response, starting from the RIGHT, going to the LEFT for addition, subtraction, and multiplication problems.

Error Analysis 1:

(x²-x-6)/(x²+9x+14)

=(x-3)(x+2)/(x+2)(x+7)

=(x-3)/(x+7)

Error Analysis 2:

(x²-6x-27)/(2x²+2x)÷(x²+14x+45)/(x²)

=(x(x-7)(x+3))/2(x+1)(x+9)(x+5)

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The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Answer:

Let us set up a ratio to find the relationship between side lengths of the two triangles.

25:10

5:2

We can divide both sides by two, but there's no need as the smaller triangle has multiples of two.

So, if XZ is 6, let's place it into the ratio and find what "x" is.

5(3) : 2(3)

15 : 6

x = 15

==============================================

Explanation:

The formula to use is n*(n-1)/2

Plug in n = 12 to get 12*(12-1)/2 = 12*11/2 = 132/2 = 66

That formula is from the nCr combination formula when r = 2.

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

Here's a visual way to see why that rule works.

Imagine there are only 4 teams. We'll make a table that has 4 rows and 4 columns. The team names are A,B,C,D.

\(\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & & & & \\\cline{1-5}B & & & & \\\cline{1-5}C & & & & \\\cline{1-5}D & & & & \\\cline{1-5}\end{array}\)

In the table, cross out the cells where one team pairs up with itself. That's along the main diagonal pointing to the northwest (or southeast).

\(\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & & X & & \\\cline{1-5}C & & & X & \\\cline{1-5}D & & & & X\\\cline{1-5}\end{array}\)

Let's also cross out any cell below the main diagonal.

\(\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & X & X & & \\\cline{1-5}C & X & X & X & \\\cline{1-5}D & X & X & X & X\\\cline{1-5}\end{array}\)

We do this because a mirrored copy is found above the diagonal.

We started with 4*4 = 16 cells. Then subtracted off the diagonal to get 16-4 = 12 cells left over. Then divide in half because we crossed off the lower half to get 12/2 = 6 different matchups among the 4 teams.

Those 6 matchups are:

The order doesn't matter. A matchup like "A vs B" is the same as "B vs A".

We'll take this concept to extend it to n teams. We have n*n = n^2 cells to start with. Subtract off the n cells along the diagonal to get n^2-n = n(n-1) cells remaining.

Then we split that in half to get the formula n(n-1)/2.

(1) The wise man requested to be paid in grains of rice. (2) The king realized it at the 21st square. (3) \(2^{63\) rice grains. (4) This legend demonstrates the concept of exponents and exponential growth.

What is exponents ?

Exponents are a mathematical operation that involves raising a number to a certain power or exponent.

(1)According to the legend, the wise man who invented the game of chess requested to be paid in grains of rice, with each square of the chessboard receiving twice the number of grains as the previous square.

(2) In the legend, it is said that the king realized the wise man's request was going to be impossible to fulfill at the 21st square, when he would have had to pay 1,048,576 grains of rice.

(3) On the final square of the chessboard, the king would have had to pay \(2^{63\) grains of rice if it were possible to fulfill the wise man's request.

(4) This legend demonstrates the concept of exponents and exponential growth. Each square of the chessboard receives twice the number of grains as the previous square, which leads to a rapidly increasing number of grains of rice. This concept is important in many fields, including mathematics, economics, and science, where exponential growth can have significant implications.

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Answer:help people figure out how to best allocate income between savings and spending.

Step-by-step explanation:Those who don't have an effective cash flow plan in place risk going into debt to cover their living expenses. Cash flow plans can help people figure out how to best allocate income between savings and spending.

                                                                                        -Amelia<33

good luck hope this helped!!

Answer:

6

Step-by-step explanation:

15/2.5=6

The 95 percent confidence interval is (0.20, 0.32).

a. We can construct a 95% confidence interval to estimate the percentage of yellow peas as follows:

Let p = proportion of yellow peas = 155/595 = 0.26

Sample size = n = 595

Standard error = SE = √(p × (1-p) / n) = √(0.26 × (1-0.26) / 595) = 0.03

95% confidence interval = p ± 1.96 × SE

= 0.26 ± 1.96 × 0.03

= 0.26 ± 0.06

So, the 95% confidence interval is (0.20, 0.32).

b. Yes, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow, as the 95% confidence interval does not include the expected value of 0.25.

Therefore, the 95 percent confidence interval is (0.20, 0.32).

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Answer:

i need a picture

Step-by-step explanation:

Answer:

Vota Trump

Step-by-step explanation:

Answer: \(f^{-1} (x)=x^{2} -7\)

Step-by-step explanation:

To find the inverse of a function replace f(x) with x and the original x with y

\(f(x)=\sqrt{x+7} \\x=\sqrt{y+7}\)

Now we can solve for y

Square both sides so we can cancel out the root

\(x=\sqrt{y+7}\\x^{2} =\sqrt{y+7}^{2} \\x^{2} =y+7\)

Now subtract 7 from both sides

\(x^{2} =y+7\\x^{2} -7=y+7-7\\x^{2} -7=y\)

Now replace y with the inverse of f(x), \(f^{-1} (x)\)

f⁻¹=x²+7

Hope it helps.

Do comment if you have any query.

Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16

Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

Given:

Number of tanks of goldfish = 5

Number of fishes in a tank = 40

Step 1: Find the total number of fishes

Hence, the total number of fishes will be = 5 x 40 = 200 fishes

Step 2: Find the percentage of fin rot

Given:

Number of fishes inspected = 5

Number of fin rot =4

Therefore, the percentage of fin rot will be

So, the percentage of fish with fin rot is 80%

Step 3: Estimate the number of goldfishes with fin rot

since 80% of the fishes is estimated to have fin rot

Then

Total estimate of fin rot =

=> 160 fishes

Hence, the estimated number of goldfish in the store that has fin rot = 160

Answer:

.9

Step-by-step explanation:

1.2^2+a^2=1.5^2

1.44+a^2=2.25 then subtract 1.44 from both sides

a^2=.81 then square root both sides

a=.9

Answer:

Step-by-step explanation:

area =area of rectangle 1 +area of rectangle 2 + area of rectangle 3 + area of triangle

= 17*6 + 9*9 + 8*6  + (1/2) * 3*7

= 102 + 81 + 48 + 10.5

= 241.5 sq . ft

Answer:  241.5 ft²

Step-by-step explanation:

I divided the image into 3 rectangles and 1 triangle:

top rectangle: length = 17, height = 6              -->     A = 17 x 6 = 102

middle rectangle: length = 9, height = 9         -->     A = 9 x 9  =   81

bottom rectangle: length = 6, height = 8        -->      A = 6 x 8  =  48

triangle: base = 3, height = 7                            --> A = (3 x 7)/2 =  10.5

Total                                                                                             = 241.5

Answer: why do we even need math

Step-by-step explanation:

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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Answer:

x = - 9, x = 2

Step-by-step explanation:

\( {x}^{2} - 11x + 18 = 0 \\ \\ {x}^{2} - 9x - 2x + 18 = 0 \\ \\ x(x +9 ) - 2(x + 9) = 0 \\ \\ (x + 9)(x - 2) = 0 \\ \\ x + 9 = 0 \: \: or \: \: x - 2 = 0 \\ \\ x = - 9 \: \: or \: \: x = 2 \\ \)

The interval where function f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)

We have,

The function f(x) crosses the x-axis at (-3, 0), (-1.1, 0), and (0.9, 0), it means that f(x) is negative for x values less than -3, between -1.1 and 0.9, and greater than 0.

Therefore, we can say that:

f(x) < 0 for x < -3 and -1.1 < x < 0.9

And,

The function f(x) has a minimum value of (0, -3) and a maximum value of (-2.4, 17).

This means that f(x) is positive for x values greater than -2.4. Therefore, we can say that:

f(x) > 0 for x > -2.4

Now,

Combining these inequalities, we can say that f(x) is negative over the intervals (-∞, -3) and (-1.1, 0.9), and positive over the interval (-2.4, ∞).

So,

The interval where f(x) is negative and greater than 0 is:

(-∞, -3) U (-1.1, 0)

Thus,

The interval where f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)

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8. The length of the support is 7. 9 m

9. The length of the conveyer is 12m

3. a = 59m

A = 44°

B = 52°

4. c = 88. 6 mm

b = 49. 1 m

B = 34°

8. We have the angle to be 20 degrees

Opposite side = x

hypotenuse = 23m

Using the sine ratio

sin θ = opposite/ hypotenuse

\(sin 20 = \frac{x}{23}\)

Cross multiply

\(sin 20\) × \(23 = x\)

\(x = 0. 3420\) × \(23\)

x = 7. 9 m

The length of the support is 7. 9 m

9. The angle of elevation is 37. 3 degrees

Hypotenuse = 19 . 0m

Opposite = x

Using the sine ratio

sin θ = opposite/ hypotenuse

\(sin 37. 3 = \frac{x}{19}\)

cross multiply

\(x = 0. 6059\) × \(19\)

x = 11.5

x = 12 m in 2 significant figures

The length of the conveyer is 12m

3. To determine the sides and angles, we use the sine rule;

\(\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}\)

For side a, we use the Pythagorean theorem

\(c^2 = a^2 + b^2\)

\(85^2 = a^2 + 67^2\)

\(a = \sqrt{89^2-67^2}\)

\(a = \sqrt{3432}\)

a = 58. 58, a = 59m

To find angle A and B, use the sine rule

\(\frac{59}{sin A } = \frac{85}{sin 90}\)

cross multiply

\(sin A\) × \(85\) = \(sin 90\) × \(59\)

make sin A subject of formula

\(sin A = \frac{59}{85}\)

\(sin A = 0. 6941\)

A = \(sin^-^1(0. 6941)\)

A = 44°

\(\frac{67}{sin B} = \frac{85}{sin 90}\)

cross multiply

\(sin B\) × \(85\) = \(sin 90\) × \(67\)

make sin b subject of formula

\(sin B = \frac{67}{85}\)

\(sin B = 0. 7882\)

B = \(sin^-^1( 0. 7882)\)

B = 52°

4. To find the sides, we use the sine rule;

\(\frac{74. 0}{sin 56. 6} = \frac{c}{sin 90}\)

Cross multiply

\(sin 56. 6\) × \(c = sin 90\) × \(74\)

make 'c' subject of formula

\(c = \frac{74}{0. 8348}\)

c = 88. 6 mm

To find length b, we use the Pythagorean theorem

\(c^2 = a^2 + b^2\)

\(b^2 = c^2 - a^2\)

\(b^2 = 88. 8^2 - 74^2\)

\(b = \sqrt{7885. 44 - 5476}\\\\ b = \sqrt{2409. 44}\)

b = 49. 1 m

\(\frac{74. 0}{sin 56. 6} = \frac{49. 1}{sin B}\)

cross multiply

\(sin B = \frac{40. 99}{74. 0}\)

B = \(sin^-^1(0. 5539)\)

B = 34°

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Answer:

mode of this question is 71

Answer:

71

Step-by-step explanation:

because mode is the number that occurs most frequently

Answer:

see explanation

Step-by-step explanation:

(1)

(a)

sin(a) = \(\frac{opposite}{hypotenuse}\) = \(\frac{15}{17}\)

(b)

cos(a) = \(\frac{adjacent}{hypotenuse}\) = \(\frac{8}{17}\)

(c)

tan(a) = \(\frac{opposite}{adjacent}\) = \(\frac{15}{8}\)

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

(2)

(a)

sin(b) = \(\frac{opposite}{hypotenuse}\) = \(\frac{8}{17}\)

(b)

cos(b) = \(\frac{adjacent}{hypotenuse}\) = \(\frac{15}{17}\)

(c)

tan(b) = \(\frac{opposite}{adjacent}\) = \(\frac{8}{15}\)

Answer:

30

Step-by-step explanation:

Add all the sides and you get 30.

Hope this helps! Pls give brainliest!

Answer:

30

Step-by-step explanation:

6+9.5+6.5+4+4 = 30