Use linear approximation, i.e. the tangent line, to approximate
and find the equation of the tangent line……

Let's start by trying out different combinations and see if they give us a rectangle:

- If we use the two 4 ft sections as the width, we have 8 ft. For the length, we can use one of the 6 ft sections, which gives us a length of 6 ft. However, we still have a 6 ft section left that we cannot use to complete the rectangle. This combination doesn't work.

- If we use the two 6 ft sections as the width, we have 12 ft. For the length, we can use one of the 4 ft sections, which gives us a length of 4 ft. However, we still have an 8 ft section left that we cannot use to complete the rectangle. This combination doesn't work.

- If we use the 8 ft section as the width, we have 8 ft. For the length, we need to use both 6 ft sections, which gives us a length of 12 ft. We used all sections and we have a rectangle. This combination works.

Therefore, Patty's garden could be 8 ft by 12 ft.

The calculated value of the probability using the given parameters is 0.0154

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

n = 4

x = 3

p = 1/6

The probability is then calculated as

P(x = x) = nCr * p^x * (1 - p)^(n - x)

Substitute the known values in the above equation, so, we have the following representation

P(x = 3) = 4C3 * (1/6)^3 * (1 - 1/6)

Evaluate

P(x = 3) = 0.0154

Hence, the probability is 0.0154

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The Answer would be 57

Invest in stocks and bonds directly by purchasing them through a brokerage account. Indirect investments  can be made through mutual funds.

Assets acquired or invested  to build wealth and save money based on hard-earned income or appreciation. Investing primarily means getting extra income or income from an investment over a certain period of time.  Stocks, bonds and cash are the three main types of investments.

Stocks - represent ownership in a company and their value varies depending on market demand and company performance. Stocks may offer potential growth over the long term, but they also carry more risk than other  investments.  

Bonds - are essentially loans that investors make to governments or companies, usually offering a fixed interest payment and repayment of principal at maturity. Bonds generally offer lower yields than stocks, but are considered  less risky.

Cash - refers to investments that are highly liquid and can be easily converted to cash, such as savings accounts, money market accounts, and certificates of deposit (CDs). Cash investments usually have lower returns than stocks and bonds, but  are considered  the least risky types of investments.

You can invest in stocks and bonds directly by buying them through a brokerage account. This can be done online or through a financial advisor. Financial investments can be made directly through a bank or credit union. Such investments  can be invested indirectly through investment funds. A mutual fund is  money from many investors  managed by a professional investment manager. A mutual fund invests in a diversified portfolio that includes stocks, bonds or cash, depending on the fund's investment objective. Investors can buy shares of  mutual funds, and the value of the shares will rise or fall based on the performance of the underlying investments.

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Answer:

The chance of drawing a yellow marble is 3/14. The chance of drawing a black marble is 6/14, or 3/7. 3/14 * 3/7 = 9/98.

Step-by-step explanation:

answer is 9/98

The equation that represent the situation is:

y = 29x

The graph that represent the situation is shown below.

The graph that corresponds to the sketched graph is Graph A.

From the question, we are to write and graph an equation to represent the given situation

From the given information, we have that

"You put 11 gallons of gasoline (x) in your car. You know that this amount of gasoline will allow you to drive 319 miles (y)"

From this information, we can calculate the rate

Rate = 319 miles / 11 gallons

Rate = 29 miles / gallon

This is equivalent to the slope,

Slope = Change in y / Change in x

Thus, we can write that

y/x = 29

y = 29x

This is the equation that represent the situation.

From this equation, we can sketch the graph that represent the situation.

The graph is shown below.

The graph that corresponds to the sketched graph is Graph A.

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Using De Morgan's law and the associative law of disjunction, the simplified expression for [(p∧q') → r']' is p' ∨ q ∨ r.

The solution to the logical expression [(p∧q') → r']', can be solved as follows:

1. Applying De Morgan's law to the expression [(p∧q') → r']':

[(p∧q') → r']' = [(p∧q')' ∨ r]

2. De Morgan's law is applied again to the negated conjunction (p∧q')':

(p∧q')'= (p' ∨ q) ∨ r

Then, the inner parentheses are removed using the associative law of disjunction, and then the expression is simplified thus: p' ∨ q ∨ r

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1kg of prawn costs $18.

Let's use algebra to determine how much 1 kg of prawns would cost.

We know that 3kg of fish cost $12, so the cost per kg of fish is:

$12 ÷ 3kg = $4/kg

We can set up an equation since we also know that the combined cost of 3 kg of fish and 1 kg of prawn is $30:

3($4/kg) + 1($x/kg) = $30

Simplifying the left side of the equation, we get:

$12/kg + $x/kg = $30

Subtracting $12/kg from both sides, we get:

$x/kg = $18

Therefore, 1kg of prawn costs $18.

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Option A is correct i.e. No, she should divide 1 / 2 by 2 to get 1 / 4.

No, Lucky's claim is not correct. The walking path is 1 / 2 miles long and is divided into 2 equal sections. Therefore, each section of the walking path is:

(1 / 2) miles ÷ 2 = 1 / 4 miles

This is equivalent to 0.25 miles, not 1 mile. Therefore, Lucky's claim that each section of the walking path is 1 mile long is incorrect

Therefore, option A is correct i.e. No, she should divide 1 / 2 by 2 to get 1 / 4.

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Answer:

a. 110°

Positive coterminal angle: 110° + 360° = 470°

Negative angles:

b. 145°

Positive coterminal angle: 145° + 360° = 505°

Negative angles:

c. -30°

Positive coterminal angle: -30° + 360° = 330°

Negative angles:

Note: To find coterminal angles, we add or subtract multiples of 360° to the given angle. To find negative coterminal angles, we simply add a negative sign in front of the angle.

By using addition, we find that the number in the top brick of the pyramid with a base of -3 and -5 is -8,

The pyramid is of two layers with base of two bricks numbered as -3 and -5. and the third brick is on the top of them whose value is unknown.

Using the rule that the missing number in any brick is the sum of the two bricks below it, we can work our way up the pyramid

The bottom layer has two bricks with values of -3 and -5, so the brick above them must be the sum of these two values

x = -3 + (-5) = -8.

Therefore, the value in the top brick of the pyramid is -8

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--The given question is incomplete, the complete question is given

" In the pyramid of 3 bricks, the missing number in any brick is the sum of the two bricks below it. What is the number in the top brick 'X'? the number on two bricks at base is -3 and -5."--

The measure of the angles are A = 33 degrees, B = 107.5 degrees and 39.5 degrees

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

The triangle

The measure of angle C is calculated using

c² = a² + b² - 2ab * cos(C)

So, we have

14² = 21² + 12² - 2 * 21 * 12 * cos(C)

Evaluate

196 = 585 - 504 * cos(C)

Subtract and divide

cos(C) = 0.7718

Take the arc cos

C = 39.5 degrees

Using the list of options, we have

A = 33 degrees, B = 107.5 degrees and 39.5 degrees

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Answer:

To find the surface area of the figure, we need to break it down into its component shapes and calculate their surface areas, then add them up.

The figure can be divided into a rectangular prism (the bottom part) and two triangular prisms (the top part).

The rectangular prism has dimensions 32 m × 26 m × 12 m. Its surface area is:

2(32 × 26) + 2(32 × 12) + 2(26 × 12) = 2(832 + 384 + 312) = 2(1528) = 3056 m²

Each of the two triangular prisms has base 32 m, height 15 m, and slant height 17 m (using the Pythagorean theorem). The surface area of each triangular prism is:

2(1/2)(32)(15) + 2(1/2)(32)(17) + 2(1/2)(15)(17) = 480 + 544 + 255 = 1279 m²

Therefore, the total surface area of the figure is:

3056 + 1279 + 1279 = 5614 m²

Rounding to the nearest tenth, the surface area is 5614.0 m².

To calculate the confidence interval, we'll use the formula:

CI = sample proportion ± z* (standard error)

where:

- sample proportion = p_hat = 23/50 = 0.46 (proportion of students in the sample who used tutoring and found it beneficial)

- z = 1.96 (for a 95% confidence level)

- standard error = sqrt(p_hat * (1 - p_hat) / n) = sqrt(0.46 * 0.54 / 50) = 0.101

Plugging these values into the formula, we get:

CI = 0.46 ± 1.96 * 0.101

CI = [0.263, 0.657]

Therefore, we can say with 95% confidence that the true proportion of Mesa students who have used tutoring and found it beneficial is between 0.263 and 0.657.

The measure of angles m∠1,m∠2, and m∠3 are 133°, 47°, and 43° respectively

47° and m∠1 are on a straight line and their sum is equal to 180° so;

m∠1 + 47° = 180° {sum of angles on a straight line}

m∠1 = 180° - 47° {subtract 47° from both sides}

m∠1 = 133°

47° and m∠2 are vertical angles hence they are equal so;

m∠2 = 47°

m∠2 and m∠3 are complementary angles so their sum is equal to 90°

m∠3 + 47° = 90°

m∠3 = 90° - 47°

m∠3 = 43°

In conclusion, the measure of angles m∠1,m∠2, and m∠3 are 133°, 47°, and 43° respectively

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Answer:

The number of times the coin landed on heads is 32 - 8 = 24 since there were 32 flips in total and 8 of them resulted in tails.

The ratio of heads outcomes to tails outcomes can be expressed as 24:8. To simplify this ratio, we can divide both the numerator and denominator by their greatest common factor, which is 8.

So, 24/8 = 3 and 8/8 = 1. Therefore, the ratio of heads outcomes to tails outcomes in simplified form is 3:1.

The value of x in the corresponding angle is 15

Corresponding angles are one of the types of angles that are formed when two parallel lines are intersected by the transversal. These are formed in the matching corners or corresponding corners with the transversal.

To find the value of x, we have to equate both sides;

10x - 38 = 7x + 7

collect like terms

10x - 7x = 7 + 38

3x = 45

Divide both sides by the coefficient of x

3x / 3 = 45 / 3

x = 15

The value of x is 15

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For the market to achieve market equilibrium, D. The monthly supply of milk must increase by 8 billion gallons.

In order to reach a state of market balance, characterized by the amount of milk demanded equating to the amount supplied each month, there needs to be a boost in the monthly milk supply.

There is a monthly shortage of 8 billion gallons due to the difference between the supply of 10 billion gallons and the required amount of 18 billion gallons. Hence, it is imperative to augment the monthly milk supply by 8 billion gallons to fulfill the stipulated market demand.

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[tex] \huge \green{\underbrace{ \red{\rm \: Answer}}}[/tex]

D. The monthly supply of milk must increase by 8 billion gallons.

[tex]\rule{1000pt}{1pt}[/tex]

Thankyou:D

The pie chart can best be used to display parts of a whole. That is option B.

The pie chart representation is a typical example of a way data can be represented following a result analysis in a circular form that shows percentages of a whole, and represents percentages at a set point in time.

The major properties of a pie chart is it's central angle, area, and arc length.

The pie chart is used to represent the display of part of a whole data set in a circular form.

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Answer:

Step-by-step explanation:

Then the amount deposited will be represented by a positive integer.

Money deposited: 2000

Money withdrawn: 1642

Balance left: 2000-1642

                   :358

Tara would be required to repay the debt in 90.42 days, or roughly 90 days and 10 hours.

The simple interest is calculated as,

Simple interest = Principal x Rate x Time

Where the loan's principal, interest rate, and term are represented by the variables principal, rate, and time, respectively.

In this case, the maturity value, which includes the principal and interest, is $2,572.92 and the principal is $2,500. The rate is 8.75%. Let's begin by computing the interest on the loan:-

Interest = Maturity value - Principal

Interest = $2,572.92 - $2,500

Interest = $72.92

Calculate the interest below,

Interest = Principal x Rate x Time / 365

$72.92 = $2,500 x 0.0875 x Time / 365

$72.92 x 365 = $2,500 x 0.0875 x Time

Time = $72.92 x 365 / ($2,500 x 0.0875)

Time = 90.42 days

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The trigonometric identity sin(x + y) = (√95 + 3√17)/27

Trigonometric identities are identities containing trigonometric ratios.

Given that tanx = 1/√8 and siny = √17/6 and angles x and y are both in Quadrant 1, we need to find the value of sin(x + y)

So, using the trigonometric identity sin(x + y) = sinxcosy + cosxsiny

First we need to find sinx, cos x and cosy

Using trigonometric identity 1 + tan²x = sec²x

sec²x = 1 + tan²x

= 1 + (1/√8)²

= 1 + 1/8

= (8 + 1)/8

= 9/8

sec²x = 9/8

secx = √(9/8)

= ±3/2

secx = 1/cosx

1/cosx = ±3/2

cosx = ±2/3

Now sinx = √(1 - cos²x)

= √(1 - (2/3)²)

= √[(1 - 4/9)]

= √[(9 - 4)/9]

= √(5/9)

= ±√5/3

Also, cosy = √(1 - sin²y)

= √(1 - (√17/6)²)

= √(1 - 17/36)

= √[(36 - 17)/36]

= √(19/36)

= ±√19/6

Since sin(x + y) = sinxcosy + cosxsiny, substituting the positive values of the variables into the equation since they are in the first quadrant, we have that

sin(x + y) = sinxcosy + cosxsiny

sin(x + y) = √5/3 × √19/6 + 2/3 × √17/6

= √95/27 + √17/9

= √95/27 + √17/9

= 1/9(√95/3 + √17)

= 1/9(√95 + 3√17)/3

= (√95 + 3√17)/27

So, sin(x + y) = (√95 + 3√17)/27

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Answer:

You didn't tell us what S is equal to, but just do this: 15-S=__

Step-by-step explanation:

Answer:

54 neighbors received cookies from Grace.

Step-by-step explanation:

The roots of the given quadratic functions are -

x = (- 6 ± √42)/2

Given is that Inga is solving the quadratic equation -

2x² + 12x - 3 = 0

The quadratic equation is given as -

2x² + 12x - 3 = 0

We can write the roots of the equation as -

x = {- 12 ± √(144 + 24)}/4

x = (- 12 ± √168)/4

x = (- 12 ± 2√42)/4

x = (- 6 ± √42)/2

Therefore, the roots of the given quadratic functions are -

x = (- 6 ± √42)/2.

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Answer:

4/3 × (4 5/6 - 1/2) is greater.

Step-by-step explanation:

What is inside the parenthesis is the same in both expressions. So what makes them different is multiplying by 3/4 or by 4/3.

Multiplying by 3/4 will make the value smaller. It is essentially "a shrink" multiplier.

On the other hand, 4/3 is bigger than one. If you times something by 1 it stays the same. If you multiply by something greater than 1 the answer will be bigger than the starting number.

Since these are actual numbers, we can just do it.

3/4(4 5/6 - 1/2)

= 3/4(4 5/6 - 3/6)

= 3/4(4 2/6)

= 3/4(4 1/3)

= 3/4(13/3)

= 13/4

= 3.25

4/3(4 5/6 - 1/2)

= 4/3(4 5/6 - 3/6)

= 4/3(4 2/6)

= 4/3(4 1/3)

= 4/3(13/3)

= 52/9

= 5.7777...

Reasoning it out definitely seems like less work!

The 99% confidence interval for mean temperature of human is :

( 98.04f, 98.40f )

A data set includes 108 body temperatures of healthy adult humans having a mean of 98.2 and a standard deviation of 0.64 .

Now, We have to construct  a 99% confidence interval estimate of the mean body temperature of all healthy humans.

We use these formula for upper limit and lower limit:

u = x + Zα/2 × (s/√n) (For the upper limit)

u = x - Zα/2 × (s/√n) (For the lower limit)

We have the information from question:

x = sample mean = 98.2

s = standard deviation = 0.64

n = sample size = 108.

[tex]Z_\frac{\alpha }{2}[/tex] = critical value for a 2 tailed test performed at a 1% level of significance ( 100% - 99%) = 2.58

Now, Substitute the parameter,

For upper limit:

u = x + Zα/2 × (s/√n)

u = 98.2 + 2.58 ( 0.64/√108)

u = 98.2 + 2.58 ( 0.0616)

u = 98.2 + 0.1589

u = 98.4

For lower limit:

u = x - Zα/2 × (s/√n)

u = 98.2 - 2.58 ( 0.64/√108)

u = 98.2 - 2.58 ( 0.0616)

u = 98.2 - 0.1589

u = 98.04.

The 99% confidence interval for mean temperature of human is :

( 98.04f, 98.40f )

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x=3.42851536

to be 100% honest with you, this was kind of a guess and check, i'm sure there is some method i am forgetting from highschool, but it's been way too long since i've done this kind of problem

Answer: D

Step-by-step explanation:

A.  2(2x + 1) = 4x + 2

    4x +2 = 4x +2     because it's the same on both sides you have infinite answers

B. 3x + 7 = x

    2x=  -7

      x = -7/2      one answer

C. 3x + 6 = x + 2

      2x = -4

        x= -4/2 = -2    one answer

D. 5x + 1 = 5x - 3       if you bring 5x over it cancels out

        1 = -3                this is what you are left with and it's not true so this one has no solution

The exact values of the given trigonometric functions are:

cos(330) = [tex]\sqrt{3}/2[/tex] or 0.866

sin(330) = 1/2 or 0.5

To find the trigonometric values of cos(330) and sin(330) exactly, we can use the unit circle and the properties of the trigonometric functions.

In the unit circle, the angle of  330 degrees is equivalent to -30 degrees or [tex]-\pi/6[/tex] radians. Since cosine is an even function, we know that [tex]cos(-\theta) = cos(\theta)[/tex], so we can find cos(-30).

Using the special triangles and the reference angle of 30 degrees, we can determine the exact values:

cos(-30) = cos(30) = [tex]\sqrt{3}/2[/tex]

Similarly, the sine of -30 degrees is the same as the sine of 30 degrees:

sin(-30) = sin(30) = 1/2

Therefore, the exact values are:

cos(330) = cos(-30)= cos(30) = [tex]\sqrt{3}/2[/tex] or 0.866

sin(330) = sin(-30)= sin(30)= 1/2 or 0.5

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