Can someone help on this using the pythagorean theorem

Answer: 12 Basil leaves

Step-by-step explanation:

Given

Monica uses 3 basil leaves for every 8 tomatoes

For 32 tomatoes she needs

\(\Rightarrow 3\ \text{basil leaves}\equiv8\ \text{Tomatoes}\\\\\Rightarrow 4\times 3\ \text{basil leaves}\equiv4\times 8\ \text{Tomatoes}\\\\\Rightarrow 12\ \text{basil leaves}\equiv 32\ \text{Tomatoes}\)

Thus, she needs 12 basil leaves.

6.1). the rate of depreciation, r, is approximately 10.77%.

6.2.1). Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2).  Ncominkosi borrowed approximately R 377,510.83 from the bank.

6.1) Let's assume the original price of the laptop is P. According to the reducing balance method, the value of the laptop after 4 years can be calculated as P * (1 - r/100)^4. We are given that this value is 31% of the original price, so we can write the equation as P * (1 - r/100)^4 = 0.31P.

Simplifying the equation, we get (1 - r/100)^4 = 0.31. Taking the fourth root on both sides, we have 1 - r/100 = ∛0.31.

Solving for r, we find r/100 = 1 - ∛0.31. Multiplying both sides by 100, we get r = 100 - 100∛0.31.

Therefore, the rate of depreciation, r, is approximately 10.77%.

6.2.1) To determine the monthly installment amount, we can use the formula for calculating the monthly payment on a loan with compound interest. The formula is as follows:

\(P = \frac{r(PV)}{1-(1+r)^{-n}}\)

Where:

P = Monthly payment

PV = Loan principal amount

r = Monthly interest rate

n = Total number of monthly payments

Let's calculate the monthly installment amount for Ncominkosi's loan:

Loan amount = Total amount paid to the bank - Interest

Loan amount = R 596,458.10 - R 0 (No interest is deducted from the total paid amount since it is the total amount paid)

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 9.5% / 12 = 0.0079167 (rounded to 7 decimal places)

Number of monthly payments = 6 years * 12 months/year = 72 months

Using the formula mentioned above:

\(P = \frac{0.0079167(Loan Amount}{1-(1+0.0079167)^{-72}}\)

Substituting the values:

\(P = \frac{0.0079167(596458.10}{1-(1+0.0079167)^{-72}}\)

Calculating the value:

P≈R10,505.29

Therefore, Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2) To determine the amount of money Ncominkosi borrowed from the bank, we can subtract the interest from the total amount he paid to the bank.

Total amount paid to the bank: R 596,458.10

Since the total amount paid includes both the loan principal and the interest, and we need to find the loan principal amount, we can subtract the interest from the total amount.

Since the interest rate is compounded monthly, we can use the compound interest formula to calculate the interest:

\(A=P(1+r/n)(n*t)\)

Where:

A = Total amount paid

P = Loan principal amount

r = Annual interest rate

n = Number of compounding periods per year

t = Number of years

We can rearrange the formula to solve for the loan principal:

\(P=\frac{A}{(1+r/n)(n*t)}\)

Substituting the values:

Loan principal (P) = \(\frac{596458.10}{(1+0.095/12)(12*6)}\)

Calculating the value:

Loan principal (P) ≈ R 377,510.83

Therefore, Ncominkosi borrowed approximately R 377,510.83 from the bank.

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Answer:

Options (A), (B)

Step-by-step explanation:

Option A.

Two sides of the given triangle are equal. Therefore, the given triangle is an isosceles triangle.

Option (B).

Given triangle has a right angle. Therefore, it's a right triangle.

Option (C).

Only two sides of the given triangle are equal. Therefore, it's not an equilateral triangle.

Option (D).

Although this triangle has two acute angles (less than 90°) but the third angle is 90°. Therefore, this triangle is not an acute triangle. It's a right triangle.

Option (E).

A scalene triangle is a triangle having all sides different in measure but the given triangle is an isosceles triangle. Therefore, it's not a scalene.

Option (F).

Any angle of this triangle is not more than 90°. Therefore, the given triangle is not an obtuse triangle.

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

Explanation:

The volume of a cylinder formula is

V = pi*r^2*h

where r is the radius and h is the height.

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

For the first cylinder, we have r = 2 and h = 7. This leads us to...

V = pi*r^2*h

V = pi*2^2*7

V = pi*4*7

V = pi*28

V = 28pi

This is the exact volume in terms of pi.

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

Repeat those steps for the other cylinder (r = 2 and h = 28)

V = pi*r^2*h

V = pi*2^2*28

V = pi*4*28

V = 112pi

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

To recap so far, we have these two cylinder volumes:

We see that cylinder B has the larger volume (since 112 > 28).

The ratio of the volumes from larger to smaller is 112pi : 28pi

Divide both parts by pi to have those terms cancel and we get the ratio 112:28

Lastly, we divide each part by the GCF 28

112/28 = 4

28/28 = 1

Therefore, the ratio 112:28 fully reduces to 4:1 which makes the final answer choice A.

The larger volume is 4 times that of the smaller volume.

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

A fairly quick way to see why we get this ratio is to notice the smaller height h = 7 jumps to the larger height h = 28 by a factor of 4.

In other words,

larger height = 4*(smaller height)

28 = 4*7

The fact that the radius is kept the same at r = 2 won't have an effect on the volume ratio. These parts effectively cancel out.

So this jump of "times 4" directly connects to the ratio 4:1

We multiplied the height by 4, so the volume is also multiplied by 4 (when going from the smaller cylinder to the larger one).

A shelving company shipped 2,483 shelving units to each of 417 warehouses 1035411 shelving units did the company ship in all.

Total shelving to one = 2483

Total shelving to 417 warehouse = 417 x 2483 = 1035411

A flexible display system that can be moved and altered to meet various product dimensions is a shelving unit. A gondola is an open-sided island shelving unit. Overstocks are kept on the riser, the top shelf atop a shelving unit.

Pallet racks are used for products placed onto pallets, whereas used shelving is often used for single things or boxes. The styles of used shelving include enclosed, nut and bolt, modular, wire, clip, and record storage, among others.

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Answer:

y = 3x + 8

Step-by-step explanation:

y = mx + b

m= 6/2 = 3/1

(-1,5)

y-5 =  3/1 (x + 1)

y-5 = 3x + 3

 +5         +5

y = 3x + 8

Answer: 24

Step-by-step explanation:

Since we are given the value for m and n, we can plug them in and solve the expression.

3(4)+6(3)-6          [multiply]

12+18-6                [add]

30-6                     [subtract]

24

Now, we know the value of the expression is 24.

Answer:

 \(-x^{3} -9x^{2}\)

Step-by-step explanation:

I think.

Pls give Brainliest.

Answer:

\( 3^{ -x+3}\)

Step-by-step explanation:

We need to simplify out the given exponential expression . The given expression to us is ,

\(\rm\implies \dfrac{\dfrac{1}{3}}{3^{x-4}} \)

We can use the Law of Exponents to simplify the given expression . Recall that ,

\(\rm\implies \red{\dfrac{a^m}{a^n}= a^{m-n}}\)

Note that , we can write ,

\(\rm\implies \dfrac{1}{3}= 3^{-1}\)

Therefore our expression becomes ,

\(\rm\implies \dfrac{ 3^{-1}}{3^{x-4}}\)

Simpify using the Law of Exponents ,

\(\rm\implies 3^{ -1 - ( x - 4 )}\)

Open the brackets in exponent ,

\(\rm\implies 3^{ -1 - x +4 }\)

Simplify to get final expression ,

\(\rm\implies \boxed{\quad \blue{ 3^{-x+3} \quad}}\)

Answer:

1.2

Step-by-step explanation:

You have to subtract 7.2 - 6 = 1.2

East and south direction motion are perpendicular to each other. The hiker went approx 4 miles in south.

East or west are perpendicular (forming 90° ) to north or south directions.

North is 180° to south, and east is 180 degrees to west.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

\(|AC|^2 = |AB|^2 + |BC|^2\)

where |AB| = length of line segment AB.

Considering the diagram attached below, we deduce that the triangle ABC is right angled triangles, and thus, its sides' lengths will follow Pythagoras theorem.

The movement the hiker did in the south direction is the length of the side BC, denoted by |BC| = x miles (assume)

Then, by applying Pythagoras theorem, we get:

\(|AC|^2 = |AB|^2 + |BC|^2\\(7.2)^2 = 6^2 + x^2\\51.84 = 36 + x^2\\\\\text{Subtracting 36 from both the sides and taking root, we get}\\\\x = \sqrt{15.86} \approx 3.98 \approx 4 \: \rm miles\)

(took positive root since distance is a non-negative quantity)

Thus, the hiker went approx 4 miles in south.

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To evaluate the limit of the given function as (x, y) approaches (0, 0), we can use the following approach:

First, we can try to simplify the expression by factoring out the common factor xy^8 from the numerator. This gives:

xy^8(x^2 + y^4)

Next, we can rewrite the expression using polar coordinates, where x = r cos(θ) and y = r sin(θ). Substituting these values into the expression and simplifying, we get:

lim (r,θ)→(0,0)  (r^3 cos(θ) sin^8(θ)) (cos^2(θ) + sin^8(θ))

Now, we can see that the factor (cos^2(θ) + sin^8(θ)) is bounded between 0 and 1 for all θ, since the terms are either 0 or positive and sum to 1.

Therefore, we can focus on evaluating the limit of the other factor:

lim (r,θ)→(0,0)  r^3 cos(θ) sin^8(θ)

Since |cos(θ)| ≤ 1 and |sin(θ)| ≤ 1 for all θ, we can bound the expression as follows:

|r^3 cos(θ) sin^8(θ)| ≤ r^3

Therefore, by the squeeze theorem, the limit of the expression as (r,θ) approaches (0,0) is 0.

In conclusion, the given limit is equal to 0.

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Given that mean= 6.56 and standard deviation(σ)= 1.19

a) P(X ≤ 5)= ( (X-µ)/ σ) < (5- 6.56)/ 1.19)

                = 0.094946

P(X ≤ 5)= 0.95

So 0.95 proportion of the survey would think $5 is too expensive for a sandwich.

b) P(X ≥ 6.75) = ( (X-µ)/ σ) < (6.75- 6.56)/ 1.19)

                      = 0.43656

0.43656 proportion of people surveyed would be willing to pay more than $6.75 for a sandwich.

c)  P(X ≤ x)= 0.35

                 = P((x- µ)/ σ ≤ (x- 6.65)/ 1.19)

                  0.35

x= (-0.3853) (1.19) + 6.56

 = 6.1015

6.1015  is the 35th percentile for how much people are willing to pay for a sandwich.

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Answer:

x=-22

Step-by-step explanation:

Let's substitute the number you are thinking of with x

(x+4)*3=(x-5)*2

3x+12=2x-10

x+12=-10

x=-22

Answer:

3x + 9 = 21

Step-by-step explanation:

Let Henry's age be x

Mary's age = 9 + 3x

21 = 9 + 3x

Can also be written as 3x + 9 = 21

The leading coefficient of the polynomial is -2, and the degree of the polynomial is 3.

To identify the leading coefficient and degree of the polynomial, we need to consider the highest power of the variable in the polynomial expression.

In the given polynomial, -2y³ is the term with the highest power of y. The coefficient of this term, which is -2, is the leading coefficient of the polynomial. The degree of a polynomial is determined by the highest power of the variable. In this case, the highest power of y is 3 in the term -2y³. Therefore, the degree of the polynomial is 3.

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The 95% confidence interval estimate of , the mean procrastination scale for first-year students at this college is equals to the (35.311, 38.488).

We have a sample of 65 first-year students selected from a large university in England, with

Sample Size, n = 65.0

Sample Mean, \(\bar x\) = 36.9

Standard deviation,s = 6.41

Significance level, α = 1- 0.95 = 0.05

Degree of freedom, df = n- 1 = 65.0 - 1

= 64.0

We have to determine the 95% confidence interval for population mean μ , so, Point estimate, \(\bar x\)

= 36.9

Critical value at α = 0.05 with df = 64.0 is

\(t_{(\frac{α}{2},df)} = 1.998\) (from student t table)

From Margin of error formula,

\(ME = t_{(\frac{α}{2},df )} \frac{s}{\sqrt{n}}\)

Substitute all known values in above formula, \(= 1.998 × \frac{6.41}{\sqrt{65}}\) = 1.5885

Thus, Margin of error is 1.5885. Now 95% confidence interval is CI = point estimate ± ME = 36.9 ± 1.5885

= (35.311, 38.488)

Hence, required value of confidence is (35.311, 38.488).

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6.25% of Year 11 students are not doing homework regularly according to the school's report.

Based on the information provided in the frequency tree, we can determine the percentage of students not doing homework regularly.

First, let's find the total number of students:

Total students = (Students doing homework regularly) + (Students not doing homework regularly)

Total students = 75 + 5 = 80

Now, let's calculate the percentage of students not doing homework regularly:

Percentage = (Number of students not doing homework regularly / Total students) * 100

Percentage = (5 / 80) * 100

Percentage = 6.25%

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To construct a 99% confidence interval for a population proportion, we can use the formula:  CI = ˆp ± Z * √(ˆp(1-ˆp)/n) ,Answer :  CI = 0.6 ± 0.083

CI = ˆp ± Z * √(ˆp(1-ˆp)/n)

Given that n = 580 and ˆp = 0.6, we can substitute these values into the formula.

First, we need to find the critical value Z for a 99% confidence level. The critical value corresponds to the desired level of confidence and is obtained from a standard normal distribution table or calculator. For a 99% confidence level, the critical value is approximately 2.576.

Now, let's calculate the confidence interval:

CI = 0.6 ± 2.576 * √((0.6 * (1 - 0.6)) / 580)

CI = 0.6 ± 2.576 * √(0.24 / 580)

CI = 0.6 ± 2.576 * 0.032

CI = 0.6 ± 0.083

The confidence interval is (0.517, 0.683) when rounded to three decimal places. This means that we can be 99% confident that the true population proportion falls within this range.

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Step 1:

Write the two equations

x - y = 2 Equation 1

x + 4y = -3 Equation 2

Step 2:

From equation 1 , make x subject of the formula and substitute in equation 2.

Step 3:

Substitute x = 2 + y in equation 2

Step 4

Substitute y = -1 in x = 2 + y to find x

x = 2 - 1

x = 1

Final answer

x = 1 , y = -1

Equation: x - y = 2x + 4y = -3 x - y = -3 Equations 1st and 2 (x - y = -3) 2 equations 1 2x - 2y = -6 equation 1 -(2x + 4y = -3) equation 2 are obtained.

In the second equation, 2x - 2y = -6, 2x -4y = 3, 6y = 3, and 6y = -3/-6 = 1/2.

2x + 4y = -3 , 2x + 4×1/2 = -3

2x +2 = -3 , 2x = -3 -2 , 2x = -5 ,x = -5/2

The last solution is y = 1/2 and x = -5/2.

What you want altered should go here. After that, click the button below. It's that simple!

Answer:

14: A

15: A

Step-by-step explanation:

The Taylor series for f(x) at x = -2 is f(x) = -73 + 88(x+2) - 63(x+2)^2 + 9(x+2)^3

To find the Taylor series for a function, we need to find its derivatives at a point and then use them to form the series.

First, we find the first few derivatives of f(x):

f(x) = 6x^3 - 9x^2 + 4x - 1

f'(x) = 18x^2 - 18x + 4

f''(x) = 36x - 18

f'''(x) = 36

Now we can use these derivatives to find the Taylor series centered at x = -2:

f(-2) = 6(-2)^3 - 9(-2)^2 + 4(-2) - 1 = -73

f'(-2) = 18(-2)^2 - 18(-2) + 4 = 88

f''(-2) = 36(-2) - 18 = -126

f'''(-2) = 36

The Taylor series for f(x) centered at x = -2 is:

f(x) = -73 + 88(x+2) - 63(x+2)^2 + 9(x+2)^3

We can check that this series converges to f(x) by comparing the series to f(x) and its derivatives using the remainder term (Taylor's theorem).

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The correct expression to find the volume of a rectangular prism is D. (3 × 6) × 15 = 270 in.3.

Expression is a word, phrase, or gesture that conveys an idea, thought, or feeling. It is an outward representation of an emotion, attitude, or opinion. Expressions can be verbal, physical, or written. They can also take the form of art, music, or dance. Expression is used to communicate and express emotions, thoughts, and ideas. It can be a powerful tool to create a connection with others and build relationships.

The correct expression to find the volume of a rectangular prism is D. (3 × 6) × 15 = 270 in.3. This expression involves multiplying the length, width, and height of the rectangular prism in order to calculate the total volume. In this case, the length is 3, the width is 6, and the height is 15. If these values are multiplied together, the result is 270 in.3, which is the total volume of the rectangular prism.

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Answer:

Step-by-step explanation:

Correct option is C

1. The expected value is 9.848

2. The standard deviation is 9.848

3. The value of P(X<12) is -9.84

4. The value of P(8) is -6.23

To answer the questions regarding the exponential distribution with parameter λ = 1/9.848:

1. The expected value or mean of the exponential distribution can be calculated as;

E(X) = 1/λ

λ = 1 / 9.848

The expected value can be calculated as 9.848

2. The standard deviation of the exponential distribution can be calculated as 1/λ

σ = 1/λ = 9.848

3. P(X<12) can be calculated using cumulative distribution function of the exponential distribution.

The CDF can be calculated as;

\(f(x) = 1 - e^(^- \lambda ^x^)\)

\(P(X < 12) = F(12) = 1 - e^(^-^(^1^/^9^.^8^4^8^) ^* ^1^2^) = -9.84\)

4. To find P(X = 8), we need to calculate the probability density function (PDF) of the exponential distribution. Substituting the given value of λ = 1/9.848 and x = 8, we have:

\(P(X = 8) = f(8) = (1/9.848) ^* ^e^(^-^(^1^/^9^.^8^4^8^) ^* ^8^) =-6.23\)

Note: The exponential distribution is continuous, so the probability of a single point is always zero. However, we can calculate the probability density at that point.

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At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

The speed of an object is the ratio of distance and time it takes for the object to travel that distance.

Mathematically,

S = D/T

where

S is velocity

D is the distance traveled or distance traveled

T is the time it takes to travel that distance

Velocity is considered a scalar quantity. A scalar size only has a size. It does not provide information about the direction of object movement.

If an object moves at a constant speed, it means that the object moves the same distance in the same time interval.

Acceleration of an object is the ratio of velocity and time. vector size. Vector quantities have both magnitude and direction.

Mathematics,

a = v/t

When an object is in motion, its acceleration is never zero.

When an object moves, it moves a constant distance over time. Therefore, body positions cannot be the same from the same coordinate system.

Given in the question:

First the plane was travelling at a constant rate of 250  miles per hour.

Initial height was 20000 feet

Now,

As the speed increases and travels at a constant rate of 400 miles per hour.

Now,

   (400 /250 ) × 20000

=  1.6 × 20000

= 32000 feet

Thus, At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

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Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

Answer:

0.125

Step-by-step explanation:

2 * 0.125 = 0.25 (or 1/4)

Answer:

0.125

Step-by-step explanation:

I think not really good at it

the following statements correctly outputs the names of voters who live in district 6 and all voters who live in district 7:

if(district == 6 || district == 7)

System.out.println("Name is " + name);

Output is any information processed by and transmitted by a computer or other electronic device. Anything visible on your computer monitor screen, such as the text you write on your keyboard, is an example of output. The information produced by a system or process as a result of a certain input is referred to as output. The inputs are what are placed into a system in the context of systems theory, and the outputs are the outcomes gained after executing a whole process or just a tiny section of a process. The system's inputs are the signals or data it receives, and its outputs are the signals or data it sends. The phrase can also refer to an activity; to "perform I/O" is to carry out an action.

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Answer: 857142/1000000

Step-by-step explanation:

i think