5. Which equation's line is steeper and explain how you know

A. y = 3x + 7
B. y=x+9

Answer:

let the third side be x

Using pythagoras theorem we get,

(58)^2 = (42)^2 + (x)^2

3364=1764+x^2

x^2=3364-1764

x^2= 1600

x=√(1,600)

x=40

\(\pink{\sf Third \: side \: of \: the \: triangle = 40}\)

As, the given triangle is a right angled triangle,

Hence, We can use the Pythagoras' Theorem,

\(\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}\)

Here,

In given triangle,

Now, by Pythagoras' theorem,

\(\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}\)

\( \sf : \implies (58)^{2} = (42)^{2} + P^{2}\)

\( \sf : \implies 58 \times 58 = 42 \times 42 + P^{2} \)

\( \sf : \implies 3364 = 1764 + P^{2}\)

\( \sf : \implies P^{2} = 3364 - 1764\)

\( \sf : \implies P^{2} = 1600\)

By squaring both sides :

\( \sf \sqrt{P^{2}} = \sqrt{1600}\)

\( \sf : \implies P^{2} = \sqrt{1600}\)

\( \sf : \implies P^{2} = \sqrt{(40)^{2}}\)

\( \sf : \implies P^{2} = 40 \)

\(\pink{\sf \therefore \: Third \: side \: of \: the \: triangle \: is \: 40}\)

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To generate a series of 100 numbers uniformly distributed in the interval [0,1] using a linear congruential generator, we can use the parameters a = 41, c = 33, m = 100, and Z0 = 48.

A linear congruential generator is a simple method for generating pseudo-random numbers. It uses a recurrence relation of the form Zₙ₊₁ = (aZₙ + c) mod m, where Zₙ is the current random number, a is a multiplier, c is an increment, and m is the modulus. In this case, we start with an initial seed value of Z0 = 48 and generate subsequent numbers using the given parameters. To compute the mean and standard deviation of the generated series, we calculate the sample mean and sample standard deviation of the 100 numbers. The sample mean is the average of the numbers, while the sample standard deviation measures the spread or dispersion of the numbers around the mean. We can then compare these computed values with the expected theoretical values for a continuous uniform distribution on the interval [0,1]. The theoretical mean of a continuous uniform distribution is (a + b) / 2, where a and b are the endpoints of the interval. In this case, the mean is (0 + 1) / 2 = 0.5. The theoretical standard deviation of a continuous uniform distribution is (b - a) / sqrt(12), which for the interval [0,1] is 1 / sqrt(12) ≈ 0.2887. Any differences between the computed and theoretical mean and standard deviation may arise due to the nature of pseudo-random number generation. Linear congruential generators are deterministic and have certain limitations in terms of randomness. Deviations from the expected theoretical values can be attributed to the algorithm used and the chosen parameters. If the generated numbers deviate significantly from the expected mean and standard deviation, it may indicate that the linear congruential generator is not adequately simulating a continuous uniform distribution.

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Answer:

1st one 20 2nd one 15

Step-by-step explanation:

From the given pattern, the missing term will be equal to 17 and the gap between the difference is +2.

Two definitions are given for an arithmetic sequence. A "series where the variances in between every two succeeding terms are the same" is what it is. Each term in an algebraic expression is created by multiplying its previous term by a specified integer (either positive, negative, or zero).

As per the given pattern mentioned in the question,

1, 2, 5, 10, __, 26, 37

Let's find out the growth from one number to another number.

From 1 to 2 = +1

From 2 to 5 = +3

From 5 to 10 = +5

It means a +2 increment is going on with the sequence.

So, the next number of increments will be + 7.

10 + 7 = 17

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Answer:

B. 38°​

Explanation:

From the given figure, angles x and 142 degrees are on a straight line.

The sum of angles on a straight line is 180 degrees, therefore:

Next, we solve the equation for x:

The correct choice is B.

Answer: i don't care

Step-by-step explanation: I am doing it for the points

sry for not knowing the answer

The annual compound rate of return on this 20-year zero coupon bond is 6%. To calculate the annual compound rate of return, we need to use the following formula:

Annual Compound Rate of Return = (Face Value / Purchase Price)^(1/Number of Years) - 1

Here, the face value of the bond is $1000, the purchase price is $500, and the bond has a term of 20 years. Substituting these values in the above formula, we get:

Annual Compound Rate of Return = (1000/500)^(1/20) - 1

Simplifying this expression, we get:

Annual Compound Rate of Return = 1.06 - 1

Annual Compound Rate of Return = 0.06 or 6%

Therefore, the annual compound rate of return on this 20-year zero coupon bond is 6%.

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The width of the cooling tower is 36 meters.

A cooling tower is a vent that is built for the purpose of releasing waste heat back to the atmosphere.

Now we can model the system using;  x²/324 - (y² - 90)²/1600. Thus, the width can be obtained from;

2 × ✓324

= 2 × 18

= 36 meters

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Missing parts;

Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.

36 meters

48 meters

80 meters

89 meters

To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

Rearranging the equation, we get n = PV/RT.

Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.

Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.

To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:

1. Recall the ideal gas equation: PV = nRT

2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).

3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):

  n/V = (1.524 g/L) / (22.4 L/mol)

4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):

  M = (n/V) * (RT/P)

5. Substitute the values and solve for M:

  M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)

6. Calculate the molecular weight of the gas:

  M ≈ 32.0 g/mol

Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

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Answer:

Step-by-step explanation:

- Hint: In this question we asked to find the Simple interest. Here, we will calculate simple interest for 4 years at 8% per annum by using the formula of simple interest (SI) =PRN100 .

Complete step-by-step solution -

To find the simple interest first we will know about simple interest.

Simple interest is based on principal amount for a fixed period of time. The amount which we deposit or take loan from the bank is known as principal amount. The period of time for which the money is lent is known as time on interest.

Now, we will calculate here simple interest,

SI =PRN100

Where P (principal amount) = Rs. 3000

R (Rate of interest) = 8%

N (number of period) = 4 years

So, finding simple interest by putting all the value, we get

=3000×8×4100

=30×8×4

=960 Rs.

Answer:

28.095 cm^2

Explanation:

To determine the area of the given shape, we have to determine the area of the complete rectangle, then subtract the areas of each of the cut-out semi-circles as seen below;

From the shape, let's determine the length and width of the rectangle;

Length(l) = 2 cm + 5 cm + 2 cm = 9 cm

Width(w) = 1 cm + 4 cm + 1 cm = 6 cm

So the area of the complete rectangle will be;

Let's now determine the area of the top semi-circle given that the radius is 2cm (radius = diameter/2 = 4/2 = 2cm);

Given that the two semi-circles by the side of the rectangle have the same radius(r) which is 2.5cm (r = diameter/2 = 5/2 = 2.5cm), let's go ahead and determine their area;

So the area of the shape will be;

Therefore, the area of the shape is 28.095 cm^2

Answer:

11.8

Step-by-step explanation:

I simply just did multiplication

I multiplied the whole numbers alone and did the same with the fraction

Example: -2*-4=8

2/3*3/7

then you add the two products and get your answer

Answer:

100, 102, 104

Step-by-step explanation:

Hi there!

Let x be equal to the first number in the set of the three consecutive even numbers.

We're given that the sum of three consecutive even numbers is 306.

Because x is the first number, the next would be x+2, and then x+4. These are our even numbers.

We can now set up an equation:

\((x)+(x+2)+(x+4)=306\)

Combine like terms:

\(x+x+x+2+4=306\\3x+6=306\\3x=300\\x=100\)

Therefore, the first number in the set of 3 numbers is 100.

The next two even numbers after 100 is 102 and 104.

Therefore, the three numbers are 100, 102 and 104.

I hope this helps!

Answer:

Below

Step-by-step explanation:

A geometric sequence is a sequence where you keep multiplying a term by the ratio to generate the next one.

The first term is 3/4

Let n0 = 3/4

The next term is n1.

To get n1 we must multiply n0 by the ratio 4.

● n1 = n0×4

This formula gives us the second term. We need a general one that can generate all the terms of the sequence.

Let S(n) be a term of this sequence.

To get n we have multiplied n0 (the first term) by 4 (the ratio) one or many times. Precisely, n times.

So:

● S(n )= n0 ×4^n

no is 3/4

● S(n)= (3/4) × 4^n

This formula generates any term from this geometric sequence. If you want to calculate the 77th term then just replace n with 77.

Answer:

Step-by-step explanation:

To find the next term, multiply the previous term by constant ratio

a₁ = 3/4

\(a_{2}=\frac{3}{4}*4=3*1 = 3\\\)

a₃ = a₂ * constant ratio = 3 * 4 = 12

a₄ = a₃ * constant ratio = 12 *4 = 48

Geometric sequence :

3/4, 3,12, 48, 192,.......

The number of solution for the equation  x₁ + x₂ + x₃ = 14 where x₁ , x₂ , x₃  are integers for different condition are

a. 91 solution for each variable greater than or equal to zero

b. 66 solution when each variable greater than or equal to one.

Total number of solution for the equation x₁ + x₂ + x₃ = 14.

a. Each variable x₁ , x₂, x₃ is an integer greater than or equal to zero.

When x₁ = 0 and x₂ , x₃ have different values

0 + 0 + 14 = 14

0 + 1 + 13 = 14

0 + 2 + 12 = 14

0 + 3 + 11 =14

0 + 4 + 10 =14 .......so on

0 + 13 + 1 = 14

Total outcome = 14

Two place needs to be fill one place is fixed by certain number.

Total number of possible solution is equal to

= ¹⁴C₂

= ( 14! ) / ( 14 - 2 )! 2!

= ( 14 × 13 ) / ( 2 × 1 )

= 7 × 13

= 91

b. Each integer is an integer greater than or equal to one

When x₁ = 1 and x₂ , x₃ have different values

1 + 1+ 12 = 14

1 + 2 + 11 = 14

1+ 3 + 10 =14

1 +4 + 9 =14 .......so on

1+ 12 + 1 = 14

Total outcome = 12

Total number of possible solution when each variable is greater than or equal to 1

= ¹²C₂

= ( 12! ) / (12 - 2)! 2!

= ( 12 × 11 ) / 2

= 66

Therefore , total number of solution for the equation having integer variable x₁ + x₂ + x₃ = 14 is

a. Each variable greater than or equal to zero has 91 solution.

b. Each  variable greater than or equal to one has 66 solution.

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To solve the matrix equation X = [1 -1 2; -14 -2 0; 4 0 1; 9 -5 11], where X is a 4 x 3 matrix, we can utilize the given structure of the matrix equation. By equating the corresponding elements of the matrices on both sides, we can find the values of the matrix X.

The given matrix equation X = [1 -1 2; -14 -2 0; 4 0 1; 9 -5 11] implies that the matrix X has four rows and three columns. To solve this equation, we can write the matrix X as a block matrix:

X = [k₁ 0 0 0; 0 k₂ 0 0; 0 0 k₃ 0; 0 0 0 k₄]

By equating the corresponding elements of X and the given matrix on the right-hand side, we can solve for the values of k₁, k₂, k₃, and k₄. Comparing the first row, we have:

k₁ = 1, 0 = -1, and 0 = 2

These equations do not hold true, indicating that there is no solution for the matrix equation. Therefore, the system of equations is inconsistent, and we cannot find a matrix X that satisfies the given equation.

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Answer:

x - 5

Step-by-step explanation:

Again, we can just write the width as (x² - 25) / (x + 5) which will be x - 5.

Answer:

area = length x width

x² - 25 = x + 5 · width

(x - 5)(x + 5) = (x + 5)w

(x - 5)(x + 5) / (x + 5) = (x + 5)w / (x + 5)

x - 5 = w

Step-by-step explanation:

1. write down the formula of area.

2. since the area is a difference of squares, factor them into two binomials, and replace the length by its measure. you can use w for width

3. to get width, divide the one of the binomials with the length that matches together to get w.

The length of Nigel's bedroom is 11 feet while the width is 9 feet

An equation is an expression that shows the relationship between numbers and variables.

For Colleen room:

length = 8 ft, width = 12 ft

Perimeter = 2(length + width)

substituting:

Perimeter = 2(8 + 12) = 2(20)

Perimeter = 40 feet

For Nigel room:

length = l ft, width = 3/4 times that of Colleen = (3/4)(12) = 9 feet

Perimeter = 2(length + width)

But Colleen and Nigel room has same perimeter

substituting:

40 = 2(l + 9)

l + 9 = 20

l = 11 feet

The length is 11 feet.

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Answer:

Step-by-step explanation:

Cups: servings

8 : 22  :: x : 3

Product of means = product of extremes

22*x = 3*8

   \(x = \dfrac{3*8}{22}=\dfrac{3*4}{11}=\dfrac{12}{11}=1\dfrac{1}{11}\)

Start with the slope formula.

m = y₂ - y₁ / x₂ - x₁

m = -6 - 3 / 5 - -2

m = -9 / 7

So the slope is -9/7.

The transformations to the graph of the quadratic function are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Additionally, when the function is multiplied by |a| > 1, it is said that the function is vertically stretched by a factor of a.

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Answer:

Jeff, 4.5 hours; Julia 9 hours.

Step-by-step explanation:

To solve the problem, we need to write two equations using the given information.

So, writing the first equation we have:

We know that Jeff can weed the garden twice as fas as his sister Julia, so:

Also, from the statement we know that they can weed the garden in 3 hours, so, writing the second equation we have:

Then, we need to substitute the first equation into the second equation in order to isolate Julia's rate, so, solving we have:

We have that Julia could weed the garden by herself in 9 hours.

So, calculating how long will it take to Jeff, we have:

We have that Jeff could weed the same garden by himself in 4.5 hours.

hope this helps!

Answer:

(x + 2) (5x + 3)(5x - 3)

Step-by-step explanation:

\(25x^2(x+2)-9(x+2) \\ \\ = (x + 2)(25 {x}^{2} - 9) \\ \\ = (x + 2) \{ ({5x})^{2} - {(3)}^{2} \} \\ \\ = (x + 2) \{(5x + 3)(5x - 3) \}\\ \\ = \purple{ \bold{(x + 2) (5x + 3)(5x - 3) }} \\ are \: the \: required \: factors\)

Population is the total number of members of a specific species or group that are present in a given area or region at any given moment.

It is a key idea in demography and is frequently used in a number of disciplines, including ecology, sociology, economics, and public health.

The given data is- Population in the year 2000 = 19400 Continuous growth rate per year = 7%.

Let P(t) be the function which models the population t years after 2000, then using the given data, we have

P(t) = 19400 * (1 + 0.07t) (as the given growth rate is continuous, we use an exponential function with base

e). The function that models the population t years after 2000 is given by the formula, P(t) = 19400 (1 + 0.07t).

Now we need to use this function to estimate the fox population in the year 2008. Here t is 8 years (since 2008 is 8 years after 2000). So, by putting t = 8 in the above function, we get

P(8) = 19400 (1 + 0.07*8)= 19400 (1.56)≈ 30240. Hence, the fox population in the year 2008 is approximately 30240.

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The largest possible difference between two different 3-digit numbers with the same digits in reverse order is 792.

Let's assume the two numbers are ABC and CBA. The largest possible difference is achieved when the digits A and C have the largest possible difference.

If A > C, then the difference would be (ABC - CBA) = (100A + 10B + C) - (100C + 10B + A) = 99A - 99C = 99(A - C).

If A < C, then the difference would be (CBA - ABC) = (100C + 10B + A) - (100A + 10B + C) = 99C - 99A = 99(C - A).

Since we want the largest possible difference, we want to maximize the difference between A and C. The maximum possible difference between two single-digit non-zero numbers is 9. So, we want A = 9 and C = 1.

Therefore, the two numbers are 901 and 109, and the largest possible difference is (901 - 109) = 792.

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The surface area that will be frosted with icing is 205in²

It will be equal to the sum between the top surface, which measures:

here, we have,

S = 13in*9in = 117 in²

And the four lateral sides, two of them measure:

s' = 2in*9in = 18in²

The other two measures:

s'' = 13in*2in = 26in²

Then the total surface area that must be frosted is:

SA = 117 in² + 2*( 18in²) + 2*(26in²) = 205 in²

So we conclude that the correct option is C.

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