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(B) Distinct parallel lines

Answer:

  B.  Distinct parallel lines

Step-by-step explanation:

These two equations have the same slope 4/3 which means they are parallel.

y = mx + b

m is slope

b is y-intercept

\(y = \frac{4}{3} x + \frac{5}{3}\)

\(y - 8 = \frac{4}{3} (x + 6)\)

     \(y = \frac{4}{3} x + 16\)

Answer:10 hexagonal, 30 rectangular and 40 triangular pieces of fabrics

Step-by-step explanation:

This question is a ratio/proportion question

The ratio of hexagonal pieces use to rectangular pieces used and to triangular pieces used can be expressed as 1:3:4

Total pieces of fabrics used = 80

Total ratio = 1 + 3 + 4 = 8

We can calculate each ratio as a proportion of the total ratio

pieces of hexagonal used = (1/8) * 80 =10

Pieces of rectangular used = (3/8) * 80 =30

Pieces of triangular used = (4/8) * 80 = 40

And hence the pieces of each shapes used will be 10 hexagonal, 30 rectangular and 40 triangular pieces of fabrics

And the total number of bugs designs made = (80/8) = 10 (since it will require 8 pieces of fabrics(1 + 3 +4) to make a bug design)

Yes, Victor needs to have similar portion of the population in the sample.

What is population size?

The number of objects inside a geographical area that has been arbitrary assigned as the population size.

In a fair, unbiased poll

Population proportion plus random error equals sample proportion.

According to the Normal Approximation, the standard deviation of the distribution of these random mistakes across all feasible samples is

\(\sqrt{\frac{\text{Population proportion}(1-\text{Population proportion})}{n}}\)

The sample estimate's variance from the actual population value is known as the random error. Numerous alternative summaries, such as sample averages or discrepancies between two sample proportions or averages, are likewise consistent with the observation that random mistakes follow the normal curve.

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Answer: The 32 electricians are expected to finish the job in 27 days.

Step-by-step explanation:

A system will function if exactly 3 out of 5 componet function with probability of functioning 0.9. The probability the system will function is equals to the 0.9914.

Binomial distribution is a probability distribution used in statistics that defines as a value will take one of two independent values under a set of parameters or assumptions. Formula, P ( X = x)

= nⁿCₓ pˣ(1 -p)⁽ⁿ⁻ˣ⁾

where, P -->binomial probability

We have provided that k out of n system is one which have a group of n components and system will function atleast k of components. Also, consider that components function independently of one another. So, The distribution of the number of components functioning is Binomial, X ~ Binom( n,p).

Probability of functioning of each component in 3 out of 5 system = 0.9

that is Probability of success, p = 0.9 and n = 5.

Now for the system to function at least 3 components must function.

X ~ Binom( 5,0.9)

a) The probability the system will function is determined by using binomial probability formula,

P (X ≥ 3) = 1 - P (X < 3)

= 1 - P (X = 0) - P (X = 1) - P (X = 2)

= 1 - ⁵C₀ 0.9⁰ ( 1-0.9)⁵ - ⁵C₁ 0.9¹ ( 1-0.9)⁴ - ⁵C₂ 0.9²(1 -0.9)³

= 1 - (0.1)⁵ - 5(0.9)(0.1)⁴ - 10(0.9)²(0.1)³

= 1− 0.00001 - 0.00045 − 0.0081

= 0.99144

Hence, required probability value is 0.9914.

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A. 3n + 5

Jose will only age by one every year. So we add one every year and since there are five years, the answer will be his age (3n) plus 5.

To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:

w = c1V1 + c2V2 + c3V3

We can write this as a matrix equation:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

We can solve this system of equations using row reduction:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

R2 = R2 - 6R1

R3 = R3 - 2R1

R4 = R4 + 15R1

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 -23 67 -59 | | -32 |

R4 = R4 + 23R2

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 0 174 -294 | | 225 |

R3 = R3 - (12/27)R2

R4 = (1/174)R4

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 0 -1 22/3 | | c3 | | -13/3 |

| 0 0 1 -98/87 | | 25/58 |

R1 = R1 + 4R3

R2 = R2 - 59R3

R4 = R4 + (98/87)R3

| 1 0 -13 -10/3 | | c1 | | 21/29 |

| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |

| 0 0 1 -98/87 | | c3 | | 25/58 |

| 0 0 0 1390/2391 | | 1009/2391 |

R1 = R1 + (13/1390)R4

R2 = (1/27)R2

R3 = R3 + (98/1390)R4

| 1

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Answer:

363=90bags

then you look into it and say

440=200bags

The system of linear equations which has the rank of coefficient matrix equal to augmented matrix and equal to the number of unknowns, has only one solution called the unique solution.

Two types of system of equations exist- consistent and inconsistent.

Inconsistent means that it has no solution , i.e. the solution does not exist , here

Rank of augmented matrix is not equal to that of coefficient matrix.

Consistent system means a solution of the equation exists i.e.

rank of augmented matrix = rank of coefficient matrix.

Now, a consistent system can be of two types again - It may have a unique solution ,i.e.

rank of augmented matrix = rank of coefficient matrix = no. of unknowns

or an infinite number of solutions, where

rank of augmented matrix = rank of coefficient matrix < no. of unknowns   (here we need to assign an arbitrary value to a free variable to find its solutions).

For e.g. let us consider the system -

x + y+ z = 0

2x + 3y + 4z = 1

Since , (0,0,0) is obviously satisfying the equation and so is a solution to this system , the given system is a consistent system .

Also, for a system to be consistent , either a unique solution exists or an infinite number of solutions exist. There is no particular number of solutions.

Here, we see that (-1,1,0) is also a solution other than the zero solution.

We can clearly see that the number of unknown variables , x,y,z is 3 and the number of equations is 2.

Thus, The system if there are fewer equations than variables has infinite solutions, equal number of equations as the unknowns has the unique solution.

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MN+NO=MO

Where N is the midpoint of MO

Therefore:

MN = NO

MN = 8

NO = 8

8 + 8 = MO

MO = 16

Now:

MO + OQ = MQ

If O is the midpoint of MQ:

MO = OQ

OQ = 16

Therefore:

MQ = 16 + 16 = 32

Answer: 11/74

Step-by-step explanation:

We have to think about what number can be divided from both 33 and 222. 33’s factors are 11 and 3. 222’s are 3, 6, 74, 37, and probably more. The only one the two numbered have in common is 3. So, divide north the numbers toe and denominator by 3 to get 11/74.

The 12th mortgage payment is 23,998.11 pesos, which is calculated based on the loan amount, 2 years of accrued interest, and the monthly mortgage payment formula.

To calculate the amount of the 12th mortgage payment, we need to break down the steps involved:

1. Calculate the loan amount after 2 years of accruing interest:

The loan amount after 2 years will be the sum of the initial loan amount and the accrued interest. Since the interest is compounded semi-annually at a rate of 15%, the formula for calculating the future value (FV) of the loan after 2 years is:

FV = PV * (1 + r/2)²ⁿ

Where PV is the present value (loan amount), r is the interest rate, and n is the number of compounding periods.

In this case:

PV = 2,000,000 pesos

r = 15% = 0.15

n = 2 years

FV = 2,000,000 * (1 + 0.15/2)²²

FV = 2,000,000 * (1 + 0.075)⁴

FV ≈ 2,479,095.31 pesos

2. Calculate the monthly mortgage payment for the first 5 years:

The monthly mortgage payment during the first 5 years is half of the payments from the 6th to the 30th year. Since the mortgage is for 30 years, there are 360 monthly payments.

The formula for calculating the monthly mortgage payment is:

PMT = PV * (r/12) / (1 - (1 + r/12)⁽⁻ⁿ⁾)

Where PMT is the monthly payment, PV is the loan amount, r is the monthly interest rate, and n is the number of months.

In this case:

PV = 2,479,095.31 pesos (calculated in step 1)

r = 12% = 0.12

n = 360 months (30 years)

PMT = 2,479,095.31 * (0.12/12) / (1 - (1 + 0.12/12)⁽⁻³⁶⁰⁾)

PMT ≈ 23,998.11 pesos

3. Calculate the amount of the 12th mortgage payment:

Since the first monthly mortgage payment is made exactly 2 years after the loan is requested, the 12th mortgage payment corresponds to the payment made in the 13th month.

Therefore, the amount of the 12th mortgage payment is approximately 23,998.11 pesos.

In conclusion, the amount of the 12th mortgage payment is approximately 23,998.11 pesos. This calculation takes into account the initial loan amount, accrued interest over 2 years, and the monthly mortgage payment formula. It is important to note that the calculations provided are based on the information and assumptions given in the question.

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Answer:

x(-8)

Step-by-step explanation:

the equation for g(x) is g(x) = (x - 3)² - 6.

The function g(x) can be obtained by applying a horizontal and vertical shift to the graph of f(x) = x². The horizontal shift of three units to the right can be achieved by replacing x in f(x) with (x - 3), which moves the graph to the right. The vertical shift of six units down is accomplished by subtracting 6 from f(x).

Therefore, the equation for g(x) is g(x) = (x - 3)² - 6. This equation represents a parabola that has the same shape as f(x) = x² but is shifted three units to the right and six units down in the coordinate plane.

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Answer:

Step-by-step explanation:

(-5/3)(-5/3)= 25/9= 2 7/9

a

because it has the highest values from all the options from all the above

A rectangular tank 3600 bricks measuring 1/5m by 1/8m by 1/10m into the tank before the water overflows.

To find bricks can be put into the tank before the water overflows,  the volume of water in the tank and then determine the volume of each brick.

The volume of water in the tank  length, width, and depth:

Volume of water = length × width × depth = 3m × 2m × (3/4)m

The volume of each brick:

Volume of each brick = length × width × height = (1/5)m × (1/8)m × (1/10)m

Divide the volume of water in the tank by the volume of each brick:

Number of bricks = (Volume of water) / (Volume of each brick)

Now let's substitute the given values into the formulas and

Volume of water = 3m × 2m × (3/4)m = 9/2 m³

Volume of each brick = (1/5)m × (1/8)m × (1/10)m = 1/400 m³

Number of bricks = (9/2 m³) / (1/400 m³)

= (9/2) / (1/400)

= (9/2) × (400/1)

= 9 × 400 / 2

= 3600

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The value of x is

sin(2x) = (14√32)/81*

cos(2x) = -17/81**, and

tan(2x) = -(14√32)/17

Given that **sin(x) = 7/9** and **x** is in the first quadrant, we can find the values of **sin(2x)**, **cos(2x)**, and **tan(2x)** without explicitly determining the value of **x**.

To find **sin(2x)**, we can use the double-angle formula for sine: **sin(2x) = 2sin(x)cos(x)**.

We already know that **sin(x) = 7/9**. To find **cos(x)**, we can use the Pythagorean identity: **cos(x) = √(1 - sin^2(x))**.

Plugging in the value of **sin(x)**, we have **cos(x) = √(1 - (7/9)^2) = √(1 - 49/81) = √(32/81) = √32/9**.

Now, we can substitute the values of **sin(x)** and **cos(x)** into the double-angle formula to find **sin(2x)**:

**sin(2x) = 2sin(x)cos(x) = 2 * (7/9) * (√32/9) = (14√32)/81**.

Moving on to **cos(2x)**, we can use the double-angle formula for cosine: **cos(2x) = cos^2(x) - sin^2(x)**.

We already have the values of **sin(x)** and **cos(x)**, so we can substitute them into the double-angle formula:

**cos(2x) = (√32/9)^2 - (7/9)^2 = (32/81) - (49/81) = -17/81**.

Lastly, to find **tan(2x)**, we can use the identity: **tan(2x) = sin(2x)/cos(2x)**.

Plugging in the values we obtained earlier, we have:

**tan(2x) = (14√32)/81 / (-17/81) = -(14√32)/17**.

Therefore, without explicitly finding the value of **x**, we have determined:

**sin(2x) = (14√32)/81**,

**cos(2x) = -17/81**, and

**tan(2x) = -(14√32)/17**.

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Answer:

Line A = 3

Line B = - 1

Step-by-step explanation:

To find the gradient, you need two points on a line right. The formula for gradient is

\( \frac{y2 - y1}{x2 - x1} \)

So on line A, try to find 2 points (coordinates)

You have (-2,1) , (-1,4) , (0,7)

Choose any two

Let's say (-1,4) and (0,7)

Gradient =

\( \frac{7 - 4}{0 - - 1} = \frac{3}{1} = 3\)

Gradient of line A is 3

For line B, let's take (1,7) and (2,6)

Gradient =

\( \frac{7 - 6 }{1 - 2} = \frac{1}{ - 1} = - 1\)

Gradient of line B = - 1

the simplest fraction is: 3/5

in decimal form its: 0.6

Answer: 3y+6

Step-by-step explanation:

Answer:

17.5 units

Step-by-step explanation:

a² + b²= c²

9² + 15² = c²

81 + 225 = c²

c² = 306

c = √306

c = 17.5

Jerri rides 22 miles per hour against the wind.

        w × (1 ÷ 2) = 21

       a × (1 ÷ 2) = 21

        w = a + 20

        w = a + 20

       (21 × 2) = a + 20

       42 = a + 20

       22 = a

Therefore, Jerri rides 22 miles per hour against the wind.

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The given equation is (1/2)a + (2/3) b = 50

and b = 30

Substituting the given value of b is above the equation we get

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a+\left(\frac{2}{3}\right)\times30=50 } \end{gathered}$}\)

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow \left(\frac{1}{2}\right)a+20=50 } \end{gathered}$}\)

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a=50-20=30 } \end{gathered}$}\)

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow a = 30 \times 2 = 60 } \end{gathered}$}\)

Therefore, a = 60 and b = 30 is a solution of the given equation.

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Answer:

$(8m + 13n)

Step-by-step explanation:

Given that :

Total Cost of 6 bouquet = 6m

Total cost of 8 chocolate = 8n

Total amount spent = $(6m + 8n)

Total amount left = $(2m + 5n)

Hence, amount had at first :

Total amount. Spent + total amount. Left

(6m + 8n) + (2m + 5n)

(6m + 2m + 8n + 5n)

$(8m + 13n)

Answer:

A) 98% Confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B

= (0.51, 0.57)

This means that the true proportion of all thay would chose opinion B can take on values between the range of (0.51, 0.57)

B) For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion of all US buyers of this particular app who would have chosen Opinion B = 0.54

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 98% confidence interval for sample size of 1500 is obtained from the z-tables.

Critical value = 2.33

Standard error = σₓ = √[p(1-p)/n]

p = sample proportion = 0.54

n = sample size = 1500

σₓ = √(0.54×0.46/1500) = 0.0128685664 = 0.01287

98% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.54 ± (2.33 × 0.01287)

CI = 0.54 ± 0.02998)

98% CI = (0.51, 0.57)

98% Confidence interval = (0.51, 0.57)

B) The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?

For this confidence interval to be obtained using sample data, a couple of conditions are necessary to be satisfied. They include;

- The sample data must have been obtained using a random sampling technique.

- The sampling distribution must be normal or approximately normal.

- The variables of the sample data must be independent of each other.

On the second point, the condition for a binomial distribution to approximate a normal distribution is that

np ≥ 10

and n(1-p) ≥ 10

The quantity np is the actual sample mean which is the actual number of buyers that chose Opinion B while n(1-p) is the number of buyers that did not chose Opinion B.

For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

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Answer:

Scouts are on the third side in the sense they are running

Step-by-step explanation:

A regular hexagonal shape of perimeter 270 has each side of                 270/6 = 45  

Let´s call d  the run distance  then

d = 2/5 * 270      d = 108 m

We don´t have fig 9 available therefore if  X is a vertex in the hexagon or at the middle point of one side, scouts are 108 m from the starting point which means they had run 2,4 sides of the hexagon. If X is not either a vertex or a middle point of a side then, we have two solutions for the question depending on the sense the scouts took when began the run (clockwise or counterclockwise)

The average number of intersections the traffic engineer would need for each type of traffic signal to reject the null hypothesis at the 0.01 level of significance with a power of 0.90 is six

To test the effectiveness of these signals, the engineer must reject the null hypothesis, which states that there is no significant difference in the mean delays between the three types of signals. The engineer wants to reject the null hypothesis at the 0.01 level of significance with a power of 0.9. In other words, they want to be 90% sure that they can detect a significant difference if it exists.

Using the data provided in the study, the engineer can calculate the sample size needed for each type of signal. They need at least five intersections for pretimed signals, six intersections for semi-actuated signals, and four intersections for fully actuated signals to reject the null hypothesis at the desired level of significance with a power of 0.9.

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Answer:

4h-1

Step-by-step explanation:

subtracted it with a scientific calculator and that was the answer