Write the equation of a line parallel to 2x – 3y = 7 through
(6,2).​

Answer

1-right

2-not a triangle

3-acute

4-obtuse

5-right

6-obtuse

7-acute

Step-by-step explanation:

Answer:

-6\(\sqrt{7}\) /434

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

First we are going to set up our general equation (what is being asked of us). Marina bought pears, pineapples, and kiwis and spent $13.50 on them. The equation for that is

pi + pe + k = 13.5

Now we need to figure out how to eliminate most of those unknowns and put 2 of them in terms of the other 1. It looks like everything is based on the number of pineapples she bought. First it says she bought 9 more pears than pineapples, so obviously, there are more pears than pineapple, so

pe = pi + 9

And if she bought 2 fewer than kiwis thatn pears, and pears = pi + 9, then the number of kiwis she bought was

kiwis = (pi + 9) - 2 which simplifies down to pi + 7.

Now we'll put all of those into the equation:

pi + (pi + 9) + (pi + 7) = 13.5 What I have done is create an equation that is not parallel. In other words, I have the NUMBER of the kinds of fruit on one side of the equation, and the COST of the fruit on the other side, and that's not cool. We have to have EITHER a NUMBER of fruit equation OR a COST of fruit equation, but not both in the same equation. To amend that, we will figure in the cost of each of these kinds of fruit by the correcpsonding number of that kind of fruit. Pineapples cost $1.50 each, so the expression for pineapples is 1.5pi; pears cost $.50 each, so the expression for pears is.5(pi + 9); kiwis cost $.30 each, so the expression for kiwis is .3(pi + 7). NOW we can set up the equation:

1.5pi + .5(pi + 9) + .3(pi + 7) = 13.5 and simplify:

1.5pi + .5pi + 4.5 + .3pi + 2.1 = 13.5 and simplify some more by combining like terms:

2.3pi = 6.9 so

pi = 3. Ok we have 3 pineapples. Now we go back up to the expression for pears:

pe = pi + 9 so

pears = 12. Now we go back to the expression for kiwis:

k = pi + 7 so

kiwis = 10. And there you go!

Answer:

Step-by-step explanation:

The first debt that Alice would have to pay based on the Stack method would be the third debt. Option C

From the stack method, the debt that Alice would have to pay off first would be the debt that has the highest interest rate.

The amount of 150 dollars would then be added to the debt that has the second highest rate.

Hence the amount of debt that would be paid off first would be the first debt based on the stack method.

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Answer:

1. (a)  [-1, ∞)

   (b)  (-∞, -1) ∪ (1, ∞)

2. (a)  (1, 3)

    (b)  (-∞, 1) ∪ (3, ∞)

3. (a)  9.6 m and 0.4 m

   (b)  03:08 and 15:42

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Part (a)

When x < 0, the function is f(x) = x².

Since the square of any non-zero real number is always positive, the range of the function f(x) for x < 0 is (0, ∞).

When x ≥ 0, the function is f(x) = sin(x).

The minimum value of the sine function is -1 and the maximum value of the sine function is 1.  As the sine function is periodic, the function oscillates between these values.  Therefore, the range of function f(x) for x ≥ 0 is [-1, 1].

The range of function f(x) is the union of the ranges of the two separate parts of the function.  Therefore, the range of f(x) is [-1, ∞).

Part (b)

The domain of the function g(x) = ln(x² - 1) is the set of all real numbers x for which (x² - 1) is positive, since the natural logarithm function (ln) is only defined for positive input values.

Find the values of x:

\(\implies x^2-1 > 0\)

\(\implies x^2 > 1\)

\(\implies x < -1, \;\;x > 1\)

Therefore, the domain of function g(x) is (-∞, -1) ∪ (1, ∞).

Part (a)

To determine the interval where f(x) < 0, we need to find the values of x for which the quadratic is less than zero.

First, set the function equal to zero and solve for x:

\(\begin{aligned} x^2-4x+3&=0\\x^2-3x-x+3&=0\\x(x-3)-1(x-3)&=0\\(x-1)(x-3)&=0\\ \implies x&=1,\;3\end{aligned}\)

Therefore, the function is equal to zero at x = 1 and x = 3 and so the parabola crosses the x-axis at x = 1 and x = 3.

As the leading coefficient of the quadratic is positive, the parabola opens upwards. Therefore, the values of x that make the function negative are between the zeros.  So the interval where f(x) < 0 is 1 < x < 3 = (1, 3).

Part (b)
Since the square root of a negative number cannot be taken, and dividing a number by zero is undefined, function f(x) has to be positive and not equal to zero:  f(x) > 0.

As the parabola opens upwards, the values of x that make the function positive are less than the zero at x = 1 and more than the zero at x = 3.

Therefore the domain of g(x) is (-∞, 1) ∪ (3, ∞).

Part (a)

The range of a sine function is [-1, 1]. Therefore, to calculate the maximal and minimal possible water depths of the bay, substitute the maximum and minimum values of sin(t/2) into the equation:

\(\textsf{Maximum}: \quad 5+4.6(1)=9.6\; \sf m\)

\(\textsf{Maximum}: \quad 5+4.6(-1)=0.4\; \sf m\)

Part (b)

To find the times when the depth is maximal, set sin(t/2) to 1 and solve for t:

\(\implies \sin \left(\dfrac{t}{2}\right)=1\)

\(\implies \dfrac{t}{2}=\dfrac{\pi}{2}+2\pi n\)

\(\implies t=\pi+4\pi n\)

Therefore, the values of t in the interval 0 ≤ t ≤ 24 are:

Convert these values to times:

Part A: The equation that can be used to determine the dimensions, in meters, of the field is 5500 = 2x² + 10x

Part B: width is 50 meters.

The formula for calculating the area of a rectangle is expressed with the equation;

A = lw

Such that the variables are expressed as;

We then have that;

l = 2x + 10

Substitute the values

5500 = (2x + 10)(x)

expand the bracket

5500 = 2x² + 10x

2x² + 10x - 5500

x² + 5x - 2750

x² + 55x - 50x - 2750

x(x + 55) - 50(x + 55)

x = 50 meters

Length = 2(50) + 10

Length = 100 + 10 = 110 meters

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Answer:

7

Step-by-step explanation:

Answer:

To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:

EAR = (1 + r/n)^n - 1

where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.

For daily compounding, n = 365 (since there are 365 days in a year), so we have:

EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%

To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:

EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%

Therefore, the effective annual rate for hourly compounding is approximately 7.27%.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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In the picture, we see two similar triangles, this means that ther is a factor k which satisfies:

h = 6k

and

40 = 10k

Isolating k in each equation:

This means that:

Answer:

we need to to find what percentage 9 is of 90

from looking at this we can see that 90 is just 9*10

so 9% of students took a vanilla cupcake

Hope This Helps!!!

Answer: 3.5

Step-by-step explanation:

Since 10% x 10 = 100%

So we have to do 35 ÷ 10

35 ÷ 10 = 3.5

In conclusion, 10% of 35 = 3.5

Hope this helps!

The mean of the sampling distribution of sample means is 5.3, and its standard deviation is 0.186.

By dividing the sum of the provided numbers by the total number of numbers, the mean—the average of the given numbers—is determined.

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3, regardless of the sample size. This is a fundamental property of the sampling distribution of the mean.

However, if we want to be more precise, we can use the formula for the standard error of the mean (SEM) to calculate the standard deviation of the sampling distribution of sample means:

SEM = σ / √(n)

where σ is the population standard deviation, n is the sample size, and sqrt represents the square root.

In this case, σ = 1.1 and n = 35, so:

SEM = 1.1 / √(35) = 0.186

Therefore, the mean of the sampling distribution of sample means is 5.3, and its standard deviation is 0.186.

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Answer:

Simple Linear Regression Correlation

Step-by-step explanation:

When it snows normally the schools continue .But constant snowing affects the schools continuity. As more and more snow falls more schools are closed.

There may be a situation where all the schools are closed at a certain temperature.

So it is a simple linear regression correlation because in it there are two variables and one variable is dependent on the other. In this example the schools are dependent on the average snowfall.

If there's a snow blizzard or extreme weather all the schools are definitely closed .

It can be represented by a graph.

Answer:

The interest rate = 1.68%

Step-by-step explanation:

Sue invests £9000 in an account for one year.

She pays £30.24 at a rate of 20%

So 20% of the interest =£ 30.24

Let the interest be x

X0.2= 30.24

X=£ 151.2

The total interest was£ 151.2

The rate R at which generated this interest

R = (100*151.2)/(1*9000)

R= 15120/9000

R= 1.68%

The interest rate = 1.68%

To prove the identity (sec²α - 1)cos²α = sin²α, we will manipulate the left-hand side (LHS) of the equation and show that it simplifies to the right-hand side (RHS). Here's the step-by-step proof:

Starting with the LHS:

(sec²α - 1)cos²α

We know that sec²α = 1/cos²α. Substituting this into the LHS, we get:

(1/cos²α - 1)cos²α

Now, we can simplify further:

1/cos²α * cos²α - 1 * cos²α

= 1 - cos²α

Using the trigonometric identity sin²α + cos²α = 1, we can substitute 1 - cos²α as sin²α:

= sin²α

Thus, we have shown that (sec²α - 1)cos²α simplifies to sin²α, which proves the given identity.

Therefore, (sec²α - 1)cos²α = sin²α.

Account Compounding Interest after 6 years

1 quarterly

A1 = -$1798.42

2 monthly $

A2 = -$1798.01

3 daily $

A3 =  -$1797.96

1) An account with quarterly compounding: After 6 years, the formula to calculate the interest is:

Interest = Principal \(\times\)(1 + (rate / \(n))^{(n * t)}\) - Principal

Substituting the given values:

Principal = $2200

Rate = 3% = 0.03

n = 4 (quarterly compounding)

t = 6 years

Interest = $2200 \(\times\) (1 + (0.03 / \(4))^{(4 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0075)^{(24)}\) - $2200

Interest ≈ $401.58 - $2200

Interest ≈ -$1798.42 (rounded to two decimal places).

2) An account with monthly compounding: After 6 years, the formula remains the same, but the compounding frequency changes:

   Principal = $2200

   Rate = 3% = 0.03

   n = 12 (monthly compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(12))^{(12 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.0025)^{(72)}\) - $2200

Interest ≈ $401.99 - $2200

Interest ≈ -$1798.01 (rounded to two decimal places)

3) An account with daily compounding: Using the same formula with the compounding frequency:

   Principal = $2200

   Rate = 3% = 0.03

   n = 365 (daily compounding)

   t = 6 years

Interest = $2200 \(\times\)(1 + (0.03 / \(365))^{(365 \times 6)}\) - $2200

Interest = $2200 \(\times\)\((1.000082)^{(2190)}\) - $2200

Interest ≈ $402.04 - $2200

Interest ≈ -$1797.96 (rounded to two decimal places)

In all three cases, the interest earned is negative, indicating that the accounts would have lost money rather than gained interest.

This suggests that there might be an error in the calculations or the provided interest rates. It's important to verify the given information to ensure accurate calculations and resolve any discrepancies.

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Answer:

93,600

Step-by-step explanation:

4x104= 416

416x225 = 93,600

Answer: 120 yds

Step-by-step explanation:

48+30+24+18+120 yds

Answer:

cosU = \(\frac{3}{4}\)

Step-by-step explanation:

cosU = \(\frac{adjacent}{hypotenuse}\) = \(\frac{TU}{ST}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\)

Expression A decays at a rate of 5% every three months, while Expression B grows at a rate of 12% every four months  and  Expression A has an initial value of 624, while expression B has an initial value of 725 , Option B and E are the correct statements.

It is a mathematical statement tat consists of variables , constants and mathematical operators.

It is given that

The company's records show the sales of short boards decrease every three months as represented by expression A, where t is the number of years that the boards have been for sale.

The company's records show that the sales of long boards increase every four months as represented by expression B, where t is the number of years that the boards have been for sale.

\(\rm Expression\; A = 624(0.95)^{4t}\\\\Expression \; B = 725(1.12)^{3t}\)

From observing both the expression the initial value is when t = 0

when t = 0,

A = 624

B = 725

and so Expression A decays at a rate of 5% every three months, while expression B grows at a rate of 12% every four months  and  Expression A has an initial value of 624, while expression B has an initial value of 725 , Option B and E are the correct statements.

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When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

We should reject H₀   for values of | x₁| > 5,26     |x₁| > 6,12

Step-by-step explanation:

Sample mean    μ₀  =  5,7

Sample size       n₁  = 24

Sample standard deviation   s =  1

Significance level    α  = 0,05        CI = 95 %

Hypothesis criteria: Valves don´t meet the specification, which means pressure could be higher or lower than nominal

Normal Distribution where n < 30 we should use a two-tail t-student test

degree of freedom     df =  24 - 1  = 23

And with df = 23  and  α = 0,025 we find in t-tables the value for

t(c) =  - 2,0687     ( on the left tail )

Test Hypothesis:

Null Hypothesis                                       H₀            x  = μ₀

Alternative Hypothesis                           Hₐ            x  ≠ μ₀

To compute  t(s)

t(s) = ( x  -  μ₀ ) / s/√n

t(s) = ( x - 5,7 )*4,80

t(s) =  4,80*x  -  27,34

Then   for values of  t(s)   |t(s)| > 2,0687 we have to reject H₀

If we make   t(s)  =  t(c)  we find

-2,0687 = 4,8*x - 27,34

x  = ( 27,34 - 2,07 ) / 4,8      and on the other tail  x  = 6,12

x = 5,26

Therefore for values of 5,26 ( under )   and above 6,12 we shoud reject the Null hypothesis

Answer:

x < -1

Step-by-step explanation:

Let the unknown number be x

nine more than sum of eight times a number and seventeen, is expressed as;

9 >  8x + 17

Subtract 17 from both sides

9 - 17 > 8x+17-17

-8 > 8x

8x < -8

Divide both sides by 8

8x/8 < -8/8

x < -1

Hence the quotient is x < -1

Answer:

C. $755 i got it right

Step-by-step explanation:

If you make only the minimum payment each month, the total cost of the computer will be $755.00, which is $155 more than the original cost of the computer ($600).

percentage, a relative value indicating hundredth parts of any quantity.

To calculate the total cost of the computer if you make only the minimum payment each month, we need to use the simple interest formula:

A = P(1 + rt)

where A is the total amount paid, P is the principal or balance, r is the annual interest rate expressed as a decimal, and t is the time in years.

P = $600

r = 12.9% or 0.129 (annual interest rate)

t = 2 years

To find the monthly interest rate, we divide the annual interest rate by 12 (the number of months in a year):

Monthly interest rate = 0.129 / 12 = 0.01075

Now, we can use this monthly interest rate to calculate the minimum monthly payment:

Minimum monthly payment = 1% x P = 0.01 x $600 = $6

Therefore, the minimum monthly payment is $6.

To find the total cost of the computer over the 2-year period, we need to calculate the total amount paid (A) by making the minimum monthly payment each month:

A = P(1 + rt)

A = $600(1 + 0.01075 x 2 x 12)

A = $600(1 + 0.258)

A = $755.00

Therefore, if you make only the minimum payment each month, the total cost of the computer will be $755.00, which is $155 more than the original cost of the computer ($600).

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Step-by-step explanation:

The volume of a hemisphere is given by :

\(V=\dfrac{2}{3}\pi r^3\)

Taking differentiation,

\(\dfrac{dV}{dr}=2\pi r^2\)

So,

\(dV=2\pi r^2\times dr\)

Put r = 21 m and dr = 0.03 cm = 0.0003 m

\(dV=2\pi \times 21^2\times 0.0003\\\\dV=0.831\ m^3\)

Hence, this is the required solution.