could anyone give me some quick help with this?

Answer:

270m^2

Step-by-step explanation:

30m*18m/2 = 270m^2

Answer:

270

Step-by-step explanation:

Answer: y = (1/3)x-2

Step-by-step explanation:

You can rearrage the equation to:

\(3y=x-9\)

Then solve for y:

\(y=\frac{1}{3} x-3\)

We now have our slope of 1/3. We can plug in our point and slope to the equation y=mx+b to get the y-intercept:

\(-1=\frac{1}{3}(3)+b\)

\(-1=1+b\)

\(b=-2\)

Now we have our slope and y-intercept we can form the equation:

\(y=\frac{1}{3}x-2\)

The probability of randomly picking a school or library-related issue from the ballot is 9/19 or approximately 0.474 (rounded to three decimal places).

To determine the probability of a randomly picked issue being school or library related, you'll need to consider the total number of issues and the number of school and library issues combined.

There are 7 school-related issues, 10 ordinance-related issues, and 2 library-related issues, making a total of 19 issues on the ballot. To find the probability of picking a school or library issue, combine the number of school and library issues: 7 + 2 = 9.

Now, divide the number of school and library issues (9) by the total number of issues (19): 9/19.

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Answer:

Step-by-step explanation:

25/8

8x3+1=25

Using the lowest common factor of the shuttles' run times, they will depart again for the campus simultaneously at 10.25 A.M.

We can use the lowest common factor (LCM) of their run time to determine when they depart again for the campus.

The lowest common factor of 30 and 20 is 60 because both 30 and 20 can divide 60 evenly without a remainder, showing that it takes 60 minutes for the two shuttles to depart for the campus at the same time.

We can conclude that every 60 minutes or hour, the two shuttles simultaneously depart for the campus.  Every hour, the shuttle departing from Ball Hall completes 2 runs, while the shuttle departing from Lot A completes 3 runs.

Thus, using the lowest common factor, the next time both shuttles will depart for the campus at the same time is 10:25 A.M.

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Answer:

Base: \(15\), Height: \(19\)

Step-by-step explanation:

Let the base be \(b\). Then the height is \(b+4\).

By the area of a triangle theorem, we have that \(bh/2=b(b+4)/2=142.5\).

Multiplying by \(2\) and expanding gives \(b^2+4b=285\), so \(b^2+4b-285=0\). We see that this quadratic factors into \((b-15)(b+19)=0\). Because the base is a side length and must be positive, we have that the base is \(15\).

The height is then \(15+4=19\).

Answer:

1.25 gallons per second

Step-by-step explanation:

To find out the amount of water per second, we must divide the gallons by the time.

50/40 = 1.25

Answer: 1.25

Step-by-step explanation: If they use 50 gallons of water every 40 seconds you just divide 50 and 40 which equals 1.25

n⁴ - 2n³ - 23n² + 24n + 144 is the standard form of given zeroes.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.

                              A linear equation is an equation that raises a variable to the first power. ax+b = 0 is an example of a 1 variable. x is a variable and a and b are real numbers.  

Roots : -3(mult . 2), 4(mult.2)

the function is given as

     f(n) = (n + 3)² (n - 4)²

         = (n + 3) (n + 3 ) ( n - 4 ) ( n - 4)

        = (n² + 6n + 9) (n² - 8n + 16 )

        = n⁴ - 8n³ + 16n² + 6n³ - 48n² + 96n + 9n² - 72n + 1

collecting like term,

    f(n) = n⁴ - 2n³ - 23n² + 24n + 144

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the probability of event B happening is 0.50 or 50%. This means that the occurrence of event A has no impact on the likelihood of event B happening, and vice versa.

How to solve the question?

If A and B are independent events, then the occurrence of A does not affect the probability of B happening. Mathematically, this can be written as P(B|A) = P(B), where P(B|A) represents the conditional probability of B given that A has occurred.

Using the formula for the probability of the intersection of two events, we have:

P(A AND B) = P(A) * P(B|A)

Since A and B are independent, we can substitute P(B|A) with P(B):

0.30 = 0.60 * P(B)

Solving for P(B), we get:

P(B) = 0.30 / 0.60 = 0.50

Therefore, the probability of event B happening is 0.50 or 50%. This means that the occurrence of event A has no impact on the likelihood of event B happening, and vice versa. It's important to note that independence is a key assumption when using the multiplication rule to calculate the probability of the intersection of two events. If the events are not independent, this rule cannot be used, and other methods such as the addition rule or Bayes' theorem must be used to calculate probabilities.

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Answer:

28 percent............

The simplification of the expression, ∛8x⁴y⁸ / 125 is \(\frac{2\sqrt[3]{x^{4}y^{8} } }{5}\).

The exponential expression can be solved as follows:

Therefore, let's simplify the expression.

To simplify the expression we have to deal with the exponential by applying it laws and also the cube root.

∛8x⁴y⁸ / 125

let's solve them individually,

125 = 5³ = 5 × 5 × 5

8 = 2³ = 2 × 2 × 2

Therefore,

∛8x⁴y⁸ / 125 = \(\frac{2\sqrt[3]{x^{4}y^{8} } }{5}\)

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Step-by-step explanation:

Types of fees and charges

Monthly account keeping or service fee. The fee you pay for an organisation to manage your bank account. ...

Internet banking fee. ...

EFTPOS transaction fee. ...

ATM transaction fee. ...

Non-bank or foreign ATM fee. ...

Telephone banking transaction fee. ...

Branch withdrawal fee. ...

Cheque withdrawal fee.

The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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Answer:

  5.80 hours

Step-by-step explanation:

The temperature difference is decaying from (77 -10) = 67 to (35 -10) = 25. The time required for that to happen satisfies ...

  25 = 67e^(-kt)

  ln(25/67) = -kt . . . . . divide by 67, take natural logs

  t = ln(25/67)/(-0.17) ≈ 5.80 . . . hours

Answer:

0.75

Step-by-step explanation:

Answer:

$1.33 per ticket cost

Step-by-step explanation:

5 / $3.75 = $1.33 per 1 ticket cost

Answer:

Your solution is (3/2, -7/2)

Step-by-step explanation:

y = x - 5

y = -3x + 1

First, see that these two equations equal y. This means you can set them equal to each other.

x - 5 = -3x + 1

Combine like terms.

[add 3x to both sides]

4x -5 = 1

[add 5 to both sides]

4x = 6

Isolate x further by dividing both sides by 4.

x = 6/4

Simplify the fraction.

x = 3/2

Now that we know x, plug its value (3/2) back into one of the original equations to find y.

y = (3/2) - 5

Simplify by subtracting.

[convert 5 to have a denominator of 2]

y = 3/2 - 10/2

y = -7/2

Your solution is (3/2, -7/2)

Check this by plugging these values into the equation you have not yet checked.

-7/2 = -3(3/2) + 1

Simplify.

[multiply]

-7/2 = -9/2 + 1

[convert 1 to have a denominator of 2]

-7/2 = -9/2 + 2/2

[add]

-7/2 = -7/2

This equation is true; therefore your solution is correct.

Hope this helps!

Answer:

A.

\( x = \frac{7\sqrt{6}{3} \)

\( y = \frac{7\sqrt{6}}{3} \)

Step-by-step explanation:

Reference angle = 60°

Opposite = \( \frac{7\sqrt{2}}{2} \)

Hypotenuse = x

Adjacent = y

✔️To find x, apply the trigonometric function SOH:

Sin 60° = Opp/Hyp

\( sin 60° = \frac{\frac{7\sqrt{2}}{2}}{x} \)

\( \frac{\sqrt{3}}{2} = \frac{\frac{7\sqrt{2}}{2}}{x} \) (sin 60 = √3/2)

\( \frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2}*\frac{1}{x} \)

\( \frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2x} \)

Cross multiply

\( \sqrt{3}*2x = 7\sqrt{2}*2 \)

\( 2\sqrt{3}*x = 14\sqrt{2} \)

Divide both sides by 2

\( \sqrt{3}*x = 7\sqrt{2} \)

Divide both sides by √3

\( x = \frac{7\sqrt{2}}{\sqrt{3}} \)

Rationalize

\( x = \frac{7\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}} \)

\( x = \frac{7\sqrt{6}{3} \)

✔️To find y, apply the trigonometric function TOA:

Tan 60° = Opp/Adjacent

\( Tan 60° = \frac{\frac{7\sqrt{2}}{2}}{y} \)

\( \sqrt{3} = \frac{\frac{7\sqrt{2}}{2}}{y} \) (tan 60 = √3)

\( \sqrt{3} = \frac{7\sqrt{2}}{2}*\frac{1}{y} \)

\( \sqrt{3} = \frac{7\sqrt{2}}{2y} \)

Cross multiply

\( \sqrt{3}*2y = 7\sqrt{2} \)

\( 2\sqrt{3}*y = 7\sqrt{2} \)

Divide both sides by √3

\( y = \frac{7\sqrt{2}}{\sqrt{3}} \)

Rationalize

\( y = \frac{7\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}} \)

\( y = \frac{7\sqrt{6}}{3} \)

5/8 of the total has been sold, so we just do 64*5/8=40 houses that had been sold this year. Hope this helped!

Answer:

P (X | CI) = 0.7313

Step-by-step explanation:

X = event of getting a job

CI = Campus interview

P (X | CI) = p ( CI ∩ X) / P ( CI ) = P( CI | X)P(X) / P( CI | X)P(X) + P( CI | X')P(X')

P (X | CI) = 0.93 * 0.17 / 0.93 * 0.17 + 0.07 * (1 - 0.17)

P (X | CI) = 0.93 * 0.17 / 0.93 * 0.17 + 0.07 * 0.83

P (X | CI) = 0.1581 / 0.1581 + 0.0581

P (X | CI) = 0.1581 / 0.2162

P (X | CI) = 0.73126735

P (X | CI) = 0.7313

Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = \(\frac{1-7}{2-0}\) = \(\frac{-6}{2}\) = - 3

the line crosses the y- axis at (0, 7 ) ⇒ c = 7

y = - 3x + 7 ← equation of line

The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

The linear graph represents the given parameter

For the graph, we have the points

(0, 7) and (25, 0)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 7

Using the point (2.5, 0) on y = mx + 7, we have

m(2.5) + 7 = 0

2.5m + 7 = 0

Evaluate

m = -2.8

So, we have

y = -2.8x + 7

Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

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The pairs of complementary angles are:

1) 36° and 54°

4) 23° and 67°

5) 5° and 85°

Two angles A and B are complementary if the sum of the measures is equal to 90°.

For the given options, the 3 correct ones are:

1) 36° and 54°

The sum gives:

36° + 54° = 90°

So these are complementary.

4) 23° + 67° = 90°

These are also complementary.

5) 5° + 85° = 90°

These are also complementary.

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The surface area of the solid is 281 ft².

Given that, a solid figure made of a rectangular prism and a square pyramid,

We need to find its surface area,

To find the same, we will find the lateral surface area of square pyramid, and total surface area of rectangular prism,

So,

Surface area = 2×side×slant height + 2(length·width+width·height+height·length)-base area of the square pyramid,

= 2×5×5 + 2(4·12+12·5+4·5)-5²

= 50+256-25

= 281 ft²

Hence the surface area of the solid is 281 ft².

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Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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Have a GREAT day!!!

Answer:

The answer is

(f.g)(x)= x^5-2x^3+2x^2-8x+4

Step-by-step explanation:

Hope this helps:)

I guess the chef is making the mixture for the sheriff... Let x be the amount of dressing with 5% vinegar that is required, and y the amount of 15% vinegar dressing (both amounts in mL).

The sheriff wants 390 mL of the mixed dressing, so that

x + y = 390

x mL of the 5% dressing contains 0.05x mL of vinegar, while y mL of the 15% dressing contains 0.15y mL of vinegar. The resulting mixture should have a concentration of 9% vinegar, so that it contains 0.09 (390 mL) = 35.1 mL of vinegar. This means

0.05x + 0.15y = 35.1

Solve for x and y :

y = 390 - x

0.05x + 0.15 (390 - x) = 35.1

0.05x + 58.5 - 0.15x = 35.1

23.4 = 0.10x

x = 234

y = 156

If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:

Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).

Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).

Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).

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Answer:

(-7, -46)

Step-by-step explanation:

Based on the information, the confidence interval doesn't contradict the claim.

Based on the information, the following vs be deduced:

Mean = 2.87

Sample size = 35

Population standard deviation = 1.36

Critical value = 2.576

Standard error = Standard deviation / ✓Sample size

= 1.36 / ✓35

= 0.2299

The margin of error will be:

= 2.576 × 0.2299

= 0.5922

The 99% confidence interval will be 2.5678 < U < 3.7522

In conclusion, the confidence interval doesn't contradict the claim. Hence, the publication claim of 2.87kg is inside the 99% confidence interval.

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Answer and Step-by-step explanation:

Given Asin(wt + phi), we know that sin (A + B) = sinAcosB + sinBcosA. This means:

Asin(wt + phi) = Asin(wt)cos(phi) + Asin(phi)cos(wt).

Let Acos(phi) = c2 and Asin(phi) = c1 we have:

Asin(wt + phi) = c2sin(wt) + c1cos(wt)

Answer:

Step-by-step explanation:

In order to prove that Asin(ω⁢t+ϕ) equals c2sin ω⁢t+ c1cos ω⁢t we need use the sin (A+B) sum identity.

The sin sum identity is sin(A+B)= sinA × cosB + cosB × sinA

Now lets plug in our info.

Asin(ω⁢t+ϕ)= (sin wt × cosϕ) + (cos wt × sinϕ)

We know that Asin= c1 and Acos= c2.

Once we input c1 and c2 and solve, our end result becomes c2sin(wt)+c1cos(wt)​