use the graphing tool to solve the system

Answer:3rd one

Step-by-step explanation:DO THIS CAREFULLY

The angle of elevation that the instruments have to record to be at the correct height is given as 79°

We have 2x + 70 = 180

We have to find the value of x

2x = 110

x = 55

y/sin x = 225/sin70

This is the use of sine rule

From here we would have

y = 225(sinx/sin70)

Remember x = 55

y =  225(sin55/sin70)

y = 196.1378

tanθ = 1000/y

tan θ = 1000/196.1378

tanθ = 5.098

θ = tan⁻¹5.098

= 78.90°

Hence the conclusion is that the angle of elevation has to be 78.9 degrees for it to be at the correct height.

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A simple random sample of 64 kitchen toasters should be taken to determine the mean operational lifetime with a margin of error of 8 hours and a 95% confidence level.

A confidence interval estimates the range within which a population parameter (in this case, the mean operational lifetime) is likely to lie, based on a sample statistic. The margin of error is the maximum amount by which the sample statistic might deviate from the true population value.

The sample size (n) can be calculated using the formula: n = (Z * σ / \(E)^2\) where Z is the Z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the margin of error. The Z-score is a measure of how many standard deviations a data point is from the mean of a distribution. It can be looked up in a Z-score table, or calculated using software, for a specific confidence level. Commonly used confidence levels include 90%, 95%, and 99%.

To calculate the sample size needed for a confidence interval with a margin of error of 8, we need to use the formula:

n = (\((z-value)^2\) * σ\(^2)\) / (\(E^2\))

Where:
- n is the sample size
- z-value is the critical value for the desired confidence level (let's assume a 95% confidence level, so z-value is 1.96)
- σ is the population standard deviation (given as )
- E is the margin of error (given as 8)

Plugging in the values, we get:

n = \(((1.96)^2 * ^2) / (8^2)\)
n = \((3.8416 * ^2) / 64\)
n = 0.2373 *

Rounding up to the nearest whole number, the sample size needed is:
n = 64

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We must solve for x using the addition principle, the equation is as follows

In conclusion, the answer is x = -9

John Barker's repair shop in Ontario is required to calculate the HST payable or refund for the first reporting period. The HST rate is 13% and the amount before HST sales is $150,000. The total HST collected from sales is $19,500 and the total ITCs are $19,790. The net HST payable/refund is $19,500 - $19,790 and the correct option is d) A refund of $5,980.

Given the following information for John Barker's repair shop in Ontario, we are required to calculate the HST payable or refund for the first reporting period. The HST rate for Ontario is 13%.Amount Before HST Sales $150,000 Equipment purchased $96,000 Supplies purchased $83,000 Wages paid $19,000 Rent paid $17,000Let's calculate the total HST collected from sales:

Total HST collected from Sales= HST Rate x Amount before HST Sales

Total HST collected from Sales= 13% x $150,000

Total HST collected from Sales= $19,500

Let's calculate the total ITCs for John Barker's repair shop:Input tax credits (ITCs) are the HST that a business pays on purchases made for the business. ITCs reduce the amount of HST payable. ITCs = (HST paid on eligible business purchases) - (HST paid on non-eligible business purchases)For John Barker's repair shop, all purchases are for business purposes. Hence, the ITCs are the total HST paid on purchases.

Total HST paid on purchases= HST rate x (equipment purchased + supplies purchased)

Total HST paid on purchases= 13% x ($96,000 + $83,000)

Total HST paid on purchases= $19,790

Let's calculate the net HST payable or refund:

Net HST payable/refund = Total HST collected from sales - Total ITCs

Net HST payable/refund = $19,500 - $19,790Net HST payable/refund

= -$290 Since the Net HST payable/refund is negative,

it implies that John Barker's repair shop is eligible for an HST refund. Hence, the correct option is d) A refund of $5,980.

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Answer:

2 hours and 5 minutes or 125 minutes

Step-by-step explanation:

25minutes per class

5 classes

25 * 5 = 125 minutes = 2 hours and 5 minutes

The function shown below is decreasing on the interval -7 < x < -4.The graph of the function is shown below.

We can see from the graph that the function is decreasing between the x-values -7 and -4.

On the interval -7 < x < -4, as x increases, the value of the function decreases.

Therefore, we can conclude that the interval for which the function shown below is decreasing is -7 < x < -4.

This is because the function is decreasing between these values of x.

Any value of x greater than -4 and less than -7 will result in an increase in the value of the function.

The graph of the function is shown below.

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The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

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Answer:

Your answer is A, 3x - 2x.

Step-by-step explanation:

Triple a number means to multiply it by 3.

Double a number means to multiply it by 2.

Difference means to subtract.

Hope this helps!

Answer:cim not sure tho

Step-by-step explanation:

Answer:

\(g(x) = -3x\)

Step-by-step explanation:

Given

\(f(x) = 3x\)

Required

Reflect over \(y = 0\)

This means that we reflect over the x-axis

And the rule of reflection is:

\((x,y) \to (x,-y)\)

Hence:

\(f(x) = 3x\)

Will become:

\(g(x) = -f(x)\)

So, we have:

\(g(x) = -3x\)

Answer:

Where's the grid?

Step-by-step explanation:

The area of the given shape is 78.5 unit²

Given,

The shape is 1/4th part of circle.

The radius is given as 10 units

We have to find the area of the shape.

Here,

The area of a circle is pi times the radius squared (A = π r²).

Area of circle = π × r²

Then

Area of 1/4th part of circle = π × r² / 4

That is,

Area of 1/4th part of circle = 3.14 × 10² / 4

Area of 1/4th part of circle  = 314 / 4

Area of 1/4th part of circle = 78.5 unit²

That is,

The area of the given shape is 78.5 unit²

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Answer:

3/25

Step-by-step explanation:

0.12 multiplied by 100 equals 12

which means 12/100 is 0.12

now simplify

6/50

3/25

Answer:

I didn't Sanderstead sorry

Answer:

150 ft

Step-by-step explanation:

Answer:

  D) A″ (3, 2), B″ (3, 0), C″ (−1, 0), D″ (−1, 2)

Step-by-step explanation:

You want the coordinates of points A", B", C", D" after A(-5, 1), B(-5, 3), C(-1, 3), and D(-1, 1) have been translated by <2, -3> and reflected across the origin.

The translation transformation is given in the problem statement:

  (x, y) ⇒ (x +2, y -3)

The reflection transformation is ...

  (x, y) ⇒ (-x, -y) . . . . . . . reflection across the origin

The composition of these transformations is ...

  (x, y) ⇒ (-(x +2), -(y -3))

  (x, y) ⇒ (-x-2, -y+3)

Using this transformation on the given points, we find ...

  A(-5, 1) ⇒ A"(-(-5)-2, -1+3) = A"(3, 2)

  B(-5, 3) ⇒ B"(-(-5)-2, -3+3) = B"(3, 0)

  C(-1, 3) ⇒ C"(-(-1)-2, -3+3) = C"(-1, 0)

  D(-1, 1) ⇒ D"(-(-1)-2, -1+3) = D"(-1, 2)

Please find attached a diagram with the completed table

In order to determine which number is  a counterexample of the conjecture, we are to divide each number by 2 and 4. A counterexample of this conjecture would only be divisible by either 2 or 4 but not both of them

Dividing the numbers by 2

12 / 2 = 6

19 / 2 = 9.5

22 / 2 = 11

28 / 2 = 14

30 / 2 = 15

Dividing the numbers by 4

12 / 4 = 3

19 / 4 = 4.75

22 / 4 = 5.5

28 / 4 = 7

30 / 4 = 7.5

22 and 30 are counterexamples because they are divisible by 2 but not by 4

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The inequality to represent the acceptable length of the lumber is 11 ≥ x ≤ 61.

The minimum and maximum length is 11 and 61 inches.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

The minimum length will be:

= 36 - 25

= 11 inches

The maximum length will be:

= 36 + 25

= 61 inches

Therefore, the inequality is 11 ≥ x ≤ 61.

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Answer:

x < 57

Step-by-step explanation:

Answer:

200+64=264

Step-by-step explanation

You mulitply the 2 figures i.e 8x5x5 and 8x8x1 to find the volume of each shape then simply add and you get 264.

Answer:

264 is the correct answer hope this helps you :)

Step-by-step explanation:

The function is \(e^{(x^3)}\) whose Maclaurin expansion is 1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

The Maclaurin series of a given function is represented as a sum of terms with increasing powers of x and decreasing factorials. The Maclaurin series you provided is:

1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

This series can be rewritten as:

∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

This expansion resembles the Maclaurin series for \(e^x\), which is:

\(e^x\) = ∑ \(x^n\)/n! for n=0 to infinity.

However, in the given series, the powers of x are in multiples of 3. To adjust the standard exponential function to match the provided series, you can use the substitution \(x^3\) = u:

\(e^u\) = ∑ \(u^n\)/n! for n=0 to infinity.

Now, substitute \(x^3\) back for u:

\(e^{(x^3)}\) = ∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

Therefore, the function whose Maclaurin expansion matches the given series is f(x) = \(e^{(x^3)}\).

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The possible values that a correlation coefficient, r, can take are bounded between -1 and +1, where the correlation coefficient (r) is a statistical measure that quantifies the degree and direction of the linear relationship between two variables.

It ranges from -1 to +1, where a value of -1 represents a perfect negative correlation, a value of 0 represents no linear correlation, and a value of +1 represents a perfect positive correlation.

The magnitude of the correlation coefficient indicates the strength of the relationship between the two variables. It is a numerical value that ranges from -1 to +1. The value of r indicates the degree of association between two variables.

A positive value of r indicates a positive correlation, meaning that as one variable increases, the other variable tends to increase as well. A negative value of r indicates a negative correlation, meaning that as one variable increases, the other variable tends to decrease.

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Of the four different sets provided along with the question statement, option (B) {(1, -4), (5, 0), (5, -9)} is not a function.

As per the question statement, we are provided with 4 different set of numbers, as

A. {(3, 2), (-4, 1), (5, -9)}

B. {(1, -4), (5, 0), (5, -9)}

C. {(1, -4), (0, 5), (-9, 5)}

D. {(1, -4), (5, 0), (5, -9)}

We are required to determine the set which does not belong to a function from the above mentioned options.

To solve this question, we need to know that every input to a function has a distinct output, i.e., the same input cannot have two different outputs, or two different outputs cannot be result of one input. Also, we need to know that the corresponding inputs and outputs of a function are represented in a set form as {(i₁, o₁), (i₂, o₂), (i₃, o₃), ...], where "iₙ"  

[n = 0, 1, 2, 3, ...] denotes individual input values to a function, and "oₙ"

[n = 0, 1, 2, 3, ...] denotes individual output values to the same.

In Option (B), we can see that, (i₂ = i₃ = 5), while (o₂ = 0) and (o₃ = -9), i.e.,

Same inputs producing different output values, which is impossible in the case of a function.

Hence, {(1, -4), (5, 0), (5, -9)} is not a function.

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Answer:1. true and 2.true

Step-by-step explanation:

Answer:

y= 1/2x + -3

Step-by-step explanation:

it starts at -3, and climbs by 1/2 points every time. (remember, 1/2 can be read as rise/run. Rise one, run 2)

The mean, variance, and standard deviation for the number who got their flu shots are 130, 45.5, and 6.74, respectively.

Given that the probability of adults aged 70 and over who got their flu shot is 65%, and the sample size is 200. We can consider this situation as a binomial distribution with parameters n = 200 and p = 0.65.

The mean of the binomial distribution is given by:

μ = np = 200 × 0.65 = 130

The variance of the binomial distribution is given by:

σ^2 = np(1 - p) = 200 × 0.65 × (1 - 0.65) = 45.5

The standard deviation of the binomial distribution is the square root of the variance:

σ = √45.5 = 6.74

Therefore, the mean, variance, and standard deviation for the number who got their flu shots are 130, 45.5, and 6.74, respectively.

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From the figure , and by using congruent complements theorem, the angle that is congruent to angle4 is (a) angle1  .

The "Congruent Complements Theorem" states that if two angles are complementary to same angle, then they are congruent. In other words, if two angles add up to 90 degrees, and they both complement the same third angle, then they are equal in measure.

The ∠4 and ∠5 are the complements and ∠1 and ∠5 are complements.

Which proves that :  ∠1 and ∠4 are complimentary to the same angle that is ∠5.

Therefore, the ∠ 1 is congruent to angle 4 .

The given question is incomplete , the complete question is

From the figure below , the angle 4 and angle 5 are complements and angle 1 and angle 5 are complements , By using the congruent complements theorem, which angle is congruent to angle4 ?

(a) angle1

(b) angle2

(c) angle3

(d) angle5

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Answer:

Step-by-step explanation:

The Probability of Landing a heads is (1/2)

Now, to find the probability of landing it five times in a row, it is

1/2 x 1/2 x 1/2 x 1/2 x 1/2

( 1/2 is multiplied to the number of times to get a head )

The final answer will be,

Probability of landing heads 5 times in a row = 1/32