7. The table shows the linear relationship between the total amount Mrs. Jacobs will be



charged for a skating party and the number of children attending.




Which equation best represents y, the total amount in dollars Mrs. Jacobs will be



charged for



x number of children attending the skating party?

You want all of the answers or just one?

Answer:

Step-by-step explanation:

opposite sides of a parallelogram are equal . So,

NM = OL

2x + 5 = x + 10

2x - x = 10 - 5

x = 5

substitute the value of x

NM = 2x + 5

=2*5 + 5

=15

for NO also substitute 5 inplace of x

The main answer, incorporating the continuity correction, is P(X < 8.5), where X represents a random variable.

To calculate the probability of X being fewer than 8 (excluding 8) with continuity correction, we can use the normal approximation to the binomial distribution.

Assuming X follows a binomial distribution, we can approximate it with a normal distribution by adjusting the boundaries of the interval. In this case, since we want fewer than 8 (excluding 8), we use the continuity correction and consider the interval as (X < 8.5).

We can then calculate the probability using the cumulative distribution function (CDF) of the normal distribution for X = 8.5. The resulting probability represents the likelihood of observing fewer than 8 (excluding 8) occurrences.

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Answer:

Step-by-step explanation:

are the what???

The semimajor axis of Halley's Comet's orbit is approximately 17.91 AU. To find the semimajor axis of Halley's Comet's orbit, we can use Kepler's third law, which relates the orbital period (T) and the semimajor axis (a) of an object in an elliptical orbit:

T^2 = 4π^2a^3/GM,

where T is the orbital period, G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2), and M is the mass of the central body (in this case, the Sun).

First, we need to convert the orbital period from years to seconds:

T = 76 years = 76 × 365.25 days × 24 hours × 60 minutes × 60 seconds = 2.399 × 10^9 seconds.

Next, we can rearrange the equation to solve for the semimajor axis (a):

a = (T^2 * GM / (4π^2))^(1/3).

The mass of the Sun, M, is approximately 1.989 × 10^30 kg.

Plugging in the values, we have:

a = (2.399 × 10^9 seconds)^2 * (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (1.989 × 10^30 kg) / (4π^2)^(1/3).

Calculating this expression, we find:

a ≈ 17.91 astronomical units (AU).

Therefore, the semimajor axis of Halley's Comet's orbit is approximately 17.91 AU.

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Answer:

Both Cos^2(theta)

Step-by-step explanation:

Your teacher would likely want you to refer to the Reciprocal Identities and Pythagorean Identities.

Convert csc(theta) to = 1/ sin(theta)

\(sin(\alpha )*csc(\alpha ) - sin^2(\alpha )\\\\sin(\alpha )*\frac{1}{sin(\alpha )} - sin^2(\alpha )\\\\1-sin^2(\alpha )\\\\cos^2(\alpha )\)

Answer:

C is the correct one

Step-by-step explanation:

I’ve done it before

Answer:

5310

Step-by-step explanation:

6% of 4500=270

270x3years=810

4500+810=5310

Lara will be paying the total amount is $5310

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

Given that, Lara borrowed $4500 for some home repairs. She will be paying 6% in simple interest over the next three years.

We need to find the total amount she will be paying on the loan,

So, the formula for simple interest is - SI = PRT / 100

P = principal, r = rate and t = time

Therefore,

SI = 4500 x 6 x 3 / 100

= 45 x 18 = 810

The interest = $810

She will pay = interest + principal = 810 + 4500 = $5310

Hence, Lara will be paying the total amount is $5310

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Answer:

Step-by-step explanation: 3√2

The height of the kite is approximately 27.3 feet.

In this problem, we are given the length of the released string and the angle it makes with the ground. We need to find the height of the kite above the ground. We can solve this problem by using the tangent function in trigonometry.The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side.

In this case, the height of the kite is opposite to the angle, and the released string is adjacent to the angle. Therefore, we can set up a proportion using the tangent function and solve for the height of the kite.

The formula for the tangent function is: tan(θ) = opposite / adjacentIn our problem, the angle θ between the kite's string and the ground is 36°.

The length of the released string is 40 feet. Therefore, we can write:tan(36°) = height / 40 feetWe need to solve for the height of the kite, which is the unknown variable.

Rearranging the formula gives us:height = 40 feet × tan(36°).Using a calculator, we can evaluate tan(36°) to be approximately 0.7265.
Plugging in the values to the formula gives us:height = 40 feet × 0.7265height ≈ 29.06 feetRounding this answer to the nearest tenth gives us:height ≈ 27.3 feet.

Therefore, the height of the kite is approximately 27.3 feet.

The height of the kite can be found using the tangent function in trigonometry. We set up a proportion between the height of the kite and the length of the released string, with the angle between the kite's string and the ground being the included angle. We solved for the height of the kite by rearranging the formula and plugging in the values. The height of the kite was found to be approximately 27.3 feet.

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Answer:

I think it's 336 I'm not entirely sure though

Answer:

first it's adding 4 then it starts adding 8

Step-by-step explanation:

Answer:

If your data represents the following X, Y coordinates (11, 2), (15, 10), and (19, 18) then the slope can be calculate

X = 11 15 19

Y = 2 10 18

m = (y2 -y1)/(x2 - x1)

m = (10 - 2)/(15 - 11)

M = 8/4 = 2

I hope you find this useful.

If your data represents the following X, Y coordinates (11, 2), (15, 10), and (19, 18) then the slope can be calculate

X = 11 15 19

Y = 2 10 18

m = (y2 -y1)/(x2 - x1)

m = (10 - 2)/(15 - 11)

M = 8/4 = 2

I hope you find this useful.

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

Answer:

\( m\angle 2 = 88\degree - m\angle 1 \)

Step-by-step explanation:

\( m\angle 1 + m\angle 2 = m\angle WUV\)

\( m\angle 2 = m\angle WUV- m\angle 1 \)

\( m\angle 2 = 88\degree - m\angle 1 \)

Answer:

2 units right

Step-by-step explanation:

Answer:

It would have been translated down 2.

Step-by-step explanation:

If only the y-intercept changed. The intercept was only decreased by 2. The y axis goes up and down, so down two.

The only solution to the equation \(\(c_1y_1 + c_2y_2 = 0\)\) trivial solution\(\(c_1 = c_2 = 0\)\). The vanishing Wronskian at x = 0 implies there is no differential equation of specified form with \(\(y_1\)\) and \(\(y_2\)\) as solutions.

To show that the functions \((y_1 = d\sin(x^2)\)\) and \(\(y_2 = d\cos(x^2)\)\) are linearly independent, we need to demonstrate that no non-trivial linear combination of them can equal zero for all values of x.

Suppose there exist constants \(\(c_1\)\) and \(\(c_2\)\) such that \(\(c_1y_1 + c_2y_2 = 0\)\) for all x. Then we have:

\(\(c_1d\sin(x^2) + c_2d\cos(x^2) = 0\)\)

Dividing both sides by \(d\), we get:

\(\(c_1\sin(x^2) + c_2\cos(x^2) = 0\)\)

This equation must hold for all values of \(x\). Let's evaluate it at \(x = 0\):

\(\(c_1\sin(0^2) + c_2\cos(0^2) = c_2 = 0\)\)

Since \(c_2\) is zero, the equation becomes:

\(\(c_1\sin(x^2) = 0\)\)

This equation holds for all \(x\) if and only if \(c_1 = 0\) as well. Therefore, the only solution to the equation \(\(c_1y_1 + c_2y_2 = 0\)\) is the trivial solution with \(c_1 = c_2 = 0\). Hence, \(y_1\) and \(y_2\) are linearly independent.

Next, we need to calculate the Wronskian of \(y_1\) and \(y_2\) to determine if it vanishes at \(x = 0\). The Wronskian of two functions \(f(x)\) and \(g(x)\) is given by:

\(W(f, g) = f(x)g'(x) - f'(x)g(x)\)

For \(y_1 = d\sin(x^2)\), we have:

\(y_1' = d\cos(x^2)\)

For \(y_2 = d\cos(x^2)\), we have:

\(y_2' = -d\sin(x^2)\)

Now, let's calculate the Wronskian of \(y_1\) and \(y_2\):

\(W(y_1, y_2) = y_1y_2' - y_1'y_2\)

Substituting the values, we get:

\(W(y_1, y_2) = d\sin(x^2)(-d\sin(x^2)) - (d\cos(x^2))(d\cos(x^2))\)

\(W(y_1, y_2) = -d^2\sin^2(x^2) - d^2\cos^2(x^2)\)

Now, let's evaluate the Wronskian at \(x = 0\):

\(W(y_1, y_2) = -d^2\sin^2(0^2) - d^2\cos^2(0^2) = 0\)

We see that the Wronskian vanishes at \(x = 0\).

The fact that the Wronskian vanishes at \(x = 0\) implies that the functions \(y_1\) and \(y_2\) are linearly dependent in some neighborhood of \(x = 0\). This means that there cannot exist a differential equation of the form \(y'' + p(x)

)y' + q(x)y = 0\) (where \(p(x)\) and \(q(x)\) are continuous functions) with both \(y_1\) and \(y_2\) as solutions. If such an equation existed, the functions would be linearly independent everywhere, and the Wronskian would not vanish.

Therefore, the vanishing Wronskian at \(x = 0\) implies that there is no differential equation of the specified form with \(y_1\) and \(y_2\) as solutions.

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From the calculation, all three inequalities are satisfied, which means that the given measurements produce one triangle.

To determine whether the given measurements produce one triangle, two triangles, or no triangle at all, we can use the Law of Sines and the Triangle Inequality Theorem.

Given:

a = 10

b = 13.6

A = 33°

Determine angle B:

Angle B can be found using the equation: B = 180° - A - C, where C is the remaining angle of the triangle.

B = 180° - 33° - C

B = 147° - C

Apply the Law of Sines:

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

a/sin(A) = b/sin(B) = c/sin(C)

We can rearrange the equation to solve for side c:

c = (a * sin(C)) / sin(A)

Substituting the given values:

c = (10 * sin(C)) / sin(33°)

Determine angle C:

We can use the equation: C = arcsin((c * sin(A)) / a)

C = arcsin((c * sin(33°)) / 10)

Apply the Triangle Inequality Theorem:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

In this case, we need to check if a + b > c, b + c > a, and c + a > b.

If all three inequalities are satisfied, it means that the measurements produce one triangle. If one of the inequalities is not satisfied, it means no triangle can be formed.

Now, let's perform the calculations:

B = 147° - C (from step 1)

c = (10 * sin(C)) / sin(33°) (from step 2)

C = arcsin((c * sin(33°)) / 10) (from step 3)

Using a calculator, we find that C ≈ 34.65° and c ≈ 6.16.

Now, let's check the Triangle Inequality Theorem:

a + b > c:

10 + 13.6 > 6.16

23.6 > 6.16 (True)

b + c > a:

13.6 + 6.16 > 10

19.76 > 10 (True)

c + a > b:

6.16 + 10 > 13.6

16.16 > 13.6 (True)

All three inequalities are satisfied, which means that the given measurements produce one triangle.

In summary, with the given measurements of a = 10, b = 13.6, and A = 33°, we can determine that one triangle can be formed. The measures of the angles are approximately A = 33°, B ≈ 147° - C, and C ≈ 34.65°, and the lengths of the sides are approximately a = 10, b = 13.6, and c ≈ 6.16.

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19)

The given system of equations is,

The above system of equations can be written in matrix form as,

Here,

Therefore, equation (1) can be written as,

Therefore,

Now, we need to calculate the inverse of A.

(Note:

Let a 2x2 matrix P is of the form given below.

The inverse of the matrix P is,

)

Similar to the inverse matrix of 2x2 matrix P, the inverse matrix of A can be written as,

Now, put the values in equation (2) to find the solution to the system of equations.

Therefore, the solution to the system of equations using inverse matrix is x=2 and y=-1.

Answer: 2 one number 2

Step-by-step explanation:

It's is number 2

The required solution of the quadratic equation  (4y - 3)² = 72 is y = 3 ± 6√2/4. Option A is correct.

What is simplification?

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
Given expression, (4y - 3)² = 72

Simplifying the above expression:
(4y - 3)² = 72

4y - 3 = ±√72
4y - 3 = ±6√2
y = 3 ± 6√2/4

Thus, the required solution of the quadratic equation  (4y - 3)² = 72 is y = 3 ± 6√2/4. Option A is correct.

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The ending inventory amount is p68,000: (200 x 65) + (300 x 68) + (150 x 70) - (500 x 68) = 68,000.

1. Calculate the total cost of the beginning inventory: 200 units x p65 = p13,000

2. Calculate the total cost of the first purchase: 300 units x p68 = p20,400

3. Calculate the total cost of the second purchase: 150 units x p70 = p10,500

4. Calculate the total cost of the units sold: 500 units x p68 = p34,000

5. Calculate the total cost of the ending inventory amount : (13,000 + 20,400 + 10,500) - 34,000 = p68,000

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Answer:

there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

Step-by-step explanation:

To choose three different members from the club to be president, vice president, and treasurer, you can follow these steps:

Step 1: Calculate the number of ways to choose the president:

Since there are 15 club members in total, the number of ways to choose the president is 15.

Step 2: Calculate the number of ways to choose the vice president:

After selecting the president, there are 14 remaining members. The number of ways to choose the vice president from these 14 members is 14.

Step 3: Calculate the number of ways to choose the treasurer:

After selecting the president and vice president, there are 13 remaining members. The number of ways to choose the treasurer from these 13 members is 13.

Step 4: Calculate the total number of ways to choose the president, vice president, and treasurer:

Since each step is independent, you can multiply the number of choices at each step: 15 * 14 * 13 = 2,730.

Therefore, there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

Answer:

x = -7

Step-by-step explanation:

9 ( x - 5 ) = -108

9x - 45 = -108

add 45 to each side of the equation:

9x = -63

divide both sides by 9:

x = -7

Answer:

x = - 7

Step-by-step explanation:

9(x - 5) = - 108

9x - 45 = - 108

9x - 45 + 45 = - 108 + 45

9x = - 63

9x ÷ 9 = - 63 ÷ 9

x = - 7

The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Population: The containers of blueberries that are being sent to Stop and Shop.

Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

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Considering the definition of parallel line, the equation of the line d is y= 3x -7.

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts.

In this case, the line is y=3x-4

where:

Since two lines are parallel if they have the same slope, the parallel line has a slope of 3.

The line passes through the point (2, -1). Replacing in the expression for a line:

-1= 3× 2 + b

-1= 6 + b

-1 -6= b

- 7= b

Finally, the equation of parallel line is y= 3x -7.

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Answer:

$490

Step-by-step explanation:

Answer:

100 square inches

Step-by-step explanation:

20*4=100

(a) The z-score corresponding to x = 25 is -1. (b)The z-score corresponding to x = 42 is 2.4.(c) The raw score corresponding to z = -3 is 15. (d)  The raw score corresponding to z = 1.5 is 37.5.

For a normal distribution with mean μ = 30 and standard deviation σ = 5:

(a) To find the z-score corresponding to x = 25, we use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (25 - 30) / 5 = -1

Therefore, the z-score corresponding to x = 25 is -1.

(b) To find the z-score corresponding to x = 42, we again use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (42 - 30) / 5 = 2.4

Therefore, the z-score corresponding to x = 42 is 2.4.

(c) To find the raw score (x) corresponding to z = -3, we use the formula:

z = (x - μ) / σ

Rearranging the formula, we get:

x = μ + zσ

Substituting the values, we get:

x = 30 + (-3) x 5 = 15

Therefore, the raw score corresponding to z = -3 is 15.

(d) To find the raw score (x) corresponding to z = 1.5, we use the same formula:

x = μ + zσ

Substituting the values, we get:

x = 30 + 1.5 x 5 = 37.5

Therefore, the raw score corresponding to z = 1.5 is 37.5.

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10y−7z

Plug in the numbers for y and z.

(10)(9)−(7)(3)

= 69

Answer:

69

Step-by-step explanation:

10y-7z

Plug in y and z

10(9)-7(3)

Solve using order of operations

90-21=69

Answer:

In all 32 games Katy played catcher.

Step-by-step explanation:

total number of games played + 32

number of losing games = 8

To find the number of games won by the baseball team, we will subtract 8 (no. of games lost) from 32 (no. of total games played):

32 - 8 = 24 (no. of winning games)

As, Katy was catcher in both winning and losing games;

winning games + losing games = total games in which Katy was catcher

24 + 8 = 32

So, Katy was catcher in all the 32 games the baseball team played!