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Part A: The student that simplified the give trigonometrical identity expression incorrectly is student B.

Part B: The correct complete solution is shown below

From the question, we are to determine the student that simplified the expression incorrectly.

Part A:

The student that simplified the expression incorrectly is student B.

The student is went wrong in step 3.

From step 2, the student divided (1 + tan²θ) by (tanθ/cotθ). The student is supposed to divide [(1 + tan²θ)/tanθ] by cotθ

Part B:

The correct solution is shown below

[(1 + tan²θ)/tanθ] ÷ cotθ

(sec²θ/tanθ) ÷ cotθ

Which can be written as:

(sec²θ/tanθ) ÷ 1/tanθ

Then,

(sec²θ/tanθ) × tanθ/1

= sec²θ/1

= sec²θ

Hence, the correct simplified expression is sec²θ

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Answer:

Primero, podemos establecer las siguientes ecuaciones:

La suma de los kilómetros que caminan Mateo y Leo es igual a 15:

 Mateo + Leo = 15

Mateo camina 1/5 más que Leo:

 Mateo = Leo + 1/5Leo

 Mateo = 6/5Leo

Podemos utilizar la segunda ecuación para despejar una de las variables en términos de la otra. Por ejemplo, despejando Leo:

   Leo = 5/6Mateo

Luego, podemos sustituir esta expresión en la primera ecuación para obtener una ecuación con una sola variable:

   Mateo + 5/6Mateo = 15

   11/6Mateo = 15

   Mateo = 15*6/11

   Mateo = 8.18 Km

Finalmente, podemos utilizar una de las ecuaciones que relaciona a Mateo y Leo para obtener la distancia que recorre Leo:

   Leo = 5/6Mateo

   Leo = 5/6*8.18

   Leo = 6.82 Km

Por lo tanto, Mateo recorre 8.18 Km y Leo recorre 6.82 Km.

Answer:

200km

Step-by-step explanation:

Well.. if 2 cities were 200m apart, 200 cm apart, or 200 mm apart, they would be considered one city. The only logical choice is 200km.

Answer:

a

Step-by-step explanation:

There are 2 ounces of jam in the large jar and 2/3 ounce of jam in each small jar.

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are commonly used to represent and manipulate linear transformations and systems of linear equations.

The elements of a matrix are typically denoted by lowercase letters with subscripts, such as aij or bij, where i and j refer to the row and column indices, respectively. For example, a 3x3 matrix might look like this:

| a11 a12 a13 |

| a21 a22 a23 |

| a31 a32 a33 |

This matrix has three rows and three columns, and the element in the first row and second column is denoted by a12.

Matrices can be added, subtracted, multiplied, and divided, and these operations follow specific rules that are defined in matrix algebra. For example, to add or subtract two matrices of the same size, we simply add or subtract the corresponding elements. To multiply two matrices, we multiply the rows of the first matrix by the columns of the second matrix and sum the products.

Let's represent the number of ounces of jam in the large jar as "L" and the number of ounces of jam in each small jar as "S". Then we can write the system of equations:

1L + 2S = 8

1L - 1S = 2

We can write this system in matrix form as:

[1 2; 1 -1][L;S] = [8;2]

To solve for L and S, we can use matrix algebra to isolate [L;S]:

[L;S] = [1 2; 1 -1]⁻¹ [8;2]

First, we need to find the inverse of the coefficient matrix [1 2; 1 -1]. The inverse is:

[1 -2; 1 1]/3

So we can substitute this into our equation:

[L;S] = [1 -2; 1 1]/3 [8;2]

[L;S] = [2;2/3]

So there are 2 ounces of jam in the large jar and 2/3 ounce of jam in each small jar.

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The complete question is:

the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.

a. The exponential growth equation to represent the price y of a new HD television t years from now is:

y = $2500[tex](1 + 0.04)^t[/tex]

where t is the number of years from now.

b. To predict when a new HD television will cost $3000, we can set y = $3000 and solve for t:

$3000 = $2500[tex](1 + 0.04)^t[/tex]

1.2 = [tex]1.04^t[/tex]

ln(1.2) = t ln(1.04)

t = ln(1.2) / ln(1.04)

t ≈ 3.97

Therefore, a new HD television will cost $3000 approximately 4 years from now.

c. To determine when the amount in Jason's savings will exceed the cost of a new television, we can use the formula for continuous compound interest:

A = [tex]Pe^(rt)[/tex]

where A is the amount in savings after t years, P is the principal amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.

In this case, P = $2200, r = 0.047 (since the annual interest rate is 4.7%), and we want to find the time t when A = $2500. Plugging these values into the formula, we get:

$2500 = $2200[tex]e^(0.047t)1.13636 = e^(0.047t)[/tex]

ln(1.13636) = 0.047t

t = ln(1.13636) / 0.047

t ≈ 7.22

Therefore, the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.

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Answer:

A
b
D

Step-by-step explanation:

The sun revolves around the Earth." Statements 1 and 4 are true.

As the question asks for statements that are not true, I will go through each statement and determine if it is true or false. Statement 1: "Water boils at 100 degrees Celsius."

This statement is true. Water boils at 100 degrees Celsius at sea level under normal atmospheric conditions.

Statement 2: "The moon is made of cheese." This statement is not true. The moon is not made of cheese. It is primarily composed of rock and does not contain any dairy products.

Statement 3: "The sun revolves around the Earth." This statement is not true.

The Earth revolves around the sun in an elliptical orbit. The concept that the Earth is at the center of the solar system and the sun revolves around it was disproven by the heliocentric model proposed by Nicolaus Copernicus in the 16th century.

Statement 4: "Gravity only exists on Earth." This statement is not true. Gravity exists everywhere in the universe. It is a fundamental force that attracts objects with mass towards each other.

While the strength of gravity may vary depending on the mass of the objects and their distance apart, it is present throughout the universe.

To summarize, the statements that are not true are: 2. "The moon is made of cheese." 3. "The sun revolves around the Earth." Statements 1 and 4 are true.

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Answer:

distance traveled in 1 hour = x/3

To find the distance traveled in 9 hours, we can multiply the distance traveled in 1 hour by 9:

distance traveled in 9 hours = (x/3) * 9

Simplifying this expression gives:

distance traveled in 9 hours = 3x

Therefore, the car will travel 3 times the distance it travels in 3 hours when it travels for 9 hours.

[tex]g^{2} +4g-32=0[/tex]

[tex]g^{2} + 8g - 4g - 32=0[/tex]

[tex]g(g+8)-4(g+8) = 0[/tex]

[tex](g+8)(g-4) = 0[/tex]

[tex]g+8=0 \implies \bf g = -8[/tex]

[tex]g-4=0 \implies \bf g = 4[/tex]

[tex]\implies g = 4 \ or \ -8[/tex]

The standard deviation of the distribution is given as follows:

[tex]\sigma = 17.2[/tex]

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean of the distribution of IQ scores is given as follows:

[tex]\mu = 100[/tex]

X = 140 is the 99th percentile, as approximately 1% of the population have IQ scores above this limit, hence when X = 140, Z = 2.327, meaning that the standard deviation is obtained as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.327 = \frac{140 - 100}{\sigma}[/tex]

[tex]2.327\sigma = 40[/tex]

[tex]\sigma = \frac{40}{2.327}[/tex]

[tex]\sigma = 17.2[/tex]

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Answer:

a)10

Step-by-step explanation:

(xx)=(2×2)=4

2(4)=8

8+2=10

answer: a) 10

Using the multiplier formula, the eventual change in aggregate expenditure due to the inflow of R10 billion into South Africa and using the marginal propensity to consume (MPC) is R6 billion.

The multiplier formula is used to compute the amount of new income generated from the flow of extra income.

The multiplier formula uses the MPS (marginal propensity to save) to compute the multiplier as follows:

M = 1 / MPS

The marginal propensity to save gives the proportion of income that will be saved.

The marginal propensity to save (MPS) = 0.4

M = 1 / MPS

M = 1/0.4)

= 2.5

Change in aggregate expenditure = R25 billion (2.5 x R10 billion)

Thus, we expect the aggregate expenditure in South Africa to increase by R25 billion following the inflow of R10 billion investment.

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Step-by-step explanation:

We can simplify the given expression using the rules of absolute values:

l-80-20l – 100 + l-100l

= -(20l + 80) - 100 + 100 (since |x| = -x when x is negative)

= -20l - 80

= -20(l + 4)

Therefore, the simplified expression is -20(l + 4).

Answer:

100

Step-by-step explanation:

[tex] | - 80 - 20| - 100 + | - 100| \\ = | - 100| - 100 + | - 100| \\ = 100 - 100 + | - 100| \\ = | - 100| \\ = \boxed{100}[/tex]

____________

hope it helps!

a.) The area covered by algae for 10 days after it was spotted would be = 35.7 m²

The area covered by the algae when it was first spotted = 12.5 m²

For every week(7 days) = 2(12.5)

But 10 days = x

Make X the subject of formula;

X = 10× 2(12.5)/7

X = 250/7

X = 35.7 m²

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Answer:

-6 and -7

Step-by-step explanation:

-6 + -7 = -13

-6 * -7 = 42

Answer:

a) To calculate how much Vanessa will have to pay back after 2 years, we need to add the interest to the principal.

The interest can be calculated using the simple interest formula:

Interest = Principal x Rate x Time

where,

Principal = $5,000 (the amount borrowed)

Rate = 4% (expressed as a decimal, 0.04)

Time = 2 years

So,

Interest = $5,000 x 0.04 x 2

Interest = $400

The total amount Vanessa will have to pay back is the sum of the principal and the interest:

Total amount = Principal + Interest

Total amount = $5,000 + $400

Total amount = $5,400

Therefore, Vanessa will have to pay $5,400 after 2 years.

b) To calculate how much interest Vanessa will pay, we can use the same formula for simple interest:

Interest = Principal x Rate x Time

Plugging in the given values, we get:

Interest = $5,000 x 0.04 x 2

Interest = $400

Therefore, Vanessa will pay $400 in interest over the 2-year period.

Inequality y 5x - 7 has solutions (-5, -3), (-4, 2), and (-1, 0).

In order to address an inequality • You can multiply or divide each side by the same positive amount; • You can add the same amount to each side; • You can take the same amount away from each side. If you multiply or divide each side by a negative value, the inequality sign must be reversed.

Let's examine each point individually:

(-5, -3)

y ≥ 5x - 7

-3 ≥ 5(-5) - 7

-3 ≥ -32

The inequality is true, so (-5, -3) is a solution.

(-4, 2)

y ≥ 5x - 7

2 ≥ 5(-4) - 7

2 ≥ -27

The inequality is true, so (-4, 2) is a solution.

(1, -2)

y ≥ 5x - 7

-2 ≥ 5(1) - 7

-2 ≥ -2

The inequality is not true, so (1, -2) is not a solution.

(-1, 0)

y ≥ 5x - 7

0 ≥ 5(-1) - 7

0 ≥ -12

The inequality is true, so (-1, 0) is a solution.

(3, 0)

y ≥ 5x - 7

0 ≥ 5(3) - 7

0 ≥ 8

The inequality is not true, so (3, 0) is not a solution.

(4, 1)

y ≥ 5x - 7

1 ≥ 5(4) - 7

1 ≥ 13

The inequality is not true, so (4, 1) is not a solution.

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Answer:

see explanation below

Step-by-step explanation:

4. ∠A = 35, a = 8.9, find c

since side a is opposite to m∠A and c is the hypotenuse, we can use sin(∠A) = opp/hypo equation

5. sin(35) = 8.9/c

=> c = 8.9/sin(35) = 8.9/0.5736 = 15.516

6. 15.5

The value of x in the infinite geometric series, x = (7 ± i√107) / 26.

We can start by simplifying the left-hand side of the equation:

-1 + 1/x + x + x² + ...+ xⁿ + ...

= -1 + (1/x) * (1/(1 - x))

Using the formula for the sum of an infinite geometric series:

1 + r + r² + ... = 1/(1 - r) for |r| < 1

We can simplify the left-hand side further:

= -1 + (1/x) * (1/(1 - x))

= -1 + (1/(x - x²))

Now we have:

-1 + (1/(x - x²)) = 10/3

Multiplying both sides by 3(x - x²), we get:

-3(x - x²) + 3 = 10(x - x²)

Simplifying, we get:

13x² - 7x + 3 = 0

Using the quadratic formula, we can solve for x:

x = (7 ± √(7² - 4133)) / (2*13)

x = (7 ± i√(107)) / 26

Since the expression is defined only for |x| < 1, we can discard the solution with the plus sign, leaving:

x = (7 - √(-143)) / 26

x = (7 - 3i√13) / 26

Therefore, the solution for x is x = (7 ± i√107) / 26.

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Answer:

X = 18

Step-by-step explanation:

7x is the opposite angle if 3x, so 10x= 180 180÷10 = 18

The length of the diameter of the circle of the radius 4 cm is 8 cm and other solutions are added below

See attachment for the circle

This is calculated as

Diameter (d) = 2 * Radius (r)

So, we have

d = 2 * 4 cm

d = 8 cm

The number of 90° sectors that will fit inside the circle is

Sectors = (360°/90°)

Sectors = 4

See attachment for the circle

The shape created inside the circle by joining the ends of five equally spaced radii is a regular pentagon.

The length (L) of one chord is

L = 2 × r × sin(c/2)

For 6 chords created by the 5 radii, we have

Total length = 6 × 2 × r × sin(c/2)

Where

c = 360/6 = 60

So, we have

Total length = 6 × 2 × 4 × sin(60/2)

Evaluate

Total length = 24 cm

Each sector of 90° in a circle has an angle of

Angle = (360/6)°

Angle = 60°

If sectors of 45° were used, the shape created inside the circle by joining the ends of the radii would be a nonagon

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The linear equation representing the situation is y = 0.75x - 2.25, and according to this equation, the height of the sprout after 14 days would be 8.25 inches.

To create a linear equation that represents the relationship between the height of the bean sprout and the number of days after planting.

Therefore, the slope of the line is:

slope = change in height / change in days = (7.5 - 3) / (13 - 7) = 1.5

The intercept of the line can be found by substituting one of the data points into the point-slope form of a line:

y - y1 = m(x - x1)

where m is the slope, x1 and y1 are the coordinates of one of the data points. We choose the first data point (7, 3):

y - 3 = 1.5(x - 7)

y - 3 = 1.5x - 10.5

y = 1.5x - 7.5

Therefore, the linear equation that represents the relationship between the height of the bean sprout (y) and the number of days after planting (x) is:

y = 1.5x - 7.5

To find the height of the sprout after 14 days, we substitute x = 14 into the equation:

y = 1.5(14) - 7.5

y = 10.5

Therefore, the height of the sprout after 14 days is predicted to be 10.5 inches.

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Answer: Let's call the first angle "x".

From the problem statement, we know that the second angle is two times the first, so:

Second angle = 2x

We also know that the third angle is 170° more than the second angle, so:

Third angle = Second angle + 170°

Third angle = 2x + 170°

We know that the sum of the three angles in a triangle is 180°, so we can set up an equation:

x + 2x + (2x + 170°) = 180°

Simplifying and solving for x:

5x + 170° = 180°

5x = 10°

x = 2°

So the first angle is 2°. Using this value, we can find the other two angles:

Second angle = 2x = 2(2°) = 4°

Third angle = 2x + 170° = 2(2°) + 170° = 174°

Therefore, the three angles in the triangle measure 2°, 4°, and 174°.

Step-by-step explanation:

For the function g, the vertex form equation is [tex]g(x) = -2(x - 5)^{2} + 9.[/tex]

In algebra, the idea of an equation is a logical assertion that shows the equivalence of several mathematical expressions. For instance, the equations 3x + 5 & 14, that are separated by the 'same' sign, make up the equation 3x + 5 = 14.

A mathematical equation, such as 6 × 4 = 12 x 2, states that two quantities or values are equivalent. a meaningful noun. Equations are used when more than one factor has to be considered in order to fully understand or explain a situation.

Substituting the first point (7,1) into the equation for g(x), we get:

[tex]1 = a(7 - 5)^{2} + 9[/tex]

we get

[tex]-8 = 4a[/tex]

Dividing both sides by 4,

[tex]a = -2[/tex]

Now that we have found the value of a, we can write the equation for g(x) as:

[tex]g(x) = -2(x - 5)^{2} + 9[/tex]

Therefore, the equation in vertex form for the function g is [tex]g(x) = -2(x - 5)^{2} + 9[/tex].

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Answer:

f1(x) = (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2))

Step-by-step explanation:

To find f1(x), we need to differentiate the given function f(x) with respect to x using the product rule and the chain rule. Here are the steps:

f(x) = (7 sin x + 3 cos x) tan-1 x

f1(x) = d/dx [(7 sin x + 3 cos x) tan-1 x]

= (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2)) (d/dx)x

= (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2))

Therefore, f1(x) = (7 cos x - 3 sin x) tan-1 x + (7 sin x + 3 cos x) (1/(1+x^2)).

Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]

Answer:

The third one

Step-by-step explanation:

if you look at it, and actually solve it its 88.

The answer of the given question based on Statistics to find minimum monthly premium payments is option D) Plan 2, since it has lower monthly premium payments.

Probability is  measure of  likelihood or chance of an event occurring. It is expressed as  number between 0 and 1, where 0 indicates an impossible event and 1 indicates  certain event

Assuming that the coverage details are similar, we can compare the monthly premium payments for each plan based on the different categories of coverage:

Individual: Plan 1 has a monthly premium of $87.32, while Plan 2 has a monthly premium of $11.77. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Spouse: Plan 2 has a monthly premium of $735.00, while Plan 1 has a monthly premium of $890.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Child: Plan 2 has a monthly premium of $606.00, while Plan 1 has a monthly premium of $750.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Family: Plan 2 has a monthly premium of $1,400.00, while Plan 1 has a monthly premium of $1,600.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Based on these comparisons, we can see that Plan 2 has a lower monthly premium for all categories of coverage. Therefore, the answer is option D: Plan 2, since it has lower monthly premium payments.

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Answer:

Below

Step-by-step explanation:

I suppose you are looking for the ORIGINAL price

x = original

 32% is .32 in decimal

    so    .32 * x = $ 179.20

                     x = 179.20/.32 = $ 560.