Identify the slope of the line. Interpret the slope in the context of this problem. Y=-2.3332x+123.98

Answer:

Answer:

D

Step-by-step explanation:

The total annual FICA tax for an annual salary of $38,480 is D $2,943.72.

FICA tax comprise of Social security tax + Medicare tax

Where:

Hence:

FICA tax=($38,480×6.2%)+($38,480×1.45%)

FICA tax=$2,385.76+$557.96

FICA tax= $2,943.72

Inconclusion the  total annual FICA tax for an annual salary of $38,480 is D $2,943.72.

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The point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0.

To graph the equation 2x + 3y = 6, we can rewrite it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Starting with the given equation, we isolate y to one side:

3y = -2x + 6

y = (-2/3)x + 2

Now, we have the equation in slope-intercept form, y = (-2/3)x + 2. The slope is -2/3, and the y-intercept is (0, 2).

To find the point where the graph intersects the x-axis, we need to determine the coordinates where y is equal to zero. This occurs when the line crosses the x-axis.

Setting y = 0 in the equation, we have:

0 = (-2/3)x + 2

(-2/3)x = -2

x = (-2)(-3/2) = 3

Therefore, the point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0, indicating the point of intersection with the x-axis on the graph.

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Answer:

Step-by-step explanation:

x+y = -17

x-y = 41

------------

2x = 24

x = 12

y = -x-17 = -29

Answer: 19

Step-by-step explanation:

Using the sum of an arithmetic series formula,

\(\sum^{30}_{n=2} (an+b)=2407 \implies 29(16a+b)=2407 \implies 16a+b=83\\\\\sum^{40}_{n=1} (an+b)=4220 \implies 20(41a+2b)=4220 \implies 41a+2b=211\)

Multiplying the second equation by 2 gives us \(32a+2b=166\).

Subtracting this from the second equation, we get that \(9a=45 \implies a=5\).

Substituting this back into the first equation, we get that \(b=3\).

Therefore, \(2a+3b=2(5)+3(3)=19\)

Answer:

16.86 ft/s

Step-by-step explanation:

Given that,

Angular speed of a carousel, \(\omega=14\ rev/min\)

The diameter of the carousel, d = 23 feet

We need to find the speed of the carousel and jump on.

\(\omega=14\ rev/min=1.46\ rad/s\)

Radius, r = 11.5 feet

Let v is the velocity. So,

\(v=r\omega\\\\=11.5\times 1.46\\\\=16.79\ ft/s\)

Hernce, the correct option is (d) "16.86 ft/s"

Answer:

Step-by-step explanation:

area of rectangle=6×4=24 ft²

area of semicircle

\(=\frac{1}{2} \pi (3)^2\\= \frac{9}{2} \pi \\=4.5 \pi \\\approx 4.5\times 3.14\\\approx 14.13 ft^2\\total~area=24+14.13\\=38.13 ~ft^2\)

As x → - ∞, f(x) → - ∞ and As x → ∞, f(x) → ∞.

A function can be thought of as an output for any set of defined or valid input.

According to the given question we have to determine the end behaviour of the given polynomial of degree 7, end behaviour is observing how the graph is as x approaches negative infinity or positive infinity.

For any polynomial the end behaviour will mainly depend upon the highest power of the polynomial.

Given, 2x⁷ - 5x³ - 2x + 1.

Here highest term is 2x⁷ as x approaches positive infinity the function will also reach towards positive infinity.

On the other case if x is very very small and going towards negative infinity the function also reach towards negative infinity.

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The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.

a) We are given the equation 8 tan θ = 3 cos θ.

Dividing both sides of the equation by cos θ, we have:

8 tan θ / cos θ = 3

Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:

8 (sin θ / cos θ) / cos θ = 3

Simplifying further, we get:

8 sin θ / cos^2 θ = 3

Now, multiplying both sides of the equation by cos^2 θ, we have:

8 sin θ = 3 cos^2 θ

Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:

8 sin θ = 3(1 - sin^2 θ)

Expanding the equation, we get:

8 sin θ = 3 - 3 sin^2 θ

Rearranging the terms, we have:

3 sin^2 θ + 8 sin θ - 3 = 0

Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.

b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.

To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.

In this case, the equation factors as:

(3 sin θ - 1)(sin θ + 3) = 0

Setting each factor equal to zero, we have two equations:

3 sin θ - 1 = 0    or    sin θ + 3 = 0

For the first equation, solving for sin θ, we get:

3 sin θ = 1

sin θ = 1/3

Taking the inverse sine (sin^-1) of both sides, we find:

θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)

For the second equation, solving for sin θ, we have:

sin θ = -3

Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).

Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.

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The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

A is the answer

Step-by-step explanation:

if its wrong than its C

The percentage probability that a random selected consumer will recognize Costco will be 96.3%.

Given, the total number of consumers who recognized the brand was 1036. And the total number of consumers who didn't recognize the brand was 40. Therefore, the total number of our sample will be :

⇒1036 + 40

⇒1076

Now, we know that probability(P) of an event = f/n

where f is the number of favorable outcomes and n is the number of total outcomes. Here, number of favorable outcome is 1036.

Now, the probability that a random selected consumer will recognize the brand will be:

⇒ P = f/n

⇒ P = 1036/1076

⇒P = 0.96282

Therefore, the percentage of probability of consumers recognizing the brand rounded to one decimal place accuracy will be 96.3%.

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The surface area of the sphere, to the nearest whole number, is 1318 cm².

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

The surface area of a sphere is expressed as:

SA = 4πr²

Where r is the radius of the sphere and π is the mathematical constant pi.

Given that the volume V is 4500 cm³.

First, we solve for the radius:

Volume =  (4/3)πr³

4500 = (4/3)πr³

4500 × 3 = 4πr³

13500 = 4πr³

r³ = 13500/4π

r = ∛( 13500/4π )

Now that we have the radius, we can calculate the surface area of the sphere using the formula:

SA = 4πr²

Substituting the radius we found:

SA = 4 × π × ∛( 13500/4π )²

SA = 1318 cm²

Therefore, the surface area is approximately 1318 cm².

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Answer: My teacher told me to use 180 and divide something.

Step-by-step explanation:

Answer:

isnt itjust 15?

Step-by-step explanation:

1 +1+1+1 = 4  5+3+3 = 11 then 11+4 = 15 if this is incorrect im sorry

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The powers, (index) and coefficients of the polynomial indicates;

(A) The standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

(B) 4

(C) Positive zeroes; 2 or 0, negative zeroes; 0 or 2, complex zeroes; 0 or 2 or 4

(D) ±1/2, ±1, ±3/2, ±2, ±3, ±6

(E) Please find attached the graph of the polynomial created with MS Excel

(F) Four complex roots

A polynomial is a mathematical expression that consists of variables and coefficients joined together by addition, subtraction and multiplication, with the exponents of the variables consisting of positive integer values.

Part A) The polynomial in standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

Part B) The degree of the polynomial is 4, as the highest power of the polynomial is 4

Part C) The use of the Rule of Signs, to determine the options for the number of positive zeroes, negative zeroes and complex zeroes, can be presented as follows;

Positive zeroes options; The number of time the signs coefficients of the expression; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6, changes are two as follows;

+6 to -12, and from -12 to +9, therefore, the number of possible positive zeroes are 2 or 0, positive zeroes

The negative zeroes options; The negative zeroes options can be found by changing the sign of all the coefficients as follows; -2·x⁴ - 3·x³ - 9·x² + 12·x - 6, therefore, the number of times the sign of the coefficients change are again from -6 to +12, and from +12 to -9, which is 2 times, therefore;

The possible number of negative zeros are 2 or 0, negative zeroes

Whereby there are possibly 0 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 4

Whereby there are 2 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Whereby there are possibly 0 negative zeros and 2 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Part D) The rational roots theorem indicates that for a polynomial the rational roots are in the form p/q, where p is a factor of the constant term, and q is a factor of the leading coefficient.

The constant term is 6, and the leading coefficient is 2. The factors of 6 are ±1, ±2, ±3, and ±6 and the factors of 2 are; ±1, ±2 therefore;

p/q = ±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±2/2, ±3/2, ±6/2, which can be summarized as; ±1/2, ±1, ±3/2, ±2, ±3, ±6

Part E) Please find attached a screenshot of the graph of the polynomial created with MS Excel

Part F) The attached graph of the polynomial, created with MS Excel, indicates that there are no real zeros of the polynomial, therefore, there are four complex zeroes of the polynomial

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Answer:

Step-by-step explanation:

nth term = 3*(2n - 1 )

n =1  ;    first term = 3*( 2*1 - 1) = 3* (2-1)  = 3*1 = 3

n = 2 ; second term = 3*( 2*2 - 1) = 3* (4-1)  = 3*3 = 9

n = 3 ;  third term = 3*( 2*3 - 1) = 3* (6-1)  = 3*5 = 15

The probability that exactly 6 out of the first 11 customers buy a magazine: is 0.0002443605632.

A discrete probability distribution known as a geometric distribution may be used to describe the likelihood of experiencing success for the first time following a string of failures. Up until the first success, a geometric distribution can undergo an infinite number of trials.

Given:

The owner of the small deli shop suspects that only 9.8% of his customers buy a magazine.

p = 0.098

To find the probability that exactly 6 out of the first 11 customers buy a magazine:

Number of trials = 11 and outcome = 6,

Applying an excel formula,

= BINOM.DIST(6,11,0.098,FALSE)

= 0.0002443605632

Therefore, the probability is 0.0002443605632.

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Answer: Is reinforced with other material

Step-by-step explanation:

The options are:

A is expensive to build.

B usually cracks under heavy weights.

C looks like any other road.

D is reinforced with other material.

The passage best supports the statement that a concrete road are reinforced with other material. According to the information given in the passage, steel plays a vital role in keeping the road surface flat.

Steel bars are embedded in concrete so that the stresses cannot crack the slab. Therefore, it indicates that concrete road is reinforced with other material.

Answer:

y=4x+12

Step-by-step explanation:

Answer:13 1/2

Step-by-step explanation:

We're given:

If the shop sold " \(9\dfrac{9}{10}\)  times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply \(9\dfrac{9}{10}\) by 9 ounces:

\(9\dfrac{9}{10}\times9\)

Convert the fraction into an improper fraction:

\(=\dfrac{99}{10}\times9\)

Multiply:

\(=\dfrac{891}{10}\)

The shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.