Suppose you work as ski instructor over winter break earning $12 per hour. The amount of your weekly paycheck (before taxes are taken out) could be written F(x) = 12x.​

\(\Large{\underline{\mathcal{Given: }}}\)

radius = 12m

volume = ❓

\(\Large{\underline{\mathcal{solution :}}}\)

volume of a sphere:

☞4/3 πr³ cu.units

☞4/3 × 22/7 × 12 × 12 × 12

☞ 7214 m³

Answer:

0.90, 3/4, -5/16 , -0.52, -1/5Step-by-step explanation:

Answer:

x > 90

Step-by-step explanation:

To solve this, we will use the multiplication property of equality. We need to multiply both sides by 6, this will get us x > 90.

Answer:

99cm

Step-by-step explanation:

A meter is equal to 100cm

The rope is a metre (m) long but a centimetre (cm) less.

100cm - 1cm = 99cm

A rose garden is formed by rectangular and semi-circular parts. If the gardener wants to build a fence around the garden, then total 134.95 feet of fence are required.

The perimeter is defined as calculating the outer length of boundaries of shape.

We have a rose garden is formed by joining a rectangle and a semicircle, as present in above figure. We have to determine the feet of fence are required to build a fence around the garden.

From the above figure, length of rectangular part, l = 34 ft

Width of rectangular part, w = 26 ft.

Also, diameter of semi-circular part, d

= 26 ft

Radius of of semi-circular part, r = d/2

= 26/2 ft = 13 ft

So, the perimeter of semi-circular part, Pₛ= π× r = π× 13 ft

= 40.95 ft.

Here, the fence required for the rectangle shape is three sides that two long sides and one wide side. The fourth side of the width is already covered by the semi-circular part. So, the perimeter formula for the rectangle shape, Pᵣ = 2l + w. Therefore, perimeter of garden

= Pₛ + Pᵣ

= 40.95 ft + 2×34 ft + 26 ft

= 68 ft + 26 ft + 40.95 ft

= 134.95 ft.

Hence, required value is 134.95 feet.

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Complete question:

The above figure complete the question. a rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 34 feet long and 26 feet wide. if the gardener wants to build a fence around the garden, how many feet of fence are required? (use the value for , and do not round your answer. be sure to include the correct unit in your answer.)

Random assignment is the process of placing research participants into the conditions of an experiment in such a way that each participant has an equal chance of being assigned to any level of the independent variable.

Random assignment helps to ensure that the groups being compared in an experiment are equivalent at the start of the study, minimizing the influence of confounding variables and increasing the internal validity of the research.

By randomly assigning participants to different conditions, researchers can infer that any observed differences between groups after the experiment are due to the manipulation of the independent variable rather than preexisting differences between the groups.

Random assignment can be achieved through various methods, such as using random number tables, computer-generated randomization, or random assignment software.

It is an important aspect of experimental design and helps to strengthen the causal inferences that can be drawn from the research findings.

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Answer:

For 100 miles he uses 3.571 gallons of gasoline.

In equation form it is y/x*100

Step-by-step explanation:

Unitary Method

He travels 28 miles per gallon of gasoline.

For 1 mile he uses  1/28 gallons

For 100 miles he uses 1/28 * 100= 100/28= 3.571 gallons of gasoline.

Let x be the miles and y be the gallons of gasoline used to travel x miles.

Then for 1 mile  the gallons of gasoline used will be y/ x gallons.

For 100 miles  the gallons of gasoline used will be y/x *100 gallons.

In equation form it is y/x*100 gallons for 100 miles where x is the number of miles and y is the amount of gallons.

To solve a homogeneous differential equation of the form m(x, y)dx + n(x, y)dy = 0, we can use the substitution y = vx.

By following the steps above, you can solve a homogeneous differential equation and obtain the solution in terms of x and y.

1. Compute the derivative of y with respect to x: dy/dx = v + x * dv/dx.
2. Substitute the values of y and dy/dx in the original equation: m(x, vx)dx + n(x, vx)(v + x * dv/dx)dx = 0.

3. Simplify the equation by dividing through by dx: m(x, vx) + n(x, vx)(v + x * dv/dx) = 0.

4. Rearrange the terms to isolate dv/dx: n(x, vx) * dv/dx = -m(x, vx) - n(x, vx) * v.

5. Divide through by n(x, vx): dv/dx = (-m(x, vx) - n(x, vx) * v) / n(x, vx).

6. This is now a separable differential equation. Separate the variables and integrate both sides: ∫(1 / n(x, vx)) dv = -∫[(m(x, vx) + n(x, vx) * v) / n(x, vx)] dx.

7. Integrate both sides with respect to v and x, respectively.

8. Solve for v.

9. Substitute the value of v back into the equation y = vx.

10. This will give you the general solution of the homogeneous differential equation in terms of x and y.

In conclusion, by following the steps above, you can solve a homogeneous differential equation and obtain the solution in terms of x and y.

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The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:

1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).

The area below z=1.04 is approximately 0.851, rounded to three decimal places.

(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:

1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.

The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.

(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:

1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

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Answer:

(7, -6)

(-7, -6).............

..

Answer: -7,-6

Step-by-step explanation:

So if we look at a graph 7,6 is on the right upper quadrant since its completely positiv, once we relfect the x axis then it becomes 7,-6 then once we reflect across the why axis it finally becomes -7,-6

Answer:

angle s equals to angle t

Step-by-step explanation:

the triangle is an isosceles triangle so...angle s equals to angle t

The expression log3(x^10z^5) can be written as the sum of two logarithms: 10log3(x) + 5log3(z).

To express the given expression as the sum and/or difference of logarithms, we use the logarithmic property log_a(b^c) = clog_a(b). In this case, we have log3(x^10z^5). By applying the property, we can separate the exponents as coefficients of the logarithms. The exponent 10 in x^10 becomes the coefficient in front of the logarithm log3(x), and the exponent 5 in z^5 becomes the coefficient in front of the logarithm log3(z).

Therefore, the expression log3(x^10z^5) can be written as the sum of two logarithms: 10log3(x) + 5log3(z). This notation represents the same value as the original expression but is written in a different form that separates the variables x and z with their respective exponents as coefficients.

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Answer: \(\frac{-7}{8}\)

Step-by-step explanation:

    First, we will need to find the slope of line r.

\(\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1}} =\frac{9-1}{8-1}=\frac{8}{7}\)

    Next, we know that perpendicular slopes are negative reciprocals of one another. To find the slope of line s, we will find the negative reciprocal of line r's slope.

\(\displaystyle \frac{8}{7} \rightarrow \frac{-7}{8}\)

Each person need to pay $ 80.88345.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Bill without tax = 105.73

Tax = 6%

So, bill amount after tax = 105. 73 + 105. 73 x 6/100

                                        = 105.73 + 6.3438

                                        = $112.0738

Addition of 20% tip = 112.0738 + 211.46 = $323.5338.

If the amount is divided among 4 people, each will pay

= 323.5338/4

= $ 80.88345

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Answer:

I think it is 0.12P because 16-4 is 12 so yeah. that is what I think

Answer:

The triangular prism has two triangular bases and three rectangular lateral faces.

First, we need to find the area of each triangular base. Using the formula for the area of a triangle:

base x height / 2

We can calculate the area of one triangular base as:

(10 x 12) / 2 = 60 units²

Now we need to find the area of each rectangular lateral face. All three faces have the same dimensions of 10 units by 14 units, so the area of each face is:

10 x 14 = 140 units²

To find the total surface area of the prism, we add up the areas of both triangular bases and all three rectangular faces:

Total surface area = 2 x (area of triangular base) + 3 x (area of rectangular face)

Total surface area = 2 x 60 units² + 3 x 140 units²

Total surface area = 120 units² + 420 units²

Total surface area = 540 units²

Therefore, the surface area of the triangular prism is 540 square units.

Answer:

133+9x+2=180 (sum of interior angle on the same side of transversal is 180°)

9x=180-135

x=5

Answer:

2 months

Step-by-step explanation:

To solve this equation create an expression for the cost of each club. Use the slope-intercept form of y=mx+b where m is the monthly fee and b is the flat fee. So the 2 expressions would be A) 29x+14 and B) 22x+28. Since we want to find when these are equal, set the expressions equal to each other. This gives the equation 29x+14=22x+28. Then, solve for x.

When solved, x=2. This means that after 2 months the cost of each will be the same.

Answer:

Step-by-step

2/7

Answer: Northeast - unless you are at the South Pole, in which case you are still facing North.

Step-by-step explanation

Sequence:

Facing North

90 degrees left = facing West

180 degrees right = facing East

reverse = facing West

45 degrees left = facing Southwest

reverse = facing Northeast

Answer:

Step-by-step explanation:

The speed of the object is 12121 m per week.

What does it mean to do speed?

The object is moving at a speed of 2 centimeters every 7 seconds.

We need to find the speed in m per week.

2 cm = 0.02 m

1 week = 604800 s

7 s =  \(1.65 * 10^{-6} week\)

Speed = distance/time

So,

\(v = \frac{0.02 m}{1.65 * 10^{-6 } week}\)

\(v = 12121.21 m/ week\)

or v = 12121 m/ week

So, the speed of the object is 12121 m per week.

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The limit is -243/75 or -3.24.

To compute the limit using the Maclaurin series for trigonometric and inverse trigonometric functions, express each term in the given expression using their respective series expansions. Break down each term:

1. The Maclaurin series expansion for tangent (tan) function is:

tan(x) = x + (x³)/3 + (2x⁵)/15 + (17x⁷)/315 + ...

Substitute 9x for x in this series expansion to get the Maclaurin series for tan(9x):

tan(9x) = 9x + (81x³)/3 + (2 x (729x⁵))/15 + (17 × (6561x⁷))/315 + ...

2. The Maclaurin series expansion for cosine (cos) function is:

cos(x) = 1 - (x²)/2 + (x⁴)/24 - (x⁶)/720 + ...

Again, substitute 9x for x in this series expansion to get the Maclaurin series for cos(9x):

cos(9x) = 1 - (81x²)/2 + (6561x⁴)/24 - (59049x⁶)/720 + ...

3. The cubic term, 243x³, does not require substitution or approximation.

Now, rewrite the given expression using the Maclaurin series for trigonometric and inverse trigonometric functions:

lim(x->0) [tan(9x) - 9x cos(9x) - 243x³]/75

= lim(x->0) [(9x + (81x³)/3 + (2 × (729x⁵))/15 + (17 × (6561x⁷))/315) - 9x(1 - (81x²)/2 + (6561x⁴)/24 - (59049x⁶)/720) - 243x³]/75

Now, simplify and collect the terms with the same power of x:

= lim(x->0) [(9x - 9x) + (81x³/3 - 81x³/2) + (2 × (729x⁵)/15) - (17 × (6561x⁷)/315) + (9x³/2) - (81x⁵/24) + (729x⁷/80) - (17 × (6561x⁷)/315) - 243x³]/75

The terms (9x - 9x) and (81x³/3 - 81x³/2) cancel out, leaving:

= lim(x->0) [(2 × (729x⁵)/15) - (17 × (6561x⁷)/315) + (9x³/2) - (81x⁵/24) + (729x⁷/80) - (17 × (6561x⁷)/315) - 243x³]/75

Now, simplify further and remove the common factor of x³ from the remaining terms:

= lim(x->0) [(2 × (729x²)/15) - (17 x (6561x⁴/315) + (9x/2) - (81x²/24) + (729x⁴80) - (17 x. (6561x⁴)/315) - 243]/75

Finally, take the limit as x

approaches 0 by directly substituting x = 0 into the expression:

= [(2 × (729(0)²)/15) - (17 x (6561(0)⁴)/315) + (9(0)/2) - (81(0)²/24) + (729(0)⁴/80) - (17 × (6561(0)⁴)/315) - 243]/75

= [-243]/75

Simplifying further:

= -243/75

Therefore, the limit is -243/75 or -3.24.

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It is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques.

Multicollinearity is a statistical phenomenon where two or more independent variables in a regression model are highly correlated with each other. This can cause problems in the regression model as it becomes difficult to distinguish the individual effects of the independent variables on the dependent variable.
When multicollinearity is present in a regression model, the p-values of the slopes of the independent variables are affected. The p-value measures the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. The null hypothesis in a regression model is that the slope of the independent variable is zero, meaning that there is no relationship between the independent variable and the dependent variable.
Multicollinearity can cause the standard errors of the slopes to increase, leading to inflated p-values. In other words, the significance of the relationship between the independent variable and the dependent variable may be underestimated. This is because the highly correlated independent variables are both trying to explain the same variation in the dependent variable, leading to an unreliable estimate of the effect of each independent variable on the dependent variable.
Therefore, it is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques. This can help to ensure that the regression model produces reliable estimates of the effects of the independent variables on the dependent variable.

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In elliptic geometry, which is a non-Euclidean geometry, the first four Euclidean postulates are not valid.

However, we can still examine how they are violated and discuss the corresponding proofs in hyperbolic geometry.

1. First Postulate (Postulate of Line Existence):

Euclidean Postulate:

Given any two distinct points, there exists a unique line that passes through them.

Violation in Elliptic Geometry:

In elliptic geometry, any two distinct points do not have a unique line passing through them.

Instead, there are multiple lines that pass through any two points.

Proof in Hyperbolic Geometry:

In hyperbolic geometry, we can prove that given any two distinct points, there are infinitely many lines passing through them.

This can be demonstrated using the Poincaré disk model or the hyperboloid model.

2. Second Postulate (Postulate of Line Extension):

Euclidean Postulate:

Any line segment can be extended indefinitely to form a line.

Violation in Elliptic Geometry:

In elliptic geometry, a line segment cannot be extended indefinitely since the lines in this geometry are closed curves.

Proof in Hyperbolic Geometry:

In hyperbolic geometry, we can show that a line segment can be extended indefinitely by demonstrating the existence of parallel lines that do not intersect.

3. Third Postulate (Postulate of Angle Measure):

Euclidean Postulate:

Given a line and a point not on the line, there exists a unique line parallel to the given line.

Violation in Elliptic Geometry:

In elliptic geometry, there are no parallel lines.

Any two lines will eventually intersect.

Proof in Hyperbolic Geometry:

In hyperbolic geometry, we can prove the existence of multiple parallel lines through a given point not on a line.

This can be achieved by showing that the sum of angles in a triangle is always less than 180 degrees.

4. Fourth Postulate (Postulate of Congruent Triangles):

Euclidean Postulate:

If two triangles have three congruent sides, they are congruent.

Violation in Elliptic Geometry:

In elliptic geometry, two triangles with three congruent sides may not be congruent.

Additional conditions, such as congruent angles, are necessary to determine triangle congruence.

Proof in Hyperbolic Geometry:

In hyperbolic geometry, we can prove that two triangles with three congruent sides are congruent.

This can be demonstrated using the hyperbolic version of the SAS (Side-Angle-Side) congruence criterion.

In summary, in elliptic geometry, the first four Euclidean postulates are not valid, and their corresponding proofs in hyperbolic geometry show how these postulates are violated or modified to fit the geometrical properties of the respective geometries.

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The Average speed is 17.4 mph.

The average speed is calculated by dividing the total distance travelled by the total amount of motion time.

The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.

Average speed = Distance travelled/ Time taken

Given:

Distance = 5 4/5 = 29/5 miles

Time= 1/3 hours

So, Average speed = Distance travelled/ Time taken

Average speed= 29/5 x 3/1

                         = 87/5

                         = 17.4 mph

Hence, the Average speed is 17.4 mph.

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The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.

Given that,

From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.

Whether the claim is true or false must be determined.

The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.

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Answer:

y in (7,y) = 14

Step-by-step explanation:

A General Linear function is as the following:

y = mx + c, Where: m: slope of the line, c: y-intercept

Given that:

Point 1 (P1) = (1,5)

Point 2 (P2) = (3, 11)

Point 3 (P3) = (7,y)

By substituting in the linear function with P1:

5 = m + c  ---> (1)

By substituting in the linear function with P2:

11 = 3m + c   ---> (2)

By multiplying equation (1) times 3 and subtracting eq. (2) from it:

(15 = 3m + 3c) - (11 = 3m + c) =

4 = 2c

Then, c = 2

By substituting with "c" in eq. (1):

5 = m + 2

Then, m = 3

Hence,

the function of this line is:

y = 3x + 2

So,

to get "y" in P3, we are going to substitute with 7:

y = 3(7) + 2

then "y" in P3 = 23


Another Solution:

by getting the slope of the line:

\(Slope = \frac{\triangle y}{\triangle x}\) Where: Δy: change in y points, Δx: change in x points

by utilizing P1 & P2 in slope formula:

\(slope = \frac{11 - 5}{3 - 1} = \frac{6}{2} = 3\)

By substituting with P1 in the linear function:

5 = 3 + c

Then, c = 2

the function of the line is:

y = 3x + 2

So,

to get "y" in P3, we are going to substitute with 7:

y = 3(7) + 2

then "y" in P3 = 23



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