What is the diameter of circle 0 if the radius is 4​

a) The parametric equations of the line are: x(t) = −2 + 3t, y(t) = 4 − 2t, z(t) = 3 + 4t and The symmetric equation of the line are: (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) The line intersects yz-plane at (0, 8/3, 17/3)

The given points on the line are:

(x₁, y₁, z₁) = (−2, 4, 3)

(x₂, y₂, z₂) = (1, 2, 7)

The direction ratios of this line are:

⟨a, b, c⟩ = ⟨x₂ − x₁, y₂ − y₁, z₂ − z₁⟩

             = ⟨1 + 2, 2 − 4, 7 − 3⟩

             = ⟨3, −2, 4⟩

a) Parametric equations of the line:

These are given by:

x(t) = x₁ + at = −2 + 3t

y(t) = y₁ + bt = 4 − 2t

z(t) = z₁ + ct = 3 + 4t

Symmetric equation of the line:

This is given by:

              (x − x₁)/a = (y − y₁)/b = (z − z₁)/c

              (x + 2)/3 = (y − 4)/−2 = (z − 3)/4

b) When a line intersects the yz-plane, its x-coordinate is zero.

Using the parametric equations of the part (a):

                                   x = 0

                          −2 + 3t = 0

                                  3t = 2

                                    t = 2/3

Substitute this in the parametric equations corresponding to y and z as well:

                                   y = 4 −2t

                                      = 4 − 2(2/3)

                                      = 8/3

                                   z = 3 + 4t

                                      = 3 + 4(2/3)

                                      = 17/3

Hence, the required point is: (x, y, z) = (0, 8/3, 17/3)

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Using Trigonometry, the value of x in the right triangle is 17.1

Since we have a right angle triangle ; The angle L can be obtained thus ;

L = 180 - (90+67)

L = 23

Using Trigonometry:

Sin23° = opposite/ hypotenuse

Opposite= 6.7

hypotenuse= x

Sin23° = 6.7/x

x = 6.7/sin(23°)

x = 17.14

Therefore, the value of x to the nearest tenth is 17.1

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The value of f(1) by using the attached graph is f(1) = -2.

A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.

Given:

The graph shown in the question is representing the function value,

To find f(1) = ?

The value of f(1) will be equal to the value of x as the graph is linear so,

f(1) = value of y at x = 1

value of y at x = 1 = -2  (From the graph)

Thus, f(1) = -2.

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Answer:

Step-by-step explanation:

The perimeter of a rhomboid: The perimeter of a rhomboid is the sum of all sides of the figure i.e. P= (a +b + a +b) = 2(a + b).

B is the base of the rhomboid and a is the length of the side of the rhomboid.

Hope this helped! If so, plz mark brainliest.

Answer:

The regression equation is:

\(y=3.77+0.36 x\)

Step-by-step explanation:

The general form of a regression equation is:

\(y=\alpha +\beta x\)

Here,

α = intercept

β = slope

Compute the value of intercept and slope as follows:

\(\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 29 \cdot 186 - 28 \cdot 173}{ 5 \cdot 186 - 28^2} =3.767\approx 3.77 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 5 \cdot 173 - 28 \cdot 29 }{ 5 \cdot 186 - \left( 28 \right)^2} =0.363\approx 0.36\end{aligned}\)

The regression equation is:

\(y=3.77+0.36 x\)

To answer this question we will use the following formula for compounded monthly interest:

where A₀ is the initial amount, r is the annual interest as a decimal number and 12 is the number of years.

Notice that:

Therefore, substituting t=42, r=0.02, and A₀=120000 we get:

Simplifying the above result we get:

Answer: $277,769.75.

Given:-

To find the value by factorization.

So now we simplify,

So the values are 0 and 14.

Answer: 17

Step-by-step explanation:

2x + 56=22

- 56 -56

2x = -34

divide 2x by both sides

x = -17

Answer:

infinitely many solutions

Step-by-step explanation:

14x + 6 = 2(5+7x)-4

14x + 6 = 10 + 14x - 4

14x + 6 = 14x + 6

infinitely many solutions because both sides of the equation are equal

Graphs are used to show the relationship between two variables. In the given graph, as the value of x increases, the value of y decreases.

Given that:

\(y = \frac{10}{x}\)

The above function is an inverse function.

This means that:

As the value of x increases, the value of y decreases

Take for instance:

\(x= 1\)

\(y = \frac{10}{1} = 10\)

Now, \(x = 2\)

\(y = \frac{10}{2} = 5\)

Notice that:

As x increases from 1 to 2, the corresponding values of y decreases from 10 to 5

Hence, (b) is correct

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Answer:

90 dollars

Step-by-step explanation:

so first you need to solve for the rate of change or slope with the equation

y 2 - y1 / x2 - x1

here i think the independent variable is number of roses since the dollars rely on the number of roses (sorry for my explanation its kinda bad)

so since number of roses is independent we know that it is x and that the price in dollars is y

anyways we have to substitute two values into the equation

y 2 - y1 / x2 - x1

(3, 9) (6, 18)

18 - 9 / 6 - 3

9 / 3

3

knowing that the rate of change is 3, to find the price for 30 roses all we have to do is:

let p be price

p = 3x

p = 3(30)

p = 90 dollars

Answer:

3 ≠ -12

Step-by-step explanation:

2x + 3 = 2(x-6)

2x + 3 = 2x - 12

3 ≠ -12

Answer:

3 ≠ -12

Step-by-step explanation:

2x + 3 = 2(x-6)

2x + 3 = 2x - 12

3 ≠ -12

Answer:

she makes 22 cookies batches

Step-by-step explanation:

22*3=7 2/3

7 2/3 / 3 = 22

Answer:

C. 7°F

Step-by-step explanation:

Answer:

1/2 or 0.5

Step-by-step explanation:

Slope (m) =

ΔY/ΔX=

1/2=

0.5

(more in depth)

ΔX = 3 – 13 = -10

ΔY = -5 – 0 = -5

-10/-5 = 1/2 = 0.5

The value of the missing side lengths x and y are 5√2 and 5 respectively.

The figure in the image is a right triangle.

Angle θ = 45 degree

Hypotenuse = x

Opposite to angle θ = y

Adjacent to angle θ = 5

To solve for side x and side y, we use the trigonometric ratio.

Note that:

Cosine = adjacent / hypotenuse

tangent = opposite / adjacent

Solving for x:

Cosine = adjacent / hypotenuse

Plug in the values

cos( 45 ) = 5/x

x = 5 / cos( 45 )

x = 5√2

Solving for side y:

tangent = opposite / adjacent

Plug in the values

tan( 45 ) = y/5

y = tan( 45 ) × 5

y = 5

Therefore, the value of side length x is 5 units.

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Answer:dddddd

ddddddddStep-by-step explanation:

Step-by-step explanation:

1. 3:4, 6:8, 9,12

So 12:15 is the same thing as 12/15 you need to simplify so 12 devided by 2 is 4 and 15 divided by 3  is 5 so question to is 4:5

the ratio of 3to4 is 7.42069 and 12 to 1362 the others r to hard for my big brain

Step-by-step explanation:

Answer:

93

Step-by-step explanation:

125(.80)=100, 100(.93)=93

Answer:

\(Mean = 4.35\)

\(SD = 0.5655\)

Step-by-step explanation:

Given

\(n = 5\)

\(p = 0.87\)

Solving (a): Mean

\(Mean = np\)

\(Mean = 5 * 0.87\)

\(Mean = 4.35\)

Solving (b): Standard Deviation (SD)

\(SD = np(1 - p)\)

\(SD = 5 * 0.87(1 - 0.87)\)

\(SD = 5 * 0.87 * 0.13\)

\(SD = 0.5655\)

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

let's relist the 10 names, as there was some "mixing" going on in your text :

Dorothy

Anthony

Harold

Margaret

Tiffany

Nancy

Angela

Paul

Patrick

Jeremy

so, whatever happens, the totally possible cases are 10 (as we are only taking about these 10 names, no other name can suddenly appear in all the scenarios).

in each scenario one student is randomly chosen.

a) the probabilty to pick a student with name ending "k".

we look through the list and find only 1 student, whose name ends with "k" : Patrick.

that means the number of desired cases is 1.

and the probabilty is therefore

1/10 = 0.1

b) the probability to pick a student with name beginning "C".

we look and look and look. none of the 10 names start with a "C".

that means the number of desired cases is 0.

and the probabilty is

0/10 = 0

c) the probability that the name of the picked student contains "m" or "M".

we find 2 names : Margaret and Jeremy.

that means that the number of desired cases is 2.

and the probabilty is therefore

2/10 = 1/5 = 0.2

d) in how many ways can we pick 7 elements out of 10, when the sequence of the pulled 7 elements does not matter (e.g. ... Nancy, Paul ... is the same as ... Paul, Nancy, ...). and no student can be pulled more than once (no repetitions).

that means we have to calculate the combinations of 7 items out of 10 without repetition :

C(10, 7) = 10! / (7! × (10-7)!) = 10! / (7! × 3!) =

= 10×9×8 / (3×2) = 5×3×8 = 120

there are 120 possibilities to build the math club.

e) now we pick 4 students out of 10. but as we give them prices based on ranking, the sequence matters (e.g. Nacy first, Paul second is different to Paul first, Nancy second).

but we still have no repetition, as nobody can win more than one price.

that means we need to calculate the permutations of 4 items out of 10 without repetition :

P(10, 4) = 10! / (10-4)! = 10! / 6! = 10×9×8×7 = 5,040

there are 5040 different ways to distribute the 4 prices among the 10 students.

The total surface area of the prism is determined as  216 cm².

The surface area of the prism is calculated by applying the following formula.

The area of the two triangular faces is calculated as follows;

Area of the two triangles = 2 (¹/₂ x base x height )

Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )

Area of the two triangles = 24 cm²

The area of rectangular faces is calculated as follows;

A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )

A = 192 cm²

The total surface area of the prism is calculated as follows;

Area = 24 cm² + 192 cm²

Area = 216 cm²

The sketch of the triangular prism is in the image attached.

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The media personality's argument is flawed because they are basing their conclusion on a single year's data and ignoring the overall trend of increasing global temperatures. To counter this argument, one can make the following points:

1. While it is true that the annual increase in temperature may be less than the margin of error, the trend of increasing temperatures over several decades cannot be ignored. The margin of error is a statistical concept that takes into account the uncertainty in the measurement, but it does not negate the overall trend.

2. Global temperature records show that the Earth's temperature has been steadily rising over the past century, with the 10 warmest years on record occurring since 2005. This trend cannot be explained by natural variability alone and is consistent with the effects of human-caused climate change.

3. The consequences of rising global temperatures, such as melting glaciers, rising sea levels, and more frequent extreme weather events, are already being felt around the world. Ignoring this trend could have devastating consequences for future generations.

In summary, the media personality's argument is based on a flawed understanding of statistics and ignores the overall trend of increasing global temperatures. The best counterargument is to highlight the overwhelming evidence of climate change and its potential consequences.

Answer:

13

Step-by-step explanation:

Square root of 169 =  13

Answer:

13

Step-by-step explanation:

y^2= 169

y=?

√169= 13

Answer:

C

Step-by-step explanation:

General equation of a tangent function is: y=atanb(theta-c)+d

Based on the graph, it moved pi/2 to the right.

So, the answer is C.

The result of a transformation on the parent tangent function is g(x) = tan( x - (π / 3 ). The correct option is C.

A parent function in mathematics is the simplest function in a family of functions that keeps the definition of the entire family.

The general equation of a tangent function is represented as below:-

y=atanb(Ф-c)+d

Based on the graph, it moved π/2 to the right. Therefore, the result of a transformation on the parent tangent function is g(x) = tan( x - (π / 3 ). The correct option is C.

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Work done lifting the bucket and rope to the top of the building is 4005.75 Joules

To express this concept mathematically, the work W is equal to the force f times the distance d, or W = fd. If the force is being exerted at an angle θ to the displacement, the work done is W = fd cos θ.

Initially bucket hold = 25kg. Sand

Sand leaks 0.1 kgs each meter it is lifted

At height x meter bucket hold = (25 - 0.1x) kg of sand

Length of rope = 15 meter

density of rope = 0.4kg / meter

weight of rope = 15 (0.4) = 6kg.

At height x meter, weight of rope = (6 - 0.4x)

Total weight at height x meter = (25-0.1x) + (6-0.4x)

                                                   = (31 - 0.5x) kg

force = (31-0.5x) g Newtons. = [(31-0.5x) 9.8] Newton

Work = force × displacement

\(Work= \int_{0}^{15}9.8(31-0.5x)dx\)

          \(=9.8[31x-0.5 \frac{x^2}{2} ]_{0}^{15}\)

          \(=9.8[31(15)-0.25(15)^2]-0\)

          \(=4005.75 joules\)

Hence, work done 4005.75 Joules

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The transformation of f(x) to g(x) is :

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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Answer: 16 + 8x

Step-by-step explanation:

The area of the entire shape is (4+x) times (4+x), while the white region is (x * x).

Subtracting the white region from the entire shape gives us the area of the shaded region

(4+x)^2 - x^2

16 + 8x + x^2 - x^2  = 16 + 8x

Answer:

vertically opposite angle

Step-by-step explanation: