Make a table of values using multiples of /4 for x. (If an answer is undefined, enter UNDEFINED.)
y = cos x
x y
0
pi/4
pi/2
3pi/4
pi
5pi/4
3pi/2
7pi/4
2

The angle measure that corresponds to angle S is angle H.

Given information:

Figure 1 and Figure 3 are congruent figures.

That means, they have the same type of shape but have different sizes.

Therefore, as per the diagram,

PT ≅ GF

TR ≅ FD

RS ≅ DH

SQ ≅ HE

QP ≅ EG.

PTRSQ ≅ GFDHE.

Now, for angle measures,

Angle P is congruent to the angle G.

Angle T is congruent to the angle F.

Angle R is congruent to the angle D.

Angle S is congruent to the angle H.

Angle Q is congruent to the angle E.

As per the congruency of the figures,

∠S ≅ ∠H.

Therefore, ∠S ≅ ∠H.

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The length of the third side of the right triangle is √2. And the second option AAS Congruence Theorem is correct.

In a kite, the two pairs of congruent adjacent sides form two identical triangles. The AAS (Angle-Angle-Side) Congruence Theorem states that if two triangles have two corresponding angles and a corresponding side that are congruent, then the triangles are congruent.

Using Pythagoras rule we can calculate the length third side which is the hypotenuse as follows:

hypotenuse = √(1² + 1²)

hypotenuse = √(1 + 1)

hypotenuse = √2

In conclusion, the length of the third side of the right triangle is √2. And the second option AAS Congruence Theorem is correct.

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Answer:

distance between two cities will be 9 000 000 km

Answer:

Step-by-step explanation:Scale of a map is 1:3000000 i.e, 1cm on map =30km so distance of towns on map =3.5cm Actual distance = 3.5×30=105km

Answer:

Step-by-step explanation:

Number of field goals = 51

That is 75% of the total which is x

75% x = 51

75/100 * x = 51     Multiply by 100

75x = 51*100

75x = 5100           Divide by 75

x = 5100/75

x = 68

The total number of kicks was 68

Answer: \(2x^{2} y^{3} (\sqrt[3]{4x^{2} y} )\)

Step-by-step explanation:

\(\sqrt[3]{32x^{8} y^{10} } =\sqrt[3]{2^{3} \cdot 2^{2} \cdot x^{2} \cdot (x^{2} )^{3} \cdot y \cdot (y^{3})^{3} } =2x^{2} y^{3} (\sqrt[3]{4x^{2} y} )\)

Answer:

Option C :

               \(\sqrt[3]{32x^8y^10} = 2x^2 y^3 \sqrt[3]{4x^2 y}\)

Step-by-step explanation:

\(\sqrt[3]{32x^8y^{10}}} = ( 32 x^8 y^{10})^{\frac{1}{3}}\)

              \(= ( 2^5 \times x^8 \times y^{10})^{\frac{1}{3}}\\\\= ( 2^{5\times\frac{1}{3}} \times x^{8 \times \frac{1}{3}} \times y^{10 \times \frac{1}{3}})\\\\=(2^{\frac{3}{3} + \frac{2}{3}}} \times x^{\frac{6}{3} + \frac{2}{3}} \times y^{\frac{9}{3} + \frac{1}{3}})\\\\= 2 \times 2^{\frac{2}{3}} x^2 \times x^{\frac{2}{3}} \times y^3 \times y^\frac{1}{3}\\\\=2x^2 y^3 \times 2^{\frac{2}{3} \times }x^{\frac{2}{3}} \times y^{\frac{1}{3}}\\\\=2x^2 y^3 (2^2x^2 y)^{\frac{1}{3}}\\\\= 2x^2y^3 \ \sqrt[3]{ \ 4 x^2 \ y }\)

The correct solutions are, Local Maximums: (1, 5) Local Minimums: (1, 3) Saddle points: DNE.

The given equation is: 2 = (z² - 6x) (y² - 8y)

To find the critical points, differentiate the given equation partially with respect to x and y.

Differentiating the given equation with respect to x and y, we get

2y² - 16y - 6 = 0(2z² - 12)

= 0

Solving both the equations, we get

y² - 8y - 3 = 0z²

= 6

Critical points are obtained at (1, 5) and (1, 3).

Classification of the critical points is as follows:

Local Maximums: (1, 5)

Local Minimums: (1, 3)

Saddle points: DNE

Saddle points are not obtained.

Therefore, the answer is:

Local Maximums: (1, 5) Local Minimums: (1, 3) Saddle points: DNE.

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Answer:

69

Step-by-step explanation:

Answer: yes

A prime factor is number that can only divided by itself and one

Since, 17 can only be divided by 17 and 1, the student is correct

Step-by-step explanation:

Answer:

The given three sides can not form a triangle.

Step-by-step explanation:

Given three sides:

Length of first side = 7.7 cm

Length of second side = 4.0 cm

Length of third side = 1.7 cm

To find:

Whether these three sides can possibly be the three sides of a triangle ?

Solution:

Here, we can use the property of sides of a triangle:

The sum of the lengths of any two sides must be greater than the length of third side.

Now, let us try to verify this property.

Length of first side + Length of second side = 7.7 + 4.0 = 11.7 cm which is greater than the length of third side i.e. 1.7 cm

Length of first side + Length of third side = 7.7 + 1.7 = 9.4 cm which is greater than the length of second side i.e. 4.0 cm

Length of second side + Length of third side = 4.0 + 1.7 = 5.7 cm which is not greater than the length of first side i.e. 7.7 cm

Therefore, the property does not hold true.

It can be concluded that, the given three sides can not form a triangle.

Answer:

isyllus is correct

they can not from a triangle

Step-by-step explanation:

On solving the provided question, we can say that equation, k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.

A mathematical equation is a formula that links two assertions and signifies equivalence with the equals sign (=). In algebra, a mathematical statement that proves the equality of two mathematical expressions is referred to as an equation. The equal sign, for instance, separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14. There is a mathematical formula that explains the link between the two phrases that appear on either side of a letter. Frequently, the symbol and the single variable are the same. like in 2x - 4 = 2, for example.

a. f(x) = 2x+4 represents the function where you multiply the input by 2, then add 4 to the result.

b. g(x) = 2(x+4) represents the function where you add 4 to the input, then multiply the result by 2.

c. h(x) = 4x+2 represents the function where you multiply the input by 4, then add 2 to the result.

d. k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.

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For the given function f(x), x-intercepts are 1,2 and 6 and the y-intercept is -12

Given :

\(f(x) = x^{3} -9x^{2} +20x -12 \\\)

One of the factors of f(x) is (x-6)

Dividing f(x) by (x-6), we get :
\(\frac{x^{3} -9x^{2} +20x -12 \\}{x-6} = x^{2} -3x +2\)

Now expanding, \(x^{2} -3x +2\)

\(x^{2} -3x +2 = x^{2} -2x -x +2 =x(x-2) -(x-2) = (x-2)(x-1)\)

Hence, \(x^{3} -9x^{2} +20x -12 = (x-6)(x-1)(x-2)\)

For x-intercept, f(x) = 0 . Then

(x-6)(x-1)(x-2) =0

x = 1,2 and 6

For y-intercept, x=0 in f(x)

f(0) = -12

Hence, the x-intercepts are 1,2, and 6 and the y-intercept is -12.

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The z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.

The determination of the z-coordinate of the mass center of the homogeneous paraboloid of revolution requires a long answer.

Firstly, we need to define the mass density of the paraboloid. Since it is a homogeneous object, its mass density is constant throughout its volume.

Let us denote this density as ρ.

Next, we need to find the volume of the paraboloid.

The volume of a paraboloid of revolution with a height h and a base radius r is given by V = (π/2) * r^2 * h/3.

In this case, the height of the paraboloid is 4 units and the radius of the base is 2 units. Thus, the volume of the paraboloid is:
V = (π/2) * (2)^2 * 4/3 = (8π/3) units^3

Now, we can find the mass of the paraboloid by multiplying its volume by its density:
M = ρ * V = ρ * (8π/3) units^3

The next step is to find the x and y coordinates of the mass center of the paraboloid.

We can do this by using double integrals:
x = (1/M) * ∬(paraboloid) x * ρ * dV
y = (1/M) * ∬(paraboloid) y * ρ * dV

Since the paraboloid is symmetric about the z-axis, we know that its mass center will lie on this axis, and thus, its x and y coordinates will be zero.

Finally, we need to find the z-coordinate of the mass center. We can do this by using the same double integral, but this time we integrate over the z-axis:
z = (1/M) * ∬(paraboloid) z * ρ * dV

To set up the double integral, we can use cylindrical coordinates, with ρ ranging from 0 to 2 and θ ranging from 0 to 2π.

The z-coordinate of any point on the paraboloid is given by z = (1/16) * (x^2 + y^2), so we can substitute this into the double integral:
z = (1/M) * ∫(0 to 2π) ∫(0 to 2) ∫(0 to (1/16)*(ρ^2)) ρ * z * ρ * ρ * dρ dθ dz

After evaluating this integral, we get:
z = (3/5) * h = (12/5) units

Therefore, the z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.

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Answer:

18x-6 is the expression equivalent to -3(-6x+2)

Using Algebraic expression solution ,

The cost of three hats is $18 .

We have given that,

A hat company charge for design fee $4 per hat .

i.e design fee of one hat = $4

total cost of 5 hats = $30

let the cost of one hat without design fee be $x and total cost of one hat is $(x+4) .

using the above statement, we get an algebraic expression,

5( x+ 4)= 30

we solve the above algebra expression,

=> 5x + 20 = 30

=> 5x = 10

=> x = 2

so, cost of a hat without design fee is $2

and total cost of one hat is $6.

we have to calculate cost of 3 hats .

cost of one hat in hat company= $ 6

cost of three hats in hat company= $(6×3)

= $18

Hence, the total cost of 3 hats is $18.

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Match the Data Visualisation terms as follows:

1. Numpy: Working with arrays and matrices.

2. Bar chart: Representing categorical data with rectangular bars.

3. Pip: Package installer for Python.

4. S: Statistical library for Python.

The following are the meanings of the given terms:

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Answer:

Step-by-step explanation:

thanks im an introvert thats obsessed with learning what more is there in life

This is so amazing wow

Answer:

186.5

Step-by-step explanation:

Thats It

The correlation coefficient can be used to get a better understanding and to determine the extent of a strong relation between two variables.

In a statistical setting, two or more variables are said to be connected if their values fluctuate in such a way that as the value of one variable rise or falls, the value of the other variable does the same (although it may be in the opposite direction).

For instance, there is a relationship between the two variables "hours worked" and "revenue earned" if a rise in hours worked is correlated with an increase in income earned. When considering the two factors "price" and "purchasing power," the ability of a person to purchase items reduces as the price of those goods rises (assuming a constant income).

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The proportion of a normal distribution between z-scores of -0.25 and +0.25 is 0.1974, between -0.67 and +0.67 is 0.4994, and between -1.20 and +1.20 is 0.7699.

The normal distribution is a bell-shaped curve that is symmetrical about the mean. The area under the curve is equal to 1 and the z-score represents the standard deviations from the mean

a) The proportion of a normal distribution between z = -0.25 and z = +0.25 is 0.1974.
b) The proportion of a normal distribution between z = -0.67 and z = +0.67 is 0.4994.
c) The proportion of a normal distribution between z = -1.20 and z = +1.20 is 0.7699.

These proportions can be found by using a calculator with normal distribution functions.

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The probability of selecting a pen from the first box is 1/8 (since there is only 1 pen out of 8 items in the box). The probability of selecting a crayon from the second box is 3/6 (since there are 3 crayons out of 6 items in the box).

To find the probability of both events happening together, we multiply the probabilities:

P(pen and crayon) = P(pen) x P(crayon)

P(pen and crayon) = (1/8) x (3/6)

Simplifying the fraction 3/6 to 1/2:

P(pen and crayon) = (1/8) x (1/2)

Multiplying the numerators and denominators:

P(pen and crayon) = 1/16

Therefore, the probability of selecting a pen from the first box and a crayon from the second box is 1/16.

Answer:

210 x 297 mm

Hope that this helps!

In inferential statistics, we calculate statistics of sample data to estimate the characteristics of the entire population from which the sample was taken. The process involves drawing inferences about a population from a random sample of data taken from that population.

The sample statistics are used to estimate the parameters of the population. To make an inference, we use a hypothesis test or confidence interval based on the sample statistics. The key to inferential statistics is random sampling, which allows us to make generalizations about the population based on the characteristics of the sample.

In order to ensure that the sample is representative of the population, we use a variety of sampling techniques, including simple random sampling, stratified sampling, cluster sampling, and systematic sampling.

Each of these techniques has its own advantages and disadvantages, and the choice of technique depends on the characteristics of the population being studied and the research questions being asked.

Once we have a representative sample, we use statistical methods to draw conclusions about the population. This allows us to make predictions and to test hypotheses about the population with a high degree of confidence.

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The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.

The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.

Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.

Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):

y - 1 = (-1/8)(x - 2)

Simplifying and putting the equation in slope-intercept form:

y = (-1/8)x + 9/8

Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

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Answer:

Step-by-step explanation:

The required density in grams per milliliter is 6.72 grams/milliliter.

Given that,

The density of a specific material is such that it weighs 7 pounds per pint of volume. Express this density in grams per milliliter is to be detrmined.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Fraction is defined as the number of compositions that constitutes the Whole.

here,
Density = 7 pounds / pint
1 pint = 473 milliliters,
1 pound = 453 grams
Density =7 * 453 / 473 grams / milliliters
Density = 6.72 grams / milliliters

Thus, the required density in grams per milliliter is 6.72 grams/milliliter.

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Answer:

1) The linear equation in point and slope form is y - 67 = -4 × (x - 14)

2) The variables are;

a) The number of candies available = y

b) The number of days Jennifer eats the candies =

c) The slope, m = -4

3) Jennifer received 123 pieces of candies on Halloween

Step-by-step explanation:

The given parameters are;

The number of candies Jennifer eats everyday = 4 pieces

The number of days for which Jennifer eats the daily 4 candies = 14

The number of candies left at the end of the 14th day = 67 candies

1) We note that the rate of decrease in the number of candies = 4 candies/day

Therefore, the slope of the linear equation is m = -4

The y-intercept = The initial amount of candies Jennifer has = c = 67 + 14× 4 = 123 candies

The linear equation in point and slope form is given as follows;

y - 67 = -4 × (x - 14)

2) The variables are;

a) The y-value represents the number of candies available on a specific day

b) The x value represents the number of days Jennifer eats the candies'

c) The slope = The rate of decrease in the number of candies per day = -4

3) The number of candies Jennifer receives on Halloween is given by the y-intercept of the straight line equation as follows;

y - 67 = -4 × (x - 14)

y - 67 = -4·x + 56

y = -4·x + 56 + 67 = -4·x + 123

y = -4·x + 123

Comparing the above equation, with the general form of the straight line equation, y = m·x + c, where, the constant term, c = The y-intercept, we have;

The y-intercept of the equation y = -4·x + 123 = 123 = The initial amount of candies Jennifer received on Halloween.

An appropriate parametrization for the given piecewise-smooth curve is:
C(t) = C1(t) for 0 ≤ t ≤ 1
C(t) = C2(t-1) for 1 ≤ t ≤ 2
C(t) = C3(t-2) for 2 ≤ t ≤ 3

To parametrize the given piecewise-smooth curve, we can divide it into three segments and parametrize each segment separately.

For the first segment from (1,2,3) to (0,−6,7), we can use the following parametrization:
C1(t) = (1-t)(1,2,3) + t(0,-6,7) = (1- t, 2-8t, 3+10t) for 0 ≤ t ≤ 1
For the second segment from (0,−6,7) to (6,4,2), we can use the following parametrization:
C2(t) = (1-t)(0,-6,7) + t(6,4,2) = (6t, -6+10t, 7-5t) for 0 ≤ t ≤ 1
For the third segment from (6,4,2) back to (1,2,3), we can use the following parametrization:
C3(t) = (1-t)(6,4,2) + t(1,2,3) = (5-5t, 4-2t, 2+t) for 0 ≤ t ≤ 1
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The given function is linear, and it can be expressed in form f(x) = ax + b, f(x) = 1x + 0, or simply f(x) = x.

To determine if the given function is linear, we need to check if it can be expressed in form f(x) = ax + b, where a and b are constants.

The given function is f(x) = (5/1)x.

Let's rewrite the function in the required form:

f(x) = (5/5)x

Since 5/5 = 1, we can simplify the function to:

f(x) = 1x + 0

Here, a = 1 and b = 0.

So, the given function is linear, and it can be expressed in form f(x) = ax + b, f(x) = 1x + 0, or simply f(x) = x.

In Mathematics, a linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line. In case, if the function contains more variables, then the variables should be constant, or it might be the known variables for the function to remain it in the same linear function condition.

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-7 open parentheses -4 close parentheses times 18 is 504, it looks like -7(-4)18

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

A statement;-7 open parentheses -4 close parentheses times 18

Here, open parentheses means '(' and close parentheses means')'

So, it means;

-7(-4)18

Its value;-7(-4)18

=28x18

=504

Therefore, the algebra value will be 504 and stated as -7(-4)18.

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