A line has a slope of - 1/4 and passes through the point (4,2). Through which of the following points does the line also pass?

A. (-8,-4)
B. (0,12)
C. (8,4)
D.(8,1)

The required probability for P(all numbers are chosen), P(none of them are chosen), P (precisely four are chosen) are 0.24094, 0.75906,  0.1473 respectively.

A probability is a number that mirrors the opportunity or probability that a specific occasion will happen. Probabilities can be communicated as extents that reach from 0 to 1, and they can likewise be communicated as rates going from 0% to 100 percent.

The complete likelihood of picking any 20 arbitrary balls out of 80 is ⁸⁰C₂₀ . We use mix since the request for determination doesn't make any difference

a) P(all numbers are chosen)

¹⁰C₁₀ are our numbers,⁷⁰C₁₀ is the choice of other ten numbers separated from our numbers.

So, ¹⁰C₁₀×⁷⁰C₁₀ /⁸⁰C₂₀ = 0.24094

b) P(none of them are chosen)

Since our numbers are not really chosen, we accept that every one of the numbers chose are from the other 70.

So, 1 - 0.24094 = 0.75906

c) P (precisely four are chosen)

Just four from our numbers are chosen and the rest 16 from the other 70 numbers.

Then, ¹⁰C₄×⁷⁰C₁₆ /⁸⁰C₂₀ = 0.1473

Thus, required probabilities are 0.24094, 0.75906,  0.1473 respectively.

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The equation of the line perpendicular to 4x + 3y = -24 that passes through the point (-8, 3) is 4y = 3x + 36.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

4x + 3y = -24 and point (-8, 3).

Calculate the slope,

3y = -4x - 24

y = -4 / 3 x - 8

so, m = -4 / 3

The slope of the perpendicular line, M = - 1 / m

M = - 1 / -4 / 3 = 3 / 4

Calculate the equation of the line as shown below,

y - 3 = 3 / 4 [x - (-8)]

y - 3 =  3 / 4 [x + 8]

4y - 12 = 3x + 24

4y = 3x + 36

Therefore, the equation of the line perpendicular to 4x + 3y = -24 that passes through the point (-8, 3) is 4y = 3x + 36.

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The equation of best fit is y = (-22/5)x + 10.

What is an equation of a line?

The equation of a line is given by:

y = mx + c where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The following coordinates are given:

Pick two coordinates.

(0, 10) and (25, -100)

The equation of best fit.

y = mx + c

Now,

m = (-100 - 10) / (25 - 0)

m = -110 / 25

m = -22/5

Now,

(0, 10) = (x, y)

10 = (-22/5) x 0 + c

c = 10

Now,

y = mx + c

y = (-22/5)x + 10

Thus,

Using the coordinates the equation of best fit is y = (-22/5)x + 10.

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The completed two-column table to prove that ABCD is a rectangle is presented as follows;

Step     Statement                      [tex]{}[/tex]      Reason

1   [tex]{}[/tex]       ΔABD ≅ ΔDCA                     Given

[tex]{}[/tex]            [tex]\overline{AD}[/tex] ≅ [tex]\overline{BC}[/tex]                            

2.         [tex]\overline{BD}[/tex] ≅ [tex]\overline{BD}[/tex]                             Reflexive property

3.         [tex]\overline{CA}[/tex] ≅ [tex]\overline{CA}[/tex]                [tex]{}[/tex]              Reflexive property

4. [tex]{}[/tex]      ∠CAD ≅ ∠BDA                       CPCTC

5.  [tex]{}[/tex]       [tex]\overline{AE}[/tex] ≅ [tex]\overline{ED}[/tex]                 Side length of isosceles triangle ΔAED

6.     [tex]{}[/tex]    [tex]\overline{AB}[/tex] ≅ [tex]\overline{ED}[/tex]                              CPCTC

7.  [tex]{}[/tex]       ΔABD ≅ ΔBCD                     SSS

8.        ΔDCA ≅ ΔABC         [tex]{}[/tex]             SSS

9.      ∠B ≅ ∠C ≅ ∠D ≅ ∠A   [tex]{}[/tex]          CPCTC

10.   [tex]{}[/tex] ∠B = ∠C = ∠D = ∠A [tex]{}[/tex]                Definition of congruency

11.   [tex]{}[/tex] ∠B + ∠C + ∠D + ∠A = 360°   [tex]{}[/tex]   Angles in quadrilateral

12.  [tex]{}[/tex] 4·∠B = 360°                              Substitution property

13.   [tex]{}[/tex] ∠B = ∠C = ∠D = ∠A = 90°       Substitution property

14.  [tex]{}[/tex]ABCD is a rectangle                 Definition of a rectangle

A rectangle is a quadrilateral that has four interior angles that are right angles (90°) each and in which the length of the adjacent sides are different.

The details of the reasons used to prove that ABCD is a rectangle are presented as follows;

Reflexive property

The reflexive property of congruency states that a part is congruent to itself

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent

Isosceles triangle

An isosceles triangle is a triangle with a pair of congruent sides and a pair of congruent base angles

SSS

The Side-Side-Side (SSS) congruency postulate states that two triangles are congruent if the three sides of one triangle are congruent to the three sides of the other triangle

Definition of congruency

A geometric shape is congruent to another geometric figure if they have the same measurement

Angles in a quadrilateral

The sum of the interior angles in a quadrilateral is 360°

Substitution property

The substitution property of equality states that if a = b then b can substitute a in equations and expressions, without changing their value

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Answer:

5/2 is the simplest g will form.....

The dimensions of the hallway in meters (m) are 8.89 m (length)  and 2.29  (width ).

The unit of length is essential information. There are different units for the length. In the International System Units (SI), the standard unit for length is the meter (m).  Nonetheless, there are other units, for example: inches (in) and feet(ft).

1 in = 0.0254 m

1 ft= 0.3048 m

The question gives the following dimensions in inches:

Therefore, you should know the relation between the units for solving this question.

   1 in-------- 0.0254 m

   350 in------- x m

x=350*0.0254

x=8.89 m

   1 in-------- 0.0254 m

   90 in------- x m

x=90*0.0254

x=2.29 m

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3 is the standard deviation of the  population.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The given data is {5, 8, 8, 5}

We need to find the standard deviation.

Before finding standard deviation we need to find the mean and then variance.

The mean of the population = Sum of the terms /  Number of Terms

=5+8+8+5/4

=26/4

=6.5

The variance of the population = (5 - 6.5)² + (8 - 6.5)² + (8 - 6.5)² + (5 - 6.5)²

= (-1.5)² + (1.5)² + 1.5² + (-1.5)²

= 2.25 + 2.25 + 2.25 + 2.25

= 9

Standard deviation is square root of variance

Standard deviation=√variance

=√9

=3

Hence, the standard deviation of the  population is 3.

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Using simple unitary method, the time taken to take the length of the football field is 25min.

The system for naming or representing numbers is known as the number system or numeral system. We are aware that a number is a mathematical value that aids in the measurement and counting of items as well as in several mathematical operations.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Loth travels 60 ft in 5 min.

Loth travels 1 ft in 5/60 min.

Loth travels 300 ft in 5/60 * 300 min.

=1/12 * 30

=25min

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Answer:

A- 0.01

B- 200(1+0.01t)

C- 2t+200

Step-by-step explanation:

Answer:

The statement that is true about the given equation is that it has no solution. This can be seen by rearranging the terms on both sides of the equation and then solving for y. When we do this, we get:

3(-y + 7) = 3(y + 5) + 6

-3y + 21 = 3y + 15 + 6

-6y = -12

y = 2

However, when we substitute this value of y back into the original equation, we find that it does not satisfy the equation. This means that there is no value of y that can make the equation true, so the equation has no solution.

Step-by-step explanation:

The solution is Square ABCD is reflected about the side BC

Option A.

Option C.

Option D.

What is Reflection?

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the figure be a square

Now , the sides of the square ABCD is AB , BC , CD and DC

The square ABCD is reflected about the side BC

So , the possible relations are

The reflected square will be A'B'C'D'

where length of side AB = A'B'

length of side BC = B'C'

length of side CD = C'D'

length of side DA = D'A'

So ,

The vertex B is the midpoint of side AA'

And the vertex C = C'

And , the length of the side CD = C'D'

Hence , The vertex B is the midpoint of side AA'

And the vertex C = C'

And , the length of the side CD = C'D'

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The category has an error in the table is A. breakfast.

A survey in human subjects research is a set of questions designed to elicit specific information from a specific group of people. Surveys can be conducted by phone, mail, or the internet, as well as on street corners or in shopping malls.

Historically, survey research has included large amounts of population-based data collection.

The primary goal of this type of survey research was to quickly obtain information describing the characteristics of a large sample of individuals of interest.

The category has an error in the table is breakfast. In this case, the children should be 45 and not 30.

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Answer:

Step-by-step explanation:

4% = 4/100

4/100 x 30 = 1.2

30 + 1.2 = 31.20 (nearest cent)

Answer:

31.20

Step by step explanation: I got it from delta

The equation of the straight line would be y = (-5/2) + 15.5.

The general equation of a straight line is -

Other possible equations of lines are -

We have a triangle ABC is defined by the points A(3, 8), B (7, 5), and C(2, 3).

Assume the equation of the line to be -

y = mx + c

The slope of line BC will be -

m{BC} = (3 - 5)/(2 - 7)

m{BC} = - 2/- 5

m{BC} = 2/5

So -

m{BC} x m{l} = - 1

m{l} = -1/(2/5)

m{l} = -5/2

The equation will be -

y = (-5/2)x + c

For the point A(3, 8) -

y = (-5/2)x + c

8 = (-5/2) x 3 + c

8 = -7.5 + c

c = 8 + 7.5

c = 15.5

Therefore, the equation of the straight line would be -

y = (-5/2) + 15.5

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Answer:

The equation of the straight line would be y = (-5/2) + 15.5.

Step-by-step explanation:

Domain of square root is not all real numbers.

Domain of a function:

The domain of a function is the set of input values (x) for which it produces an output value.

Like if we consider a function y = f(x)

then input inside function that is x is know as domain of function.

First we write square root function as y =

So inside root negative numbers are not allowed so value of x should be positive numbers  means x>=0.

So domain of square root function [0, ∞).

Domain of square root function is positive real numbers.

Not all real numbers because in all real numbers both positive and negative real numbers come.

Negative real numbers can not be input for square root function.

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In the preceding equation, x has the value -2/11.

A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality. Usually, it only has one variable and an equal sign. as in 2x - 4 Equals 2.

Equations can be categorized as identities or conditional equations.

6x+2x-17+6x-1-3x+20=0

14x-3x=18-20

11x=-2

x= -2/11

Therefore, in the preceding equation, x has the value -2/11.

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The value of x in 1 1/8=2 1/4x by using inverse operation is 1 / 2.

Addition and subtraction, multiplication, and division are examples of inverse operations, which are pairs of mathematical operations where one operation reverses the effects of the other.

Given:

1 1/8=2 1/4x

Solve the above equation by using the inverse operation.

Solve the mixed fraction into improper fractions as shown below,

9 / 8 = 9 / 4 x

x = 9 / 8 × 4 / 9

x = 1 / 2

Therefore, the value of x in 1 1/8=2 1/4x by using inverse operation is 1 / 2.

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Using exponential function, the annual rate of change in the school is 1.74%

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function)

In this problem, the annual rate of change can be calculated as

A = P(1 + r)ˣ

Let's substitute the values into the equation and solve;

305 = 275(1 + r)⁶

r = 0.0174

r = 0.0174 * 100

r = 1.74%

The annual rate of change is 1.74%

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a) The system of equations that represents this situation is given as follows:

b) The number of cups of regular lemonade sold is given as follows: 60.

c) The number of cups of pink lemonade sold is given as follows: 80.

The amounts are obtained with a system of equations, in which the variables are as defined in the problem.

They sell 140 cups, hence:

x + y = 140.

y = 140 - x.

They earn a total of $90, hence, considering the amount earned per cup:

0.5x + 0.75y = 90.

Replacing the first equation into the second, the variable x is obtained as follows:

0.5x + 0.75(140 - x) = 90.

0.25x = 15

x = 15/0.25

x = 60.

Then the variable y has a value of:

y = 140 - x = 140 - 60 = 80.

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Answer:

AD = 16

Step-by-step explanation:

Using the Pythagorean Theorem:

A2 + D2 = C2

122 + D2 = 202

144 + D2 = 400

D2 = 256

D = 256 = 16

Answer:

3072, -12288, 49152

Step-by-step explanation:

[tex]-3*-4=12\\12*-4=-48\\-48*-4=192\\192*-4=-768\\-768*-4=3072\\3072*-4=-12288\\-12288*-4=49152\\\\Answer= -3,12,-48,192,-768,3072,-12288,49152[/tex]

The height and radius of the cup that will use the smallest amount of paper are 3.86 cm and 2.72 cm. The result is obtained by using the first derivative .

To find the height and radius of a cone for the smallest surface area, we can use the first derivative dS/dh. We then equate it to 0 for the maximum value.

The volume of a cone-shaped paper drinking cup is 30 cm³. Find the height and radius for the smallest amount of paper!

The radius of the cone can be expressed as

V = 1/3 (πr²h)

30 = 1/3 (πr²h)

90 = πr²h

r² = 90/πh

The surface area of the cone can be expressed as

S = πrs

[tex]S = \pi r \times \sqrt{h^{2} + r^{2}}[/tex]

[tex]S = \pi \sqrt{\frac{90}{\pi h}} \times \sqrt{{h^{2} + \frac{90}{\pi h}[/tex]

[tex]S = \pi \sqrt{\frac{90}{\pi h}} \times \sqrt{\frac{(\pi h^{3} + 90)}{\pi h}[/tex]

[tex]S = \sqrt{90} \times \sqrt{\frac{(\pi h^{3} + 90)}{h^{2}}[/tex]

[tex]S = \sqrt{90} \times \sqrt{\pi h + \frac{90}{h^{2}} }[/tex]

The 1st derivative is

[tex]\frac{dS}{dh} = \sqrt{90} \times (\pi - \frac{180}{h^{3}}) \times [(\pi h + \frac{90}{h^{2}})^{-\frac{1}{2} } ][/tex]

[tex]0 = \sqrt{90} \times (\pi - \frac{180}{h^{3}}) \times [(\pi h + \frac{90}{h^{2}})^{-\frac{1}{2} } ][/tex]

The height for the smallest amount of paper is

π - 180/h³ = 0

π = 180/h³

h³ = 180/π

h³ = 57.32

h = 3.86 cm

The radius for the smallest amount of paper is

r² = 90/πh

r² = 90/π(3.86)

r² = 7.42

r = 2.72 cm

Hence, the dimension of the cone-shaped paper drinking cup for the smallest amount of paper is

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The dimensions such as length is 18 and width is 16 or length is 32 and width is 9 will produce an enclosed area of 288ft.

We know that,

P = l + 2w

50 = l + 2w

50 - 2w = l

A = l x w

288 = (50 - 2w)w

288 = 50w -2w²

2w² - 50w + 288

By dividing throughout by 2

w² - 25w + 144

This is in quadratic equation form.

By applying quadratic formula,

w = (-(-25) ± [tex]\sqrt{(-25)^{2}-4*1*144[/tex]) / 2

w = (-(-25) ± 7)/2

w1 =  (-(-25) + 7)/2

w1 = (25 + 7) / 2

w1 = 16

w2 =  (-(-25) - 7)/2

w2 = (25 - 7) / 2

w2 = 9

By substituting the values in eq1,

A = l x w

if w = 16

288 = l x 16

l = 288/16

l = 18

if w = 9

288 = l x 9

l = 288/9

l = 32

The dimensions will be length is 18 and width is 16 or length is 32 and width is 9.

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The exponential function f(x) = 400(1. 02)ˣ is $400 does the y-intercept mean in the context of the issue.

Given that,

Samra's guardians made a yearly compounding investment on her behalf in a 529 college savings plan. The exponential function f(x) = 400(1. 02)ˣ can be used to describe the growth of the savings plan on an annual basis, x.

We have to find what does the y-intercept mean in the context of the issue.

We know that,

The exponential function is f(x) = 400(1. 02)ˣ.

In this instance, the significance of the y-intercept in relation to the situation at hand is that the beginning value of the investment is equal to $400.

Therefore, The exponential function f(x) = 400(1. 02)ˣ is $400 does the y-intercept mean in the context of the issue.

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The term​ annuity is best described as​ a stream of equal installments made at equal time intervals​.

An annuity is a term used to define a series of payments of equal size at equal intervals. Equal time intervals such as months, quarters, or years, and uniform payments are the two characteristics that make a series of payments an annuity. Therefore, a series of payments can be an annuity however all series of payments are not annuities. If the series of payments is of different values or at different intervals, it is not considered to be an annuity. An annuity that provides for payments for the remainder of a person's lifetime is known as a life annuity.

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The Laplace transformation in the given function is = 5 - 8e⁻⁷ˣ/ x

Rewrite f in terms of the unit step function:

[tex]f(t) \left \{ {{y=5} for 0\leq t \leq 7\atop {x=-3}} \rightfor t\leq 7[/tex]

⇒ f(t) = 5{u(t) -u(t -7) - 3u (t -7)}

        = 5u(t) - 8u (t-7)

Recall the time-shifting property of the Laplace transform:

L I u(t - c)f(t -c) I

= e⁻ᵃˣ L[f(t)]

and the Laplace transform of a constant function,

L(K) = [tex]\frac{k}{a}[/tex]

So we have

L{f(t)} = 5u(t) - 8u (t-7)

        = 5 L[1] - 8e⁻⁷ˣ

        = 5 - 8e⁻⁷ˣ/ x

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All the elements in DUE are {16,18,19,20,21}. And the elements are combined elements of D and E.

The set containing all the components that are present in both sets A and B, or both sets A and B combined, is referred to as the union of two sets A and B. The symbol "aUb" stands for the union of the sets a and.

Given, sets D = {16,19.21},

E = {16,18, 19,20},

and F = {15, 17, 18,19,21}.

To find the elements in the set DUE:

Here, we have to find the collection of sets D and E

And we have the elements of,

D = {16,19.21}

And E = {16,18, 19,20}.

To find the union of sets, we take all the elements in the union set.

And while doing, we should not repeat the elements.

And put the elements in the ascending order.

So, the union of set D and E is,

DUE = {16,18,19,20,21}

Therefore, the DUE is {16,18,19,20,21}.

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Answer:

20%

Step-by-step explanation:

90 of 450 can be written as:

90

450

To find percentages, we need to find an equivalent fraction with a denominator of 100. Multiply both the numerator & denominator by 100

90

___

450

×

100

100

= (

90 × 100

450

) ×

1

100

=

20

100

Therefore, the answer is 20%

If you are using a calculator, simply enter 90÷450×100 which will give you 20 as the answer.