Write an equation for a parabola with x-intercept (-3,0) and (2,0) which pae through the point (1,-20)

The COUNTIF function to count the number of students who have been elected to offices in student organizations in Cell Q8 is ‘=COUNTIF(M2:M31, "Elected")’.

The COUNTIF function is a premade function in Excel, which counts cells as specified. It is one of the statistical functions which is used to count the number of cells that meet a criterion. In the given situation, Lael wants to count the number of students who have been elected to offices in student organizations from the data available in the excel spreadsheet. The COUNTIF function is used to determine the total by using the formula: ‘=COUNTIF(M2:M31, "Elected")’ in the Cell Q8.

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The rate at which the volume of the box of height 10 inches is changing when the width is 8 inches and the length is 6 inches is 440 cubic inches per second

The volume of a rectangular box is the product of the length, the width and the height of the box.

The height of the rectangular box, h = 10 inches

The rate of change of the length of the box is; [tex]\frac{dl}{dt}[/tex] = 2 in/sec

The rate at which the width is decreasing is; [tex]\frac{dw}{dt}[/tex] = 4 in/sec

When the length is 8 inches and the width is 6 inches, we get;

[tex]\dfrac{dV}{dt} = \dfrac{d}{dt} \left(l\cdot w \cdot h\right)[/tex]

[tex]\dfrac{dV}{dt} =h\times \left(l\cdot \dfrac{dw}{dt} + w \cdot \dfrac{dl}{dt} \right)[/tex]

When l = 8, and w = 6, we get;

[tex]\dfrac{dV}{dt} =10\times \left(8\times 4 + 6 \times 2 \right)=440[/tex]

The rate at which the volume of the rectangular box is changing in cubic inches per second is therefore;

[tex]\dfrac{dV}{dt} =440 \ in^3/sec[/tex]

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The school will purchase 80 chairs and 10 tables.

A system having more than two equations is known as a system of equations.

Given that, the school can spend $5200 and the cost of one table is $200 and the cost of one chair is $40.

Let x represents the number of chairs purchased and y represents the number of tables purchased.

The total cost of purchasing x chairs and y tables is:

Total cost = 40x + 200y

Since the budget of the school is $5200 only, substitute "Total cost =5200" into the above equation,

5200 = 40x + 200y

Since each table requires 8 chairs, it follows:

x = 8y

Hence, the system of equations is:

5200 = 40x + 200y      (1)

x = 8y                            (2)

To solve the system of equations, substitute x = 8y into equation (1):

5200 = 40(8y) + 200y

5200 = 320y + 200y

5200 = 520y

y = 10

Substitute y = 10 into equation (2):

x = 8(10)

x = 80

Hence, the school will purchase 80 chairs and 10 tables.

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The slope intercept form of the given line equation is y=-5/6 x+1.

The given equation of a line is 5x+6y=6.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Here, the equation can be written in slope intercept form as

5x+6y=6

6y=6-5x

y=-5/6 x+1

Therefore, the slope intercept form of the given line equation is y=-5/6 x+1.

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In the given triangle, the length of missing side is 15.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the given triangle,

Side BD = 5, CE = 3 and AE = 9

Let the side AD is x,

Since, line BC and DE and parallel to each other,

Therefore, by side splitter theorem,

A line that is parallel to one side of a triangle and crosses the other two sides equally divides the side in proportional ratio.

Implies that,

AD/BD = AE/EC

x/5 = 9/3

x/5 = 3

x = 15

The value of side AD is 15.

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Using the Pythagoras threoem,

the possible value of k are 6 or 1 in right angled triangle.

We have given that,

There is a triangle say, ∆ABC with vertices A(1,2) ,B(k , 2) and C(6,7).

and angle, B = 90°

that is this is a right angled triangle with angle ABC is 90° .

we have to find out the value of k .

Using Pythagoras threoem,

AB² + BC² = AC²---(*)

where, AB ,BC and AC are sides of ∆ABC.

using distance formula, we find length of sides of ∆ABC . let coordinates of A (a₁,b₁) and B(a₂,b₂)

AB = √(a₂ - a₁)² + (b₂-b₁)²

put a₁ = 1 , b₁ = 2 , a₂ = k , b₂ = 2

AB² = (k - 1)² + (0) = (k-1)²

similarly we can easily calculate the length of other sides of ∆ABC.

BC² = (6-k)² + 25

AC²= (5)² + (5)² = 50

putting all sides value in above formula,

50 = (k-1)² + (6-k)²+ 25

=> 25 = k² + 1 - 2k + 36 + k² - 12k

=> 2k² - 14k + 12 = 0

=> k²- 7k +6 = 0

this is a quadratic equation we solve it and find out value of k

using , roots formula

k = { -(-7) +- √(-7)^2 - 4(1)(6)}/2×1

=> k = either( 7 + √25) /2 or (7- √25)/2

=> k = either 6 or 1

Hence , the possible value of k are 6 or 1

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The foot and orientation of the normal vector of this plane whose ray would cross (1,1,1) is (0,1,1) and 2.

Given:

we have three points:

Q(1,0,0),

R(0,1,0),

and S(0,0,1)

when the plane passes through Q,R, and S, then the vectors

QR = (-1,1,0) and QS = (-1,0,1)

lie in the plane. Thus the cross-product

n = I i  j  k  I

      -1 1 0

      -1 0 1 I

= i + j + k is normal to the plane.

If r=⟨x,y,z⟩ determines an arbitrary point P in the plane, the vector

v = QP = ⟨x-1,y−0,z−0⟩

ray = (1,1,1)

v = QP = (1-1, 1-0, 1-0)

= (0,1,1)

lies in the plane and so is perpendicular to n. In this case,

n⋅v = 1(0)+1(1)+1(1)

= 0+1+1

= 2

Hence the foot and orientation f the normal vector of this plane is (0,1,1) and 2.

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The correct option C 0.28; for the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed.

This problem involves a binomial probability distribution.

Now that five thumbtacks have been thrown, we want to determine the likelihood that at least two of them will land pointing up. As it is written;

P(X ≥ 2) = P(2) + P(3) + P(4) + P(5)

Based on the histogram

P(5) = 0.02

P(4) = 0.02

P(3) = 0.05

P(2) = 0.19

So,

P(X ≥ 2) = 0.19 + 0.05 + 0.02 + 0.02

P(X ≥ 2) = 0.28

Thus, the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed is 0.28.

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A thumbtack that is tossed can land point up or point down. The probability of a tack landing point up is 0.2. A simulation was conducted in which a trial consisted of tossing 5 thumbtacks and recording the number of thumbtacks that land point up. Many trials of the simulation were conducted and the results are shown in the histogram.

Based on the results of the simulation, which of the following is closest to the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed?

A 0.09

B 0.19

C 0.28

D 0.72

E 0.91

Using simple Units Measurement System,

Dressmaker cut total 40 pieces of length 18 inch from 15 of given rolls of ribbon.

We have given that,

total length of roll of ribbon = 6 feet

the length of ribbon cut by dressmaker = 18 inch

As we know , 1 inch = 2.5 cm --(1)

then 1 feet = 30cm --(2)

from (1) and (2) , we get

1 feet = 12 inch

total length of roll ribbon in inch = 6×12

= 72 inches

we have total number of ribbons = 5

so, total number of inches = 5 ×72 = 360 inches

As per question given that dressmaker need to cut 18 inch piece for making dress .

So, total number of 18 inch pieces Dressmaker has is equal to ratio of total length of ribbon / length of ribbon dressmaker needed

= 720/18

= 40

Hence, total 40 pieces of length 18 inch dressmaker have.

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Answer:

Step-by-step explanation:

solving by elimination means to get rid of one of the variables,  pick either one,  X or Y  and use the other equation to make it zero.

3x - y = 5

4x + y = 9

+______  add the two equations, column for column,

7x + 0y = 14

now solve for x,  that is, get x by itself

7x / 7 = 14/7

x = 2

Now that you've solved for x,  plug that x into either equation.

3(2) - y = 5

6-y = 5

6-5 = y +5-5

1 = y

Now you have both :)

There are three major forms of linear equations:

Point slope form:

The point-slope form, as its name suggests, identifies a point on a line and its slope. Not frequently is this form provided to assist with line graphing. To get from a verbal or visual representation of a line to its slope-intercept or standard form, however, is where it is more frequently utilized.

Slope intercept form:

A line's slope and y-intercept are communicated using the slope-intercept form. Technically speaking, it is an exception to the point-slope form.

Standard form:

An equation's conventional form is as follows:

Ax+By=C

Where A is not a negative number and B, C, and all three are whole numbers.

Hence we get the required answer.

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Answer: 20 & 37

What we know:

Process:

10*2=20

20 is a product of 10 because (10*2=20)

37 is not a product of 10 because there are no whole numbers that 10 can be multiplied with to make 37

At the null hypothesis, it is tested if there is not enough evidence that the means are difference, that is, if the subtraction is of zero, hence:

[tex]H_0: \mu_d = 0[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the means are difference, that is, if the subtraction is different of zero, hence:

[tex]H_1: \mu_d \neq 0[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with 5 + 5 - 2 = 8 df and a significance level of 0.05, hence the critical value is of:

|t| = 2.306.

For each sample, the mean and the standard error are given as follows:

For the distribution of differences, the mean and the standard error are given as follows:

The test statistic is given by the division of the sample mean by the standard error, hence:

t = -11.8/17.19

t = -0.69.

The absolute value of the test statistic is less than the critical value for the two-tailed test, hence:

The data is given by the image at the end of the answer.

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Integral value is finite since the given integral converges when the function is [tex]\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx[/tex].

Given that,

Analyze the integral to see if it is convergent or divergent. convergent integrals should be evaluated.

[tex]\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx[/tex]

We have to simplify the equation.

Finding the area of the curve's undersurface is the process of integration. To do this, draw as many little rectangles as necessary, then add up their areas.

We know that,

I= [tex]\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx[/tex]

Let p = x²then xdx= dp/2

Then

I= [tex]\int\limits^\infty_\infty {3/2e^{-p} } \, dp[/tex]

I= 3/2([tex]e^{-p}[/tex])infinity to minus infinity

I= 3/2 ([tex]e^{-x^{2} }[/tex])infinity to minus infinity

I=0

Therefore, integral value is finite since the given integral converges when the function is [tex]\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx[/tex].

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The component form of the force vector required to move the object of 300 pounds is (272, 127)

Suppose we have a vector v  with angle θ to the positive x-axis, then the horizontal and vertical components of the vector are given as:

vx = v cos θ

vy = v sin θ

In the given problem, the vector is a force vector of 300 pounds.

w = 300

θ = 25⁰

Hence,

horizontal component = wx = w cos 25⁰

                                         = 300 . cos 25⁰ = 272

vertical component = wy = w sin 25⁰

                                         = 300 . sin 25⁰ = 127

Hence, the component form of the given force vector is (272, 127)

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Answer:

Its D on edge

Step-by-step explanation:

The true statement is option (a) If the sample size is bigger, the interval is narrower.

Given:

for a given confidence level and population or sample standard deviation the following is true in the interval estimation of the population mean.

In a confidence interval, to find the standard error we divide the standard deviation by the sample size. When the sample size is large the value of standard error decreases. When the value of standard error decreases the width of the confidence interval also decreases. Therefore we can say If the sample size is bigger, the interval is narrower.

that is,

error α standard deviation / sample size

Here when sample size is large the error decreases because both are inversely proportional when error decreases the standard deviation or confidence intervals decrease because both are directly proportional.'

Therefore The true statement is option(a) If the sample size is bigger, the interval is narrower.

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Full question:

For a given confidence level and population standard deviation, which of the following is true in the interval estimation of the population mean?

(a) If the sample size is bigger, the interval is narrower.

(b) If the sample size is smaller, the interval is narrower.

(c) If the population size is bigger, the interval is narrower.

(d) If the population size is smaller, the interval is narrower.

The E(T) is 4 when A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on).

Given that,

A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on). The heads and tails are recorded in order. The game is over and the winner is the person who throws the tail if there is a head followed by a tail (HT sub-sequence).

We have to find what is the anticipated game length. Let the game continue for T number of coin tosses. Find E (T).

We know that,

Here,

E(T )=first time sequence HT occurs

E(T) = P(first H)× P(expected number till 1st T |first H)+ P(first T)× P(expected number till 1st HT |first T)

E(T) =0.5×(1+2)+0.5×(1+E(T))

0.5×E(T)=0.5×4

E(T) =4

Therefore, The E(T) is 4 when A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on).

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Answer:

Yes, the measurements 3cm, 4cm and 5cm are possible to create a triangle!

Step-by-step explanation:

The correct answer is amount of dilute solution is 4 gallons and amount of concentrated solution is 6 gallons.

Let the dilute amount of solution be x and the amount of salt in the solution be 0.13x

Then the concentrated amount be 10-x  and the amount of salt in the solution be 0.33x (x-10).

Solving the equation

⇒ 0.13x + 0 .33 (10 - x ) = 2.5

⇒ 0.13x + 3.3 - 0.33x  = 2.5

⇒ -0.2 x = 2.5 - 3.3

⇒ -0.2x = - 0.8

⇒ x = 4

Hence, the amount of dilute solution is 4 gallons and amount of concentrated solution is 6 gallons.

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The point-slope form of the line is y - 2 = 1/3(x - 3).

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

The equation of the line into point slope-form is equal to

y - y1 = m(x - x1)

slope(m) = 1/3

(3,2)....x1 = 3 and y1 = 2

now we sub

y - 2 = 1/3(x - 3)

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The correct option is B is correct that is by setting access to private on the class fields using the correct notation.

Given that,

Data hiding refers to the protection of sensitive data from outside code for an object. This is achieved using Options

A) Making use of the class methods' private access specifier.

B) By setting access to private on the class fields using the correct notation.

C) Using the class methods' public access specifier.

D) Using the class definition's private access specifier.

Whichever choice is accurate must be determined.

We know that,

The private modifier limits access to a class's methods or properties from any code that is outside the class, but the public access modifier permits a code from inside or outside the class to access the class's methods and properties.

Therefore, The correct option is B is correct that is by setting access to private on the class fields using the correct notation.

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The conclusion of step 4 and step 5 are not valid . Therefore, this is an invalid proof that all isosceles triangles.

Each step is valid, but the conclusion is not. At the end of step 4, there are a series of isometric maps that lead A to D and C to F, as claimed.. After the final rotation in Step 5, the sequence of isometries takes B to E and C to F —but here’s the hitch—there is no reason why it should still take A to D, in fact it can’t take A to D unless the rotation angle is zero.

If the rotation angle in Step 5 is zero, then the isometries take [A,B,C] to [D,E,F] and the two triangles are indeed similar. But this requires the dilation in Step 2 to have made A′B′ congruent to DE , in other words, it requires assuming the triangles are similar before performing any of of the transformations.

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Complete Question:

This is an invalid proof that all isosceles triangles are similar. Explain which step is invalid and why. 1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF. 2. Dilate triangle ABC to a new triangle A'B'C' using center C and scale factor DF/AC so that A'C= BC - DF = EF. 3. Translate by directed line segment CF to take A'B'C' to a new triangle A" B" F. Since translation preserves distance, A"F = A'C=DF and B" F = BC = EF. 4. Since A"F=DF, we can rotate using center F to take A" to D. 5. Since B" F = EF, we can rotate using center F to take B" to E. 6. We have now established a sequence of dilations, translations, and rotations that takes A to D, B to E, and C to F, so the triangles are similar.

The answer is all real numbers greater than or equal to -3, as domain and range.

What is the domain and range of function?

A function's domain and range are its components. A function's range is its potential output; its domain is the set of all conceivable input values. Domain, Function, and Range. If a function f: A B exists that maps every element in A to an element in B, then A is the domain and B is the co-domain. The image of an element 'a' under a relation R is provided by 'b,' where (a,b) R. The set of photographs makes up the function's range.

The domain of a relation or a function is the set of all possible values for an input in that relation/function.

The range of a relation or function is the set of all possible values that can be the result of a relation or function.

From the graph, nothing can be seen on the left side of x = - 3 and the graph is continuous and going in the direction of infinity on the right side of the x axis.

Hence all real numbers greater than or equal to -3

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y-intercept of the function = 4

What in mathematics is a y-intercept?

A point on the y-axis at which the slope of a line passes is referred to as an intercept in mathematics.

It is a place on the y-axis where a straight line or a curve crosses. This is shown by writing the equation for a line as y = mx+c, where m denotes the slope and c the y-intercept.

Here the given function is

f(x) = 4 – 5x

Which can be rewritten as

f(x) = – 5x + 4

Which is of the form f(x) = mx + c

Where m = - 5 , c = 4

Hence y-intercept of the function = 4

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The complete question is -

What is the y-intercept of the function f(x)=4 – 5x?

–5

–4

4

5

By using the concept of relation, it can be proved that

If R is a Reflexive relation, then [tex]R^{-1}[/tex] is a Reflexive relation

If R is a Symmetric relation, then [tex]R^{-1}[/tex] is a Symmetric relation

If R is a Transitive relation, then [tex]R^{-1}[/tex] is a Transitive relation

What is a relation?

Relation on a set [tex]X_1, X_2,....,X_n[/tex] is the subset of the cartesian product

[tex]X_1 \times X_2 \times..... \times X_n[/tex]

A)

Let R be a reflexive relation .

Let (x, x) ∈ R

Then (x, x) ∈ [tex]R^{-1}[/tex]

So [tex]R^{-1}[/tex] is reflexive

B)

Let R be a symmetric relation such that [tex]xR^{-1}y[/tex] holds
so yRx holds

Since R is symmetric, xRy holds

[tex]yR^{-1}x[/tex] hold

[tex]R^{-1}[/tex] is symmetric

C)

Let R be a transitive relation such that [tex]xR^{-1} y[/tex] and [tex]yR^{-1}z[/tex] holds

Then yRx and zRy holds

Since R is transitive

zRx holds

[tex]xR^{-1}z[/tex] holds

[tex]R^{-1}[/tex] is transitive

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Complete Question

Let R Be A Relation On A Set A. Prove The Following: A) If R Is Reflexive, Then [tex]R^{-1}[/tex] Is Reflexive. B) If R Is Symmetric, Then [tex]R^{-1}[/tex]Is Symmetric. C) If R Is Transitive, Then [tex]R^{-1}[/tex] Is Transitive.

The correct answer is mean.

The characteristic which is being calculated here is the mean or the average of the data set.

(20.73 + 20.76 + 20.68 + 20.75)/4

when we divide it by 4 because there are four data sets

= 82.92 / 4

= 20.73

The complete question is 'Francine makes several measurements of the mass of a metal block and the data set is shown in the table below. The measurement mass of metal blocks(g) are a) 20.73 b) 20.76 c) 20.68 d) 20.75 . After analyzing the given data set, Francine calculates a value of 20.73 g so which of these characteristics has been calculated?'

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Maintenance primarily involves modifying programs to meet new business needs, but also debugging of errors that were not detected when testing the developed code.

Preventive maintenance schedules can be regular or periodic (time-based). When an issue is discovered, corrective maintenance is performed. Maintenance is predetermined and follows a factory schedule. Condition-based maintenance occurs when a situation or condition indicates the need for maintenance.

What is modifying a program?

A program modification is defined as a programmatic change that does not clearly qualify as a new program or a nonsubstantive change, such as a new program composed primarily of course work from a previously approved program; an approved program to be offered at an off-campus location; a change in the.

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Full Question:_____ primarily involves modifying programs to meet new business needs, but also debugging of errors that were not detected when testing the developed code.

Answer:

Please see the attachment below.

Step-by-step explanation:

Please give the brainliest, really appreciated.

The given pair of events are independent when your first coin flip results in heads. and your second coin flip results in heads.

Events that occur independently of any other events are referred to as independent events. if we flip a coin in the air and get the head, we will then flip the coin again, but this time we will get the tail. The occurrence of both events is unrelated in either instance. Tossing the coin the first time does not affect the outcome of the second toss.

Note that the events are not mutually exclusive as it is possible that both the first and the second toss are headed.

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Answer: 3 and 1

Step-by-step explanation: 3 is a prime number, which means its only factors are the number itself and 1. The number 3 is not divisible by anything else. You can only multiply 3 and 1.