On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 7 kg weighs 63 N. Find the weight
of an object whose mass is 10 kg.

The average rate of change of g(x) over the interval [-3, 3] is 2.

For a function f(x), we define the rate of change over an interval (a, b) as:

(f(b) - f(a))/(b - a)

Here we have the interval [-3, 3] and the function:

g(x) = x^2 + 2x + 8

Then the average rate of change over that interval will be:

[ g(3) - g(-3)]/(3 - (-3))

The values in the denominator are:

g(3) = 3^2 + 2*3 + 8 = 9 + 6 + 8  =23

g(-3) = (-3)^2 + 2*-3 + 8 = 9 - 6 + 8 = 11

Replacing that we get:

[23 - 11]/(3 + 3) = 12/6 = 2

The average rate of change over that interval is 2.

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The sample mean is 16 times used to compute the confidence interval.

What is the z test?

If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.

The given sample value 100 observation,

Sample mean = (Lower limit + Upper limit) / 2 = (14.355 + 17.645) / 2 = 16

Hence, the sample mean is 16 time used to compute the confidence interval.

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According to the SAS congruence rule, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Congruent triangles have the same size and shape. This implies that the corresponding sides and angles are also equal.

The Side-Angle-Side (SAS) rule is used to determine whether a given set of triangles is congruent.

According to the SAS rule, triangles are congruent if two sides and the included angle of one are equal to two sides and the included angle of another.

As shown in Figure

If AC = PQ, BC = PR, and angle C = angle P, then triangle ABC is congruent to triangle QRP according to the SAS rule.

Thus, the SAS rule can be used to determine whether or not two triangles are congruent.

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The explanation about counterexample for the conjecture is describe below.

The term counterexample alludes to an occasion or model that offers the expression bogus. This is utilized in rationale to check in the event that an assertion is valid or not. Counter model will quite often counter the explanation being talked about with admirable sentiments.

The inquiry needs to show the relationship that might exist among perimeter and area of a rectangle.

The counterexample gave the aspects that gave the border which is 40 however neglected to give area of 1 square unit

Thus, A rectangle with length 19.99 units and width 0.01 unit has a perimeter of 40 units and an area of 0.1999 square unit.

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The expression for the sequence 48, 49, 50, 51, is aₙ = n + 47

The sequence is an arithmetic progression. Therefore, the expression of the sequence can be ascertain with the arithmetic formula as follows:

aₙ = a + (n - 1)d

where

Therefore,

a = 48

d = 49 - 48 = 1

Hence,

aₙ = 48 + (n - 1)1

aₙ = 48 + n - 1

aₙ = 48 - 1 + n

aₙ = n + 47

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Proved that a quadrilateral is a square then the quadrilateral is also a rectangle.

A quadrilateral is a closed shape created by uniting four points, any three of which cannot be collinear. Four sides, four angles, and four vertices make up a quadrilateral.

Quadrilaterals have a few characteristics as follows:

Each side of figure has four sides.

Each of them has four vertices.

The Two diagonals are present.

The sum of all interior angles is 360 degrees.

Given to prove if a quadrilateral is a square, then the quadrilateral is a rectangle.

The Square has four equal sides, and all four angles.

Rectangle has equal opposite sides, and all four angles are the right angle.

Thus, the two sides of the square can be increased to form a rectangle.

Hence, We have Proved that if a quadrilateral is a square then the quadrilateral is also a rectangle.

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The four types of representation of linear functions are graphs, tables , equations or verbal descriptions.

A linear function is of the mathematical form y = ax + b. This function can be represented in various ways.

The four types of linear function representations are:

       Example: a linear function is of the form: y = mx+c

        The variable y is twice the value of variable x (y = 2x)

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The odd for the event happening is 0,45%.The probability of event happening is quite posssible but it has less probability the event is not on the odds than the event is not happening.

Probability of event happening always count as two probability where it is 0 and 1 ,or the event is happening and not. To count odds for the event happening you can use this formula: odds = event happening : total probability/experiment x 100%. As per given the odds is 47 and total experiment is 47, the calculation will be:

odds = [tex]\frac{21}{47}[/tex] x 100% = 0.44680851063%

odds = 0,45%

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The time Fireman Fred spends running in 4 weeks, found from the average time it takes him to run 1 kilometer is 6.6 hours.

An average is the ratio of the sum of a set of values to the number of values in the set.

The distance Fireman Fred runs 4 morning in a week = 3 kilometers

The time it takes to run a kilometer = 8 minutes and 15 seconds

15 seconds = 0.25 minutes, therefore;

The time it takes to run a kilometer = 8.25 minutes

The time Fireman Fred spends running in 4 weeks is found as follows;

The distance Fireman Fred runs in a week = 3 × 4 kilometers = 12 kilometers per week

The total distance he runs in 4 weeks, D, is obtained using the equation;

D = 4 weeks × 12 kilometers per week = 48 kilometers

The total time = Time per kilometer × Number of Kilometers

The total time = 8.25 minutes/kilometer × 48 kilometers = 396 minutes

There are 60 minutes in one hour, therefore;

396 minutes = 396 minutes × (1/60) hour/minutes = 6.6 hours

The time Fireman Fred spends running over 4 weeks is 6.6 hours

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The Height and volume of the pyramid is ,

i) Height = 15.35cm

ii) Volume= 690.75 [tex]cm^3[/tex].

What is pyramid ?

 A three-dimensional shape is a pyramid. Flat triangular sides that are joined at a common point known as the apex define the polygonal base of a pyramid. By fusing the bases together at the peak, a pyramid is created. The lateral face, a triangular feature formed by the connection of each base edge to the apex, is present.

Here slant height l = 16cm and sides of the rectangular base is ,

length l = 15cm and width w = 9 cm.

Side length = 9/2 = 4.5cm

Using Pythagorean theorem ,

=> Height h =  [tex]\sqrt{16^2-4.5^2}[/tex]

=> height h = 15.35 cm

Now volume of pyramid is ,

=> V = 1/3 * Base area * height cubic unit

=> V = 1/3 *15*9*15.35

=> V = 690.75 [tex]cm^3[/tex]

Hence the Height and volume of the pyramid is ,

i) Height = 15.35cm

ii) Volume= 690.75 [tex]cm^3[/tex].

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The two functions are a part of the same family of functions

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

Equations

y= -80(x-1)^{2} + 80

y=-0.49(x-12)^2 +70

These equations can be re-expressed properly as follows

So, we have the following representation

y= -80(x-1)² + 80

y=-0.49(x-12)² +70

From the above representations, we can see that the degrees of both equations are 2

This means that the equations are quadratic equations

This is so because a quadratic equation is represented as y= a(x - h)² + k

Hence, the two functions are a part of the family of quadratic equation  functions

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The mean of a observed values approaches the population mean more and more as the number of data points gathered rises.

The average calculated from the group members, distribution, or population is known as the population mean.

Thus, choose a population with a finite mean and a random sample of observations. The mean of a observed values approaches the population mean to a greater extent as the number of data gathered rises.

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The constant of proportionality in the equation c = 8m will be; 8.

A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.

We have been given C = 8m is an equation and the relationship between c and m is direct.

This means that dividing both sides of the equation by m, we have;

C/m = 8m/m

c/m = 8

Therefore, the constant of proportionality is 8

It is found that the constant of proportionality for which c = 8m will be 8.

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Answer:

Step-by-step explanation:

y = (2x^2-2x+3x-3)(x-4)

y = (2x^2+x-3)(x-4)

y = 2x^3+x^2-3x-8x^2-4x+12

y = 2x^3-7x^2-7x+ 12

a : 2x^3

b : 2

c : 3

d

lim x-> +oo x^3(2-7/x-7/x^2 + 12/x^3)

lim x-> +oo  +oo(2-7/oo - 7/oo + 12/oo)

lim x->+oo   +oo(2-0-0+0)

lim x->+oo    +oo

lim x-> -oo x^3(2-7/x-7/x^2 + 12/x^3)

lim x-> -oo  -oo(2-7/-oo - 7/-oo + 12/-oo)

lim x-> -oo   -oo(2-0-0+0)

lim x-> -oo    -oo

e

y = 2x^3-7x^2-7x+ 12

y’ = [2(x+h)^3 - 7(x+h)^2 - 7(x+h) + 12 - 2x^3 +7x^2 + 7x - 12]/h

y’ = [2(x^3+h^3+3x^2h+3h^2x) -7(x^2+h^2+2xh)-7x-7h-2x^3+7x^2+7x]/h

y’ = [2x^3+2h^3+6x^2h+6h^2x-7x^2-7h^2-14xh-7h-2x^3+7x^2]/h

y’ = [2h^3+6x^2h+6h^2x-7h^2-14xh-7h]/h

y’ = h (2h^2 + 6x^2 + 6hx - 7h - 14x - 7)/h

y’ = 2h^2 + 6x^2 + 6hx - 7h - 14x - 7

lim h->0  (6x^2 - 14x - 7)

y’ = 6x^2 - 14x - 7

y’’ = [6(x+h)^2 - 14(x+h) - 7 - 6x^2 + 14x + 7]/h

y’’ = [6(x^2+h^2+2xh) -14x-14h -6x^2+14x]/h

y’’ = [6x^2+6h^2+12xh-14h-6x^2]/h

y” = h(6h+12x-14)/h

y” = 6h + 12x - 14

lim h->0 (12x-14)

y” = 12x -14

12x - 14 = 0

6x - 7 = 0

x = 7/6

(2 *7/6+3)(7/6-1)(7/6-4)

(7/3 + 3) ( 1/6) (-17/6)

(16/3)(-17/36)

4/3 * -17/9

-68/27

turning point (7/6 ; -68/27)

f

(2x + 3)(x - 1)(x - 4) = 0

x = -3/2

x = 1

x = 4

A( -3/2,0)

B (1,0)

C (4,0)

g

y= 12

D (0, 12)

Answer:

a.  2x³

b.  2

c.  3

d.  As x → -∞, f(x) → -∞.   As x → ∞, f(x) → ∞.

e.  (-0.4, 13.6) and (2.8, -18.6).

f.  (-1.5, 0),  (1, 0),  (4, 0)

g.  (0, 12)

h.  See attachment.

Step-by-step explanation:

Given polynomial:

[tex]y=(2x+3)(x-1)(x-4)[/tex]

Leading term and Leading coefficient

The given polynomial is in factored form.

To find the leading term and the leading coefficient, simply multiply the variable terms of the factors:

[tex]\implies 2x \cdot x \cdot x = 2x^3[/tex]

Therefore:

Degree of the polynomial

The degree of the polynomial is the exponent of the leading term.

Therefore, the degree of the given polynomial is 3.

End behaviour

As the degree of the polynomial is odd and the leading coefficient is positive, the end behaviour of the function is:

Turning points

The x-values of the turning points are when the derivative of the function equals zero.

Expand the polynomial:

[tex]\implies y=(2x+3)(x-1)(x-4)[/tex]

[tex]\implies y=(2x+3)(x^2-5x+4)[/tex]

[tex]\implies y=2x^3-10x^2+8x+3x^2-15x+12[/tex]

[tex]\implies y=2x^3-7x^2-7x+12[/tex]

Differentiate:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=6x^2-14x-7[/tex]

Set it to zero and solve for x:

[tex]\implies 6x^2-14x-7=0[/tex]

Solve using the quadratic formula:

[tex]\implies x=\dfrac{-(-14) \pm \sqrt{(-14)^2-4(6)(-7)}}{2(6)}[/tex]

[tex]\implies x=\dfrac{14 \pm \sqrt{364}}{12}[/tex]

[tex]\implies x=\dfrac{14 \pm 2\sqrt{91}}{12}[/tex]

[tex]\implies x=\dfrac{7\pm \sqrt{91}}{6}[/tex]

[tex]\implies x \approx-0.4, \;2.8\; \; \sf (1\;d.p.)[/tex]

Substitute the found values of x into the original polynomial to find the y-values of the turning points:

[tex]x=\dfrac{7- \sqrt{91}}{6}\implies y=13.6\; \; \sf (1\;d.p.)[/tex]

[tex]x=\dfrac{7+ \sqrt{91}}{6}\implies y=-18.6\; \; \sf (1\;d.p.)[/tex]

Therefore, the turning points of the polynomial (to the nearest tenth) are:

x-intercepts

The x-intercepts are when the function equals zero.

As the function is already in factored form, simply equal each of the factors to zero and solve for x:

[tex]\implies (2x+3)=0 \implies x=-1.5[/tex]

[tex]\implies (x-1)=0 \implies x=1[/tex]

[tex]\implies (x-4)=0 \implies x=4[/tex]

Therefore, the x-intercepts are:

y-intercept

The y-intercept when x = 0:

[tex]\implies y=(2(0)+3)(0-1)(0-4)[/tex]

[tex]\implies y=3 \cdot -1 \cdot -4[/tex]

[tex]\implies y=12[/tex]

Therefore, the y-intercept is:

Sketch the graph

To sketch the graph:

The moment of inertia of a cube with mass m = 0.500kg and side lengths s = 0. 030m about an axis which is both normal (perpendicular) to and through the center of a face of the cube is I = 2.205x10^-4 kg/m^2.

Here Given mass m = 0.5 kg

And side length = 0.03 m

Moment of inertia I = mass x radius of rotation squared

I = mr^2

In this case, the radius of rotation is about an axis which is both normal (perpendicular) to and through the center of a face of the cube.

Calculating from the dimensions of the the box, the radius of rotation r = 0.021 m

Therefore, I = 0.5 x 0.021^2 = 2.205x10^-4 kg/m^2

Hence the answer is the moment of inertia of a cube with mass m = 0.500kg and side lengths s = 0. 030m about an axis which is both normal (perpendicular) to and through the center of a face of the cube is I = 2.205x10^-4 kg/m^2.

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The 10 yearly payments worth is $ 7299806.

The current value of a future sum of money or stream of cash flows at a certain rate of return is known as present value (PV). A discount rate or the interest rate that could be earned if invested is added to the future value for present value.

it is given that

PMT =$ 900000

Rate = 4%

years = 10

using the formula

PV = [tex]A * \frac{1 - \frac{1}{(1+R)^{N} } }{R}[/tex]

PV = (900000/0.04) × (1 - (1/ (1+0.04)^10))

PV = $ 7299806

the payment you receive today is $7299806

so, it is better to accept 10 annual payments as it has a higher value.

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Annual percentage rate is 14.925% of credit card rate 0.04089.

The phrase annual percentage rate of charge (APR), which can also be referred to as a nominal APR or an effective APR (EAPR), refers to the interest rate for the entire year (annualized), as opposed to only a monthly fee or rate, as applied on a loan, home loan, credit card, etc. An annual percentage rate, or APR, is a figure that expresses the entire cost of borrowing money as a proportion of the loan's principle. An accurate picture of how much it costs to borrow money is intended to be provided by the APR on a loan or credit card.

Given,

Daily rate = 0.04089

Rate = 365

Annual percentage rate = Daily Rate% ×Rate

Annual percentage rate = 0.04089 × 365

Annual percentage rate = 14.925%

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Answer:

b=21

Step-by-step explanation:

-3=3(-8)+b

-3=-24+b

+24 +24

21=b

Hopes this helps

When the null hypothesis is rejected in ANOVA analysis, we can test for differences between treatment means by doing a t-test.

It is statistically possible to compare the means of two or more groups of data using the ANOVA approach. It includes comparing the null hypothesis, which states that the means of the groups are equal, to the alternative hypothesis, which states that at least one of the means is different. If the null hypothesis is disproved, it signifies that the group means deviate significantly from one another.To test for these differences, we may use a t-test, which is a statistical test used to evaluate if the means of two groups are significantly different from one another. With the use of a t-test, we may assess if there are any statistically variations in terms of the 2 groups.

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Answer:

x = 10

Step-by-step explanation:

[tex]\frac{x-4}{4}[/tex] = [tex]\frac{15}{x}[/tex]  ( x > 0 )

x(x - 4) = 15(4)

x² - 4x - 60 = 0

( x + 6 )( x - 10 ) = 0

x = 10

Because it only considers the worst possible outcomes, the maximin decision criterion has the least downside risk.

Wald's maximin model is a non-probabilistic decision-making model in game theory and decision theory.

It says that while choosing a course of action, the decision-maker should choose the one whose greatest (highest) loss is better than the least (minimum) loss of all other options that are feasible under the current conditions. The approach that maximizes one's own lowest payout is referred to as "maximin" in non-zero-sum games.

When given a choice between numerous options, the maximin approach instructs managers to consider each option's worst-case outcome. This presupposes that each choice has a number of possible outcomes.

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By applying the operation of addition we observed that the sum of two number are belong to the given set

take any two numbers suppose a and b

and applying the operation addition

Irrational numbers are not closed under addition.

The closure property of addition in irrational numbers say that sum of two irrational number is always a rational number, But this is not true. It is not necessary that the sum is always irrational some time it may be rational.

This can be understood with the help of an example:

let (2+√2) and (-√2) be two irrational number. Their sum is (2+√2)+(-√2) = 2, which is clearly a rational number.

Hence, irrational numbers are not closed under addition.

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Answer:

x= -1.5

Rounded: x= -2

Step-by-step explanation:

3(-6x)+5=32

-18x+5=32

      -5. -5

-18x=27

/-18.  /-18

x=-1.5

And I guess I round to a whole number

x=-2

Hopes this helps please mark brainliest

3(-6x) + 5 = 32

multiply out left side:

-18x + 5 = 32

subtract 5 from both sides:

-18x = 27

divide both sides by-18:

x = -3/2

or

x = -1.5

Answer:

[tex]\textsf{1.} \quad 2[/tex]

[tex]\textsf{2.} \quad -4[/tex]

[tex]\textsf{3.\quad und\:\!efined}[/tex]

[tex]\textsf{4.} \quad 0\;\;\textsf{(zero)}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Given points:

Substitute the given points into the slope formula:

[tex]\implies \textsf{Slope}=\dfrac{3-(-1)}{2-0}=\dfrac{4}{2}=2[/tex]

Given points:

Substitute the given points into the slope formula:

[tex]\implies \textsf{Slope}=\dfrac{6-(-10)}{2-6}=\dfrac{16}{-4}=-4[/tex]

Given points:

Substitute the given points into the slope formula:

[tex]\implies \textsf{Slope}=\dfrac{5-2}{3-3}=\dfrac{3}{0}=\textsf{und\:\!efined}[/tex]

Given points:

Substitute the given points into the slope formula:

[tex]\implies \textsf{Slope}=\dfrac{3-3}{5-2}=\dfrac{0}{3}=0[/tex]

The monthly payment needs to pay is  15,505.3.

What is the percent deposit?

Deposit Percentage refers to the percentage of total Deposit Exposures represented by any Deposit Lender's Deposit Exposure.

We have,

Car price to pay 137,825,

saved up a 10%

The rest can pay in 8 monthly deposits.

So, firstly we divide the total price amount by 10 to get the deposit amount,

137,825 /10 = 13,782.5

then minus this amount from the total amount,

137,825 - 13,782.5 = 1,24,042.5

again divide this amount by 8 to get monthly deposit,

monthly each payment = 1,24,042.5/8

= 15,505.3

Hence, the monthly payment needs to pay is  15,505.3.

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The probabilities of random survey of students are

Total number of engineering majors = 34

Total number of business majors = 24

Total number of science majors = 22

Total number of liberal arts majors = 16

Total number of students = 34 + 24 + 22 + 16

= 96 students

The probability = Number of favorable outcomes / Total number of outcomes

The probability of engineering majors = 34 / 96

= 17/48

The probability of business majors = 24 / 96

= 1/4

The probability of science majors = 22/96

= 11/48

The probability of liberal arts majors = 16/96

= 1/6

Hence, the probabilities are

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Answer:So for an isosceles right triangle with side length a , the hypotenuse has a length of a√2 . Similarly, if the hypotenuse of an isosceles right triangle has length of a , the legs have a length of a√2ora√22 each

Step-by-step explanation:

An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.

FOR EXAMPLE What is the length of the legs of an isosceles right triangle if the hypotenuse is 8 units?

2 Answers By Expert Tutors. For an isoceles right trangle, the legs each have length x and the hypotenuse has length x √2. Therefore, since the hypotenuse has length 8√2, the legs must each be of length 8.