3√y^2=6√x y=n√x

Find n​

The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The curve of the ball's path is given below.

d = -16t² + 32t + 9

The number of seconds to reach Jane is given as,

0 = -16t² + 32t + 9

16t² - 32t - 9 = 0

16t² - 36t + 4t - 9 = 0

4t(4t - 9) + 1(4t - 9) = 0

(4t - 9)(4t + 1) = 0

t = 9/4, -1/4

t = 2.25, -0.25

The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.

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Answer: 3 sports drinks

Step-by-step explanation:

6 divde by 2= 3

36 divided by 12 =3

in other words

3x2=6

12x3=36

hope this helps

Answer:

Step-by-step explanation:

the second because it has the squared sign most quadratic equations have squarred symbols

Answer:

is will end up costing 9.28

Step-by-step explanation:

all u need to do was divide the 4.06 by the 7 then the answer to that u multiple it by 16 and then u have ur final answer

Answer: $9.28

Step-by-step explanation:

Each bottle should cost 0.58 cents because 0.58 * 7=$4.06. SO if you multiply 0.58 by 16 (bottles) it will give you $9.28

The lateral surface area of a prism having a base of 18 inches, 12 inches, and a height of 8 inches is 240 inches² and the total surface area is 672 inches².

The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas in addition to the lateral surface area.

Given:

The side of the base of the prism, A = 18 inches,

The side of the base of the prism, B = 12 inches,

The height of the prism, h = 8 inches,

Calculate the lateral surface area of the prism by the formula given below,

[tex]lateral \ surface \ area = Sum \ of \ sides\times height[/tex]

Lateral surface area = (A + B) × h

Lateral surface area = (18 + 12) × 8

Lateral surface area = 240 inches²

Now calculate the total surface area by the formula given below,

[tex]S = (2 \times Base \ Area) + (Base \ perimeter \times height)[/tex]

S = (2 × 18  × 12) + (18 + 12)  × 8

S = 432 + 240

S = 672 inches²

Therefore, the lateral surface area of a prism having a base of 18 inches, 12 inches, and a height of 8 inches is 240 inches² and the total surface area is 672 inches².

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The 95% confidence interval that estimates proportion of 8th graders that are involved in an after school activity (0.745, 0.895) , the correct option is (a) .

In the question ,

it is given that ,

simple random sample of 100 8th graders is taken ,

that means ,

n = 100 ,

also given that , 82% of them are involved with some type of after school activity.

means ; p = 0.82 .

the level of significance (α) = 100 - 95 = 5% = 0.05 .

the critical value=  [tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.025}[/tex] = 1.959964   ......from the Z table .

the lower limit of the 99% confidence interval is = p - [tex]Z_{\alpha /2}[/tex]*SE

and the upper limit for the 99% confidence interval is=  p + [tex]Z_{\alpha /2}[/tex]*SE  .

the standard error is √(p(1-p)/n

= √(0.82(1 - 0.82)/100

= 0.0384

So , the lower limit is ⇒ 0.82 - 1.959964*0.0384

On simplification ,

we get ,

lower limit is = 0.7447006 ≈ 0.745 .

the upper limit is =  p + [tex]Z_{\alpha /2}[/tex]*SE  

= 0.82 + 1.959964*0.0384

On Simplification ,

we get ,

upper limit is = 0.8952994 ≈ 0.895 .

Therefore , the confidence interval is (0.745, 0.895) .

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Answer:

$13 overpayment

Step-by-step explanation:

We can find the amount Trevor should pay each month by dividing the $26,555 by 36 months:

               ($26,555/(36 months)) = $737.64 per month

Since Trevor decide to round up to the nearest dollar, he will pay $738 each month.  That's an overpayment of $0.361 each month.

After 36 months of overpaying by $0.361 each month, Trevor will have overpaid:

  ($0.36/month)*(36 months) = $13 overpayment

The truth value of the ~[P v (Q v R)] >~ (S v P) is true.

Truth-value, in logic, is the degree to which a particular proposition or assertion is true (T or 1) or false (F or 0). Because the truth-value of a compound proposition is a function of, or a quantity depending upon, the truth-values of its component components, logical connectives like disjunction and negation can be conceived of as truth-functions.

Given, ~[P v (Q v R)] >~ (S v P) since P v (Q v R) is true, thus ~ [ P v ( Q v R ) ] is false, therefore the implication is true.

⇒~[T v (F v T)] >~ (F v T)

⇒[F v (F v T)]>(T v T)

⇒[F v (F v T)]>(T v T)

⇒F v T

⇒T

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The equation of the line normal to the curve y = square root(3x² + 2x) at point (2,4) is given as follows:

y - 4 = -4/7(x - 2).

The equation of the line normal to a curve follows the point-slope definition of a linear function, given as follows:

y - y' = m(x - x').

The function in this problem is defined as follows:

y = square root(3x² + 2x).

Then the derivative of the function, applying the chain rule, is given as follows:

y' = (6x + 2)/(2 x square root(3x² + 2x))

y' = (3x + 1)/square root(3x² + 2x)

At x = 2, the numeric value of the derivative is of:

y' = 7/square root(16) = 7/4.

The slope of the normal line is calculated as follows:

m x 7/4 = -1

m = -4/7.

(as the normal line is perpendicular to the tangent line, which has slope equals to the numeric value of the derivative at the point).

The coordinates of the point at (2,4), hence:

x' = 2, y' = 4.

Then the definition of the normal line is given as follows:

y - 4 = -4/7(x - 2).

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The true or false values of the statements are:

From the question, we have the graph which represents the given parameters that can be used in our computation

Analysing the graph, we have:

The graph crosses the y-axis at y = 18

This means that the y-intercept of the graph is

y-intercept  = 18

This in other words mean that:

The cost of the book is $18

So, (a) is true

Also, the graph crosses the x-axis at x = 90

This means that the x-intercept of the graph is

x-intercept  = 90

This in other word mean that:

Giselle gets $18 if she pulls all the weed (i.e. 90 weeds) in the garden

So, (b) and (d) are true

The amount paid by her grandma is calculated as

Amount = 18/90

Amount = 1/5

So, (c) is true

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The ratio of p : q in its simplest form is 5 : 1

The unknown numbers are p and q

(p - 5) / (q - 5) = 9/1

(p + 20) / (q + 20) = 7/3

From equation (1)

cross product

1(p - 5) = 9(q - 5)

p - 5 = 9q - 45

p = 9q - 45 + 5

p = 9q - 40

From equation (2)

3(p + 20) = 7(q + 20)

3p + 60 = 7q + 140

Substitute p = 9q - 40 into 3p + 60 = 7q + 140

3p + 60 = 7q + 140

3(9q - 40) + 60 = 7q + 140

27q - 120 + 60 = 7q + 140

27q - 60 = 7q + 140

27q - 7q = 140 + 60

20q = 200

divide both sides by 20

q = 200/20

q = 10

Substitute q = 10 into p = 9q - 40

p = 9q - 40

p = 9(10) - 40

p = 90 - 40

p = 50

In conclusion, the ratio of p to q = 50 : 10

= 50/10

= 5/1

= 5:1

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Answer: below

Step-by-step explanation:

A. x=20+2n n= number of months

y=10(1+0.15)^n

B.

x 20,22,24,26,28,30....40

y 12.5,13.225,15.2,....40.5

C. The solution is 11 months because at 10 months even though the number of animals surpass the number of homes, you cannot have half a animal.

D.

In step 1, y was made the subject of the second equation to get:

y=5x-4

To proceed, the next step is to substitute the expression into the other equation, not the equation we solved for y.

8x+2y=-12

8x+2(5x-4)=-12

8x+10x-8=-12

18x=-12+8

18x=-4

x=-[tex]\frac{4}{18}[/tex]

x=[tex]\frac-{2}{9}[/tex]

answer=  the value of x is -2/9

Answer:

Step-by-step explanation:

0 is the answer

At a = √25/π^2 - 0.04 revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.

In the given question, we have to find how many revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.

r = acosti + asintj + 0.2tk, length = 10 unit

So |r| = [tex]\int^{2\pi}_{0}\sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}dt[/tex]

From the given equation,

x = acost, y = asint, z = 0.2t

dx/dt = -asint, dy/dt = acost, dz/dt = 0.2

10 = [tex]\int^{2\pi}_{0}\sqrt{(-a\sin t)^2+(a\cos t)^2+(0.2)^2}dt[/tex]

10 = [tex]\int^{2\pi}_{0}\sqrt{a^2\sin^2 t+a^2\cos^2t+0.04}dt[/tex]

As we know that sin^2x+cos^2x = 1. So

10 = [tex]\int^{2\pi}_{0}\sqrt{a^2+0.04}dt[/tex]

10 = [tex]\sqrt{a^2+0.04}\int^{2\pi}_{0}dt[/tex]

10 = [tex]\sqrt{a^2+0.04}\cdot[t]^{2\pi}_{0}[/tex]

10 = √(a^2+0.04)∙[2π-0]

2π√(a^2+0.04) = 10

Divide by 2π on both side, we get

√(a^2+0.04) = 5/π

Taking square on both side, we get

a^2+0.04 = 25/π^2

Subtract 0.04 on both side, we get

a^2 = 25/π^2 - 0.04

taking square root on both side, we get

a = √25/π^2 - 0.04

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The right question is:

How many revolutions will the circular helix

r = acosti + asintj + 0.2tk

make in a distance of 10 units measured along the z-axis?

Answer:

Hi

Step-by-step explanation:

I am just reply to see if i really understand that problem

Let's assume s the present age of the son, and f the present age of the father.

The age of the son After 10 years is equal to the age of the father before 20 years:

s+10=f+10-20

f=3s

=> s+10=f-10

=> s+10=3s-10

=> 2s=20

=> s=10 and  f=30

We utilize a two factors, independent measurements ANOVA, where, factor has 2 level and a factor likewise has 2 levels.

A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.

Factors and multiples are a part of our daily life. For example, they are employed in arranging objects in a box, handling money, recognizing patterns in numbers, solving ratios, and working with expanding

A number totally divides the provided number without leaving any residual is said to be the factor of that number.

The components of a number might be positive or negative. For example, let us find the factors of 8. Since 8 is divisible by 1, 2, 4, and 8, we may list the positive factors of 8 as, 1, 2, 4, and 8. Apart from this, 8 has negative elements as well, which might be stated as, -1, -2, -4,

According to our question-

Degrees of freedom for the F-test of the two way ANOVA

In this case, we utilize an ANOVA with two independent variables and two factors, each with two levels.

So, here,

= 2 for the number of layers of A

= B's level count is 2,

Moreover, n = sample size in each treatment condition is equal to 10.

So we have,

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of interaction effect (A x B) = ( - 1)( - 1) ( - 1)

= (2-1)(2-1) (2-1)

= 1

And = df of within variation (i.e. error variation) =

= 2 x 2 x (10 - 1) (10 - 1)

= 36

Consequently, the df value for the F-ratio measuring factors-primary A's impact is

= () ()

= (1, 36) (1, 36)

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Answer:

100 metere is 1 km

Thanks for the question

Answer:

50 degrees

Step-by-step explanation:

100 - 60 degrees

therorem

Answer:

box plot becauase wire width is numerical :)

Step-by-step explanation:

There is enough evidence to conclude that the doctor's claim is true.

We have given that,

population mean μ = 11 pounds

sample size n = 25

sample mean x = 12 ponds

standard deviation σ = 4 pounds

so the null hypothesis is H₀ : μ = 11 pounds

and the alternative hypothesis is Hₐ : μ > 11 pounds

now we will calculate test statistics,

t = (x-μ)/(σ/√n)

 = (12 - 11)/(4/√25)

 = 1/(4/5)

t = 1.25

p-value from the z-table is 0.10565

the result is non significant at p < 0.01.

Hence the null hypothesis rejected .

Therefore there is enough evidence to conclude that the doctor's claim is true.

The level of significance is the measurement of the statistical significance. It defines whether the null hypothesis is assumed to be accepted or rejected. It is expected to identify if the result is statistically significant for the null hypothesis to be false or rejected.

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Answer:

Answer Option C: SSA test

The disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values ​​is m, the alternative will be -1/m.

A relationship between two terms on either side of an equal sign is depicted by a straightforward equation.

Simple equations also pursue one or a mixture of the four arithmetic computations of addition, simple arithmetic, multiplication, and division.

There are three basic forms of the system of equations: point-slope form, standard form, and slope-intercept form.

So, Shannon's error:

In a rectangle, the neighboring sides are perpendicular to one other, whereas parallel runs between the opposing sides.

The slope of line segments is equal, and the slope, of a perpendicular line to some other line with a slope, m, is -1/m , thus the slopes of the axis of symmetry should be equal, which gives:

The equation should consist of two sets of linear equations with equal slopes: B. Pair y = -x + 6 and y = -x - 5

Therefore, the slopes of the other two lines are -1/-1 = 1 and the equations of the other two lines are y = x - 4 and y = x - 5 respectively.

Therefore, the disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values ​​is m, the alternative will be -1/m.

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Considering definition of probability, the probability that a student chosen from the class at random has either blonde hair or brown hair is 36.

Probability is the possibility that a phenomenon or an event will happen, given certain circumstances and it is expressed as a percentage.

The union of events is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs and it is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

Two events, A and B, are incompatible when they have no element in common and it is true that P(A∩B)=0. Then:

P(A∪B)= P(A) + P(B)

You know:

The probability that a student chosen from the class at random has either blonde hair or brown hair is calculated as:

P(blond hair or brown hair)= P(blond hair) + P(brown hair)

Then:

P(blond hair or brown hair)= 12 + 24

P(blond hair or brown hair)= 36

Finally, the probability in this case is 36.

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Answer: 1 decameter

Step-by-step explanation:

Answer:

1 decameter

Step-by-step explanation:

1 decameter is 10 meters or 1000 centimeters

The area of the given irregular figure is 143 square inches.

What is area of irregular figure?

We divide an irregular shape into its component common shapes before calculating its area. After that, we add the areas of each shape. For instance, if a square and a triangle make up an irregular polygon, the area of the polygon is equal to the sum of their areas.

We have to divide the given irregular figure into known shapes.

That is rectangle and square.

Rectangles with sides '7 in and 10 in' and '12 in and 4 in' and the square of side 5 in.

So, the area of irregular figure is,

Area = Area of rectangle + Area of rectangle + Area of square

= (7 x 10) + (12 x 4) + 5^2

= 70 + 48 + 25

Area = 143

Hence, the area of the given irregular figure is 143 square inches.

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The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).

We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;

x⁴ divided by 3x equals 2x³

3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³

subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27

3x³ divided by 3x equals x²

3x + 4 multiplied by x² equals 3x³ + 4x²

subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27

9x² divided by 3x equals 3x

3x + 4 multiplied by 3x equals 9x² + 12x

subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27

-15x divided by 3x equals -5

3x + 4 multiplied by -5 equals -15x - 20

subtract -15x - 20 from -15x + 27 will result to a remainder of 47

using the remainder theorem, x = -4/3 from the the divisor 3x + 4

thus:

f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}

f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27

f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}

f(-4/3) = (5919 - 2112)/81

f(-4/3) = 3807/81

f(-4/3) = 47

Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.

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Answer:

1/3 * [tex]4\pi[/tex] * h = 207, h = 155.25[tex]\pi[/tex]

Step-by-step explanation:

Since we know the area of the base is [tex]4\pi[/tex], that means the volume of the cone is:

1/3 * [tex]4\pi[/tex] * h

If we substitue, we get:

1/3 * [tex]4\pi[/tex] * h = 207

(This is the answer! If you want to solve, go below)

Now, we just solve

[tex]4\pi\\[/tex] * h = 621

h = 621/[tex]4\pi\\[/tex]

h = 155.25[tex]\pi[/tex]

The total distance traveled by the object after 30.0 seconds is 450 meters.

For the stated function;

As, the total distance is modelled by the quadratic equation-

Let the quadratic equation be-

d = at² + bt + c

For (10, 50)

d = a(10)² + (10)b + c  ....eq 1

For (20, 200)

d = a(20)² + (200)b + c  ....eq 2

For (0, 0)

d = a(0)² + (0)b + c  ....eq 3

Solving eq 1, 2 and 3

a = 1/2 ; b = 0 and c =0

Thus, equation for the distance travelled by the object is-

d = 1/2 t²

For t = 30. sec

d = 1/2 (30)²

d = 450 m

Thus, the total distance traveled by the object after 30.0 seconds is 450 meters.

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