At what point on the curve x = 6t2 + 6, y = t3 − 2 does the tangent line have slope 1 /2 ?

Answer:

height of the candle after 6 hours= 18.6 centimeters

Step-by-step explanation:

the function gives a line with a slope of −0.4.

the height of the candle after 11 hours is 16.6 centimeters.

after 6 hours, the height will be

But slope= y2-y1/x2-x1

Y2 is the unknown

Y1 = 16.6

X1= 11 hours

X2= 6 hours

y2-y1/x2-x1= -0.4

(Y2-16.6)/(6-11)= -0.4

(Y2-16.6)/(-5)= -0.4

(Y2-16.6)= -5( -0.4)

(Y2-16.6)= 2

Y2 = 2+16.6

Y2 = 18.6 centimeters

height of the candle after 6 hours= 18.6 centimeters

z = 3i / (-1 - i )

z = 3i / (-1 - i ) × (-1 + i ) / (-1 + i )

z = (3i × (-1 + i )) / ((-1)² - i ²)

z = (-3i + 3i ²) / ((-1)² - i ²)

z = (-3 - 3i ) / (1 - (-1))

z = (-3 - 3i ) / 2

Note that this number lies in the third quadrant of the complex plane, where both Re(z) and Im(z) are negative. But arctan only returns angles between -π/2 and π/2. So we have

arg(z) = arctan((-3/2)/(-3/2)) - π

arg(z) = arctan(1) - π

arg(z) = π/4 - π

arg(z) = -3π/4

where I'm taking arg(z) to have a range of -π < arg(z) ≤ π.

Answer:

may have different df values but they all have the same denominator

Step-by-step explanation:

In a two-factor analysis of variance, the F-ratios for factor A, factor B, and the AxB interaction _____. may have different df values but they all have the same denominator

In two--factor analysis of variance, the estimates of the variance can be obtained by partitioning the total sum of squares into three components corresponding to the three possible sources of variation , viz; Between Rows, Between Columns, and Within Samples or error.

As the number of rows and columns may differ the degrees of freedom differ with them.

In other words

Total df= Rows df + Columns df + Error df

Since the variance is identically the same for each row of the c values and variance is the same for each observation in the jth column of r values the sum of squares becomes an identity.

Therefore it may have different df values but they all have the same denominator.

closed interval on x=3 and open at x=5

for all values between these numbers, y=3

so [3,5)

Answer:

Solution : ( - 8, - 5π/3 )

Step-by-step explanation:

There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. For r < 0 we have the coordinates ( - 8, 60° ) and ( - 8, - 300° ) . - 300° in radians is - 5π/3, and hence our solution is option d. But let me expand on how to receive the coordinates. Again r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.

So when r is either negative or positive, we can tell that this point is 8 units from the pole. Therefore - r = - 8 in both our second cases ( we are skipping the first two cases for simplicity ). For r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.

Our first coordinate is ( - 8, 60° ). Theta will be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Our second point for - r will thus be ( - 8, - 300° ) . - 300° = - 5π/3 radians, and our coordinate will be ( - 8, - 5π/3 ).

Answer:

Step 1: Set the expression inside the square root greater than or equal to zero. Step 2: Solve the equation found in step 1. In this case, we divided by a negative number, so had to reverse the direction of the inequality symbol. Step 3: Write the answer using interval notation.

Find the circumference:

Circumference = 2 x PI x radius:

Circumference = 2 x 3.14 x 16 = 100.48 inches.

A full circle is 360 degrees, a 45 degree angle is 1/8 of a full circle.

Arc length = 100.48 / 8 = 12.56 inches.

Answer: 0.05412

Step-by-step explanation:

Formula : Odds of having an event is given by  [tex]o=\dfrac{p}{1-p}[/tex], where p = probability that event happens.

In terms to find p , we use [tex]p=\dfrac{o}{1+o}[/tex]

Given, he back of the ticket lists the odds of winning each dollar value: 0.05 for $10, 0.04 for $25, 0.01 for $50, and 0.003 for $100.

Let X be the worth of ticket.

Then, the probability that the ticket is worth at least $25 =

[tex]P(X\geq 25)=P(X=25)+P(X=50)+P(X=100)[/tex]

[tex]=\dfrac{0.04}{1+0.04}+\dfrac{0.01}{1+0.01}+\dfrac{0.003}{1+0.003}\\\\=0.05135[/tex]

The odds that the ticket is worth at least $25 = [tex]\dfrac{0.05135}{1-0.05135}[/tex]

=0.05412

hence, the odds that the ticket is worth at least $25 is 0.05412 .

Answer:

B. y = –2.9x + 13.5

Step-by-step explanation:

You can try to use the calculator to determine the best line for the values given; you will se that the calculator form, for the linear function is

y = a + bx, where a is the y intercept and b is the slope.

To determine the slope, we apply a formula, to calculate the product of the two xy and, x², plus the sum of each column.

x    y    xy    x²  

1  .  11 = 11 → x² = 1² = 1

2 .  8 = 16 → x² = 2² = 4

3 .  4 = 12 → x² = 3² = 9

4 .  1 = 4 → x² = 4² = 16

5 .  0 = 0 → x² = 5² = 25

Total x = 1 + 2 + 3 + 4 + 5 = 15

Total y = 11 + 8 + 4+ 1 + 0 = 24

Sum of xy = 11 + 16 + 12 + 4 + 0 = 43

Sum of x² =  1 + 4 + 9 + 16 + 25 = 55

n = 5

So b =  5 (43) - (15) . (24) / 5 (55) - 15² = -2.9

a =  y media - b . x media → a = 24/5 - (-2.9) . 15/5 = 13.5

Answer:

150

Step-by-step explanation:

70% of 500 people are adults and the remainder are children.

There are 150 children

Answer:

the answer is

-x-8y=8

or, x + 8y= -8

Step-by-step explanation:

4x - 6y = 13 - (5x + 2y = 5)

or, 4x - 6y = 13

- 5x - 2y = -5

-------------------------

- x - 8y = 8

Answer:

A and B

Step-by-step explanation:

Both points are in the shaded/blue zone

I hope this helps!

pls ❤ and give brainliest pls

Answer:

Yea both A and B are correct.

Step-by-step explanation:

if you can see you can put (-12,0) inside the shaded triangle also for (-10,1)

you can give brainlist to the person above :D

Answer:

The distance is 87.5 miles

Step-by-step explanation:

We can use a ratio to solve

1 in              3.5 inches

-----------  = ----------------

25 miles          x miles

Using cross products

1x = 3.5 * 25

x =87.5

The distance is 87.5 miles

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▹ Answer

87.5 miles

▹ Step-by-Step Explanation

[tex]\frac{1}{25} * \frac{3.5}{x} \\\\1 * 3.5 = 3.5\\25 * 3.5 = 87.5 \\\\Actual Distance = 87.5 miles[/tex]

Hope this helps!

CloutAnswers ❁

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The correct answer is D. Both A and B

Explanation:

Bartering is an economic system in which products are directly exchanged for other products. For example, a pound of oranges is exchanged for a pound of rice. Due to this, in bartering, there is no money or elements such as coins or bills that represent the value of products or services. This system has both advantages and disadvantages in comparison to the use of money.

In terms of disadvantages, bartering implies individuals need products or services they can use to exchange, which might not be possible for all individuals as not all individuals might produce a product or have a product other are interested in. Also, in bartering the value of products varies, for example, a pound of blueberries can be equal to a pound of rice, three pounds of rice, or even half pound of rice, as values change according to the situation of those participating in the exchange. This means, in bartering the value fluctuates and it is more difficult to agree on the value of something, which does not occur if money is used as each product has a defined price which might just vary slightly. According to this, options A and B are advantages of money over bartering.

Answer:

x(x + 11)

Step-by-step explanation:

x^2 + 11x when factored gives a result of x(x + 11)

Answer:

x(x+11)

Step-by-step explanation:

We are given the expression:

[tex]x^2+11x[/tex]

This can be factored using the Greatest Common Factor (GCF).

The GCF of x^2 and 11x is x.

Factor out an x.

[tex]x(x+11)[/tex]

x^2+11x factored is: x(x+11).

Answer: Will continue to rise

Step-by-step explanation:

Looking at the graph one notices that after a slight dip in the unemployment rate from August 2010 to January 2011, the unemployment rate began to rise and by November 2011 was still rising.

The arrow on the graph serves to indicate the direction the unemployment rate is going and as it is pointing upwards, this means that the Unemployment rate will continue to rise.

This was down to the fact that in 2011 the US was still yet to recover from the Great Recession of 2008 - 2009.

Answer:

EDGE 2021

Step-by-step explanation:

1) 4%

2) Increase

Answer:

460 1/3

Step-by-step explanation:

175 2/3 + 456 2/3

First convert to improper fraction,

527/3 + 854/3

=> 1381/3

Then After adding convert back to mixed fraction,

=> 460 1/3

Answer:

141

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)

We know z+70 = 180 since they form a straight line

z = 110

z = 1/2 ( 79+w)

110 = 1/2 ( 79+w)

220 = 79+w

220-79 = w

141 =w

The value of w is found to be 141.

The line segment connecting any two locations on a circle's circumference is referred to as the chord of the circle.

It should be emphasised that the diameter is the circle's longest chord, which runs through its centre.

When two chords cross inside of a circle, the angle's measure is equal to the product of the lengths of the intersecting arcs and the vertical angle, divided by two.

angle formed by two chords =  1/2 (sum of intercepted arcs)

Estimate angle z by linear pair.

z + 70 = 180

z = 110

z is the angle formed between two chord of the circle.

Thus,

z = 1/2( 79 + w)   {sum of intercepted arcs}

110 =  1/2( 79 + w)

Further solving,

w = 141

Therefore, the value of arc w comes out to be 141.

To know more about linear pair, here

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9514 1404 393

Answer:

Step-by-step explanation:

1. The negative leading coefficient (-2) tells you the parabola opens downward.

__

2. The fact that the parabola opens downward tells you the vertex is a maximum.

__

3. For quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For this parabola, that is x = -4/(2(-1)) = 2. The y-value of the vertex is f(2) = -2^2+4(2)-3 = -4+8-3 = 1. The y-intercept is the constant, c = -3.

Let the largest integer equal x, the 3rd number ( smallest-number) would be x - 2

The sum of the two would be:

X + 5(x-2) = -244

Simplify:

X + 5x -10

Combine like terms

6x -10 = -244

Add 10 to both sides:

6x = -234

Divide both sides by 6

X = -234/6

X = -39

The smallest number is x-2 = -39-2 = -41

The answer is -41

10 units squared. Hope this helped.

The area of the triangle is 10 square units.

The given coordinates are A(2,0), B(6,0), and C(8,5).

The formula of area of triangle formula in coordinate geometry is the area of the triangle in the coordinate geometry is:  [tex]A=\frac{1}{2} |x_{1} (y_{2}-y_{3})+x_{2} (y_{3}-y_{1})+x_{3} (y_{1}-y_{2})|[/tex]

Now, Area=1/2|2(0-5)+6(5-0)+8(0-0)|=0.5|20|

=10 square units

Therefore, the area of the triangle is 10 square units.

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The probability that he receives an invitation to work in a bank given that he defends his diploma excellently is [tex]\mathbf{0. \overline 6}[/tex]

The reason for the above probability value is as follows;

The known parameters are;

The probability that a graduate of the Faculty of Finance will defend the diploma excellently, P(A) = 0.6

The probability that he will defend perfectly and receive an invitation to work at a bank, P(A∩B) = 0.4

The unknown parameter is;

The probability that the student will receive an invitation from the bank given that the student defend the diploma excellent, [tex]\mathbf {P(B \ | \ A)}[/tex]

The process;

[tex]\mathbf{ P(B \ | \ A)}[/tex] is found using the conditional probability formula as follows;

[tex]\mathbf {P(B \ | \ A) = \dfrac{P(A \cap B) }{P(A)}}[/tex]

Plugging in the values, we get;

[tex]P(B \ | \ A) = \dfrac{0.4 }{0.6} = \dfrac{2}{3} = 0. \overline 6[/tex]

The probability that the student will receive an invitation from the bank given that the student defend the diploma excellent, [tex]P(B \ | \ A)[/tex] = [tex]\mathbf {0. \overline 6}[/tex]

Learn more about conditional probability here;

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Answer:

0.70319018

Step-by-step explanation:

Given the following:

Number of students surveyed (n) = 15

Probability of attending tet festival (p) = 24% =0.24

Therefore,

Probability of not attending (1 - p) = (1 - 0.24) = 0.76.

The probability that at most 4 students will attend can be obtained using the binomial probability relation:

p(x) = nCx * p^x * (1 - p)^(n-x)

At most 4 students means:

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

p(x=0) = 15C0 * 0.24^0 * 0.76^(15 - 0)

p(x=0) = 1 * 1 * 0.0004701 = 0.00047018

p(x=1) = 15C1 * 0.24^1 * 0.76^(14)

p(x=1) = 15 * 0.24 * 0.021448 = 0.07721

p(x=2) = 15C2 * 0.24^2 * 0.76^(13) =

p(x=2) = 105 * 0.0576 * 0.02822 = 0.17068

p(x=3) = 15C3 * 0.24^3 * 0.76^(12)

p(x=3) = 455 * 0.013824 * 0.037133 = 0.23356

p(x=4) = 15C4 * 0.24^4 * 0.76^(11) =

p(x=4) = 1365 * 0.0033177 * 0.048859 = 0.22127

0.00047018 + 0.07721 + 0.17068 + 0.23356 + 0.22127 = 0.70319018

Answer:

y=3x+6

Step-by-step explanation:

The slope of the line is 3 and the equation will be y=3x+6

Answer:

3

Step-by-step explanation:

dont put this in cuz it wrong ‍♂️

Answer:

15/8

Step-by-step explanation:

tan(62)=P/B

tan(62)=15/8

Answer:

3/5

Step-by-step explanation:

um 3/5+2/5 = 1

The correct option is A because

The statement makes sense. There is​ 95% probability that the confidence interval limits actually contain the true value of the population​ mean, so the probability it does not fall in this range is ​100%−​95% =​5%.

From the question we are told that:

Confidence interval [tex]CI=95\%[/tex]

Mean [tex]\=x =1.9-3.5hours[/tex]

Level of significance (of the alternative hypothesis)

[tex]\alpha=100-95[/tex]

[tex]\alpha=5\%[/tex]

[tex]\alpha=0.05[/tex]

Generally

There is​ 95% probability that the confidence interval limits actually contain the true value of the population​ mean.

In conclusion

The  it does not fall in this range is Level of significance (of the alternative hypothesis)

​100%−​95% =​5%.

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Answer:

65.8

Step-by-step explanation:

Use the sin formula

100/sin (28) = x/ sin (18)

(sin (18) (100))/ sin (28) = x

x = 65.8223

x = 65.8

Answer:

65.8

Step-by-step explanation:

Accellus Correct

Answer:

0.8989

Step-by-step explanation:

Using the Newton's Raphson approximation formula.

Xn+1 = Xn - f(Xn)/f'(Xn)

Given f(x) = x³-2x+2

f'(x) = 3x²-2

If the initial value X1 = 2

X2 = X1 - f(X1)/f'(X1)

X2 = 2 - f(2)/f'(2)

f(2) = 2³-2(2)+2

f(2) = 8-4+2

f(2) = 6

f'(2) = 3(2)²-2

f'(2) = 10

X2 = 2- 6/10

X2 = 14/10

X2 = 1.4

X3 = X2 - f(X2)/f'(X2)

X3 = 1.4 - f(1.4)/f'(1.4)

f(1.4) = 1.4³-2(1.4)+2

f(1.4) = 2.744-2.8+2

f(1.4) = 1.944

f'(1.4) = 3(1.4)²-2

f'(1.4) = 3.880

X3 = 1.4- 1.944/3.880

X3 = 1.4 - 0.5010

X3 = 0.8989

Hence the value of X3 is 0.8989