2. Write an equation of a line in slope-intercept form
that passes through a point (4,-6) and has a slope of -3.

Answer:

[tex]\boxed{\sf \ \ \ 8^5 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]8*8*8*8*8 =8^5[/tex]

because we use five time 8 in the multiplication

hope this helps

Answer:

[tex]\frac{2x^2 +4x}{3x-3}[/tex]

Step-by-step explanation:

1. You multiply the reciprocal from org equations

2. Multiply straight across your new fractions

3.Remove the parentheses

-Hope this helps :)

Answer:

[tex] \dfrac{2x^2 + 4x}{3x - 3} [/tex]

Step-by-step explanation:

[tex] \dfrac{x + 2}{x - 1} \div \dfrac{3}{2x} = [/tex]

[tex] = \dfrac{x + 2}{x - 1} \times \dfrac{2x}{3} [/tex]

[tex] = \dfrac{2x(x + 2)}{3(x - 1)} [/tex]

[tex] = \dfrac{2x^2 + 4x}{3x - 3} [/tex]

Answer:

[tex]\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C[/tex]

Step-by-step explanation:

Given the function: [tex]f(x)=\dfrac{8x^3}{5}+3x-\dfrac{4}{5}[/tex]

To take the antiderivative (or integral) of a function, we follow the format below.

[tex]f(x)=x^n\\$Then its antiderivative\\Antiderivative of f(x)$=\dfrac{x^{n+1}}{n+1}[/tex]

Therefore, the antiderivative of f(x) is:

[tex]=\dfrac{8x^{3+1}}{5(3+1)}+\dfrac{3x^{1+1}}{2}-\dfrac{4}{5}x+C\\=\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C[/tex]

We want to check our result by differentiation.

[tex]\dfrac{d}{dx}\left(\dfrac{8x^{4}}{20}+\dfrac{3x^{2}}{2}-\dfrac{4}{5}x+C\right)\\=\dfrac{d}{dx}\left(\dfrac{8x^{4}}{20}\right)+\dfrac{d}{dx}\left(\dfrac{3x^{2}}{2}\right)-\dfrac{d}{dx}\left(\dfrac{4}{5}x\right)+\dfrac{d}{dx}\left(C\right)\\\\=\dfrac{32x^{3}}{20}+\dfrac{6x}{2}-\dfrac{4}{5}+0\\\\=\dfrac{8x^{3}}{5}+3x-\dfrac{4}{5}[/tex]

Answer:

c) H0: µ = 7 hours (null hypothesis)

H1: µ < 7 hours (alternative hypothesis and original claim)

Step-by-step explanation:

The hypothesis test is performed in order to see if a sample outcome gives evidence to reject a null hypothesis and support the researchers claim.

In this case, the claim is that the mean amount of sleep for adults is less than 7 hours.

For this claim, the alternative hypothesis will state the researcher's claim: the mean amount of sleep for adults is significantly less than 7 hours.

The null hypothesis will state the opposite: the mean amount of sleep for adults is not significantly less than 7 hours. In this case, it is the same to claim that the mean amount is 7 hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=7\\\\H_a:\mu< 7[/tex]

Answer:

A

Step-by-step explanation:

Given the equality y > -½, it means the values of y is greater than -½.

The values of y would range from 0 upwards. I.e. 0, ½, 1, 1½, 2. . .

Thus, when graphed on a number line, the circle that appears like "o" would start from -½, and the "o" would not be full or shaded to indicate that -½ is not included in the values of y, which are greater than -½. Since the values of y are greater than -½ the direction of the arrow that indicates values of y would point towards our far right, to indicate the values included as y.

Therefore, the graph that indicates the inequality y > ½ is A

Answer:

A

Step-by-step explanation:

Answer:

The answer is option D.

Step-by-step explanation:

To find LJ we use the sine rule

From the picture

LK / sin J = LJ / sin K

LK = 9

J = 89°

K = 23°

So now LJ is

9 / sin 89° = LJ / sin 23°

Make LJ the subject

That's

LJ = 9 sin 23° / sin 89°

LJ = 3.51

The final answer is

Hope this helps you.

Answer:

17.1 meters

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

where a and b are the legs and c is the hypotenuse.

6 and 16 are the legs, because they form the right angle. c is the hypotenuse because it is opposite the right angle.

[tex]6^2+16^2=c^2[/tex]

Evaluate the exponents.

6^2= 6*6= 36

16^2= 16*16= 256

[tex]36+256=c^2[/tex]

Add 36 and 256.

[tex]292=c^2[/tex]

Since c is being squared, take the square root of both sides of the equation. The exponent and square root will cancel and leave c by itself

[tex]\sqrt{292} =\sqrt{c^2}[/tex]

[tex]\sqrt{292}=c[/tex]

[tex]17.0880075=c[/tex]

Round to the nearest tenth. The 8 in the hundredeth place tells us to roung the 0 in the tenth place up to a 1.

[tex]17.1=c[/tex]

c= 17.1 m

The missing length, or the hyptenuse is 17.1 meters.

Answer:

Step-by-step explanation:

Given the sequence [tex]a_n = \frac{9+14n^{2} }{n+15n^{2} }[/tex]

To find the limit of the sequence, we will first divide the numerator and the denominator through by the highest power of n which is n² as shown;

[tex]\lim_{n \to \infty} \frac{9/n^{2} +14n^{2}/n^{2} }{n/n^{2} +15n^{2}/n^{2} }\\ \lim_{n \to \infty} \frac{9/n^{2} +14 }{1/n +15n^{2}/n^{2 }}\\[/tex]

As [tex]n[/tex] tends to [tex]\infty[/tex], [tex]\frac{a}{n}[/tex] tends to zero where n is any constant, The limit of tyhe sequence as n tends to infinity becomes;

[tex]= \frac{9/\infty+14 }{1/\infty+15 }\\= \frac{0+14}{0+15} \\= 14/15\\[/tex]

Therefore [tex]\lim_{n \to \infty} \frac{9+14n^{2} }{n+15n^{2} } = 14/15[/tex]

Since the limit of the sequence gave a finite number , the sequence converges.

Note that the only case when the sequence diverges id when the limit of the sequence is infinite

Answer:

a surface of a cone looks like an hyperbolic cylinder

Answer:

x = 1 and y = 4

Step-by-step explanation:

m² = 7x + 7; m³= 4y and m∧4 = 112

√(m∧4) = √112

∴ m² = √112

Hence, 7x + 7 = √112

(7x + 7)² = 112

49x² + 14x + 49 = 112

49x² + 14x - 63 = 0

7x² + 2x - 9 = 0

7x² + 9x - 7x - 9 = 0

x(7x + 9) - 1(7x + 9) = 0

(x - 1)(7x + 9) = 0

x - 1 = 0

∴ x = 1

When x = 1

m²= 7 + 7 = 14

m³= 4y and m∧4 = 112

Also m∧4/m²= m² = 112/14 = 8

Hence, m° = 2; m = 2 X 2 = 4; m² = 2 x 2 x 2  = 8; m³= 2 x 2 x2 x 2 =  16

m³ = 16 = 4y

∴ y = 16/4 = 4

Answer:

The probability of getting even 7 times out of 8 is 1/256. Hope this helps!!

Step-by-step explanation:

21/7 = 3 is the answer of your question

Answer:

A = 166.66

Step-by-step explanation:

You have the following functions:

[tex]y_1=x^2-24\\\\y_2=1[/tex]

In order to calculate the area of the given region, you first calculate the points at which the function y = x^2-24 intersects the line y=1:

[tex]1=x^2-24\\\\0=x^2-25\\\\x=\sqrt{25}=\pm 5[/tex]

Next, you take into account that the area between the two function is given by:

Where you have used the fact that y2 is above the y1 function.

Next, you calculate the following integral:

[tex]A=\int_{-5}^{5}(1-(x^2-24))dx=\int_{-5}^{5}(25-x^2)dx\\\\A=(25x-\frac{1}{3}x^3)|_{-5}^{5}\\\\A=(25(5)-\frac{1}{3}(125))-(25(-5)-\frac{1}{3}(-125))\\\\A=166.66[/tex]

Then, the area of the bounded region is 166.66

Answer:

2nd Option

Step-by-step explanation:

Standard Form: ax² + bx + c

This can be modified to fit any degree polynomial, as long as the highest degree is first, and then decreasing. So our answer is B.

Answer:

Step-by-step explanation:

Using the proportion test

Null hypothesis: p <= 0.22

Alternative hypothesis: p > 0.22

Using the formula

z score = p - P /√ (P(1-P)/n)

Where p is 74/200= 0.37, P = 0.22, n = 200.

0.37-0.22 / √(0.22(1-0.22)/200)

0.15 / √(0.22(0.78)/200)

0.15 / √(0.1716/200)

0.15/ √0.000858

0.15 / 0.02929

= 5.1212

To help arrive at a conclusion, we have to find the p value, using a p value calculator at the 0.05 level of significant, the p value is less than 0.00001... Thus we would reject the null as there is sufficient statistical evidence to prove that the proportion is higher than that reported by the polling ​organization.

Answer:

The ratio of x to y is

1.02/1 = x/y

1.02:1= x:y

Step-by-step explanation:

Rectangle p

Length = 60 cm

Width = x cm

Area = length* breadth

Area = 60 *x

Rectangle q

Length = 20% more than length of rectangle p

Length = (60*0.2) + 60

Length = 12 +60

Length = 72cm

Width = y cm

Area = 72*y

(72*y)-(72*y *0.15)= 60*x

72y - 10.8y = 60x

61.2y = 60x

61.2/60 = x/y

15.3/15= x/y

5.1/5 = x/y

1.02/1 = x/y

Answer:

0.015 radians per second.

Step-by-step explanation:

They tell us that at the moment the speed would be 6 ft / s, that is, dx / dt = 6 and those who ask us is dθ / dt.

Which we can calculate in the following way:

θ = arc sin 100/200 = pi / 6

Then we have the following equation of the attached image:

x / 100 = cot θ

we derive and we are left:

(1/100) * dx / dt = - (csc ^ 2) * θ * dθ / dt

dθ / dt = 0.01 * dx / dt / (- csc ^ 2 θ)

dθ / dt = 0.01 * 6 / (- csc ^ 2 pi / 6)

dθ / dt = 0.06 / (-2) ^ 2

dθ / dt = -0.015

So there is a decreasing at 0.015 radians per second.

The horizontal distance and the height of the kite are illustration of rates.

The angle is decreasing at a rate of 0.24 radian per second

The given parameters are:

[tex]\mathbf{Height =y= 100ft}[/tex]

[tex]\mathbf{Speed =\frac{dx}{dt}= 6fts^{-1}}[/tex]

[tex]\mathbf{Length = 200}[/tex]

See attachment for illustration

Calculate the angle using the following sine ratio

[tex]\mathbf{sin(\theta) = \frac{100}{200}}[/tex]

[tex]\mathbf{sin(\theta) = \frac{1}{2}}[/tex]

The horizontal displacement (x) is calculated using the following tangent ratio:

[tex]\mathbf{tan(\theta) = \frac{100}{x}}[/tex]

Take inverse of both sides

[tex]\mathbf{cot(\theta) = \frac{x}{100}}[/tex]

[tex]\mathbf{cot(\theta) = \frac{1}{100}x}[/tex]

Differentiate both sides with respect to time (t)

[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dx}{dt}}[/tex]

Substitute known values

[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 6}[/tex]

[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]

Recall that:

[tex]\mathbf{sin(\theta) = \frac{1}{2}}[/tex]

Take inverse of both sides

[tex]\mathbf{csc(\theta) = 2}[/tex]

Square both sides

[tex]\mathbf{csc^2(\theta) = 4}[/tex]

Substitute [tex]\mathbf{csc^2(\theta) = 4}[/tex] in [tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]

[tex]\mathbf{-4 \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]

Divide both sides by -4

[tex]\mathbf{\frac{d\theta}{dt} = -\frac{24}{100}}[/tex]

[tex]\mathbf{\frac{d\theta}{dt} = -0.24}[/tex]

Hence, the angle is decreasing at a rate of 0.24 radian per second

Read more about rates at:

https://brainly.com/question/6672465

Answer:

a. [tex]N(1)=2600[/tex]

b. [tex]N'(a) = 470/a[/tex]

c. N(a) has no maximum value, max N'(a) = 470 (when a = 1)

d. lim a→[infinity] N′(a) = 0

Step-by-step explanation:

a.

the variable 'a' is the amount spent in thousands of dollars, so $1,000 is equivalent to a = 1. Then, we have that:

[tex]N(1)=2600 + 470ln(1)[/tex]

[tex]N(1)=2600 + 470*0[/tex]

[tex]N(1)=2600[/tex]

b.

To find the derivative of N(a), we need to know that the derivative of ln(x) is equal (1/x), and the derivative of a constant is zero. Then, we have:

[tex]N'(a) = 2600' + (470ln(a))'[/tex]

[tex]N'(a) = 0 + 470*(1/a)[/tex]

[tex]N'(a) = 470/a[/tex]

c.

The value of 'ln(a)' increases as the value of 'a' increases from 1 to infinity, so there isn't a maximum value for N(a).

The maximum value of N'(a) is when the value of a is the lower possible, because 'a' is in the denominator, so the maximum value of N'(a) is 470, when a = 1.

d.

When the value of 'a' increases, the fraction '470/a' decreases towards zero, so the limit of N'(a) when 'a' tends to infinity is zero.

Answer:

(See explanation below for further details).

Step-by-step explanation:

The procedure for plotting each line consists in creating a table with at least two different points, given that Euclidean Geometry states that any line can be created with only two points,  and plotting the lines with the help of graphing tools:

(a) [tex]y = \frac{2}{3}\cdot x - 5[/tex]

(i) Table of values

       x              y

      -2         -6.333

      -1          -5.667

       0             -5

       1          -4.333  

       2         -3.667      

(ii) Plotting the line

The line is presented below in the attachment "line_1".

(b) [tex]6\cdot x - 2\cdot y + 5 = 0[/tex]

[tex]2\cdot y = 6\cdot x +5[/tex]

[tex]y = 3\cdot x +\frac{5}{2}[/tex]

(i) Table of values

       x              y

      -2           -3.5

      -1            -0.5

       0            2.5

       1             5.5  

       2            8.5    

(ii) Plotting the line

The line is presented below in the attachment "line_2".

Answer:

∠6 and ∠4

Explanation:

Exterior angles tend to be outside the polygon. The ones inside like ∠1, ∠5, and ∠3 are called interior because they are inside the polygon.

∠2 is invalid because it isn't really an angle, it's a side.

Answer:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

Step-by-step explanation:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

Answer:

B.

Step-by-step explanation:

According to SohCahToa, when using Sin to find a side value, you must use opposite over hypotenuse.

So in this case to find x, you would do the Sin(L)=x/y

Answer:

B.  Sin(L)=x/y  indeed!

Step-by-step explanation:

Answer:

a. 125.0714; 11.1835.

b. 109.4375; 10.4612.

Step-by-step explanation:

Given the following data;

70, 65, 71, 78, 89, 68, 50, 75.

Mean = 70.75

The deviation for the mean of the data is -0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25.

We would then find the square of this deviation;

[tex]=(-0.75)^2+(-5.75)^2+( 0.25)^2+(7.25)^2 +(18.25)^2+(-2.75)^2+(-20.75)^2 +(4.25)^2[/tex]

[tex]=0.5625+33.0625+0.0625+52.5625+333.0625+7.5625+430.5625+18.0625[/tex]

= 875.5

Next is to find the population variance;

[tex]V = \frac{875.5}{8}[/tex]

Variance, V = 109.4375

The population standard deviation is the square root of the population variance;

[tex]Sd = \sqrt{109.4375}[/tex]

Standard deviation, Sd = 10.4612

To find the sample variance;

[tex]V = \frac{875.5}{8-1}[/tex]

[tex]V = \frac{875.5}{7}[/tex]

Variance, V = 125.0714

The sample variance is;

[tex]Sd = \sqrt{125.0714}[/tex]

Standard deviation, Sd = 11.1835

Therefore,

a. The sample variance is 125.0714 and the sample standard deviation is 11.1835.

b. If this is a population data, the population variance is 109.4375 and the population standard deviation is 10.4612.

Answer:

C. 20.67

Step-by-step explanation:

I got it right on edge :)

Answer:1.P(exactly 2 kids are girls)=3/8

2. P(at least 1 is boy)=7/8

Step-by-step explanation:

1.P(exactly 2 kids are girls)=N(outcomes with 2 girls) /Total number of outcomes.

All possible outcomes are ggb,gbg, bgg, gbb, bgb, bbg, ggg, bbb - total 8

Outcomes where are exactly 2 girls are:

ggb,gbg, bgg - total 3 outcomes

So P(exactly 2 are girls)=3/8

2. P(at least 1 is boy)=Number of outcomes , where are at least 1 boy (1,2 or all 3 kids are boys)/ Total number of outcomes

All possible outcomes are ggb,gbg, bgg, gbb, bgb, bbg, ggg, bbb - total 8

Outcomes, where at least 1 kid is boy: ggb,gbg, bgg, gbb, bgb, bbg, bbb - total  7

P(at least 1 is boy)=7/8

Answer: The width of the garden is 6 Meters

Step-by-step explanation:

3x + x = 24

The length is 3x and the width is x

24 / 4 = 6

x= 6

The width of the garden is 6 Meters

Answer:

x = 6

Step-by-step explanation:

3x + x = 24

24 / 4 = 6

x = 6

Answer:

Increase: 1.7

Decrease: 0.3

Step-by-step explanation:

Increase:

100% + 70% = 117%

117/ 100 = 1.7 (multiplier)

Decrease:

100% - 70%= 30%

30/ 100 = 0.3 (multiplier)

Answer:

Step-by-step explanation:

y>3/2 x-1

y<3/2 x-1

graphs do not intersect any point.

so no solution.

Answer:

D

Step-by-step explanation:

no solution

Answer:

f(0) = 4 ,  f(6) = 8

Step-by-step explanation:

Since

[tex]0 < 5[/tex]  then   f(0) = 0+4 = 4

5 < 6  < 7  therefore  f(6) = 8

Answer:

The answer is below

Step-by-step explanation:

What must be applied to know if the result is true or reliable is a  test statistic, since due to it we can calculate how true or rather what is the probability that this data will occur. There are many types of  test statistic, use the one that best fits the data.

The veracity of the medium where the information comes from is also important, whether they took a representative sample or not, among other parameters.

Answer:

A ∪ B = {1,3,6,9,12,15,18,24}

Step-by-step explanation:

Let A = {3,6,9,12,15}

B = {1,6,12,18,24}

So,

A ∪ B = {3,6,9,12,15} ∪ {1,6,12,18,24}

A ∪ B = {1,3,6,9,12,15,18,24}

Answer:

{1,3,6,9,12,15,18,24}

Step-by-step explanation:

The union is joining of the elements of the sets

{3, 6, 9, 12, 15}U {1, 6, 12, 18, 24}

= {1,3,6,9,12,15,18,24}

Answer: Hope this helps <3

Step-by-step explanation:

Graphs can be used to represent functions.

See attachment for the graphs of [tex]\mathbf{x^2 + y = 2}[/tex] and [tex]\mathbf{x^2 + y^2 = 9}[/tex]

The functions are given as:

[tex]\mathbf{x^2 + y = 2}[/tex]

[tex]\mathbf{x^2 + y^2 = 9}[/tex]

Rewrite [tex]\mathbf{x^2 + y^2 = 9}[/tex] as:

[tex]\mathbf{x^2 + y^2 = 3^2}[/tex]

The above equation represents a circle of radius 3, and that has its center as the origin.

Similarly, we have:

[tex]\mathbf{x^2 + y = 2}[/tex]

Make y the subject

[tex]\mathbf{y = 2 -x^2}[/tex]

Rewrite as:

[tex]\mathbf{y = -x^2 + 2 }[/tex]

The above is a square function, that is reflected over the y-axis, and then shifted up by 2 units.

See attachment for the graphs of [tex]\mathbf{x^2 + y = 2}[/tex] and [tex]\mathbf{x^2 + y^2 = 9}[/tex]

Read more about graphs and functions at:

https://brainly.com/question/18806107