If log3=0.4771 and log2=0.3010,Find the value of log12

Answer:

Option B.

Step-by-step explanation:

According to the question, the data provided is as follows

[tex]H_o : p_1 - p_2 = 0\ (p_1 = p_2)\\\\ H_\alpha : p_1 - p_2 < 0\ (p_1 < p_2)[/tex]

Based on the above information,

The type ii error is the error in which there is an acceptance of a non rejection with respect to the wrong null hypothesis. The type I error refers to the error in which there is a rejection of a correct null hypothesis and the type II refers that error in which it explains the failure of rejection with respect to null hypothesis that in real also it is wrong  

So , the type II error is option B as we dont create any difference also the proportion is very less

Answer:

1) a+b(x)+a+(y)

b) a+b(x)-a-b(y)

2)p-q(r)-p-q(s)

b)r-2r(s)+r-2t(t)

Step-by-step explanation:

1) ax+bx+ay+by

a+b(x)+a+b(y)

b) ax+bx-ay-by

a+b(x)-a-b(y)

2) pr-ps+qr-qs

pr+qr-ps-qs

p+q(r)-p-q(s)

b) rs-2rs+rt-2t^2

r-2r(s)+r-2t(t)

Hope this helps ;) ❤❤❤

Answer:

Step-by-step explanation:

a)Use distributive property

ax + bx + ay + by = x(a + b) + y(a + b)

                            = (a + b) (x + y)

b) ax + bx - ay - by = x(a + b) - y (a +b)

                              = (a +b) (x - y)

2)

a) pr - ps + qr - qs =  p (r - s) + q( r - s)

                             = (r -s )( p + q)

Answer:

The equation of the graph after translating one unit to the left is;

[tex]y = \left | \dfrac{x}{2} - \dfrac{3}{2} \right |+3[/tex]

Step-by-step explanation:

The given equation is [tex]y = \left | \dfrac{1}{2}\cdot x - 2 \right |+3[/tex]

We note that minimum value of y = 3, where 1/2·x - 2 = 0 and x = 4

Therefore, in moving one unit to the left, we have at the y-intercept where slope of the graph has become inverted (reflection of the real graph) we add one to the x value as follows;

[tex]y = \left | \dfrac{1}{2}\cdot (x+1) - 2 \right |+3 = \left | \dfrac{x}{2} + \dfrac{1}{2} - 2 \right |+3 = \left | \dfrac{x}{2} - \dfrac{3}{2} \right |+3[/tex]

The equation of the graph becomes;

[tex]y = \left | \dfrac{x}{2} - \dfrac{3}{2} \right |+3[/tex].

Answer:

[tex]\large \boxed{\sf \ \ y=(x+5)^2+5 \ \ }[/tex]

Step-by-step explanation:

Hello, please find my work below.

[tex]y=x^2+10x+30\\\\\text{*** We can notice that ***}\\\\\text{*** } x^2+10x = x^2+2\cdot 5 \cdot x=(x+5)^2-5^2=(x+5)^2-25\\\\y=x^2+10x+30=(x+5)^2-25+30=(x+5)^2+5\\\\[/tex]

a = 1

h = -5

k = 5

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

the probability that a randomly selected college student will take between 2.5 and 5 minutes to find a parking spot in the library lot is 0.77454

Step-by-step explanation:

Given that:

mean = 4

standard deviation = 1

The objective is to find the probability that a randomly selected college student will take between 2.5 and 5 minutes to find a parking spot in the library lot.

i.e

[tex]P(2.5 \leq x \leq 5) = P(\dfrac{2.5 - \mu}{\sigma} \leq \dfrac{X-\mu}{\sigma}\leq \dfrac{5- \mu}{\sigma})[/tex]

[tex]P(2.5 \leq x \leq 5) = P(\dfrac{2.5 - 4}{1} \leq Z \leq \dfrac{5- 4}{1})[/tex]

[tex]P(2.5 \leq x \leq 5) = P(\dfrac{-1.5}{1} \leq Z \leq \dfrac{1}{1})[/tex]

[tex]P(2.5 \leq x \leq 5) = P({-1.5}\leq Z \leq 1)[/tex]

[tex]P(2.5 \leq x \leq 5) = P({Z < 1})- P(Z < -1.5)[/tex]

[tex]P(2.5 \leq x \leq 5) = 0.84134- 0.06680[/tex]

[tex]\mathbf{P(2.5 \leq x \leq 5) = 0.77454}[/tex]

Answer:

0.72

Step-by-step explanation:

hope i helped

pls mark brainliest im trying to level up

Answer:

0.719 rounded to the nearest hundredth is 0.720

Step-by-step explanation:

9 is more than 5, so you round up, and the next hundredth is 2, so you get 0.720.

Hope this helps!!!  Brainliest would be appreciated

Answer: Resultant force = 114.96 pounds at angle 81.76°

Answer: magnitude = 114.96 lbs, direction =  88.21°

Step-by-step explanation:

Vector A: 150 lbs at  40°

Vector B: 100 lbs at 170°

Slide Vector B onto Vector A so you have a head to tail connection.

Calculate the angle between the vectors (50°).

Use Law of Cosines to find the magnitude of the resultant vector.

Use Law of Sines to find the direction of the resultant vector.

Law of Cosines:  c² = a² + b² - 2ab cos θ

Given: a = 150, b = 100, C = 50°

c² = (100)² + (150)² - 2(100)(150) cos 50°

c = 114.96

Law of Sines:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c}\\\\\text{Given: a=150, c=114.96, C=50}^o\\\\\\\dfrac{\sin A}{150}=\dfrac{\sin 50^o}{114.96}\\\\\\\sin A=\dfrac{150\sin 50^o}{114.96}\\\\\\A=\sin^{-1}\bigg(\dfrac{150\sin 50^o}{114.96}\bigg)\\\\\\A=88.21^o[/tex]

Answer:

[tex] Area = 2,031ft^2 [/tex]

Total weight of gravel on the roof = [tex] 24,372 pounds [/tex]

Step-by-step Explanation:

The area Adams planned to cover with gravel can be divided into 3 rectangles as shown in the diagram attached.

We would have 3 rectangles. See the attachment below to check out how we arrive at the dimensions of the 3 rectangles.

Area of rectangle = L*W

Area to be covered by gravel = area of rectangle 1 + area of rectangle 2 + area of rectangle 3

Area to be covered with gravel = [tex] (30*17) + (13*9) + (52*27) [/tex]

[tex] Area = (30*17) + (13*9) + (52*27) = 2,031ft^2 [/tex]

Total weight of gravel on the roof = 12 pounds per square foot multiplied by total area of the roof to be covered = [tex] 12 * 2031 = 24,372 pounds [/tex]

Answer:

2031 and 16925

Step-by-step explanation:

Step-by-step explanation:

[tex]( {x}^{2})(x + 3) - (x + 3)[/tex]

[tex](x + 3)( {x}^{2} - 1) [/tex]

[tex](x - 1)(x + 1)[/tex]

[tex](x - 1)(x + 1)(x + 3)[/tex]

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

(x+1) (x-1) (x+3)

Step-by-step explanation:

. .....................

Answer:

157.5.

Step-by-step explanation:

(155 + 160) / 2

=  315/2

= 157.5.

Hey there! I'm happy to help!

We want to find whatever is in between J and K. To find the halfway point between any two numbers, you add them and then divide that result by two!

What's between 1 and 3?

1+3=4

4/2=2

So, we'll do the same here!

155+160=315

315/2=157.5

So, the midpoint is 157.5 or 157 1/2.

Have a wonderful day!

Answer:

The exact values of sinθ = -7/√58.

The exact value of  secθ = -√58/3 and

The exact value of tanθ = 7/3

Step-by-step explanation:

Given that a point on the terminal side is of an angle is (x,y) and we are given (-3, -7). So x = -3 and y = -7. The length of its terminal side is given by r = √(x² + y²) = √((-3)² + (-7)²) = √(9 + 49) = √58

We know that sinθ = y/r.

So, sinθ = y/r = -7/√58

We know that secθ = 1/cosθ = 1/x/r = r/x

So, secθ = r/x = √58/-3 = -√58/3

We know that tanθ = y/x.

So, tanθ = y/x = -7/-3 = 7/3

So, the exact values of sinθ = -7/√58.

The exact value of  secθ = -√58/3 and

The exact value of tanθ = 7/3

[tex]\dfrac{15 + 10i}{1 + 2i}=\\\\\dfrac{(15 + 10i)(1-2i)}{(1 + 2i)(1-2i)}=\\\\\dfrac{15-30i+10i+20}{1+4}=\\\\\dfrac{35-20i}{5}=\\\\7-4i[/tex]

Answer:

7-4i

Step-by-step explanation:

Multiplying the numerator and denominator by $1-2i$ gives

\begin{align*}

\frac{15+10i}{1+2i} &= \frac{15+10i}{1+2i}\cdot\frac{1-2i}{1-2i}\\

&= \frac{(15+10i)(1-2i)}{1^2 + 2^2} \\

&= \frac{5(3 + 2i)(1 - 2i)}{5} \\

&= (3 + 2i)(1 - 2i) \\

&= 3 + 2i - 6i - 4i^2 \\

&= 3 + 2i - 6i + 4 \\

&= \boxed{7 - 4i}.

Answer:

4.2 miles per/hour

Step-by-step explanation:

we know

speed  total distance covered/ total time taken to cover that distance.

Time from 9:00 Am to 11:30 Am is 2 hours 30 minutes

time = 2 1/2 hours = 5/2 hours

for distance\

By 11:30 AM, he was 13 miles from the start.

so he covered a total distance of 12 miles

At 9:00 AM, a person running a race was 2 1/2 miles from the start

until 9 am he had already ran 2 1/2 miles = 5/2 miles

since we have to take distance travelled from 9 to 11 :30 Am

we need to subtract distance travel until 9 am from total distance traveled until 11:30 pm

Distance travlled from 9:11:30 am = distance traveled from start till 11:30AM -  distance traveled from start till 9 AM

Distance traveled from 9:11:30 am =  13 - 5/2 = (26-5)/2 = 21/2

Thus, speed = 21/2 / 5/2 = 21/5 = 4 1/5 miles/hour = 4.2 miles/hour

Thus, he was running with 4.2 miles per/hour.

Answer:

The possible number of goats is 6 and the possible number of chicken is 24

Step-by-step explanation:

Let

chicken=c

Goat=g

the number of chickens could be four times the number of goats

c=4g

Total number of animals=30

c+g=30

Recall, c=4g

So,

c+g=30

4g+g=30

5g=30

Divide both sides by 5

5g/5=30/5

g=6

Recall,

c+g=30

c+6=30

c=30-6

=24

c=24

The possible number of goats is 6 and the possible number of chicken is 24 making a total of 30 animals

Answer:

n = 108

Step-by-step explanation:

Radius of the given circle = 9 in.

If this circle is dilated by a scale factor of 6, radius of the dilated circle will be

= 6 × 9

= 54 in.

Circumference of a circle is determined by the formula,

Circumference = 2πr

Where r = radius of the circle

By substituting the value of 'r' in the formula,

Circumference = 2π(54)                          

                         = 108π

By comparing it with circumference = nπ

Value of n = 108

Answer:

This question is unanwserable without the "Spider Tool" If you would like to revise it i'd be happy to help

Step-by-step explanation:

But the units are degrees

Answer:

(i) The area of the rabbit cage when the width is 5.2 m is 81.5 m²

(ii) The area of the rabbit cage if Wilson has 40 meters of wire mesh is 75 m²

Step-by-step explanation:

(i) The given relation of the area, A to the width P of the rabbit cage is A = 3·p²

The graph of the function between the values of 0 and 6 inclusive is found as follows;

A,              3·p²

0,               0

1,                1

2,               12

3,               27

4,               48

5,               75

6,               108

Please find attached the graph of A to 3·p²

From the graph, we have when the the width, p, of the rabbit cage = 5.2, the area, A ≈ 81.5 m²

The area of the rabbit cage when the width is 5.2 m = 81.5 m²

(ii) Also from the graph given that the total wire mess with Wilson = 40 meters, we have;

The formula for the perimeter of the cage = The formula for the perimeter of a rectangle = 2×length + 2×width

The formula for the perimeter of the cage = 2×3×p + 2× p = 8·p

Where the total length of the wire mesh available = 40 meters for the cage

The 40 meters of wire mesh will be used round the perimeter of the cage

∴ 40 m. = 8·p

p = 40/8 = 5 m.

At p = 5 m. the area is given as A = 75 m².

Therefore, the area of the rabbit cage if Wilson has 40 meters of wire mesh = 75 m².

Answer:

second option

Step-by-step explanation:

The range is all of the y values. In this scenario, the y values are the number of sit-ups per minute. We can eliminate the first and third options because they're talking about x when we want y. Additionally, we can eliminate the last option because that is all of the x values, therefore, the answer is the second option.

Answer:

[tex]\boxed{\mathrm{B}}[/tex]

Step-by-step explanation:

The range of a function is the set of all possible output values [tex]F(x)[/tex].

Options A and C are wrong because they talk about the input value x.

The output values are the number of sit-ups.

Option D talks about the ages (input).

Answer:

[tex]\huge\boxed{x=7\dfrac{23}{25}}[/tex]

Step-by-step explanation:

[tex]x\div3\dfrac{3}{10}=2\dfrac{2}{5}\\\\\text{convert the mixed number to the impropper fraction}\\\\3\dfrac{3}{10}=\dfrac{3\cdot10+3}{10}=\dfrac{33}{10}\\\\2\dfrac{2}{5}=\dfrac{2\cdot5+2}{5}=\dfrac{12}{5}\\\\x\div\dfrac{33}{10}=\dfrac{12}{5}\\\\x\times\dfrac{10}{33}=\dfrac{12}{5}\qquad\text{multiply both sides by}\ \dfrac{33}{10}\\\\x\times\dfrac{10\!\!\!\!\!\diagup}{33\!\!\!\!\!\diagup}\times\dfrac{33\!\!\!\!\!\diagup}{10\!\!\!\!\!\diagup}=\dfrac{12}{5}\times\dfrac{33}{10}\\\\x=\dfrac{396}{50}[/tex]

[tex]x=\dfrac{198}{25}\\\\x=\dfrac{175+23}{25}\\\\x=\dfrac{175}{25}+\dfrac{23}{25}\\\\x=7\dfrac{23}{25}[/tex]

Answer:

Associative Property.

Step-by-step explanation:

The Associative Property is the property that says that (a + b) + c = a + (b + c).

Hope this helps!

Answer:

Associate Property

Step-by-step explanation:

I found my answer at baba com

Answer:

4096/15,625

Step-by-step explanation:

The reason is because the power is distributed individually within the fraction. Since the fraction is already fully simplified, 4096/15625 multiplied by itself is also simplified.

Thus the answer is 4096/15,625 = (4^6)/(5^6)

Answer:

The owner needs 195 meters of wire

Step-by-step explanation:

If the lot is squared shaped, then its area is given by the formula:

[tex]Area =x^2[/tex]

where x is the side of the square. Then considering the value they provide for the surface, each side must be of length:

[tex]x^2=\frac{4225}{16} \,m^2\\x=\sqrt{\frac{4225}{16}} \,\,m\\x=16.25\,\,m[/tex]

Then the perimeter around this square lot is four times that side length:

Perimeter = 4 (16.25 m) = 65 m

and since the owner wants three rows of wire, the total length of wire needed is:

3 (65 m) = 195 m

Answer:

y = -3x + 6

Step-by-step explanation:

Any line perpendicular to

y = (1/3)x + 4

has a slope of -1/(1/3) = -3

and equation

y = -3x + b  .................(1)

If the line has an x intercept of 2 at (0,2), then

0 = -3(2) + b

solving

b = 6

By substituting b=6 into (1), the line required

y = -3x + 6

Answer:

y = -3x + 2

Step-by-step explanation:

y= [tex]\frac{1}{3}x +4[/tex]

Slope [tex]m_{1}=\frac{1}{3}[/tex]

slope of the perpendicular line [tex]m_{2}[/tex] = [tex]\frac{-1}{m_{1}}[/tex] = [tex]\frac{-1}{\frac{1}{3}}=-1*\frac{3}{1}=-3\\[/tex]

b= 2

Slope intercept form of required line: y = mx + b

y = -3x + 2

Answer:

The last option

Step-by-step explanation:

The centroid is the point that is equidistant from all the vertices, not the incenter. Furthermore, the incenter is formed by finding the point of concurrency (intersection) of the angle bisectors.

Answer:

(x,y) = Any point on the line

m = the slope of the line

(x₁, y₁) = A given point on the line

Step-by-step explanation:

the equation of a straight line is;

y = mx + c

where;

x and y are any point on the line

m is the slope of the line

c is the intercept on the y axis

And a given point on (x,y) can be written as (x₁, y₁)

Therefore, for the case above;

(x,y) = Any point on the line

m = the slope of the line

(x₁, y₁) = A given point on the line

Answer:

Step-by-Step Explanation:

Perimeter = 75

Sides:

2x + 3

3x + 4

2x - 9

75 = 2x + 3 + 3x + 4 + 2x - 9

2x + 3 + 3x + 4 + 2x - 9  = 7x - 2

75 = 7x - 2

75 = 7x - 2

+2        +2

77 = 7x

77 = 7x

/7     /7

2x + 3 = 2(11) + 3 = 22 + 3 = 25

3x + 4 = 3(11) + 4 = 33 + 4 = 37

2x - 9 = 2(11) - 9 = 22 - 9 = 13

Answer:

your answer is k

Step-by-step explanation:

not all the isosceles triangles are similar

Answer:

Graph (B)

Step-by-step explanation:

For x < 3,

An arrow starting with a hollow circle at x = 3 and heading towards 0 will represent the given inequality on a number line.

Similarly, x ≥ 5,

An arrow starting with a dark circle at x = 5 and heading towards 12 will represent the given inequality on a number line.

When we combine these inequalities on a number line, Graph (B) will be the answer.