For a research project on rodents, 60 groundhogs were tagged and released. Later, researchers
counted 700 groundhogs, 12 of which had tags. To the nearest whole number, what is the best
estimate for the groundhog population?

Answer:

Yellow Bin

Step-by-step explanation:

Yellow Bin

Length = 11.4 inches,

Width = 4.2 inches,

Height =  [tex]\frac{8}{3}[/tex]

Volume of the yellow bin=LWH[tex]=11.4 X 4.2 X \frac{8}{3}=127.68 \:cubic \:inches[/tex]

Red Bin

Length = 9 inches,

Width = 5.45 inches,

Height =  [tex]\frac{11}{5}[/tex]

Volume of the red bin=LWH[tex]=9X 5.45 X \frac{11}{5}=107.91 \:cubic \:inches[/tex]

The yellow bin has a greater volume since 127.68 is greater than 107.91.

Final answer:

To evaluate the expression (2a)³, we cube the numeric term, resulting in 8, and multiply the exponent of the variable 'a' by 3, which gives us the final result of 8a³.

Explanation:

The expression given, (2a)³, requires us to cubing of exponentials. Cubing in mathematics involves raising a number or expression to the third power. In this case, the number 2 and the variable a are multiplied together first, and then that result is raised to the power of three. To evaluate this expression, you would do the following steps:

Combining these results, the expression (2a)³ becomes 8a³.

Answer:

P = 54 so

arc AC = 150

Step-by-step explanation:

The measure of AC on circle P in degrees is 118degrees

To get the measure of the arc AC on the circle, we will use the formula for calculating the angle at a point.

The sum of the angle at a point is 360 degrees, hence:

arc AB + arcBC + arcCD + arc DE + arcEA = 360

If ∠APE and ∠EPD are congruent, this means that arc DE = arcEA. The equation becomes:

arc AB + arcBC + arcCD + arc DE + arcDE = 360

Substitute the given angles into the expression:

arc AB + arcBC + arcCD +2arcDE = 360

126 + 74 + 42 + 2arcDE = 360

242  + 2arcDE = 360

2arcDE = 360 - 242

2arcDE = 118

arcDE = 118/2

arcDE = 59

arcAC = 2(arcDE)

arcAC = 2(59)

arcAC = 118 degrees

Hence the measure of AC on circle P in degrees is 118degrees

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Answer:

-4

Step-by-step explanation:

Answer:

it is

Step-by-step explanation:

Any number, all by itself, is a monomial, like 5 or 2700.

Answer:

Yes it is a monomial

Step-by-step explanation:

There's only one number, there's no operations to do so its a monomial :)

Answer:

71.75 milliroentgens per hour

Step-by-step explanation:

The  intensity(I) of Radiation varies inversely as the square of the distance (D) from the machine.

This is written as:

[tex]I \propto \frac{1}{D^2} \\$Introducing the constant of Variation k$\\I = \frac{k}{D^2} \\$When D=3 meters, I=62.5 milliroentgens per hour$\\62.5= \frac{k}{3^2}\\k=62.5 X 9 =562.5\\$Substituting K=562.5 into the variation equation$\\I = \dfrac{562.5}{D^2} \\$Therefore, When D=2.8 meters$\\Intensity,I = \dfrac{562.5}{2.8^2}=$71.75 milliroentgens per hour$[/tex]

Answer:

Step-by-step explanation:

25

Answer:

27             X

__    =      __

40           100

cross multiply divide. meaning 27*100 = 40*X. -> 2700 = 40*X. also meaning the answer is 2700 divided by 40 = X.

plug 2700/40 into a calculator. answer 67.5%

Step-by-step explanation:

Answer:

help with what tho

Step-by-step explanation:

Answer:

with what I can't see it

Step-by-step explanation:

Answer: c=2

Step-by-step explanation: the square root of c^2 equals the squae root of 4 which is 2 so your left with c=2

Answer:

a) 0.30 (30%)

b) Boy: 0.13 (13%) , Girl : 0.17 (17%)

Step-by-step explanation:

Given:-

- The probability of senior girls attend spring dance, P(GA) = 0.85

- The probability of senior boys attend spring dance, P(BA) = 0.65

- The probability that an attendee wins a prize, P(W) = 0.20

Find:-

Estimate the probability that a randomly selected senior won a prize at the dance.

Construct Arguments If you knew whether the selected student was a boy or a girl, would your estimate change

Solution:-

- First realize that the probability for any senior student to attends the spring dance and winning a prize are independent events.

- So for independent events, the probability that a "girl or a boy" attends the spring dance and wins a prize can be determined:

              P ( GA & W ) = P(GA)*P(W) = 0.85*0.20 = 0.17 (17%)

              P ( BA & W ) = P(BA)*P(W) = 0.65*0.20 = 0.13 (13%)

              P ( (BA & W) U (GA & W) ) = P ( BA & W ) + P ( GA & W )

                                                         = 0.17 + 0.13

              Answer                             = 0.3 (30%)

- So the estimate probability that a randomly selected senior won a prize at the dance is 0.3 or 30% of all attendee.

- If the randomly selected senior was a girl would be the proportion of people who won the prize.

            P ( GA & W ) = 0.17 (17%)

- Similarly, If the randomly selected senior was a boy would be the proportion of people who won the prize.

            P ( BA & W ) = 0.13 (13%)                        

Answer:

a) 30%

b) the estimate wouldnt change as far as the probabilities is been maintained. thre can only be a shift in the gender probability depending on whether there are more number of boys or girls.

Step-by-step explanation:

a) Prob( all senior girl attended) = 85%

    Prob ( all senior boy attended) = 65%

    Prob( won a price)  = 20%

Prob( a senior girl attends and win a price) = 85% x 20%

           = 17%

Prob ( a senior boy attends and win a price) = 65% x 20%

           = 13%

Prob( a senior won a price)  = 17% + 13%

                = 30%

b)   The estimate wouldnt change as far as the probabilities is been maintained. thre can only be a shift in the gender probability depending on whether there are more number of boys or girls.

Answer:

The last option

Step-by-step explanation:

To find a percentage of something you need

[tex]\frac{expected}{total}*100[/tex]

The expected is correct marks, the total is the total amount - then you multiply by 100 to turn the decimal into a percentage.

Answer:

the answer is D

Step-by-step explanation:

Answer:25

Step-by-step explanation:

15x 2/5=25

Answer:

$37.50

Step-by-step explanation:

[tex]\frac{2}{5}[/tex] of Aiden's money is $15. Half of [tex]\frac{2}{5}[/tex] is [tex]\frac{1}{5}[/tex], so you have to find half of $15 to find out what [tex]\frac{1}{5}[/tex] of Aiden's money is.

15/2 = 7.5. [tex]\frac{1}{5}[/tex] of Aiden's money is $7.50.

7.5 × 5 = 37.5, so Aiden had $37.50 before he put some into his piggy bank.

Answer:

Step-by-step explanation3:45

Answer:

3:20 p.m

Step-by-step explanation:

Answer:

59.1 °

Step-by-step explanation:

-Given that Tan B=1.6732

-Angle B is equivalent to the tan inverse of the tan B value:

[tex]\angle B=Tan^{-1}B\\\\\angle B=Tan^{-1}(1.6732)\\\\=59.1350\approx59.1\textdegree[/tex]

Hence, angle B is 59.1 °

To find the measure of angle B, you can use the inverse tangent function (arctan) to find the angle whose tangent is 1.6732.

The measure of angle B is approximately 59.7 degrees.

To find the measure of angle B, you can use the inverse tangent function (arctan) to find the angle whose tangent is 1.6732. First, convert the tangent value to radians by using the formula tan(B) = opposite/adjacent. Then, take the arctan of B to find the measure in radians. Finally, convert the radians to degrees by multiplying by 180/pi.

Step-by-step:

Plugging in the given value, B ≈ 59.7 degrees to the nearest tenth of a degree.

https://brainly.com/question/2046046

#SPJ3

Answer:

p = 0.52392

Step-by-step explanation:

Here we have

p = 23% = 0.23

[tex]\hat p[/tex] = 208/800 = 0.26

n = 800

q = 1-p = 0.77

α = 5% = 0.05

Here we have

Z test given by

[tex]z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}[/tex]

From which we have

From the Cpdf we have Probability = 0.0219, z = 2.016

Therefore from the z score = 0.0683, p = 0.52392 from z table.

Answer:

all value of x are equal

Step-by-step explanation:

Answer:

1,404,928 is the volume of a cube with a side length that measures 112 ft

Answer:

1,404,928 is the volume

Answer:

none

Step-by-step explanation:

Answer:

  3/8

Step-by-step explanation:

1/4 + 1/8 = 2/8 + 1/8 = 3/8

After you give the fractions a common denominator, you can add their numerators to find the numerator of the result.

Mr. Hawkins's combined bonus payments are 3/8 of his salary.

Final answer:

Without more context, the measure of angle 6 cannot be determined from the given information that angle 5 is 120 degrees.

Explanation:

To determine the measure of angle 6, we need additional information about the context in which angle 5 and angle 6 are related. Since the question does not provide sufficient details, such as whether the angles are supplementary, complementary, or part of a geometric figure like a triangle or polygon, it's not possible to provide the measure of angle 6 based solely on the given information that angle 5 is 120 degrees. In geometry, the relationships between angles often depend on the shapes they are part of or the lines intersecting with them. If angle 5 and angle 6 are supplementary angles (angles that add up to 180 degrees), for instance, we could subtract the measure of angle 5 from 180 degrees to get angle 6. However, without more details, we cannot accurately provide the measure of angle 6.

Step-by-step explanation:

As it is a quadrilateral so sum of all angles of quadrilateral is equal to 360°

14x - 11° + 8x + 7° + 5x + 18° + 10x + 13° = 360°

37x+ 27° = 360°

37x = 360° - 27°

37x = 333°

x = 333° / 37

Therefore x = 9°

Now

<B = 8 * 9° + 7° = 79°

Hope it will help you.

Answer: The answer is 79.0°

Step-by-step explanation:

A quadrilateral will always have 360° and four sides. Keep that in mind, that's a universal rule of geometry.

Here, the sum of all sides is equal to 360°. Therefore, we make an equation:

[tex](14x-11) + (8x+7) + (5x+18) + (10x + 13) = 360[/tex]

Simplify by adding and subtracting like terms.

[tex]37x +27=360[/tex]

Isolate x by first passing the 27 to the other side.

[tex]37x = 333[/tex]

Divide by 37 to isolate x.

[tex]x = 9[/tex]

To find m∠B, we plug in x to [tex](8x+7)[/tex]

which gives you: [tex](8*9+7) = 79[/tex]

The answer is 79.0°

Curious if it is correct? Let's double check.

Plug in the x=9 to all the x values and add them up. You should get 360, which makes the answer correct.

Answer:

A student solved 3/x−4=x/7 in six steps, as shown:

Step 1:  3=x(x−4)/7  

Step 2: 21=x(x−4)

Step 3: 21=x^2−4(x)

Step 4: 0=x^2−4(x)−21

Step 5: 0=(x−7)(x+3)

Step 6: x=−3, x=7

Which statement is an accurate interpretation of the student's work?

A.The student solved the equation correctly.

B.The student made an error in step 2.

C.The student made an error in step 5.

D.Only x=7 is a solution to the original equation.

Option A is the right choice.

Step-by-step explanation:

Given:

An equation and its step-wise work.

We have to check whether the steps are correct or not.

The equation is:

⇒ [tex]\frac{3}{x-4} = \frac{x}{7}[/tex]

Solution:

⇒ [tex]21=x(x-4)[/tex]              ...cross multiplying terms.

⇒ [tex]21=x^2-4x[/tex]    

⇒ [tex]x^2-4x-21=0[/tex]

⇒ [tex]x^2-7x+3x-21=0[/tex] ...using middle term splitting

⇒ [tex]x(x-7)+3(x-7)=0[/tex]

⇒ [tex](x+3)(x-7)[/tex]

⇒ [tex]x=-3\ and\ x=7[/tex]

The student have solved the question correctly.

Answer:

The maximum dimension for box will be side length as 26.667 inches and height will be 6.667 inches and volume will be 4741 cu inches.

Step-by-step explanation:

Given:

With dimensions as

40x40 square and sides are folded in square corners.

To Find:

Maximum volume that will yield and maximum dimension for box

Solution:

Consider, a box with 40 x 40 dimensions as follows and

let a x side length square corners are cut and folded up and a new figure is formed .and for that what will be the maximum volume and dimension.

Now,

as the there 2 corner for each side i.e. 2 square on side length

Resultant length will be 40-2x

So volume is given by ,

[tex]V=l^2*h[/tex]

[tex]=(40-2x)^2*x[/tex]

[tex]V=(40^2-2*2x*40+4x^2)*x[/tex]

[tex]V=(1600-160x+4x^2)*x[/tex]

[tex]V=4x^3-160x^2+1600x[/tex]

To get Maximum volume differentiate w.r.t 'x'

[tex]V'=12x^2-320x+1600[/tex]

[tex]V"=24x-320[/tex]

Now solve for x with help of quadratic equation we get ,

12x^2-320x+1600

=4(3x-20)(x-20)

Therefore ,

3x-20=0 or x-20=0

x=20/3 or x=20

x=16.666 or x=20

Now use this values in a 2nd derivative equation,

V"=24(6.667)-320)

V"=160-320

V"=-160 <0 ,................equation(1)[Here maximum volume will be presented]

For X=20

V"=24*20-320

V"=480-320

=160>0 ..................Equation(2)[here minimum volume will presented]

Comparing equation 1 and 2 we get ,

Take as x=20/3 as the folded square length as it is gives minimum value for 2nd derivative.

So

[tex]V=(40-2x)^2*x[/tex]

[tex]V=[40-2(20/3)]^2*20/3[/tex]

[tex]V=[40-40/3]^2*6.667[/tex]

=[tex][26.667]^2*6.667[/tex]

=4740.95

=[tex]4741 cu inches.[/tex]

So side lengths =40-2x=40-2*20/3

=40(1-1/3)

=40(2/3)

=26.667 inches

And the height will be x=20/3=6.667 inches.

Answer:

The answer to your question is Vertex = (5 , -5)

Step-by-step explanation:

Data

Equation                y = - x² + 10x - 30

Process

1.- Add 30 units in both sides

                             y + 30 = -x² + 10x - 30 + 30

2.- Simplify

                             y + 30 = -x² + 10x

3.- Factor -1 in the right side

                             y + 30 = -(x² - 10x      )

4.- Complete the perfect square trinomial

                             y + 30 - 5²= -(x² - 10x + 5²)

5.- Simplify

                             y + 30 - 25 = -(x² - 10x + 25)

                             y + 5 = -(x - 5)²

6.- Find the vertex

                            Vertex = (5 , -5)

Answer:

x=-4 or x=-1/2=-0.500

Step-by-step explanation:

Answer:

x= -4 or x= -0.5

Step-by-step explanation:

use a quadratic formula calculator or graph it on desmos

You will need 592 square inches of cardboard to build the box.

To determine how much cardboard is needed to build the box, we calculate the surface area of the box.

The box has six faces: two of each dimension.

Calculating the area of each pair of faces:

Two faces of (12 in x 8 in):

2 x (12 x 8) = 2 x 96 = 192 square inches

Two faces of (12 in x 10 in):

2 x (12 x 10) = 2 x 120 = 240 square inches

Two faces of (8 in x 10 in):

2 x (8 x 10) = 2 x 80 = 160 square inches

Sum the areas of all faces:

192 + 240 + 160 = 592 square inches

Answer: A

Step-by-step explanation:

We need to get the denominators to be same first before we can do anything to the numerator.

The LCD (lowest common denominator) is [tex]3x^{3}[/tex]. To find the LCD, multiply the denominators together: [tex]x^{3}[/tex] · [tex]3x[/tex] = [tex]3x^{3[/tex].

Below, we are trying to get the denominators to equal the same or to [tex]3x^{3}[/tex].

[tex]\frac{3}{3} (\frac{4}{x^{3} } ) - \frac{x^{2} }{x^{2} } (\frac{2x-1}{3x} )[/tex]

[tex]\frac{12}{3x^{3} } - \frac{2x^{3}-x^{2} }{3x^{3} }[/tex]

Now that the denominators are the same, we can subtract the numerators from each other.

[tex]\frac{ 12 - (2x^{3} -x^{2})\\}{3x^{3} } \\[/tex]

[tex]\frac{12-2x^{3} +x^{2} }{3x^{3} }[/tex]

Now, we can just reorganize the variables.

Answer:  A or [tex]\frac{-2x^{3} + x^{2}+12 }{3x^{3} }[/tex]

Answer: n = 8.4

Step-by-step explanation:

40 - 5n = -2

First, subtract 40 from each side of the equation

-5n = -42

Then, divide each side by -5

n = 8.4

The -5 and -42 cancel each other out when dividing, so n = 8.4 is positive.

Answer:

n=8.4

Step-by-step explanation:

To solve, we need to isolate the variable, n

40 -5n =-2

Subtract 40 from both sides

40-40-5n= -2 -40

-5n= -42

Divide both sides by -5

-5n/-5=-42/-5

n=42/5

n=8.4

Answer:

  see below

Step-by-step explanation:

The angle where chords cross is the average of the intercepted arcs. Here, that is ...

  (37° +46°)/2 = (83°)/2 = 41.5°

Angle SUT is 41.5°.

_____

Comment on the error

The measure of an arc cannot be arbitrarily said to be the same as the angle where the chords cross. It will be the same if (a) the chords cross at the circle center, or (b) the opposite intercepted arc has the same measure. Neither of these conditions hold here.

Answer:

1) A

2) 41.5°

Step-by-step explanation:

SUT would have been 46° if U was the centre

Angle SUT = (37+46)/2

= 83/2

= 41.5