David cuts 4 pieces of wood for a birdhouse. When he is done, he realizes that each piece is 2 1/3 inches too short. How does the total length of the pieces compare to what their total length should have been? Explain or show how you got your answer

Answer:

The radius is 8.5

Step-by-step explanation:

Mathematically, the radius of a circle is the distance from the center of the circle to its circumference

Thus, as we have here;

The two marked lengths are radii of the inner inscribed circle and this means that they are equal in length

thus;

x + 6 = 5x-4

5x - x = 6 + 4

4x = 10

x = 10/4

x = 2.5

Now, to get the radius length, substitute the value of x in any of the lengths

from x + 6

2.5 + 6 = 8.5

Survey every 4th student who walks into the cafeteria.

Answer:

Step-by-step explanation:

I believe it is b

Answer:

X=9

Step-by-step explanation:

I know this because you can find the answer by doing 28 - 10 which equals 18 and 2 times 9 gets you 18 and would make the equation

( 2 times 9) + 10= 28

18 + 10=28

Answer:

-6, -4 , -3 , and - 1 only.

Step-by-step explanation:

−12x + 3 ≥  5

-12x  ≥  5 - 3

-12x  ≥  2

Divide both sides by -12:

x ≤ -1/6    (Note the inequality sign flips because we are dividing by a negative value).

So considering the given set, all the values except 0 and 2 fit this inequality.

Answer:

5.625 pounds or 5 5/8 pounds

Step-by-step explanation:

(2 1/4)/24 = weight of one golf ball = 0.09375

0.09375 x 60 = 5.625 pounds or 5 5/8 pounds

Answer:

5.625 pounds or 5 5/8 pounds as a fraction

Step-by-step explanation:

Answer:

As per above two statements we have:

and

Answer:

y=58×2=116 central angle of the cyclic quadrilateral is double if inscribed angle

z=90/2=45

inscribed angle is half of central angle of the cyclic quadrilateral

Answer:

FV= $1,448.01

Step-by-step explanation:

To calculate the future value of the investment, we need to use the following formula using both interest rates:

FV= PV*(1+i)^n

Interest 6% compounded semmiannually:

i= 0,06/2= 0.03

n= 2*3= 6 semesters

FV= 1,000*(1.03^6)

FV= $1,194.05

Interest 6.48% compounded quarterly:

i= 0.0648/5= 0.0162

n= 3*4= 12 quarters

FV= 1,194.05*(1.0162^12)

FV= $1,448.01

5km :20min

? km :100min

here you do cross multiplication.

SOLUTION:

5×100=500

500÷20=25KM

DONE!!!!

Step-by-step explanation:

This is called direct propotion where you do cross multiplication!!

keep that in mind

Answer :

Given : A and B are complementary angles. B and C are complementary angles.

Prove : A C

I have attached a picture of me doing it. Hope this helps, thank you :) !!

Answer:

area = 92 yd²

Step-by-step explanation:

13x8 = 104

3x8x0.5 = 12

104 - 12 = 92 yd²

Answer:

Step-by-step explanation:

Answer: 75

Step-by-step explanation: took test and got it right. this is not fake like other people

Answer:

By substituting the values of m and n into the expression, 3(4)2 - 4(18) +6= -42

Answer:

m∠C = 66°

Step-by-step explanation:

Since AB = BD, it means this triangle is an Isosceles triangle and as such;

∠BAD = ∠BDA = 24°

Thus, since sum of angles in a triangle is 180,then;

∠ABD = 180 - (24 + 24)

∠ABD = 180 - 48

∠ABD = 132°

We are told that BC = BD.

Thus, ∆BDC is an Isosceles triangle whereby ∠BCD = ∠BDC

Now, in triangles, we know that an exterior angle is equal to the sum of two opposite interior angles.

Thus;

132 = ∠BCD + ∠BDC

Since ∠BCD = ∠BDC, then

∠BCD = ∠BDC = 132/2

∠BCD = ∠BDC = 66°

Answer:

The difference is -2x10 is basically-2 times x times 10.

Step-by-step explanation:

Cuz i said so

The x values that makes the given inequality true are -10, -9, -8, -7 and -6.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -2x>10.

Divide -2 on both the sides of an inequality, we get

x<-5

So, the solution is {.......-10, -9, -8, -7, -6}

Hence, the x values that makes the given inequality true are -10, -9, -8, -7 and -6.

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Answer:

Step-by-step explanation:

if C is the right angle,

AB is the hypotenuse

AB^2=AC^2+BC^2

AC^2=13^2-5^2

AC^2=169-25=144

AC=[tex]\sqrt{144}[/tex]=12

AC=12

Answer:

Sure, where is the activity

Answer:

where is it?

Step-by-step explanation:

Answer:

(4, 3)

Step-by-step explanation:

Plug in x - 1 where y is. The equation will turn in 2x - 3(x - 1) = -1. Distribute, and you'll have 2x -3x + 3 = -1. Combine like terms (2x and -3x) and you'll have -x + 3 = -1. Subtract 3 from both sides, and you'll have -x = -4. Divide by -x (or -1) on both sides, and you'll have x = 4. Since y = x - 1, y = 3, since 4 - 1 = 3. Sorry if this sounds repetitive btw. Good luck :D

Answer:

a. 3

Step-by-step explanation:

[tex]6 {x}^{2} - 3x + 18 \\ \\ = 3(2 {x}^{2} - x + 6) \\ \\ GCF = 3[/tex]

the greatest common factor of 6x2 – 3x + 18 is 3.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life

Here, given that,

6x2 – 3x + 18

=3×(2x2-x+6)

Hence, the greatest common factor of 6x2 – 3x + 18 is 3.

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Answer:

3w² = 243

Step-by-step explanation:

Width = w

Length = 3w

Area = 243 square units

length *width = 243

3w * w = 243

3w² = 243

The equation that you can used to determine the width of the rectangle with the given area is: 3w² = 243

Area = (length)(width)

The given dimensions are:

The equation to se in finding the width (w) of the rectangle will be:

3w(w) = 243

3w² = 243

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Answer:

21

Step-by-step explanation:

Answer:

Possible lengths of [tex]XZ[/tex] are [tex]21\,\,cm,22\,\,cm,23\,\,cm,24\,\,cm,25\,\,cm[/tex]

Step-by-step explanation:

According to triangle inequality theorem,

length of one side is less than the sum of remaining two sides.

Also,

[tex]XY=11\,\,cm\\YZ=15\,\,cm\\XZ>20\,\,cm[/tex]

Therefore,

[tex]20<XZ<15+11\\20<XZ<26[/tex]

The length of [tex]XZ[/tex] is in whole centimeters.

Therefore, possible lengths of [tex]XZ[/tex] are [tex]21\,\,cm,22\,\,cm,23\,\,cm,24\,\,cm,25\,\,cm[/tex]

Answer: 60

Step-by-step explanation:

Find the total number of students.

In this case, there are 8 total students. Multiply 60 * 8 = 480

Add all the numbers up.

85 + 65 + 36 + 48 + 75 + 39 + 72 = 420

480 - 420 = 60

x = 60

Answer: A.26

Step-by-step explanation:

= 3f+g

= 3 (6)+8

=26

Answer:

(a) The equation for the number of bacteria at time t ≥ 0 is [tex]y = 200\cdot e^{0.5 \cdot t }[/tex]

(b) The average population in the bacteria for 0 ≤ t ≤ 10 is 29,482 bacteria

(c)  The growth rate of the bacteria in the first 10 hours is 14,841 Bacteria/hour

Step-by-step explanation:

(a) The given rate of growth of the bacteria population is;

[tex]\dfrac{dy}{dt} = 0.5 \cdot y[/tex]

The initial amount of bacteria = 200

At time, t ≥ 0, we have;

[tex]\dfrac{dy}{y} = 0.5 \cdot dt[/tex]

[tex]\int\limits {\dfrac{dy}{y} } = \int\limits {0.5} \, dt[/tex]

ln(y) = 0.5·t + C

[tex]y = e^{0.5 \cdot t + C}[/tex]

[tex]y = C_1 \cdot e^{0.5 \cdot t }[/tex]

When, t = 0, y = 200, we have;

[tex]200 = C_1 \cdot e^{0.5 \times 0 } = C_1[/tex]

C₁ = 200

The equation for the number of bacteria at time t ≥ 0 is therefore given as follows;

[tex]y = 200\cdot e^{0.5 \cdot t }[/tex]

(b) The expression for the average number of bacteria in the population for 0 ≤ t ≤ 10 is given as follows;

[tex]y = \int\limits^t_0 {0.5 \cdot y} \, dt[/tex]

[tex]y = \int\limits^{10}_0 {0.5 \cdot 200\cdot e^{0.5 \cdot t }} \, dt = \left[200\cdot e^{0.5 \cdot t }\right]^{10}_0 \approx 2,9682.6 - 200 = 29,482.6[/tex]

The average population in the bacteria for 0 ≤ t ≤ 10 is therefore, y = 29,482

(c)  The average rate of growth after 10 hours of growth is given as follows;

[tex]\dfrac{dy}{dt} = 0.5 \cdot y[/tex]

[tex]\dfrac{dy}{dt} = 0.5 \cdot 200\cdot e^{0.5 \cdot 10 } = 14,841.32 \ Bacteria/hour[/tex]

The growth rate of the bacteria in the first 10 hours is 14,841 Bacteria/hour

Population functions can either represent growth or decays.

The given parameter is:

[tex]\frac{dy}{dt}= 0.5y[/tex]

(a) Solve for y

We have:

[tex]\frac{dy}{dt}= 0.5y[/tex]

Integrate both sides

[tex]\int \frac{dy}{dt}= \int 0.5y[/tex]

Divide both sides by y, and multiply both sides by dt

[tex]\int \frac{dy}{y}= \int 0.5\ dt[/tex]

Integrate both sides of the equation

[tex]\ln(y) = 0.5t +c[/tex]

Take the exponent of both sides

[tex]y = e^{0.5t +c}[/tex]

This gives

[tex]y = ce^{0.5t}[/tex]

When t = 0, and y = 200.

So, we have:

[tex]200 = ce^{0.5 \times 0}[/tex]

[tex]200 = ce^{0}[/tex]

Evaluate the exponent

[tex]200 = c[/tex]

Rewrite as:

[tex]c = 200[/tex]

Substitute 200 for c in [tex]y = ce^{0.5t}[/tex]

[tex]y = 200e^{0.5t}[/tex]

Hence, the equation for y is [tex]y = 200e^{0.5t}[/tex]

(b) The average number of bacterial for 0 ≤ t ≤ 10.

The average value of the function is calculated as:

[tex]y' = y(10) - y(0)[/tex]

Calculate y(0) and y(10)

[tex]y = 200e^{0.5t}[/tex]

[tex]y(0) = 200e^{0.5(0)}= 200[/tex]

[tex]y(10) = 200e^{0.5\times 10} =29682.6318205[/tex]

So, we have

[tex]y' = y(10) - y(0)[/tex]

[tex]y' = 29682.6318205 - 200[/tex]

[tex]y' = 29482.6318205}[/tex]

[tex]y' = 29483[/tex]

Hence, The average number of bacterial for 0 ≤ t ≤ 10 is 29483

(c) The average rate over the first 10 hours of growth

We have:

[tex]\frac{dy}{dt}= 0.5y[/tex]

Substitute [tex]y = 200e^{0.5t}[/tex]

[tex]\frac{dy}{dt}= 0.5 \times 200e^{0.5t}[/tex]

[tex]\frac{dy}{dt}= 100e^{0.5t}[/tex]

When t = 10, we have:

[tex]\frac{dy}{dt}= 100e^{0.5 \times 10}[/tex]

[tex]\frac{dy}{dt}= 100e^{5}[/tex]

[tex]\frac{dy}{dt}= 14841[/tex]

Hence, the average rate over the first 10 hours of growth is 14841

Read more about population growth functions at:

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Answer:

5 < 8

-4 < 0

0 < 4

-5 < 5

-9 > -19

-5 > -8

Step-by-step explanation:

Remember, the "Alligator" or better known as the "Packman" symbol (  >  <  )

It will always want to "eat" the bigger number. so, 8 is bigger than five, so the "Packman" will want to go after the bigger number. 5 < 8

Answer: 313.1 feet

Step-by-step explanation:

\tan 82=\frac{x}{44}

tan82=

44

x

​

44\tan 82=x

44tan82=x

x=313.0763\approx \mathbf{313.1}\text{ feet}

x=313.0763≈313.1 feet

Answer:

313.1

Step-by-step explanation: