Find the circumference of a circle with a radius of 5 inches

Evaluating the exponential decay we can see that 200 years, there will be 47.43 pounds left of the material.

A general exponential decay is:

f(x) = A*(b)^x

Where A is the initial value, b is the rate of decay, x is the variable.

We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:

63.3 = 68*(b)^40

Where b defines how it decays, we can solve that equation for b to get:

(63.3/68)^(1/40) = b

0.9982 = b

Then the decay is:

f(x) = 68*(0.9982)^x

The amount left after 200 years will be:

f(200) = 68*(0.9982)^200 = 47.43

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Answer: 0.04

Step-by-step explanation:

The area \(A_1\) of the square target with side length \(s_1=20 cm\) is:

\(A_1=s_1^{2}=20^{2}=400\)

The area \(A_2\) of the shaded square with side length \(s_2=4cm\) is:

\(A_2=s_2^{2}=4^{2}=16\)

So, the probability that the dart will land in the shaded square on the target is:

\(\frac{A_{2}}{A_{1}}=\frac{16}{400}=0.04\)

Answer:

125

Step-by-step explanation:

5^3 = 5*5*5

5*5*5 = 25*5 = 125

Hope this helps :)

Have a nice day!

Answer:

125

Step-by-step explanation:

5^3 = 5*5*5

5*5*5 = 25*5 = 125

Answer:

Step-by-step explanation:

AB=√[(4+2)²+(6-11)²]=√61

BC=√[(-1-4)²+(0-6)²]=√61

AC=√[(-1+2)²+(0-11)²]=√122

AC²=AB²+BC²

So it is a right angled triangle.

The area of the triangle is (8/5)sqrt(1199) square units.

We are given that;

Coordinates= A=(-2,11) B = (4.6) C=(-1,0)

Now,

we can plug in one point on line AB, such as A(-2, 11), and solve for b:

y = mx + b 11 = (-5/6)(-2) + b 11 = (5/3) + b b = 11 - (5/3) b = (28/3)

Hence, the equation of line AB is:

y = (-5/6)x + (28/3)

Now we can set y equal to 0 (the y-coordinate of C) and solve for x:

y = (-5/6)x + (28/3)

0 = (-5/6)x + (28/3) (-5/6)

x = -(28/3)

x = -(28/3)/(-5/6)

x = (56/15)

Therefore, point D has coordinates (56/15, 0). To find the height of the triangle, we need to find the distance between points A and D using the distance formula:

\(h = AD = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) h = sqrt((56/15 - (-2))^2 + (0 - 11)^2) h = sqrt((136/15)^2 + 121) h = sqrt(18496/225 + 121) h = sqrt(45121/225) h = (3/15)sqrt(5024)\)

Now we can plug in the values of b and h into the area formula and simplify:

\(A = (1/2)bh A = (1/2)(sqrt(61))((3/15)sqrt(5024)) A = (1/10)sqrt(61)sqrt(5024) A = (1/10)sqrt(307584) A = (1/10)(16)sqrt(1199) A = (8/5)sqrt(1199)\)

Therefore, by the given triangle answer will be (8/5)sqrt(1199) square units.

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Answer:C=40 degrees D=76 degrees

Step-by-step explanation:

Because of a theorem angle c and d equal angle DEF

so here is our equation:4y+(7y+6)=116

Open the parentheses

4y+7y+6=116

-6 on both sides

4y+7y=110

11y=110

Divide both sides by 11

y=10

Now we have to substitute

C=4y=4(10)=40

D=7y+6=7(10)+6=70+6=76

Answer:

the dozen for 7.68 because it is 12 instead of 5 for 4.42 more and ur geting 7 more donuts

Answer: cos4

Step-by-step explanation: 50 meters

B. 50-√3 meters

C. 100 meters

D. 100-√3 meters

40. What expression is used to answer: "A 4-m tall man stands on horizontal ground 43 m from a tree.

The angle of depression from the top of the tree to his eyes is 22°. Estimate the height of the tree."

A. sin 22

B. cos 22

C. tan 22

D. cot 22

Answer:320000

Step-by-step explanation:

Answer:

Alhaji Shehu Shagari

Step-by-step explanation:

Alhaji Shehu Shagari the first Democratic elected president of Nigeria, He was elected in October 1979. He contested under the The National Party of Nigeria. Prior to that time, Nigeria had been under military rule for more than 13 years.

In December 1983, there was a military coup and he was overthrown.

Answer:

-2

Step-by-step explanation:

When x = -3, y is equal to -2.

The equation of circle is \(x^2+y^2=100\)

The standard equation of a circle with center (h, k) and radius r is given by:

\((x-h)^2+(y-k)^2=r^2\) ........(1)

This is the equation needed for the circle with a center at A(h, k) and a radius equal to r since it describes the relationship between the coordinates of any point on the circumference.

Now according to the question, it is given that the circle has the center at origin and length of its radius is 10.

Center = (h, k)=(0, 0)

Radius(r) = 10 units

Now, substituting the given values in (1) we get;

⇒\(x^2+y^2=100\)

Therefore, the equation of circle centered at origin with radius 10 is \(x^2+y^2=100\)

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The function g(x) = x² + 4x has a: A. minimum.

The minimum value occur at x = -2.

The function's minimum value is -4.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function g(x) = x² + 4x, we have:

a = 1, b = 4, and c = 0

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(4)/2(1)

Axis of symmetry, Xmax = -2

Next, we would determine vertex as follows;

g(x) = x² + 4x

g(-2) = -(-2)² + 4(-2)

g(-2) = -4.

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Answer:

Step-by-step explanation:

Given cotA = 40/9

1/tanA = 40/9

tanA = 9/40

According to SOH, CAH, TOA

tan A = 9/40 = opposite/adjacent

Get the hypotenuse

hyp² = opp²+adj²

hyp² = 9²+40²

hyp² = 81+1600

hyp² = 1681

hyp = √1681

hyp = 41

Het sec A

sec A = 1/cosA

Since cos A = adjacent/hypotenuse

cos A = 40/41

secA = 1/(40/41)

SecA = 41/40

Hence the exact value of secA is 41/40

The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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Answers:

==========================================

Explanations:

Answer:

multiply the length value by 3

so its 3 foot

Answer:

$10,574.40

Step-by-step explanation:

$10,574.40 is already rounded to two decimal places. Rounding to two decimal places means rounding to the hundredths place.

Answer:

(0,-3), (1,1)

Step-by-step explanation:

Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

(a) The closed form for ∑2 is 2.

(b) The closed form expression for ∑3 is 24.

(c) The closed form for the sum ∑n = 0(― 1)² ― 1 is n(1 - n) / 2.

(d) The value of -3 matches the manual computation of the four terms.

Our closed form solution is correct.

To find the closed form for ∑2, we can use the formula for the sum of the first n terms of an arithmetic series:

∑2 = n(a + l) / 2

In this case, a = 2 (the first term) and l = 2 (the last term) since we are summing a series of 2's.

We also know that there is only one term, so n = 1.

Substituting these values into the formula, we have:

∑2 = 1(2 + 2) / 2

= 4 / 2

= 2

The formula for the sum of the first n terms of an arithmetic series is:

∑n = n(a + l) / 2

In this case, we have a = 3 (the first term), l = 13 (the last term), and n = 3 (the number of terms).

Substituting these values into the formula, we get:

∑3 = 3(3 + 13) / 2

= 3(16) / 2

= 48 / 2

= 24

The formula we developed in class is:

∑n = n(a + a + (n - 1)d) / 2

In this case, we have a = 0 (the first term) and d = -1 (the common difference).

Substituting these values into the formula, we get:

∑n = n(0 + 0 + (n - 1)(-1)) / 2

= n(0 - n + 1) / 2

= n(1 - n) / 2

To test the closed form solution for ∑3 = 0(― 1)² ― 1, we substitute n = 3 into the closed form expression we derived in part (c):

∑3 = 3(1 - 3) / 2

= 3(-2) / 2

= -6 / 2

= -3

Now, let's manually compute the sum of the first four terms of ∑3 = 0(― 1)² ― 1:

0(― 1)² ― 1 + 1(― 1)² ― 1 + 2(― 1)² ― 1 + 3(― 1)² ― 1

= 0 - 1 - 2 - 3

= -6

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Roland's percent error is approximately 3.889%.

This means that his measured value differs from the actual value by 3.889% or 0.03889 in decimal form.

The positive sign indicates that Roland's measured value is slightly lower than the actual value.

To calculate Roland's percent error, we can use the formula:

Percent Error = (|Measured Value - Actual Value| / Actual Value) \(\times\) 100

Given that Roland measured a current of 0.173 amps while expecting a current of 0.180 amps, we can substitute these values into the formula:

Percent Error = (|0.173 - 0.180| / 0.180) \(\times\) 100

Simplifying the expression within the absolute value:

Percent Error = (|-0.007| / 0.180) \(\times\) 100

Since the absolute value of -0.007 is 0.007, we have:

Percent Error = (0.007 / 0.180) \(\times\) 100

Calculating the division:

Percent Error = 0.03889 \(\times\) 100

Percent Error = 3.889%.

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Answer:

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

(-9,-6.5)

Step-by-step explanation:

mid point formula

Answer:

114.29

Step-by-step explanation:

The set builder notation of the solution inequality represented on the number line is; {x: 3< x <=5}.

It follows from the task content that at point positive 3, there's an open circle which signifies that the number 3 is less than the solution.

And since the number line is shaded from positive 3 to 5, it follows that the maximum value in the solution set is 5.

The representation is therefore; {x: 3< x <=5}.

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On the number line, the solution inequality is represented by the notation x: 3=5, which is the set builder notation of the inequality.

This is further explained below.

Given the information provided in the job, it is logical to conclude that at point positive 3, there will be an open circle. This will indicate that the number 3 will be lower than the answer.

And since the shading on the number line goes from positive 3 to 5, it follows that the highest value that can be found in the set of solutions is 5.

As a result, the representation is written as:

"x: 3 x = 5."

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Answer:

slope = 3

Step-by-step explanation:

The slope of a line parallel to the given equation share the same slope. Note the slope intercept formula:

y = mx + b

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

First, isolate the variable, y. Subtract 3x from both sides:

3x (-3x) - y = 1 (-3x)

-y = -3x + 1

Next, divide -1 from both sides:

(-y)/-1 = (-3x + 1)/-1

y = 3x - 1

You are solving for the slope of a line parallel to the given equation. Since you are solving for parallel, the slope would be shared.

3 would be the slope of the line.

~

Answer:

Yes.(16.088m combined jump)

Step-by-step explanation:

Combining jumps=4.76+5.428+5.9=16.088

16.088>16

Therefore Juan qualified for the competition

Answer:

3

Step-by-step explanation:

Answer: The correct answer is 3

Step-by-step explanation:

:) it should be correct have a good day!

A. True.

In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.

The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).

The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.

A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.

For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.

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Step-by-step explanation:

at first solve first triangle with Pythagorean solving witch it c²=a²+b²

you have to change a bit so it will be c²-b²=a²

you start with 8 and 10 triangle and then you get line which is in the middle and yo udo just the same with triangle 8 and the solved side and you get x in the second triangle you have to use c²-a²=b²