=
An initial sample of 502 g of a radioactive substance decays according to the function Alt)
where t is given in years.
502e -0.033t
(a) How many grams of the substance will remain after 68 years? Round your answer to one decimal place.
(b) What is the half-life of the substance? Round your answer to one decimal place.
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Ruth's quarterly payments after the collision coverage is dropped is going to be $186.35.

First find out the annual cost of insurance after the collision insurance is dropped:

= Annual premium - Collision insurance

= 916 - 170.60

= $745.40

The quarterly payments become:

= 745.50 / 4 quarters a year

= $186.35

In conclusion, Ruth will pay $186.35 per quarter.

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Answer:

F=5+M

F=5+4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the expression (((x^3)^2))^2

a) Differentiating the function with respect to x using chain rule.

Given y = (((x^3)^2))^2

Let u = (x³)²

y = u²; dy/du = 2u

Let p = x³; dp/dx = 3x²

u = p²; du/dp = 2p

Applying the chain rule formula:

dy/dx = dy/du • du/dp • dp/dx

substitute in the formula

dy/dx = 2u•2p•3x²

Since u = (x³)² and p = x³

dy/dx = 2(x³)²(2x³)(3x²)

dy/dx = 12x^6•x^5

dy/dx = 12x¹¹

b) Using property of exponent

y = (((x^3)^2))^2

y = (x^6)²

y = x¹²

dy/dx = 12x^12-1

dy/dx = 12x^11

Answer:

A: P = 41100 - 590t

B: 34610

Step-by-step explanation:

equation = 41100-(41100-36380)/(2011-2003)t

plug it in

41100 - 590(2014-2003)=34610

Answer:

The empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 62, standard deviation of 8.

What is the approximate percentage of trees planted between 38 and 86?

38 = 62 - 3*8

86 = 62 + 3*8

So within 3 standard deviations of the mean, which, by the empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.

Answer:

500ml

Step-by-step explanation:

\(2000 \div 4 = 500\)

Answer:

500 ml

Step-by-step explanation:

2 litres= 2000 millilitres divided into 4 bowls=2000÷4=500 millilitres

The slope of the line of best fit in Robert's math class represents the relationship between a student's grade and the number of hours they study.

When Robert's math teacher plots student grades against the number of hours they study, she is creating a scatter plot on a coordinate plane.

Each point on the graph represents a student's grade and the number of hours they claim to have studied. The line of best fit is a straight line that passes as close as possible to all the data points.

The slope of this line represents the rate at which a student's grade changes as they study more hours.

Specifically, the slope tells us how much the grade changes for each unit increase in the number of hours studied.

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The total cost for the customer for the entire year is  $48,600.

The customer wants to purchase 20 subscriptions for each of their 20 employees, so they need a total of 20 x 20 = 400 subscriptions.

Each subscription costs $10 per month for a yearly commitment,

so the cost for one subscription for a year would be $10 x 12 = $120.

Therefore, the total cost for 400 subscriptions for a year would be $120 x 400 = $48,000.

In addition, they need 1 extra subscription for a different service for every two employees, so they need 20 / 2 = 10 extra subscriptions.

Each extra subscription costs $5 per month for a yearly commitment, so the cost for one extra subscription for a year would be $5 x 12 = $60.

Therefore, the total cost for 10 extra subscriptions for a year would be $60 x 10 = $600.

Adding the cost of the extra subscriptions to the cost of the regular subscriptions, the total cost for the customer for the entire year would be $48,000 + $600 = $48,600.

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Triangle DEF as shown ion figure D(-4, 6), E(2,6), F(0,8) translate by a factor of 1/2, So the new vertex are: D' (-2, 3), E' (1, 3), F' (0, 4)

Triangle is commonly represented by a graph in which the three points are labeled as A, B, and C, and the three line segments are labeled as AB, AC, and BC. The graph of a triangle typically looks like below figure.

The new coordinates of each vertex of the triangle after scaling by 1/2.

For vertex D:

x-coordinate = -4, y-coordinate = 6

New x-coordinate = (1/2) × (-4) = -2

New y-coordinate = (1/2) × 6 = 3

So the new coordinates for D' are (-2, 3)

For vertex E:

E (2, 6) ⇒ 1/2 × (2, 6) ⇒ (1, 3)

So the new coordinates for E' are (1, 3)

For vertex F:

F (0, 8) ⇒ 1/2 × (0, 8) ⇒ (0, 4)

So the new coordinates for F' are (0, 4)

D(-4, 6), E(2,6), F(0,8)  ⇒   D' (-2, 3), E' (1, 3), F' (0, 4)

Finally, plot the new points on the same coordinate plane and connect them to form the new triangle. You should see that the new triangle is a smaller version of the original triangle, with all sides and angles scaled down by a factor of 1/2.

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The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Answer:

D

Step-by-step explanation:

4 - 8 × 2 ← perform multiplication before doing subtraction

= 4 - 16

= - 12

Answer:

yaa , when X=15, y = 3;

here the value of X is five times the value of y

so when X= 10

then. y =X/5 = 10/5= 2

so the value of y will be 2

hope you like the answer

Answer:

21 and 10.5 respectively

Step-by-step explanation:

Remember circumference of a circle is given as;

C= 2×π×r; r is raduis

r = C / 2×π

=65.98/(2×3.142)= 10.50

D= 2× r = 2× 10.50= 21.0( D represent diameter)

Note π = 3.142 a known constant

Step 1

Given; The mean weight of an adult is 60 kilograms with a variance of 100. If 118 adults are randomly selected, what is the probability that the sample mean would be greater than 62.2 kilograms? Round your answer to four.

Step 2

In a set with mean and standard deviation, the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean and standard deviation, the sample means with size n of at least 30 can be approximated to a normal distribution with mean and standard deviation;

What is the probability that the sample mean would be greater than 62.2 kilograms?

Thus;

Answer;

Answer:

option a is right hope it may help u

Step-by-step explanation:

cz area unit always comes in square

and volume comes in cube so don't be confused

\(32,500 {m}^{2} \)

7,150,000

The population of Georgia is 10,500,000.

The population of Virginia is 30% less than that.

So the population of Virginia is 10,500,000 - 30% which equals 7,150,000

Answer:80

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

its just 80

The area of the enclosed shape is about 14.47 km^2.

We are given that;

056° for 9.8km and  3.5 km on a bearing of 112°

Now,

We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:

y = 180° - 56° - 112°

y = 12°

Now we can use the cosine rule to find z:

z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)

z^2 ≈ 101.87

z ≈ 10.09

Therefore, Fred is about 10.09 km away from his start point.

To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:

sin(56°) = x/9.8

x = 9.8 sin(56°)

x ≈ 8.27

The area of a triangle is given by half the base times the height, so:

A = (1/2)(3.5)(8.27)

A ≈ 14.47

Therefore, by trigonometric ratios the answer will be 14.47 km^2.

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Answer:

least to greatest

.86, 8/9, .9

Answer:

.86,8/9,9 ttttttttttttttttttftfffff

Answer:

+1 is the answer

Step-by-step explanation:

-19-(-10)

-19+10

+1

Answer:

\(y = 3x +1\)

Step-by-step explanation:

Given

\(m = 3\)

\((x_1,y_1) = (-2,-5)\)

Required

The equation

This is calculated as:

\(y = m(x - x_1) + y_1\)

So, we have:

\(y = 3(x - -2) -5\)

\(y = 3(x +2) -5\)

Open bracket

\(y = 3x +6 -5\)

\(y = 3x +1\)

Answer:

third chord length is 27.8088 cm

Between III and I chord is \(27^\circ57'30''\)

Between III and II chord is \(37^\circ36'30''\)

Step-by-step explanation:

The calculation of measurements of the triangle is shown below:-

By Cosine rule

\(BC^2 = (14.32)^2 + (18.64)^2 - 2\times 14.32 \times 18.64 cos\114^\circ26'\\\\ BC^2 = 773.330156\\\\ BC = \sqrt{773.330156}\)

BC = 27.8088 (it is the length of third chord)

By Sin rule

\(\frac{Sin A}{BC} = \frac{Sin B}{14.32} \\\\ \frac{Sin114^\circ26'}{27.8088} = \frac{Sin B}{14.32} \\\\ Sin B = \frac{14.32114^\circ26}{27.8088}\)

After solving this we will get

Sin B = 0.468829

\(<B = Sin^{-1} 0.468829\\\\ <B = 27^\circ 57'30''\)

Therefore

\(<A + <B + <C = 180^\circ\)

\(<C = 180^\circ - 114^\circ26'-27^\circ57'30''\\\\ <C = 37^\circ36'30''\)

Now,

third chord length is 27.8088 cm

Between III and I chord is \(27^\circ57'30''\)

Between III and II chord is \(37^\circ36'30''\)

The same is to be considered

The multiplicative rate of change for the function  is approximately.

To find the multiplicative rate of change for the exponential function f(x) = , we need to calculate the derivative of the function. However, it's important to note that the function you provided is not an exponential function. An exponential function has a base raised to a variable exponent.

The given functioncan be rewritten as. Now, we can proceed to find the multiplicative rate of change by taking the derivative of f(x) with respect to x.

Using the chain rule, the derivative of is:

Here, ln(2/5) is a constant representing the natural logarithm of 2/5. The multiplicative rate of change is given by the derivative, which is

The value of ln(2/5) is approximately -0.916.

It's important to note that the multiplicative rate of change is not constant for this function. It depends on the value of x and decreases exponentially as x increases.

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Answer:

5^a= 1/5^3

5^a= 5^-3

a=-3

Step-by-step explanation:

Answer:

1,3,5,7,9,11,13,15,17,19

add them all together

= 100

Step-by-step explanation:

hope this works :)

Total number of possible outcomes:

Number of ways to choose 3 numbers from 56 (56 choose 3): 56! / (3! * (56 - 3)!) = 22,957

Number of ways to choose 1 number from 49: 49

Total number of possible outcomes = 22,957 * 49 = 1,128,593

Number of favorable outcomes:

Number of ways to choose 1 number from 49: 1

Number of favorable outcomes = 1

Probability of winning the minimum award:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 1 / 1,128,593 ≈ 0.000000888, or approximately 0.0000888%

1. If Alex runs a mile in under 6 minutes, then he will have a new personal record. Alex ran a mile in 5 minutes and 45 seconds. Therefore, Alex set a new personal record. - law of Detachment

2. If you go to the water park, then you will need to bring sunscreen. If you do not bring sun screen, then you will burn. Therefore, when you go to the water park you will get a sunburn. - law of contrapositive

3. If two lines are parallel, then they never intersect. Line a and line b intersect. Therefore, line a and line b are not parallel - Law of Syllogism

4. If the measures of two angles in a triangle are 30° and 60°, then the third angle is 90°. If a triangle has a 90° angle, then it is a right triangle.  Therefore, if a triangle has two angles that measure 30° and 60°, then it is a right triangle. - Not a valid conclusion

According to the law of contrapositive, the initial assertion is accurate if and only if the contrapositive is accurate. The original assertion is untrue if the contrapositive is false. A conditional assertion that may or may not depend on another is a contrapositive.

Using deductive reasoning, a syllogism is a three-part logical argument in which two premises are joined to get a conclusion.

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Answer:

c. $100,000

Step-by-step explanation:

Calculation of the expected net profit of Ephemeral services corporation

Since we are been told that 9 other companies besides esco are as well bidding for the $900,000 government contract, it means we have to find the expected net profit by dividing 1 by 9×$900,000 .Thus ESCO can only expect to cover its sunk cost.

Hence ,

E(X) = (1/9) × $900,000

E(X)=0.111111111×$900,000

E(X)= $100,000

Therefore the expected net profit would be $100,000

The equation solved for the variable are;

h = S- 2B/p

b = S - hp/2

To determine the equation, we need to know that the subject of formula for  an equation is described as the variable that is made to stand on one end of the equality sign.

It is the variable that is being worked out.

From the information given, we have that;

S= hp + 2B.

To make the height with the variable 'h' the subject, we have;

collect the terms

hp = S - 2B

Divide by the coefficient

h = S- 2B/p

For b, we have;

S - hp = 2b

divide by the coefficient

b = S - hp/2

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