The half-life of a substance is how long it takes for half of the substance to decay or become harmless (for certain radioactive materials). The half-life of a substance is 37 years and there is an amount equal to 202 grams now. What is the expression for the amount A(t) that remains after t years, and what is the amount of the substance remaining (rounded to the nearest tenth) after 100 years?

Answer:

The number of cans that he will need to cover the court is 12 cans

Step-by-step explanation:

The court is in the shape of a rectangle. Its length is 54 feet and its width is 30 feet. The formula for the area of a rectangle is expressed as length × width. Therefore, the area of the wooden floor is

54×30 = 1620 square foot

Suppose each can of wood stain covers 135 square feet, the number of cans that would cover the rectangular floor of the court would be

1620/135 = 12

Answer:

  y = 33°

Step-by-step explanation:

The left side and the right side are parallel, so the angles marked y and 33° are alternate interior angles, hence congruent.

  y = 33°

Answer:

7-9

Step-by-step explanation:

Sebastian goes up from 0 by 7 floors. Then, he goes down by 9.

Answer:

A. increase the sample size

Step-by-step explanation:

By increasing sample size, the amount of data included in the statistical calculation is more. As the size increases, the uncertainty decreases, hence the confidence level on our estimate is higher. By having more sample, we have more accurate analysis, and our margin of error can be reduced as well.

Answer:

Step-by-step explanation:

let x be the length of third side.

10-5<x<10+5

or 5<x<15

so third side is between 5 and 15 .

Answer:  The length of the third side is greater than 5 and less than 15 units.

Step-by-step explanation: Given that the lengths of two sides of a certain triangle are 5 and 10 units.

We are to find the length of the third side of the triangle.

Let x represents the length of the third side of the given triangle.

We know that the sum of the lengths of two sides of a triangle is always greater than the length of the third side, so we must have

[tex]5+10>x\\\\\Rightarrow x<15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

[tex]5+x>10\\\\\Rightarrow x>5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

and

[tex]x+10>5\\\\\Rightarrow x>-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

From inequalities (i), (ii) and (iii), we get

[tex]5<x<15.[/tex]

Thus, the length of the third side is greater than 5 and less than 15 units.

Answer:

[tex]\frac{25}{102}[/tex].

Step-by-step explanation:

Total number of cards in a deck = 52

number of black cards in a deck = 26

Find the probability that both cards are black (without replacement).

Therefore, both events are dependent.

The probability of first card is black = [tex]P_{1}=\frac{26}{52}[/tex]

the probability of second card is black = [tex]P_{2}=\frac{25}{51}[/tex]

[tex]P=\frac{26}{52}[/tex] × [tex]=\frac{25}{51}[/tex]

   = [tex]\frac{1}{2}[/tex] × [tex]\frac{25}{51}[/tex]

   = [tex]\frac{25}{102}[/tex]

The probability that both cards are black is [tex]\frac{25}{102}[/tex].

The probability that both cards picked without replacement are black is [tex] \frac {25}{102}[/tex]

Number of black cards in deck = 26

Total number of cards = 52

Recall :

Probability = (required outcome / Total possible outcomes)

Therefore,

Ist pick :

P(black card) = 26/52

Number of black cards left = 26 - 1 = 25

Total number of cards left = 52 - 1 = 51

2nd pick:

P(black card) = 25 / 51

Therefore, probability that both cards are black is ;

[tex]P(Both \: black) = \frac{26}{52} \times \frac{25}{51} = \frac {25}{102}[/tex]

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Answer:

1. 9 hours      2. $377     3. 48 hours     4. 235 feet

Step-by-step explanation:

In all cases below, let x represent the variable sought for.

1: 2x/5=3.6,

x=5/2 *3.6=9 hours

2. x-83=294

x=83+294=377

3. x+x/3=4x/3=64

x=64*3/4=48 hours

4. If the gardenview hotel's height  is x, then (x+17)/2 will be the height of the Plaza Hotel.

The combined height  will be x + (x+17)/2 = 361 feet

Multiplying by 2 across board,

2x+x+17=722

3x+17=722

3x =722-17=705

x=705/3=235m

Answer:

It is A. my friend

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

One angle is larger than other from the SAS Inequality Theroem that state that if two congruent sides are congruent, then one of the included angle is greater than the other

Answer

m< 1 > m < 2.

Step-by-step explanation:

< 1 is opposite the longer side.

Tim has 84 more postcards than Paul.

Step-by-step explanation:

Given,

Total number of postcards = 280

Let,

Tim's share of postcards = x

Shawn's share of postcards = [tex]\frac{3}{5}\ of\ Tim's\ share[/tex] = [tex]\frac{3}{5}x[/tex]

Paul's share of postcards = [tex]\frac{2}{3}\ of\ Shawn's=\frac{2}{3}(\frac{3}{5}x)=\frac{2}{5}x[/tex]

According to given statement;

[tex]x+\frac{3}{5}x+\frac{2}{5}x=280[/tex]

Taking LCM

[tex]\frac{5x+3x+2x}{5}=280\\\\\frac{10x}{5}=280\\\\2x=280[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{280}{2}\\x=140[/tex]

Paul's share = [tex]\frac{2}{5}x=\frac{2}{5}(28)=56[/tex]

Difference = Tim's share - Paul's share

Difference = 140 - 56 = 84 cards

Tim has 84 more postcards than Paul.

Keywords: addition, fraction

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Answer:

Step-by-step explanation:

Based on what you have here as the slope we can set the slope formula equal to 34 using the points (0, 8) and (8, c) to solve for c, then use the points (0, 8) and (a, 5) to solve for a.  

c first:

[tex]\frac{c-8}{8-0}=34[/tex] and

[tex]\frac{c-8}{8}=34[/tex] and

c - 8 = 272 s0

c = 280

For a:

[tex]\frac{5-8}{a-0}=34[/tex] and

[tex]\frac{-3}{a}=34[/tex] and

-34a = 3 so

[tex]a=-\frac{3}{34}[/tex]

That seems a little weird, but when you plug those points into the slope formula to solve for the slope, it works out the way it should.

Answer:

4 trays should he prepared, if the owner wants a service level of at least 95%.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 5

Standard Deviation, σ = 1

We are given that the distribution of demand score is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

P(X > x) = 0.95

We have to find the value of x such that the probability is 0.95

P(X > x)  

[tex]P( X > x) = P( z > \displaystyle\frac{x - 5}{1})=0.95[/tex]  

[tex]= 1 -P( z \leq \displaystyle\frac{x - 5}{1})=0.95 [/tex]  

[tex]=P( z \leq \displaystyle\frac{x - 5}{1})=0.05 [/tex]  

Calculation the value from standard normal z table, we have,  

[tex]\displaystyle\frac{x - 5}{1} = -1.645\\x = 3.355 \approx 4[/tex]  

Hence,  4 trays should he prepared, if the owner wants a service level of at least 95%.

Answer:

The Statements which are true are:

(2)(6) > (–2)(2)

6/-2 < -2/-2

6/2 > -2/2

Step-by-step explanation:

Given:

6 > –2

We need to check all options which are true,

Hence we will check for all 1 by 1.

(2)(6) > (–2)(2)

It means that when 2 is multiplied on both side we get the value as

12 > -4

Since 12 is greater than -4.

Hence this statement is true.

6/2 < -2/2

It means that when 2 is divided on both side we get the value as

3 < -1

Since 3 is greater than -1.

Hence this statement is false.

(–2)(6) > (–2)(–2)

It means that when -2 is multiplied on both side we get the value as

-12 > 4

Since -12 is less than 4.

Hence this statement is false.

6/-2 < -2/-2

It means that when -2 is divided on both side we get the value as

-3 < 1

Since -3 is lesser than 1.

Hence this statement is true.

5) (2)(6) < (–2)(2)

It means that when 2 is multiplied on both side we get the value as

12 < -4

Since 12 is greater than -4.

Hence this statement is False.

6/2 > -2/2

It means that when 2 is divided on both side we get the value as

3 > -1

Since 3 is greater than -1.

Hence this statement is True.

Answer:

A,D,F

Step-by-step explanation:

I got these correct!

Answer:

D. [tex]y<\frac{2}{3}x-4\ and\ y\geq-2x+2[/tex]

Step-by-step explanation:

Given:

Let us find the equations of the lines from the graph.

First let us determine the equation of the broken line.

The slope of the broken line is positive as 'y' values increases with increase in 'x'. The slope is the ratio of the absolute value of y-intercept to that of the x-intercept.

x-intercept = 6, |y-intercept| = |-4| = 4

So, [tex]m=\frac{4}{6}=\frac{2}{3}[/tex]

Now, equation of a line with slope 'm' and y -intercept 'b' is given as:

[tex]y=mx+b[/tex]

Here, [tex]m=\frac{2}{3},b=-4[/tex].So, equation of the broken line is:

[tex]y=\frac{2}{3}x-4[/tex]

Now, from the graph, the solution is below the broken line. So, the equality sign is replaced by the less than inequality sign. So,

[tex]y<\frac{2}{3}x-4[/tex]

Now, let us determine the equation of the other line.

y-intercept, [tex]b = 2[/tex], x-intercept = 1

Slope is negative as 'y' decreases with increase in 'x'. So,

Slope, [tex]m=-\frac{2}{1}=-2[/tex]

Now, equation is given as:

[tex]y=-2x+2[/tex]

From the graph, the solution region is to the left of the line. So, the 'equal to' sign is replaced by the 'greater than or equal to' sign' as the line is also included in the solution region. So, the inequality becomes:

[tex]y\geq-2x+2[/tex]

Therefore, the last option is correct.

[tex]y<\frac{2}{3}x-4\ and\ y\geq-2x+2[/tex]

Answer:

Short-Term investment: 5000$

Intermediate-Term investment: 65000$

Long-Term investment: 30000$

Step-by-step explanation:

To construct our first equation lets define sort-term bond investment as x, long-term investment as y.

So the equation is:

[tex]x*0,04+(100000-x-y)*0,05+y*0,06=5250[/tex]

From the equation it is found that:

[tex]y=25000+x[/tex]

Instead of y, if we put 25000+x the equation will be as following:

[tex]x*0,04+75000*0,05+(25000+x)*0,06=5250[/tex]

From the equation it is found that:

[tex]x=5000[/tex]

Short-Term investment is 5000$

[tex]x+25000=y[/tex]

Long-Term investment is 30000$

Rest of the money is Intermediate-Term investment 65000$

Answer:

(-5,7) is the center

Step-by-step explanation:

Answer:

a)20$

b)46,1$

c)0,3336

d)No concerns

Step-by-step explanation:

A) To find expected difference of cost of medical care for dogs and cats we can simply subtract average costs of cats and dogs.

[tex]120-100=20[/tex]

Expected difference will be 20$.

B) To find the standard deviation of that difference, we need to square deviations and add them and square root it again.

[tex]\sqrt{(30^2+35^2)} =46,1[/tex]

Expected difference will be 46,1$.

C)We need to find the Z value to find the probability of more expensive dogs than cats in a Vet vise.[tex]Z=(0-20)/46,1=-0,434[/tex]

Z value of the function is -0,434

From the Z table that you can find at the attachment. The probability is %33,36 or 0,3336

D) This is a subjective part. I don't have any concerns

If the cutting plane was parallel to the circular base of the cones, then we would have a circular cross section (assuming the plane doesnt cut through the vertex). However, we're told than the plane intersects both nappes, or cones, so it's not possible for the plane to be parallel to the base faces. We can rule out choice A.

We can rule out choice C and choice D for similar reasons. An ellipse only forms if the plane only cuts through one cone only, which is the same story for a parabola as well.

Answer:

The average rate of change is $25.5 per hour, option B.

Step-by-step explanation:

Average Rate of Change

When we are explicitly given some function C(x), we sometimes need to know the rate of change of C when x goes from [tex]x=x_1[/tex] to [tex]x=x_2[/tex]. It can be computed as the slope of a line .

[tex]\displaystyle m=\frac{C(x_2)-C(x_1)}{x_2-x_1}[/tex]

The provided function is

[tex]C(x)=25.50x + 50[/tex]

We are required to compute the average rate of change between the points

[tex]x_1=3\ ,\ x_2=9[/tex]

Let's compute

[tex]C(3)=25.50(3) + 50=126.5[/tex]

[tex]C(9)=25.50(9) + 50=279.5[/tex]

[tex]\displaystyle m=\frac{279.5-126.5}{9-3}[/tex]

[tex]\displaystyle m=\frac{153}{6}=25.5[/tex]

The average rate of change is $25.5 per hour, option B.

He used 86 pounds of type A coffee.

Step-by-step explanation:

Cost of type A coffee = $5.40 per pound

Cost of type B coffee = $4.05 per pound

Total blend made = 138 pounds

Total cost = $675.00

Let,

x represents the pounds of type A coffee

y represents the pounds of type B coffee

According to given statement;

x+y=138    Eqn 1

5.40x+4.05y=675    Eqn 2

Multiplying Eqn 1 by 4.05

[tex]4.05(x+y=138)\\4.05x+4.05y=558.90\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](5.40x+4.05y)-(4.05x+4.05y)=675-558.90\\5.40x+4.05y-4.05x-4.05y=116.1\\1.35x=116.1\\[/tex]

Dividing both sides by 1.35

[tex]\frac{1.35x}{1.35}=\frac{116.1}{1.35}\\x=86[/tex]

He used 86 pounds of type A coffee.

Keywords: linear equation, elimination method

Learn more about elimination method at:

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Answer:

165 Hamburgers

Step-by-step explanation:

330 divided by 2 is 165

Answer:

The supply and demand curves will shift to the left i.e. there will be a decrease in demand and supply.

Step-by-step explanation:

First: Tax is a compulsory contribution to state revenue, levied by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions.

Secondly: Money supply is the total amount of monetary assets available in an economy at a specific time.

When tax is increased, this means individuals and businesses have to contribute more to the state revenue leaving both categories with lesser income or profit i.e. lesser to spend.

In the same way, when money supply decreases, there is lesser money available to both individuals and businesses

What this implies is that demand will decrease because income has decreased. Supply will also decrease because producers will not make as much profit given the increase in tax (tax is considered cost of production).

As a result of this, the demand curve shifts to the left, the supply curve also shift to the left because both demand and supply will decrease.

Answer:

53

Step-by-step explanation:

Final answer:

About 95% of households would typically be expected to have a number of cars within 2 standard deviations of the mean, as per the empirical rule for a normal distribution.

Explanation:

The question, in a broad sense, relates to the concept of a probability distribution, specifically to the normal distribution and the empirical or 68-95-99.7 rule. To answer the question about the percentage of households with a number of cars within 2 standard deviations of the mean, one needs to apply the properties of the normal distribution. Typically, about 95% of observations can be found within 2 standard deviations of the mean on a normal distribution. However, to be precise for this case, one would calculate the mean (μ) and standard deviation (σ) of the given probability distribution, then sum the probabilities of the random variable X falling between μ - 2σ and μ + 2σ to find the desired percentage of households.

About 93% of households have a number of cars within 2 standard deviations of the mean.

To determine the percentage of households that have a number of cars within 2 standard deviations of the mean, we need to perform the following steps:

       [tex]\mu = \sum xP(X=x)[/tex]

       [tex]\mu = 0(0.09) + 1(0.36) + 2(0.35) + 3(0.13) + 4(0.05) + 5(0.02) = 1.75[/tex]

       [tex]\sigma^2 = \sum (x - \mu)^2 P(X=x)\\\sigma^2 = (0 - 1.82)^2(0.09) + (1 - 1.82)^2(0.36) + (2 - 1.82)^2(0.35) + (3 - 1.82)^2(0.13) + (4 - 1.82)^2(0.05) + (5 - 1.82)^2(0.02) = 1.1675[/tex]

       [tex]\[\sigma = \sqrt{1.0764} \approx 1.0805[/tex]

      The range is from μ - 2σ to μ + 2σ.

       μ - 2σ =  1.75 - 2(1.0805) ≈ -0.411

       μ + 2σ = 1.75 + 2(1.0805) ≈ 3.911

      Since the number of cars cannot be negative, the range is from 0 to 3.911 (practically up to 3 cars).

      0.09 + 0.36 + 0.35 + 0.13 = 0.93

Thus, about 93\% of households have a number of cars within 2 standard deviations of the mean.

Complete question:

Choose an American household at random and let the random variable X be the number of cars (including SUVs and light trucks) they own. Given is the probability distribution if we ignore the few households that own more than 5 cars.

Number of cars:   0\\       1 \\      2\\      3 \\     4\\       5

Probability:        0.09 \\ 0.36\\ 0.35\\ 0.13\\ 0.05\\ 0.02

About what percentage of households have a number of cars within 2 standard deviations of the mean?

Answer:

lt is the graph of x2+3x-4

Answer:

See Graph

Step-by-step explanation:

Find the Solution for

1x2+3x−4=0

using the Quadratic Formula where

a = 1, b = 3, and c = -4

x=−b±sqrtb^2−4ac/2a

x=−3±sqrt3^2−4(1)(−4/2(1)

x=−3±sqrt9−−16/2

x=−3±sqrt25/2

Simplify the Radical:

x=−3±sqrt5/2

We get x=22x=−82

which becomes

x=1

x=−4

Here is the graph:

Answer:

[tex]x^3+2x^2-5x-6=\left(x+1\right)\left(x-2\right)\left(x+3\right)[/tex].

Step-by-step explanation:

To find [tex]\frac{x^{3} + 2 x^{2} - 5 x - 6}{x + 1}[/tex] using synthetic division you must:

Write the problem in a division-like format. To do this:

Take the constant term of the divisor with the opposite sign and write it to the left.

Write the coefficients of the dividend to the right.

[tex]\begin{array}{c|cccc}&x^{3}&x^{2}&x^{1}&x^{0}\\-1&1&2&-5&-6\\&&\\\hline&\end{array}[/tex]

Step 1: Write down the first coefficient without changes:

[tex]\begin{array}{c|rrrr}-1&1&2&-5&-6\\&&\\\hline&\1\end{array}[/tex]

Step 2:

Multiply the entry in the left part of the table by the last entry in the result row.

Add the obtained result to the next coefficient of the dividend, and write down the sum.

[tex]\begin{array}{c|rrrr}-1&1&2&-5&-6\\&&\left(-1\right) \cdot 1=-1\\\hline&{1}&{2}+\left({-1}\right)={1}\end{array}[/tex]

Step 3:

Multiply the entry in the left part of the table by the last entry in the result row.

Add the obtained result to the next coefficient of the dividend, and write down the sum.

[tex]\begin{array}{c|rrrr}{-1}&1&2&{-5}&-6\\&&-1&\left({-1}\right) \cdot {1}={-1}\\\hline&1&{1}&\left({-5}\right)+\left({-1}\right)={-6}\end{array}[/tex]

Step 4:

Multiply the entry in the left part of the table by the last entry in the result row.

Add the obtained result to the next coefficient of the dividend, and write down the sum.

[tex]\begin{array}{c|rrrr}{-1}&1&2&-5&{-6}\\&&-1&-1&\left({-1}\right) \cdot \left({-6}\right)={6}\\\hline&1&1&{-6}&\left({-6}\right)+{6}={0}\end{array}[/tex]

We have completed the table and have obtained the following resulting coefficients: 1, 1, −6, 0.

All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus, the quotient is [tex]x^{2}+x-6[/tex], and the remainder is 0.

[tex]\frac{x^{3} + 2 x^{2} - 5 x - 6}{x + 1}=x^{2} + x - 6+\frac{0}{x + 1}=x^{2} + x - 6[/tex]

Now, we factor [tex]x^{2}+x-6[/tex]

[tex]\left(x^2-2x\right)+\left(3x-6\right)\\x\left(x-2\right)+3\left(x-2\right)\\\left(x-2\right)\left(x+3\right)[/tex]

Therefore,

[tex]x^3+2x^2-5x-6=\left(x+1\right)\left(x-2\right)\left(x+3\right)[/tex]

Answer:

340 ft²

Step-by-step explanation:

perimeter of rectangle = 2 x (L+W) = 2L + 2W = 74 .....(1)

cost of two length : $1 x 2L

cost of two width: $3.50 x 2W

($1 x 2L) + ($3.50 x 2W) = $159

2L + 7W = 159 ....... (2)

(2) - (1) ...  5W = 85

W = 17

L = (74 - 2 x 17) / 2 = 20

dimension = 17 x 20 = 340 ft²

The dimensions of the rectangular lot are 162.67 feet by 325.34 feet. The perimeter equation is 2L + 2W = 74. The cost equation is L + 3.50W = 159.

Let's say the length of the rectangular lot is L feet and the width is W feet.

The perimeter of a rectangle can be defined as: 2L + 2W.

According to the question, the perimeter is 74 feet, so we can write the equation as: 2L + 2W = 74.

The cost of fencing along the two lengths is $1 per foot, so the cost for the length fencing is 1 * L dollars.

The cost of fencing along the two widths is $3.50 per foot, so the cost for the width fencing is 3.50 * W dollars.

The total cost of fencing is $159, so we can write the equation as: 1 * L + 3.50 * W = 159.

Now we have two equations:

2L + 2W = 74

L + 3.50W = 159

To solve these equations, we can use substitution or elimination method.

Let's use the elimination method:

This simplifies to: 1.50W = 244.

Divide both sides by 1.50: W = 244 / 1.50 = 162.67 feet.

Plug this value back into the first equation to find L: 2L + 2(162.67) = 74.

Simplify: 2L + 325.34 = 74.

Subtract 325.34 from both sides: 2L = -251.34.

Divide both sides by 2: L = -251.34 / 2 = -125.67 feet.

Since the dimensions of the lot cannot be negative, we discard the negative value.

Therefore, the dimensions of the lot are 162.67 feet by 325.34 feet.

Answer: the slope of the line is 2

Step-by-step explanation:

The equation of a straight line is represented in the slope intercept form as

y = mx + c

Where

m = slope

c = intercept

The given equation is y = 2x + 4

Comparing it with the slope intercept form given above,

m = 2. Therefore, the slope of the line is 2

Answer:

114

Step-by-step explanation:

z = (x − μ) / σ

0.93 = (x − 100) / 15

x ≈ 114

answer: 0.69

answer explanation:

to start take 1.38 and 1.11 and subtract to find a price of a plum which is 0.27 since 1.38 have a extra plum then take 1.11 and take away 0.27 from 1.11 and get 0.84 then divide by 2 and get 0.42 so a apple cost 0.42 and a plum cost 0.27 together cost 0.69 which is nice

To find the cost of 1 apple and 1 plum, set up and solve a system of equations based on the given costs of different fruit combinations.

To solve this problem, we need to set up a system of equations: