If 14 g of a radioactive substance are present initially and 7 years later only 7 g remain, how much of the substance will be present after 9
yr?

Answer: 50

Step-by-step explanation:

Formula for sample size(n) if population standard deviation [tex](\sigma)[/tex] is known:

[tex]n=(\dfrac{\sigma\times z_c}{E})^2[/tex] , E = Margin of error , [tex]z^c[/tex] =  Critical z-value

As per given,

[tex]\sigma= 128[/tex] kilowatt-hours.

Critical z-value for 90% confidence = 1.645

E =  30

Required sample size : [tex]n=(\dfrac{128\times1.645}{30})^2=(7.01867)^2[/tex]

[tex]=49.2617285689\approx50[/tex]

Hence,  the smallest sample size to provide a 90% confidence interval for the population mean with a margin of error of 30 or less = 50

Answer:

1.  dividing

2.  faster than

Step-by-step explanation:

Edge 2020

Answer:

The speed of a turtle can be found by distance by time.

   adding

   subtracting

   multiplying

✔ dividing

The speed of the winning turtle was the speed of the other two turtles.

   slower than

   the same speed as

✔ faster than

Answer:

The probability that the man arrives first is 0.50.

Step-by-step explanation:

Let X denote the arrival time of the man and Y denote the arrival time of the woman.

It is provided that:

[tex]X\sim U[15,45]\\\\Y\sim U[0,60][/tex]

The pdf of X an Y are:

[tex]f_{X}(x)=\frac{1}{45-15}=\frac{1}{30};\ 15<X<45\\\\f_{Y}(y)=\frac{1}{60-0}=\frac{1}{60};\ 0<Y<60[/tex]

It is provided that X and Y are independent of each other.

Then the joint pdf of X and Y is:

[tex]f_{XY}(x,y)=f_{X}(x)\times f_{Y}(y)\\\\\Rightarrow f_{XY}(x,y)=\frac{1}{30}\times \frac{1}{60}\\\\\Rightarrow f_{XY}(x,y)=\frac{1}{1800};\ 15<X<45,\ 0<Y<60[/tex]

Compute the probability that the man arrives first as follows:

[tex]P(X<Y)=\int\limits^{45}_{15} {\int\limits^{60}_{x} {\frac{1}{1800}} \, dy } \,dx[/tex]

                 [tex]=\frac{1}{1800}\times \int\limits^{45}_{15} y|^{60}_{x} \,dx\\\\=\frac{1}{1800}\times \int\limits^{45}_{15} {60-x} \,dx\\\\=\frac{1}{1800}\times |60x-\frac{x^{2}}{2}|^{45}_{15}\\\\=\frac{(1687.5-787.5)}{1800}\\\\=\frac{900}{1800}\\\\=\frac{1}{2}\\\\=0.50[/tex]

Thus, the probability that the man arrives first is 0.50.

Answer:

angle = 48 supplement = 132

Step-by-step explanation:

Answer:

angle 48 and supplement 132

Answer:

Sin A = 8/10 or 4/5

Cos A = 6/10 or 3/5

Tan A = 8/6 or 4/3

Answer:

210

Step-by-step explanation:

You can multiply 52 by 4 which is 208.

Next, you can add that to the number 2 which is 210.

Hope this Helps!!! :)

Answer:

x=9

Step-by-step explanation:

f(x) = −(x − 7)2 + 4

(substitute f(x) = 0)

0= −(x − 7)2 + 4

(distribute 2 into brackets)

0= −(2x - 14) + 4

(remove brackets and change the sign of each expression inside the brackets)

0= - 2x + 14 + 4

(add the numbers)

0= - 2x + 18

(move variable to the other side and change its sign)

2x = 18

(divide both sides by 2)

x = 9

The given expression is quadratic, parabolic graph, relative maxima and real zeros. The correct options are (a), (c) and (f).

The general form of a quadratic equation is given as ax^2 + bx + c = 0.

Here, a ≠ 0 and b and c are integers.

The degree of a quadratic equation is 2.

The given expression is f(x) = -(x - 7)² + 4

Since the degree of the expression is 2, it is quadratic.

The graph of the given equation will be parabolic.

By comparing from the general vertex form (x - h)² + k, its vertex can be found as (7, 4).

Axis of symmetry is x = 7.

y-intercept can be obtained by plugging x = 0 as,

-(0 - 7)² + 4 = 53.

Maxima or minima can be found as below,

f'(x) = 0

⇒ -2(x - 7) = 0

⇒ x = 7

In order to find the solution write the expression as follows,

-(x - 7)² + 4 = 0

⇒ -x² + 14x - 49 + 4 = 0

⇒ x² - 14x + 45 = 0

⇒ x = 5,9

Thus, the equation has real solutions.

Hence, the properties of the given equation are derived as quadratic, parabolic graph, relative maxima and real zeros.

To know more about quadratic equation click on,

https://brainly.com/question/17177510

#SPJ2

Answer:

no table

Step-by-step explanation:

This question is incomplete, the complete question is;

Find the volume of the described solid of revolution or state that it does not exist.

The region bounded by ​f(x) = x⁻⁷ and the​ x-axis on the interval ​[ 1​,​ ∞) is revolved about the​ x-axis.  

Answer: volume of the cubic units is π/13

Step-by-step explanation:

Given that;

​f(x) = x⁻⁷  

in the image, Area of ring = πR²

we substitute

Area = π (x⁻⁷)²

= π(x⁻¹⁴)

Now

Volume = ₁∫^∞ π(x⁻¹⁴) dx

= [ -π/13  x⁻¹³ ]₁^∞

= 0 + π/13

= π/13

therefore volume of the cubic units is π/13

Answer:

nnnvvg

Step-by-step explanation: mm

Answer:

First table

Step-by-step explanation:

It will be the first table as on the other ones there is two of the same X

Given:

Consider the expression is

[tex]\log_63+\log_68-\log_64[/tex]

To find:

The value of given expression.

Solution:

We have,

[tex]\log_63+\log_68-\log_64[/tex]

Using properties of logarithm, we get

[tex]=\log_6(3\times 8)-\log_64[/tex]       [tex][\because \log_am+\log_an=\log_amn][/tex]

[tex]=\log_6(24)-\log_64[/tex]

[tex]=\log_6\left( \dfrac{24}{4}\right)[/tex]       [tex][\because \log_am-\log_an=\log_a\dfrac{m}{n}][/tex]

[tex]=\log_66[/tex]

[tex]=1[/tex]                    [tex][\because \log_aa=1][/tex]

Therefore, the value of given expression is 1.

(C) 1 is the correct answer.

Answer:

251,000$

Step-by-step explanation:

Answer:

in total there are 225 books if that's what you're asking?

Answer:

0.56652

Step-by-step explanation:

Given that :

1 job takes 15 seconds

x jobs will take 60 seconds

15x = 60

x = 4

4 jobs take 60 seconds

μ = 4

Job is 4th in line :

Find the probability of ;

P(x ≥ 4) = 1 - [P(x ≥ 4) = 1 - [P(x < 3 ) + P(x < 2) + P(x < 1) + p(x < 0)]

P(μ, x) = [(e^-μ) * (μ^x)] ÷ x!

Using the poisson distribution calculator :

P(x< 3) = 0.19537

P(x< 2) = 0.14653

P(x< 1) = 0.07326

P(x< 0) = 0.01832

Hence,

P(x ≥ 4) = 1 - [P(x < 3 ) + P(x < 2) + P(x < 1) + p(x < 0)

= 1 - (0.19537 + 0.14653 + 0.07326 + 0.01832)

= 1 - 0.43348

= 0.56652

Answer: 73

Step-by-step explanation:

Answer:

[tex]n = 7\frac{1}{4}[/tex]

Step-by-step explanation:

See attachment for complete question.

From the attachment, we have:

[tex]Length = 4\frac{1}{4}ft[/tex]

[tex]Width = n[/tex]

[tex]Perimeter = 23fr[/tex]

Required

Determine n

Perimeter is calculated as:

[tex]Perimeter = 2(Length + Width)[/tex]

Substitute in values

[tex]23 = 2(4\frac{1}{4} + n)[/tex]

Convert to decimal

[tex]23 = 2(4.25 + n)[/tex]

Open Bracket

[tex]23 = 8.5 + 2n[/tex]

Collect Like Terms

[tex]2n = 23 - 8.5[/tex]

[tex]2n = 14.5[/tex]

[tex]n = 14.5/2[/tex]

[tex]n = 7.25[/tex]

[tex]n = 7\frac{1}{4}[/tex]

Answer:

5 capsules

Step-by-step explanation:

A doctor may prescribe Keflex for an ear infection. One capsule = 0.250 g of Keflex. The recommended daily dose for a child is (40.0mg of Keflex)/(kg that the child weighs).

Step 1

We convert the capsules form grams to milligrams

1 gram = 1000 milligrams

0.250grams = x

Cross Multiply

x = 0.250 × 1000 milligrams

x = 250 mg

Hence, 1 capsule = 250 mg

How many Keflex capsules would a 69-pound child take for one daily dose? (Round to the nearest whole number of capsules) Given: 1 pound = 0.453592 kg

The recommended daily dose for a child is (40.0mg of Keflex)/(kg that the child weighs).

The child weighs 69 pounds

1 pound = 0.453592 kg

69 pounds = x kg

Cross Multiply

x kg = 69 × 0.453592kg

x kg = 31.297848kg

Hence,

1 kg= 40.0 mg

31.297848 kg = x

x = 31.297848 × 40.0mg

x = 1251.91392mg

Therefore, the child would take 1251.91392 mg

From the first calculation we know that:

1 capsule = 250 mg

250mg = 1 capsule

1251.91392 mg = x capsules

250mg × x = 1251.91392 mg × 1 capsule

x = 1251.91392 mg/250mg

x = 5.00765568 capsules

Approximately = 5 capsules

Hence, a child that weighs 69 pounds takes 5 capsules of keflex

Answer:

A or C

Step-by-step explanation:

Answer:

0.004

Step-by-step explanation:

10*0.004=0.04

hope this helps

Answer:

0,004 i think

Step-by-step explanation:

Answer: The population is 523 and the sample is 112.

Step-by-step explanation:

In statistical parlance, a population is referred to as all the entire individuals or subject which makes up a certain group of interest. In the scenario above, the group of interest refers to the consumers who buys the vitamin brand each month. Hence, the population encompasses all the buyers for for a particular month which sums up to 523 customers.

The sample is a subset culled from the population. It refers to a smaller group of individuals or subject which are chosen by a sampling method from the entire population. In the scenario above, the number of randomly selected consumers who were sent surveys are the sample. The fact that not all those who were sent surveys responded does not change the fact that they were randomly selected from the larger population pool and will hence be considered to be a part of the sample.Hence the sample is 112.

Answer: (-5,1)

Step-by-step explanation:

−2.5x+y=13.5

−2.5x+y+2.5x=13.5+2.5x(Add 2.5x to both sides)

y=2.5x+13.5

Step: Substitute

5x+13.5  and 2.25x−y=−12.25:

2.25x−y=−12.25

2.25x−(2.5x+13.5)=−12.25

−0.25x−13.5=−12.25(Simplify both sides of the equation)

−0.25x−13.5+13.5=−12.25+13.5(Add 13.5 to both sides)

−0.25x=1.25

−0.25=1.25−0.25(Divide both sides by -0.25)

x=−5

Step: Substitute−5forxiny=2.5x+13.5:

y=2.5x+13.5

y=(2.5)(−5)+13.5

y=1(Simplify both sides of the equation)

Answer:

x = -4, y = 3.5

Step-by-step explanation:

-2.5x + y = 13.5 ------ (1)

2.25x - y = -12.25 ---(2)

you can substitute (1) into (2) or vice versa

We are going to substitute (2) into (1)

but first we have to rewrite it in terms of x or y

Lets do y

from (2), (after subtracting -2.25x from both sides), y = 12.25 + 2.25x ----(3)

plug in (3) into (1)

-2.5x + (12.25 + 2.25x) = 13.5

-2.5x + 12.25 + 2.25x = 13.5

-2.5x + 2.25x = 13.5 - 12.5

-0.25x = 1

x = -(1/.25)

x = -4

Now we have x

We already used (2), lets plug in x = -4 into (1)

-2.5(-4) + y = 13.5

10 + y = 13.5

y = 13.5 - 10

y = 3.5

Complete Question

The scores on a psychology exam were normally distributed with a mean of 59 and a standard deviation of 6. About what percentage of sores were less than 53. The percentage of scores that were less than 53 was %. (Type an integer or a decimal.

Answer:

The value is [tex]P(X < 53) = 0.15866[/tex]

Step-by-step explanation:

From the question we are told that

   The mean is  [tex]\mu = 59[/tex]

    The standard deviation is [tex]\sigma = 6[/tex]

Generally the percentage that were less than 53 is mathematically represented as

       [tex]P(X < 53) = P(\frac{X - \mu }{\sigma } < \frac{ 53 - 59 }{ 6 } )[/tex]

[tex]\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )[/tex]

=>    [tex]P(X < 53) = P(Z < -1 )[/tex]

Generally the probability of (Z <  -1  ) is  

         [tex]P(Z < -1 ) = 0.15866[/tex]

=>        [tex]P(X < 53) = 0.15866[/tex]

Answer:

See below

Step-by-step explanation:

All of the sides are the same length so all of the angles are the same in this equilateral triangle....each is 60°

60 = 2.5 x + 6

54 = 2.5 x

x = 21.6 °

Answer:

The coordinates of its final image are [tex](x'', y'') = (12, 13)[/tex].

Step-by-step explanation:

From Linear Algebra, we define reflection across the x-axis as:

[tex](x',y') = (x, -y)[/tex], [tex]\forall \,x,y\in\mathbb{R}[/tex]

According to the statement of problem, the following operation of translation:

[tex](x',y') = (x+3, y-7)[/tex], [tex]\forall \,x,y\in \mathbb{R}[/tex]

Where:

[tex](x,y)[/tex] - Original point, dimensionless.

[tex](x',y')[/tex] - Translated point, dimensionless.

If we know that [tex]A(x, y) = (9, -6)[/tex], we proceed to make the abovementioned operations:

Translation

[tex](x', y') = (9+3,-6-7)[/tex]

[tex](x',y') = (12, -13)[/tex]

Reflection

[tex](x'', y'') = (x',-y')[/tex]

[tex](x'', y'') = (12, 13)[/tex]

The coordinates of its final image are [tex](x'', y'') = (12, 13)[/tex].