The half life of iron-59 is 44.5 days. How much of
a 50g sample would remain after 178 days?

The surface area of a cone is given by the sum of the areas of the lateral surface and the area of the circular base.

The area of the circular base is given by:

Where r is the radius of the base.

The area of the lateral surface is given by:

Where s is the length of the slant.

Since s=17 in and the radius is half the diameter, r=8 in, the area of the cone is:

To the nearest hundredth, the area of the cone in square inches, is:

The three consecutive integers according to the expression will be 6, 8, 10

In the given question, there is an expression stated that tells the condition for a sequence in which a number is represented by 'n'. The expression is the sum of three even integers whose sum is equal to four times the smallest of numbers.

The expression is n + (n + 2) + (n + 4) = 4n. We have to find out the values for each of the numbers.

Here, First Number = n

Second number = (n + 2)

Third Number = (n + 4)

Now, We will calculate the given expression to find out the value of n.

=> n + (n + 2) + (n + 4) = 4n

=> 3n + 6 = 4n

=> n = 6

We get the smallest number n = 6 which is the first number, the second number is 8, and the third number is 10.

Hence, the numbers are 6, 8, and 10.

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SOLUTION

We want to find the distance that the top edge of the calendar is from the ceiling.

The diagram below will help us

From the diagram above x is the distance we want to find

We can see that the entire wall is 9 ft long,

Distance from the foot of the calender to the floor is 5 1/4 ft and

Halve of the calendar is 2/3 ft

So the whole calendar is

So, to find x, we will add length of the calendar which is 4/3 ft to distance from the foot of the calender to the floor which is 5 1/4 ft and subtract this from height of the wall which is 9 ft

We have

Hence the answer is

In a chemical reaction, atoms are neither CREATED nor DESTRUCTED. According to science, each side of the equation must contain the SAME amount of atoms.

You must place COEFFICIENTS in front of the chemical formulas in the equation in order to make it equal.

What does a chemical reaction always involve?

Only atoms from the reactants can end up in the products of a chemical reaction. No atoms are destroyed or made into new ones. When reactants come into touch with one another, the bonds between their atoms are broken, and the atoms then reorganize and form new bonds to create the products.

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Answers in bold

[tex]\begin{array}{|c|c|} \cline{1-2}k & P(X = k)\\\cline{1-2}0 & \boldsymbol{0}\\\cline{1-2}1 & \boldsymbol{0}\\\cline{1-2}2 & \boldsymbol{0.04}\\\cline{1-2}3 & \boldsymbol{0.18}\\\cline{1-2}4 & \boldsymbol{0.41}\\\cline{1-2}5 & \boldsymbol{0.37}\\\cline{1-2}\end{array}[/tex]

Note: The P(x) values for k = 0 and k = 1 are not actually zero, but they are small enough that they round to 0 when rounding to two decimal places.

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

Explanation:

I used a spreadsheet to compute the values in bold.

The specific command is called BINOMDIST

The template is BINOMDIST(k,n,p,0)

Let me know if you have any questions about how to use that function in a spreadsheet.

Also, I used the function called ROUND to round each value to 2 decimal places.

Example calculation

=ROUND(BINOMDIST(4,5,0.82,0),2)

This calculates the result of 0.41 and it corresponds to the value k = 4

Don't forget about the equal sign up front when computing these commands in the spreadsheet. Otherwise, it'll stay as text form.

-------------------

If you want to use a TI83 or TI84 calculator, then press the button labeled "2nd". Then press the button labeled "VARS". Scroll down until you reach "binompdf".

The template is binompdf(n,p,k)

So for example, type in binompdf(5,0.82,4) to get the P(X) value for k = 4

If you aren't able to access a spreadsheet or a TI83/84 calculator, then search out "binomial distribution calculator" and there are plenty of free ones to pick from.

In my opinion, a spreadsheet is the best option since the given data is already in tabular form. Also, many real world situations and careers use spreadsheets everyday.

Given,

The coordinates of the points is,

The coordinates of the mid point is:

Hence, the mid point of the line segment is (-1,2).

The perimeter is 54 inches

The area is 108 square inches

The perimeter of the triangle is:

15 in + 15 in + 24 in

= 54 in

The area is:

(1/2)(24)(9)

= 108 sq. in

ANSWER

0.01175 metres

EXPLANATION

We want to find how many metres are in 11.75 millimetres.

There are 1000 millimeters in 1 meter:

We will simply divide 11.75 milimetres by 1000

1000 millimetres = 1 metre

Answer:

Five times the quantity x plus four equals x minus y.

Step-by-step explanation:

Probably the most confusing part is that parenthesis are pronounced "the quantity"

Answer:

A - $4060

B - 32 copies

Step-by-step explanation:

A -

P = 1900 + 90c

P = 1900 + 90(24)

P = 1900 + 2160

P = 4060

Total if Ann sold 24 copies: $4060

B -

1900 + 90c = 4780

90c = 4780 - 1900

90c = 2880

c = 32

Total copies: 32

A population proportion's 95% confidence interval is 0.45416 ≤ P ≤ 0.66584.

Given sample size n is 318, the probability of success,

p = x ÷ n = 181 ÷ 318 = 0.56

A population proportion's 95% confidence interval is calculated as follows:

(p -  [tex]Z_{0.05}[/tex] √(p(1 - p) ÷ n) , p +   [tex]Z_{0.05}[/tex] √(p(1 - p) ÷ n)

(0.56 - 1.96 √ ((0.56(1 - 0.56) ÷ 318) , 0.56 + 1.96 √ ((0.56(1 - 0.56) ÷ 318))

(0.56 - 1.96 × 0.054) , (0.56 + 1.96 × 0.054)

(0.45416 , 0.66584)

95% confidence interval for a population proportion of 0.45416 ≤ P ≤ 0.66584.

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Given:

The vertices are P (-4, -5), L (1, -7), and K (-9, 8).

The vector is < -6,3 >.

Aim:

We need to find the image of the vertices when translating given vertices along the vector.

Explanation:

The translation vector <-6,3> means each point is being moved 6 units to the left and 3 units up.

For each vertex, we subtract 6 from each x value and add 3 to each y value.

Final answer:

Problem

Solution

For this case we can find the remain angle with this operation:

180 -39-90= 51º

And then we can use the sines law and we can do this:

And solving for x we got:

x= 14*sin(39)/sin (90) = 14*sin 39= 8.81

Answer:

7315.55

Step-by-step explanation:

just dont be lazy solve it.

Answer:

(-7, 5) is correct.

Step-by-step explanation:

[tex]2x + 3y = 1[/tex]

[tex] - 2x - y = 9[/tex]

Add these two equations, and then solve for y.

[tex]2y = 10[/tex]

[tex]y = 5[/tex]

Substitute this value of y into 2x + 3y = 1, and solve for x.

[tex]2x + 3(5) = 1[/tex]

[tex]2x + 15 = 1[/tex]

[tex]2x = - 14[/tex]

[tex]x = - 7[/tex]

So (-7, 5) is the correct solution.

The critical value (tα/2) for a 95% confidence interval for the sample size 15 is 2.009.

We have to find the critical value tα/2 for 95% confidence interval, we are given the sample size.

First we will find the alpha value to get the critical value.

=100%-95%

=1-0.95

=0.05

α=0.05

α/2=0.05/2

α/2=0.025

degrees of freedom(df)= n-1=15-1=14

We will use degrees of freedom and α/2 values to find the critical value that is tα/2.

By using the t table we get the critical value  of tα/2=2.009.

Therefore, the critical value for 95% confidence interval with sample size of 15 is 2.009.

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Answer:

indetermination

Step-by-step explanation:

Hope this helps

Step 1:

Question 1.1

Arrive time = 7:30

Departure time = 17:00

h (9:30) > 7

Garage B is cheaper

Question 1.2

Arrive time = 8:23

Departure time = 10:53

The time spent by issac and his friends is between 2 < h < 4

Since h = 2:30

Answer R11.00

Question 1.3

Karabo uses Garage B

Time spent is 4 < h < 6

Let n represent the number of nights

Cost to travel to Bali:

The cost of flight is constant so we simply add it to the cost of hostel per night times the number of nights

Cost to travel to Paris:

We can divide the given figure into different rectangular faces:

Faces 1 and 3 have the same measure, also 2 and 4, and faces 5 and 6.

Faces 1 and 3 have the following dimensions: L=100cm W=50cm.

Faces 2 and 4 have the following dimensions: L=100cm W=35cm.

Faces 5 and 6 have the following dimensions: L=50cm W=35cm.

The surface area of a rectangular face is given by:

Thus, the surface areas of the given faces are:

The surface area of the net is the addition of all of these surface areas:

The logarithm of the number 6.5 is log(6.5) = 0.8129

This is the number that represents the power by which a fixed number known as the base must be raised to result in another number.

The number is given as

6.5

The logarithm of the number is then represented as

log(6.5)

There are several ways to calculate the logarithm of the number

Some of which are:

In this case, the only way is by using a calculator

Using a calculator, we have

log(6.5) = 0.8129

Hence, the logarithm of 6.5 is 0.8129

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A sequence is a series that follows the sum general rule. The sum of the given sequence  ∑(n=1 to 4) [tex]u_{n}[/tex] is {u₁ + u₂ + u₃ + u₄ + u₅}.

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

As per the given series,  ∑(n=1 to 4) [tex]u_{n}[/tex]

The sign ∑ is used to sum the terms of the series in the given interval.

Given that n = 1 to 4

Substiute n = 1 into  [tex]u_{n}[/tex] ⇒ u₁

Substiute n = 2 into  [tex]u_{n}[/tex] ⇒ u₂

Substiute n = 3 into  [tex]u_{n}[/tex] ⇒ u₃

Substiute n = 4 into  [tex]u_{n}[/tex] ⇒ u₄

So, the sum is {u₁ + u₂ + u₃ + u₄ + u₅}.

Hence "A sequence is a series that follows the sum general rule. The sum of the given sequence  ∑(n=1 to 4)".

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Fraction - A,C,D is the incorrect option that means 18 >17 is the correct option B

Equivalent fractions with the same denominator should be used to compare fractions with different denominators. Comparing fractions: If the denominators are the same, the numerators can be compared. The greater fraction is the one with a larger numerator.

Now, comparing the fraction,

first of all write the fraction in simplest form then cross multiplication.

1.   [tex]\frac{29}{35} < \frac{20}{30}[/tex]

[tex]\frac{29}{35} < \frac{2}{3}[/tex]

87 < 70

This option is wrong.

2.    [tex]\frac{18}{34} > \frac{16}{32}[/tex]

[tex]\frac{9}{17} > \frac{1}{2}[/tex]

18 >17

This option is correct.

3.    [tex]\frac{14}{21} > \frac{17}{24}[/tex]

[tex]\frac{2}{3} > \frac{17}{24}[/tex]

48 > 51

This option is wrong.

4.   [tex]\frac{20}{15} < \frac{28}{23}[/tex]

[tex]\frac{4}{3} < \frac{28}{23}[/tex]

92 < 84

This option is wrong.

Hence, option b is correct.
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By identifying the first values of each point in the graph, we saw that the domain of the relationship is:

D: {-3, -1, 1, 3, 6}

A relation can be defined by a set of points (x, y), where the values of x are the values in the domain and the values of y are the values in the range.

Here we have the graph of a relation, and we can see the points:

(-3, 3)(-1, -1)(1, 2)(3, 0)(6, -2)

The domain of the graphed relationship will be the set of the first values of each of these points, then we can see that the domain is:

D: {-3, -1, 1, 3, 6}

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A function that models the population of 400 birds decreasing at an annual rate of 6% is  [tex]f(x) = 400(1 - 0.06)^{t}[/tex] where t is the time period.

The Exponential decay formula aids in determining the quick decrease over time, i.e. the exponential decrease. The exponential decay formula is used to calculate population decay, half-life, radioactivity decay, and so on.

Its general form is f(x) = a (1 - r)ⁿ.

Where a = the initial amount

1 - r = decay factor and n = time period.

Given:

The initial population of birds, P = 400

Rate of decay, r = 6% = 0.06

Time = t years

By using the exponential decay formula,we get

[tex]f(x) = P (1 - r)^{t}[/tex]

[tex]f(x) = 400(1 - 0.06)^{t}[/tex]

Therefore, the function that models the population of 400 birds decreased at an annual rate of 6% is  [tex]f(x) = 400(1 - 0.06)^{t}[/tex].

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The number of horse is 1, goat is 2 and sheep is 3 a man has.

The problem we are dealing with is related to the linear equation which is referred to as the algebraic condition where each term has an exponent of 1 and when this condition is graphed, it continuously comes about in a straight line.

Now w consider x to be the number of sheep, y to be the  number of  goats, and z to be the number of horses the man owns.

the actual equation for the total number of animals he owns  is :

x+ y+ z

according to the first condition:

that all sheep bar three, means

y+ z=3

similarly, for the other condition, it will be

x+ z=4   and x+ y=5

Now we adding the three  equations:

y + z +x +z +x +y=5+4 +3

2(x+y+z)=12

x+y+z=6........equation(1)

As x + y = 5

Put this in equation in (1), we get

x+y+z = 6

5 + z = 6

z = 1

x + z = 4

x + y + z = 6

y + 4 = 6

y = 2

Now we know

x + y + z = 6

x + 1 + 1 = 6

x = 4

So simplifying the other equation  we get, that the number of horse is 1, goat is 2, and sheep is 4.

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The following are the reasons for sampling:

1. To bring the population to a manageable number

2. To reduce cost

3. To help in minimizing error from the despondence due to large number in the population

4. Sampling helps the researcher to meetup with the challenge of time.

Therefore, the answer is:

c. Sampling is so easy.

The value of the missing angles are; m∠ABC = 36° and m∠DBC = 41°

We are given that;

m∠ABD = 77°

Addition angle postulate states that the sum of two adjacent angle measures will equal the angle measure of the larger angle that they form together.

Now, by addition angle postulate, we can say that;

m∠ABC + m∠DBC = 77°

Now, we are given that;

m∠ABC = (5x - 4)°

m∠DBC = (5x + 1)°

Thus, by substitution property, we have;

(5x - 4)° + (5x + 1)° = 77

10x - 3 = 77

10x = 77 + 3

10x = 80

x = 8

Thus;

m∠ABC = (5(8) - 4)°

m∠ABC = 36°

m∠DBC = (5(8) + 1)°

m∠DBC = 41°

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Given:

Given the equation

Required: Point at which the equation crosses the y axis.

Explanation:

At y -axis, the value of x is zero. Substitute 0 for x in the equation of y.

So, the point at which the equation cross the y-axis is (0, 5).

Final Answer: The point at which the equation cross the y-axis is (0, 5).