Helpppp

The half-life of Radium-226 is 1590 years. If a sample contains 300 mg, how many mg will remain after 2000 years? -------------

On the x-axis use a scale of 2 units for each grid square. on the y-axis use a scale of 10 units of each grid square. The x-coordinates range from -5 to 5. y-coordinates range from -40 to 50.

In mathematics, points and functions are represented and graphed on the coordinate plane, commonly known as the Cartesian plane. The x-axis and y-axis are two perpendicular number lines that meet at the origin to form the plane (0,0).

On the coordinate plane, points are denoted by ordered pairs (x, y), where x denotes the point's separation from the y-axis and y denotes its separation from the x-axis.

For the given coordinates the range of x and y coordinates are:

x-coordinates range from -5 to 5

y-coordinates range from -40 to 50.

Thus, we use a scale of 2 on the x-axis and 10 units on the y axis.

Learn more about coordinate plane here:

https://brainly.com/question/24134413

#SPJ1

Answer:

Let m be the mass of the object and w be the weight of the object. According to the problem, weight varies directly with mass, so we can write:

w = k * m

where k is the constant of proportionality.

To find k, we can use the information given in the problem. We know that when m = 2 kg, w = 4 N. Substituting these values into the equation above, we get:

4 N = k * 2 kg

Solving for k, we get:

k = 4 N / 2 kg = 2 N/kg

Now we can use this value of k to find the mass of an object that weighs 18 N. We can rearrange the equation above to solve for m:

m = w / k

Substituting w = 18 N and k = 2 N/kg, we get:

m = 18 N / 2 N/kg = 9 kg

Therefore, the mass of the object that weighs 18 N is 9 kg.

Answer:

Step-by-step explanation:

Circle

Solve for circumference

C≈977.04

Radius

155.5

Solution

C=2πr=2·π·155.5≈977.03532 = 977.03

Answer:

977.03

Step-by-step explanation:

C=2πr=2·π·155.5≈977.03532 = 977.03

The measure of  angle CFE is determined as 29⁰.

The measure of angle CFE is calculated by applying the following formula.

The intersecting chord theorem, also known as the intersecting chords inside and outside theorem, is a geometric property that applies to chords (line segments that connect two points on the circumference of a circle) that intersect inside or outside a circle.

Based on the angle of intersecting chord theorem, we will have the following equation.

m∠CFE = ¹/₂( arc angle CE )

arc CE = 360 - 302 (sum of angles in a circle)

arc CE = 58⁰

m∠CFE = ¹/₂ x 58

m∠CFE = 29⁰

Learn more about chord angles here: brainly.com/question/23732231

#SPJ1

Answer:  1st one

Step-by-step explanation:

Answer:

The amount of persons who have heard in 30mins would be:

45 persons

From the calculation, g increases on the interval [-3, 6) and for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)²

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: The formula is (Number/Variable, Math Operator, Number/Variable).

Since f(x) is a piecewise-defined function, we need to consider each interval separately.

For -3 ≤ x < 0, f(x) = 3, so g'(x) = 3, which is positive.

For 0 ≤ x ≤ 6, f(x) = -x + 3, which is a decreasing function, so g'(x) is also decreasing. However, since f(x) is always non-negative on this interval, g'(x) is non-negative as well.

For 6 < x ≤ 9, f(x) = -3, so g'(x) = -3, which is negative.

Therefore, g is increasing on the interval [-3, 6).

To justify this, note that g'(x) = 0 at x = 0 and x = 6, where g has local maxima. This means that g is increasing on the intervals (-3, 0) and (0, 6) and decreasing on (6, 9]. Since g is continuous, it cannot have any jumps, so it must be increasing or decreasing on each of these intervals. Since g(-3) = 0 and g(6) = 9, we know that g is increasing on the interval [-3, 6).

We can evaluate g(x) on the interval [0, 6] by integrating f(x) with respect to t from -2 to x:

g(x) = ∫_{-2}^{x} f(t) dt

On the interval [-3, 0), f(t) = 3, so we have

g(x) = ∫_{-2}^{0} 3 dt + ∫_{0}^{x} (-t + 3) dt

Simplifying the integrals, we get:

g(x) = 6 - 1/2(x-2)^2, for 0 ≤ x ≤ 6

Therefore, for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)²

Learn more about expression

brainly.com/question/14083225

#SPJ1

The expression of g in terms of x  is increases on the interval [-3, 6) and for 0 ≤ x ≤ 6 is  g(x) = [tex]6 - \frac{1}{2(x-2)^2}[/tex].

What is a mathematical expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Since f(x) is a piecewise-defined function, we need to consider each interval separately.

For -3 ≤ x < 0, f(x) = 3, so g'(x) = 3, which is positive.

For 0 ≤ x ≤ 6, f(x) = -x + 3, which is a decreasing function, so g'(x) is also decreasing.

However, since f(x) is always non-negative on this interval, g'(x) is non-negative as well.

For 6 < x ≤ 9, f(x) = -3, so g'(x) = -3, which is negative.

Therefore, g is increasing on the interval [-3, 6).

We can evaluate g(x) on the interval [0, 6] by integrating f(x) with respect to t from -2 to x:

[tex]g(x) = \int{-2}^{x} f(t) dt[/tex]

On the interval [-3, 0), f(t) = 3, so we have

[tex]g(x) = \int_{-2}^{0} 3 dt + \int_{0}^{x} (-t + 3) dt[/tex]

Simplifying the integrals, we get:

[tex]g(x) = 6 - \frac{1}{2(x-2)^2}[/tex], for 0 ≤ x ≤ 6

Therefore, for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)².

To Learn more about expression refer the below link

https://brainly.com/question/112703

#SPJ1

Check the picture below.

[tex]\sin(38^o )=\cfrac{\stackrel{opposite}{x}}{\underset{hypotenuse}{7}}\implies 7\sin(38^o)=x\implies 4.31\approx x \\\\[-0.35em] ~\dotfill\\\\ \cos(38^o )=\cfrac{\stackrel{adjacent}{y}}{\underset{hypotenuse}{7}}\implies 7\cos(38^o)=y\implies 5.52\approx y[/tex]

Make sure your calculator is in Degree mode.

Answer:

Step-by-step explanation:

You want the leg measures in a right triangle with a hypotenuse of 7 inches and an angle of 38°.

The mnemonic SOH CAH TOA reminds you of the relations between side lengths and trig functions:

  Sin = Opposite/Hypotenuse   ⇒   Opposite = Hypotenuse×Sin

  Cos = Adjacent/Hypotenuse   ⇒   Adjacent = Hypotenuse×Cos

The given triangle will have opposite and adjacent sides of ...

  opposite = (7 in)sin(38°) ≈ 4.31 in

  adjacent = (7 in)cos(38°) = 5.52 in

The leg lengths of the triangle are 4.31 inches and 5.52 inches.

The position of  √17 between 4 and 5, which is nearer 5, and the location of 6, which is between 2 and 3, which is nearer 2.

A visual representation of real numbers in a linear manner is a number line. It is a straight line that is divided into intervals or segments, each of which stands for a distinct real number value.

Number lines can be vertical or horizontally oriented, and they can also have a positive or negative orientation. Positive numbers often extend to the right or up, whereas negative numbers typically extend to the left or down. The origin of the number line, or zero, is typically situated in the middle of the line.

The number line is a crucial tool in mathematics since it offers a means of representing numerical relationships visually and carrying out fundamental arithmetic operations. For instance, positive and negative motions along a number line can be used to depict addition and subtraction, respectively, with positive movements denoting addition and negative movements denoting subtraction. On a number line, multiplication and division can alternatively be shown as repeated addition or subtraction.

If we have a number line with the proper markings, we may indicate where the square roots of 17 and 6 are located as follows:

To begin, determine the approximate square root values:

√17 is between 4 and 5, since 4² = 16 and 5² = 25.

√6 is between 2 and 3, since 2² = 4 and 3² = 9.

Place the number √17 closer to 5, between 4 and 5.

Place the number √6 between the numbers 2 and 3, closer to 2.

Since 6 and 17 are not integers and their values are not evenly spaced, it should be noted that their markings will not be evenly spaced on the number line.

To know more about Number Line, visit:

https://brainly.com/question/24644930

#SPJ1

Number line attached below,

The initial mass (in mg) of the sample is  32 mg

The mass 7 weeks after the start is 0.198 mg

Exponential decay is a process in which a quantity decreases at a rate proportional to its value. This means that the larger the quantity, the faster it will decrease.

Exponential decay is modeled by the following formula:

[tex]A = A_{0} \times (1/2)^{\frac{t}{T} }[/tex]

where A is the amount after time t, A₀ is the initial amount,

T is the half-life, and t is the time elapsed

Here we have

The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.

For the first question, we know that after 16 days, the amount is 2 mg, and the half-life is 4 days. We can plug these values into the formula:

[tex]2 = A_{0} \times (1/2)^{\frac{16}{4}}[/tex]

Simplifying, we get:

2 = A₀ × (1/2)⁴

2 = A₀ × (1/16)

A₀ = 2 × 16

A₀ = 32 mg

So the initial mass of the sample was 32 mg.

For the second question, we need to find the mass after 7 weeks, or 49 days. We can use the same formula, but with t = 49:

[tex]A = 32 \times (1/2)^{\frac{49}{4} }[/tex]

A ≈ 0.198 mg

Therefore,

The initial mass (in mg) of the sample is  32 mg

The mass 7 weeks after the start is 0.198 mg

Learn more about Exponential decay at

https://brainly.com/question/2193799

#SPJ1

Answer: To find the circumference of a circle, there are 2 formulas.

Step-by-step explanation:

The first formula is 2πr and the second formula is πd when solving any math problem. You can use either one but you would use which one is the most helpful to answer your question. Hope this helps!

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To close the expansionary gap, the government would need to decrease spending by $100 billion.

The formula to calculate the change in equilibrium output due to a change in government spending is:

∆Y = (∆G / (1 - MPC))

Where:

∆Y = change in equilibrium output

∆G = change in government spending

MPC = marginal propensity to consume

Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).

Given that MPC = 3/4, we can plug in the values into the formula:

400 = (∆G / (1 - 3/4))

∆G = (1 - 3/4) * 400

∆G = (1/4) * 400

∆G = 100

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To know more about interest rate visit:

https://brainly.com/question/14445709

#SPJ1

Answer:

$526.75 i believe

Step-by-step explanation:

Answer:

To find the median cost of these boxes of cereal, we need to order the prices from least to greatest:

$1.90, $2.30, $2.40, $2.50, $2.50, $2.70, $2.90, $3.20, $3.50, $3.90

There are 10 numbers, so the median is the average of the 5th and 6th numbers:

Median = ($2.50 + $2.70) / 2 = $2.60

Therefore, the median cost of these boxes of cereal is $2.60.

Answer:

What is the median cost of these boxes of cereal?

$3.50, $2.30, $2.50, $3.90, $2.90, $2.40, $1.90, $2.50, $3.20, $2.70

Let's put it in order first:

$1.90, $2.30, $2.40, $2.50, $2.50, $2.70, $2.90, $3.20, $3.50, $3.90

Now find the middle number (s):

$1.90, $2.30, $2.40, $2.50, $2.50, $2.70, $2.90, $3.20, $3.50, $3.90

In this case, there are 2 middle numbers so do this:

$2.50 + $2.70

= $5.20

5.20 ÷ 2

So the median cost of those cereal boxes would be $2.60.

Step-by-step explanation:

You're welcome.

Answer:

B

Step-by-step explanation:

THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE

She reduced benefit would be approximately: $2,293.52 x (1 - 0.30) = $1,605.46 per month.

Average This is an arithmetic mean calculated by adding a set of numbers and then dividing by the number of those numbers. For example, the average of the numbers 2, 3, 3, 5, 7 and 10 is 30 divided by 6, which is 5.

 If Rachel retires at  age  67, her total Social Security pension can be estimated using the following steps:

Determine Rachel's average indexed monthly income (AIME) by taking the sum of her 35 highest  earnings (in today's dollars) and dividing it by 420 (the number of months over 35 years). GOAL = $3100 x 12 x 35 / 420 = $3100

Use the formula to determine the Primary Sum Assured (PIA), which is the monthly benefit amount payable under AIME at full retirement age. PIA = 90% x $996 32% x ($3100 - $996) = $2293.52

So, if Rachel were to retire at  age  67, her  Social Security pension would be approximately $2,293.52 per month.  If Rachel decides to start collecting her benefits now at age 62, her benefit amount will be reduced by a certain percentage based on the longer period  she receives benefits. The reduction factor is based on how many months before  full retirement age he begins receiving benefits.

In 2022, a person turning 62 will have a full retirement age of 67, which means the discount factor for starting benefits at age 62 is 30%. So, if Rachel started collecting  Social Security  now at age 62, her reduced benefit would be approximately:

$2,293.52 x (1 - 0.30) = $1,605.46 per month.

Learn more about arithmetic mean here

https://brainly.com/question/13000783

#SPJ1

Answer: To find the P-value, we first need to determine the direction of the alternative hypothesis. Since the alternative hypothesis is two-tailed, we need to divide the significance level (α) by 2 before finding the critical values and the rejection region. Therefore, we have:

H0: p = 0.06

Ha: p ≠ 0.06

α = 0.05/2 = 0.025

The test statistic is z = 1.79, which represents the number of standard errors that the sample proportion is from the hypothesized population proportion under the null hypothesis. We can find the P-value by looking up the area in the standard normal distribution table beyond the test statistic in both tails:

P-value = P(Z ≤ -1.79 or Z ≥ 1.79)

= P(Z ≤ -1.79) + P(Z ≥ 1.79)

= 0.0364 + 0.0364

= 0.0728

Therefore, the approximate P-value for Elliot's significance test is 0.0728. Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion of adults who bike to work in Elliot's city has changed significantly from the previous year.

Step-by-step explanation:

Both Jeremy and Aksa could be right, depending on how they are counting the cubes for finding the volume of a prism.

A prism is a three-dimensional solid shape with a constant cross-section, usually a polygon. It is characterized by two identical end faces, parallel and congruent bases, and straight lateral faces connecting the bases.

Both Jeremy and Aksa could be right, depending on how they are counting the cubes.

If the prism has a square base with 4 cubes along each side, then there would be 16 cubes in each layer. If there are 4 layers, then the total volume would be 16 x 4 = 64 cubic units.

However, if the prism has a rectangular base with 6 cubes along one side and 4 cubes along the other side, then there would be 24 cubes in each layer. If there are 4 layers, then the total volume would be 24 x 4 = 96 cubic units.

Therefore, the answer depends on the shape of the prism and how the layers are counted.

To know more about Prism visit:

https://brainly.com/question/23963432

#SPJ1

The investment will be worth approximately $4468 after 14 years.

Annual interest rate is the rate at which an investment or loan grows in value over the course of a year, expressed as a percentage. It represents the cost of borrowing or the return on investment over one year.

The following equation can be used to determine the future value of an investment using compound interest:

FV = P * (r/n + 1)(n*t)

Where:

FV is the investment's future value.

The principal is P. (initial investment)

The annual interest rate is represented by r,

The number of times the interest is compounded annually by n (expressed as a decimal).

t is the time (in years)

In this case:

P = $1500

r = 8.5% = 0.085

n = 1 (compounded annually)

t = 14

With these values entered into the formula, we obtain:

FV = 1500 * [tex](1 + 0.085/1)^(1*14)[/tex]

     = $4467.56

Therefore, the investment will be worth approximately $4468 after 14 years.

To know more about annual interest rate visit:

https://brainly.com/question/30573341

#SPJ1

According to the question the magnitude of the resulting force is 5.83.

Magnitude is a measure of the size or intensity of a physical quantity. It is an expression of how large or small a quantity is in comparison to a reference value. Magnitude is typically used in physics and astronomy, but it can also be used in other areas such as engineering and seismology. Magnitude is not an absolute measurement; rather, it is a relative measure of how much larger or smaller one quantity is compared to another. For example, the magnitude of a star's brightness is a measure of how much brighter it is compared to other stars.

The magnitude of the resulting force can be calculated using the Pythagorean theorem. The formula for calculating the magnitude of a vector is:
[tex]\sqrt[]{(x2 + y2)}[/tex]
In this case, x = 5 and y = -3, which gives us:
[tex]\sqrt{(52 + (-3)2)}[/tex] = [tex]\sqrt{(25 + 9)}[/tex] = √[tex]\sqrt{(34)}[/tex] = 5.83.
Therefore, the magnitude of the resulting force is 5.83.

To learn more about magnitude
https://brainly.com/question/28047791
#SPJ1

Answer:

To find the set (AUB)' n C, we first need to find the union of sets A and B, which is the set of all elements that belong to either A or B or both:

AUB = {1, 2, 3, 5, 6}

The complement of AUB, denoted by (AUB)', is the set of all elements in U that do not belong to AUB:

(AUB)' = {4, 7, 8}

Next, we need to find the intersection of (AUB)' and C, which is the set of all elements that belong to both (AUB)' and C:

(AUB)' n C = {1}

Therefore, the set (AUB)' n C contains only the element 1.

Answer:

16.77 cm²

Step-by-step explanation:

Area of rectangle = L x W

L = 4.3 cm

Width = 3.9 cm

Let' solve

4.3 x 3.9 = 16.77 cm²

So, the area of the rectangle is 16.77 cm²

The range of the relation whose graph is shown include the following: C. -1 ≤ y ≤ 1.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-4, 4} or -4 ≤ x ≤ 4.

Range = {-1, 1} or -1 ≤ y ≤ 1.

Read more on domain here: brainly.com/question/17440903

#SPJ1

Answer:

The side length is [tex]\frac{6}{\sqrt{2} }[/tex].

Step-by-step explanation:

We are given the diagonal of the square: 6 meters.

Using the formula with given side length:

[tex]a=q\div\sqrt{2}[/tex]

We can see that the diagonal length of the square divided by the square root of 2 can find the missing side length.

Hence the answer is 6√2.

At first Sound level increases then for an instant it becomes constant then in decreases for a while then again becomes constant for an instant then again starts to increase .

What is sound level of a conversation?

A decibel (dB) is a unit used to measure sound. A motorbike engine operating is around 95 dB louder than a whisper (30 dB louder than typical conversation).

                          Your hearing may begin to deteriorate if exposed to noise levels exceeding 70 dB for an extended length of time. Your ears might suffer instant damage from loud noises exceeding 120 dB.

The relationship of sound level w.r.t time can be described as ,

a) At first Sound level increases then for an instant it becomes constant then in decreases for a while then again becomes constant for an instant then again starts to increase .

b) At both the instances the sound level is increasing as the slope of the tangent drawn to the curve at those points is positive but absolute value of sound level at instance (1) is clearly lower than the value of sound level at instance (3).

Learn more about sound level of a conversation

brainly.com/question/31017529

#SPJ1

Answer:

5 hours

Step-by-step explanation:

Every liter is 1000 ml, and 2000 ml divided by 400 ml would be 5 hours.

Answer:5

Step-by-step explanation: hope this helps