Draw each polar equation on the same set of polar axes, and find the points of intersection for 0≤θ<2π.

After 5 half-lives, only 3.9 g of the original 155 g of radioactive isotope will remain.

Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be represented in a variety of forms, such as the natural numbers, real numbers, and complex numbers. Numbers can be used to describe physical quantities, such as volume, mass, and time, as well as abstract quantities, such as sets, functions, and abstract objects. Numbers are also used to represent concepts such as truth, beauty, and goodness.

To calculate this, we can use the formula:
Final Mass = Initial Mass * (1/2)Number of Half Lives

In this case, the Initial Mass is 155 g, and the Number of Half Lives is 5. Therefore, the equation to use is:
Final Mass = 155 g * (1/2)⁵

Plugging the numbers into the equation, we get:
Final Mass = 155 g * (1/2)⁵
Final Mass = 155 g * (1/32)
Final Mass = 3.9 g

Therefore, after 5 half-lives, only 3.9 g of the original 155 g of radioactive isotope will remain. This is due to the fact that the half-life of a radioactive isotope is the amount of time it takes for the isotope to be reduced to half its original mass. As the number of half-lives increases, the amount of the isotope left decreases exponentially.

To know more about Equation click-

http://brainly.com/question/2972832

#SPJ1

Answer:

I cannot understand the question

Answer: 36

Step-by-step explanation:

Answer:

2x + [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

The like terms that you want to combine is 1/3 and 1/2.  You need a common denominator which would be 6

[tex]\frac{1}{3}[/tex] = [tex]\frac{2}{6}[/tex]

[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{6}[/tex]

2x + [tex]\frac{2}{6}[/tex] + [tex]\frac{3}{6}[/tex]

2x + [tex]\frac{5}{6}[/tex]  You cannot combine this with the 2 because the 2 is multiplied by x.

Helping in the name of Jesus.

Therefore, the volume of the prism is 60 cubic feet.

Volume is the amount of space occupied by a three-dimensional object or the capacity of an object. It is typically measured in cubic units such as cubic meters, cubic feet, or cubic centimeters. The formula for finding the volume of a solid object depends on its shape. In general, the volume of a shape can be found by dividing it into smaller, more easily measured shapes and adding up their volumes. This is known as the method of integration in calculus, and it is used to find the volumes of irregularly shaped objects or fluids. Understanding the concept of volume is important in many fields, such as architecture, engineering, physics, and chemistry. In these fields, volume is used to determine the capacity of containers, the displacement of fluids, and the amount of materials needed for a construction project.

Here,

The volume of a prism is given by the formula:

V = Bh

where B is the area of the base and h is the height of the prism.

Substituting the given values:

V = (20 ft)(3 ft)

V = 60 cubic feet

To know more about volume,

https://brainly.com/question/28338582

#SPJ1

Answer:

0.35 m

Step-by-step explanation:

1 m = 1000 cm

350 cm = ? m

We Take

350 / 1000 = 0.35 m

So, 350 cm = 0.35 m

Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is.

[tex]0.1x + 0.2y = 70[/tex]

[tex]y = 3x[/tex]

Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.

Let's define the variables as follows:

Let x be the number of liters of Drink B produced.

Since the company produced 3 times as many liters of Drink A as liters of Drink B, let y be the number of liters of Drink A produced, so y = 3x.

Now, let's write the system of equations:

The total amount of real fruit juice used is 70 liters, so we can write:

[tex]0.1x + 0.2y = 70[/tex]

Substituting y = 3x into the above equation, we get:

[tex]0.1x + 0.2(3x) = 70[/tex]

Simplifying the equation:

[tex]0.1x + 0.6x = 70[/tex]

[tex]0.7x = 70[/tex]

[tex]x = 100[/tex]

So, the company made 100 liters of Drink B and 3 times as many liters of Drink A, or 300 liters of Drink A.

Therefore, the system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made is:

[tex]0.1x + 0.2y = 70[/tex]

[tex]y = 3x[/tex]

Where x represents the number of liters of Drink B made, and y represents the number of liters of Drink A made.

To know more about times visit:

https://brainly.com/question/28050940

#SPJ1

Answer:

The third option:

Points: A, B, C, D

Line segments: AB, AD, AC, DC, BC

The length of XY uisng the midpoint theorem is 40 units

The midpoint theorem states that if a line segment is drawn connecting the midpoints of two sides of a triangle, then that line segment is parallel to the third side of the triangle, and its length is half the length of the third side.

In this case, we have a triangle XYZ, and points A, B, C are the midpoints of sides XY, YZ, and ZX respectively.

By the midpoint theorem, we know that AB is parallel to ZX and has a length of half of ZX.

Similarly, BC is parallel to XY and has a length of half of XY, and AC is parallel to YZ and has a length of half of YZ.

We are given that BC has a length of 20, and we want to find the length of XY.

Using the midpoint theorem, we know that

XY is twice the length of BC

So

XY = 2 * BC = 2 * 20 = 40.

Therefore, the length XY is 40 units

Read more about line segments at

https://brainly.com/question/24778489

#SPJ1

In linear equation, 44%  of the shoppers have an e-mail account and 56%  of the shoppers do not have computer access at home.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Total number of the shoppers who were surveyed = 150

a). Number of shoppers who have an e-mail account = Shoppers who have email accounts and computer access at home + Shoppers who have email accounts but no computer access at home

= 44 + 22

= 66

Percentage of the shoppers having an e-mail account = 66/150 * 100

                                                                        = 44%

b). Total number of shoppers who do not have computer access at home

= 7 + 77

=  84

Percentage of the shoppers having computer access at home

                                             = 84/150  * 100   =  56%

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

Step-by-step explanation:

x = the number

1/4 * x = 1/8   <====given,     Multiply both sides of the equation by 4

4  * 1/4   x = 4 * 1/ 8

x = 4/8 = 1/2

Step-by-step explanation:

Let the given number Be X  

SO given thatone fourth of X is one eighth

x/4 = 1/8

x  = 1/2

x = 0.5

The independent variable x represents the number of hours since the snow began to fall while the dependent variable is total amount of snow on Samir's lawn after x hours because the total amount of snow on Samir's lawn depends on the number of hours the snow fell.

The function M(6) refers to the amount of snow on Samir's Lawn after 6 hours

An independent variable is defined as the variable that causes a change.

However, a dependent variable is defined as the variable that occurs as a result or effect of a change.

The independent variable x represents the number of hours since the snow began to fall while the dependent variable is total amount of snow on Samir's lawn after x hours because the  total amount of snow on Samir's lawn depends on the number of hours the snow fell.

The function M(6) refers to the amount of snow on Samir's Lawn after 6 hours

Read more about Independent and Dependent Variables at: https://brainly.com/question/25223322

#SPJ1

The expressions that are all equivalent to 3/5 - 8/13 +2/9 are:

A mathematical expression is a combination of numbers, variables, operators, and symbols that represents a mathematical relationship or calculation. Mathematical expressions can be written using a variety of mathematical notations, such as algebraic notation, set notation, or calculus notation.

We were given the expression  3/5 - 8/13 +2/9, then we can see that the only negative value is  - 8/13 , then we can see that the only options that have a negative value of  - 8/13  is option B,D. Therefore, option B and E are correct.

Learn more about expressions at:

https://brainly.com/question/1859113

#SPJ1

complete question;

Which expressions are all 3/5 - 8/13 +2/9 ?

As a result, the vertex form of the f(x) equation is: [tex]f(x) = -(x - 5)^2 + 2[/tex]which is equivalent to choice (b).

A quadratic function is a sort of second-degree polynomial equation, meaning it has at least two squared element. A quadratic equation's generic form is: [tex]ax^2 + bx + c = 0[/tex] where the variable x and the constants a, b, and c. If the coefficient a were zero, the expression would be linear rather than quadratic. Several ways to solve a quadratic equation, including factoring, squaring the square, and utilising the quadratic formula. The negative numbers or roots of the quadratic equation are the values of x which it make the equation true and are the solutions to the quadratic equation.

given

The factored form of the quadratic function f(x), which has roots of 3 and 7, is as follows:

f(x) = a(x - 3)(x - 7) (x - 7) where "a" stands for a fixed coefficient.

We can utilise the point (1, 12) through which the function passes to determine the value of "a"

12 = a(1 - 3) (1 - 3)(1 - 7)

12 = -24a

a = -1/2

Inputting the value of "a" into the factored form yields the following results:

[tex]f(x) = -1/2(x - 3)(x - 7) (x - 7)[/tex]

By extending this phrase, we get:

[tex]f(x) = -1/2(x^2 - 10x + 21)[/tex]

We need to finish the square before we can transform this into vertex form. To achieve this, add and remove the square of the coefficient of x's half:

[tex]f(x) = -1/2(x^2 - 10x + 25 - 4)[/tex]

If we condense this phrase, we get:

[tex]f(x) = -1/2[(x - 5)^2 - 4][/tex]

As a result, the vertex form of the f(x) equation is: [tex]f(x) = -(x - 5)^2 + 2[/tex]which is equivalent to choice (b).

To know more about quadratic equation visit:

https://brainly.com/question/30098550

#SPJ1

Answer:

The third choice (the bottom one)

Step-by-step explanation:

By law of sin, an angle over the side opposite of the angle is equal to another angle over side opposite of the angle. If that doesn't make sense, refer to the picture below. The first option is not applicable because y is not opposite the angle measuring 100 degrees. Therefore, law of sin cannot be applied. The second option is not applicable because y is not opposite the angle measuring 46 degrees. The third option is applicable because the side measuring 21 unites is opposite the angle measuring 46 degrees and side y is opposite the angle measuring 34 degrees.

Answer: To test for unequal variances, we use Welch's t-test, which is a modification of the Student's t-test that adjusts for unequal variances. The null hypothesis for Welch's t-test is that the population means are equal, and the alternative hypothesis is that they are not.

The critical values for a two-tailed test at alpha level 0.10 with degrees of freedom df = 23.99 can be found using a t-distribution table or a calculator and are ±1.717.

For the first sample, we have:

Sample 1: s1 = 10.2, n1 = 22

Sample 2: s2 = 6.4, n2 = 16

Test: Two-tailed

The degrees of freedom can be calculated as follows:

df = ((s1^2 / n1) + (s2^2 / n2))^2 / ((s1^2 / n1)^2 / (n1 - 1) + (s2^2 / n2)^2 / (n2 - 1))

= ((10.2^2 / 22) + (6.4^2 / 16))^2 / ((10.2^2 / 22)^2 / 21 + (6.4^2 / 16)^2 / 15)

= 23.81

The calculated t-value is:

t = (x1 - x2) / sqrt(s1^2 / n1 + s2^2 / n2)

= (0 - 0) / sqrt(10.2^2 / 22 + 6.4^2 / 16) = 0

Since the calculated t-value is within the critical region (-1.717, 1.717), we fail to reject the null hypothesis. We can conclude that there is insufficient evidence to suggest that the population means are different.

For the second sample, we have:

Sample 1: s1 = 0.89, n1 = 25

Sample 2: s2 = 0.67, n2 = 18

Test: Right-tailed

The degrees of freedom can be calculated as follows:

df = ((s1^2 / n1) + (s2^2 / n2))^2 / ((s1^2 / n1)^2 / (n1 - 1) + (s2^2 / n2)^2 / (n2 - 1))

= ((0.89^2 / 25) + (0.67^2 / 18))^2 / ((0.89^2 / 25)^2 / 24 + (0.67^2 / 18)^2 / 17)

= 34.13

The critical value for a right-tailed test at alpha level 0.10 with degrees of freedom df = 34.13 can be found using a t-distribution table or a calculator and is 1.311.

The calculated t-value is:

t = (x1 - x2) / sqrt(s1^2 / n1 + s2^2 / n2)

= (0.89 - 0.67) / sqrt(0.89^2 / 25 + 0.67^2 / 18)

= 2.42

Since the calculated t-value (2.42) is greater than the critical value (1.311), we reject the null hypothesis. We can conclude that there is sufficient evidence to suggest that the population mean of Sample 1 is greater than the population mean of Sample 2.

For the third sample, we have:

Sample 1: s1 = 124, n1 = 12

Sample 2: s2 = 260, n2 = 10

Test: Left-tailed

The degrees of freedom can be calculated as follows:

df = ((s1^2 / n1) + (s2^2 / n2))^2 / ((s1^2 / n1)^2 / (n1 - 1) + (s2^2 / n2)^2 / (n2 - 1))

= ((124^2 / 12) + (260^2 / 10))^2 / ((124^2 / 12)^2 / 11 + (260^2 / 10)^2 / 9)

= 14.23

The critical value for a left-tailed test at alpha level 0.10 with degrees of freedom df = 14.23 can be found using a t-distribution table or a calculator and is -1.345.

The calculated t-value is:

t = (x1 - x2) / sqrt(s1^2 / n1 + s2^2 / n2)

= (0 - 0) / sqrt(124^2 / 12 + 260^2 / 10) = 0

Since the calculated t-value is not less than the critical value (-1.345), we fail to reject the null hypothesis. We can conclude that there is insufficient evidence to suggest that the population mean of Sample 1 is less than the population mean of Sample 2.

The decision rule for all three tests is:

If the calculated t-value is within the critical region, fail to reject the null hypothesis.

If the calculated t-value is greater than the critical value for a right-tailed test, reject the null hypothesis in favor of the alternative hypothesis that the population mean of Sample 1 is greater than the population mean of Sample 2.

If the calculated t-value is less than the critical value for a left-tailed test, reject the null hypothesis in favor of the alternative hypothesis that the population mean of Sample 1 is less than the population mean of Sample 2.

Step-by-step explanation:

The perimeter of the figure is 20.56 centimetres

Explain perimeter

Perimeter is the distance around the edge of a two-dimensional shape, such as a polygon or a circle. It is calculated by adding the length of all the sides of the shape. Perimeter is a fundamental measure in geometry and is used to determine the amount of material needed to enclose a shape, such as fencing or paving. It is also used to compare the size of different shapes with the same perimeter.

According to the given information

The perimeter of the figure is 4+4 + circumference of the circle with diameter 4= 8+12.56= 20.56

To know more about perimeter visit

brainly.com/question/6465134

#SPJ1

Answer:

x=26

Step-by-step explanation:

5x=3x+52

5x-3x=52

2x=52

2x/2=52/2

x=52/2

x=26

Answer:

$232,241.07

Step-by-step explanation:

To calculate the total amount in the account after 30 years of depositing $3,000 each year and earning 6% interest compounded annually, we can use the formula for the future value of an annuity:

FV = P * (((1 + r)^n - 1) / r)

where:

FV is the future value of the annuity

P is the periodic payment (in this case, $3,000 per year)

r is the interest rate per compounding period (in this case, 6% per year, compounded annually)

n is the number of compounding periods (in this case, 30 years)

Substituting the given values, we get:

FV = $3,000 * (((1 + 0.06)^30 - 1) / 0.06)

Using a calculator, we get:

FV ≈ $232,241.07

Therefore, the total amount in the account after 30 years, rounded to the nearest cent, is $232,241.07.

Answer: y=2

Step-by-step explanation:

We're given x=1 so we can plug this in 3x - y =1 and isolate to solve for y.

[tex]3(1)-y=1\\3-y=1\\-y=-2\\y=2[/tex]

The standard form equation of a circle whose diameter endpoints are  (-3,4) (2,1) is [tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5

The general form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius. This equation is derived using the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. By setting (x - h)² and (y - k)² equal to r² and then combining the two equations, we get the standard form equation of a circle.

The center of the circle lies in the middle of the diameter, so we find the midpoint of the end points:

[tex](\frac{-3+2}{2} , \frac{4+1}{2} )[/tex] = (-0.5, 2.5)

And radius of the circle is half of the diameter, which is:

[tex]\frac{\sqrt{( 2-(-3))^2 + (1-4)^2 )}}{2}[/tex] = [tex]\frac{\sqrt{26}}{2}[/tex]

Therefore, the circle equation is:

[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = [tex](\frac{\sqrt{26} }{2} )^2[/tex] = 26/4 = 6.5

[tex](x - (-0.5))^2 + (y - 2.5)^2[/tex] = 6.5

To know more about circle equation visit:

brainly.com/question/29288238

#SPJ1

Answer:

d. x > 2 or x < -2

Step-by-step explanation:

Domain describes the range of x-values in a function.

Domain

The domain of a graph is all of the x-values covered by the function. The domain does not reflect the y-values of a function. This means that answers A and B are automatically wrong.

By looking at the graph, we can tell that there is a gap where some x-values are not covered. This gap is known as a discontinuity. The discontinuity begins at -2 and ends at 2. All of the x-values in the discontinuity are not a part of the domain, and any parts of the graph that are continuous, are included in the domain. The graph is continuous at all points greater than 2 and less than -2, so all of those values are included in the domain. Now, we just need to find out if the endpoints are included in the domain.

Included Values

We know that the domain includes all x-values greater than 2 and less than -2, but we need to know if the domain includes 2 and -2. On a graph, included values will be shown as a closed circle and non-included values will be shown as an open circle. By looking at the graph, we can tell that 2 is not included but -2 is. This means that the domain is x > 2 or x < -2 because the domain does not include x = 2.

Sum of all probabilities for Leon's experiment and for Celia's experiment are 1.

The study of random events and their likelihood of occurring is the focus of the probability field, which is a subfield of statistics. It is used to predict and estimate the likelihood of future events.

Based on the problems 4, 5 and 6 as discuss in figure, we have to find out the sum of all the probabilities for Leon's experiment and for Celia's experiment.

The Results of problem 5 and problem 6 are shown in below figure.
So, The sum of all the probabilities for Leon's experiment and for Celia's experiment are;

Leon:   [tex]\frac{2}{20} + \frac{3}{20} + \frac{5}{20} +\frac{4}{20} +\frac{6}{20} = \frac{20}{20} =1[/tex]

Celia:   [tex]\frac{4}{24} + \frac{3}{24} + \frac{7}{24} +\frac{6}{24} +\frac{4}{24} = \frac{24}{24} =1[/tex]

Solution: Sum of all probabilities for Leon's experiment and for Celia's experiment are 1.

Possible explanation: It is certain that 1 of the 5 possible outcomes will result. The probability of any of the outcomes occurring is 1.

To know more about probability, visit:
https://brainly.com/question/13604758
#SPJ1

Full question -

Answer:

f(x) = 4(1.095)^x.

Step-by-step explanation:

The function f(x) = 4(1+0.1/0.5)^0.5x can be simplified using the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction).

First, we can simplify 0.1/0.5 to get 0.2.

Next, we can simplify (1 + 0.2) to get 1.2.

Then, we can simplify (1.2)^0.5 to get approximately 1.095.

Finally, we can multiply 4 by 1.095^x to get the simplified function:

The ratio of volumes and areas of bases and sides of the medium box to the small box are 27:1 and 9:1 and 27/2:1 respectively, and the volume of the large box is 24 times greater than that of the small box, which is 5,184 cubic inches.

Volume is the amount of space occupied by an object in three-dimensional space. It is measured in cubic units, such as cubic inches, cubic centimeters, or cubic meters, and can be calculated using various formulas depending on the shape of the object. For example, the volume of a rectangular prism can be calculated as length x width x height, while the volume of a sphere can be calculated as (4/3) x pi x radius^3.

In the given question,

(a) For the medium box, the length, width, and height are all tripled. Let's call the dimensions of the small box l, w, and h. Then, the dimensions of the medium box are 3l, 3w, and 3h.

The volume of the small box is V_small = lwh = 216 cubic inches.

The volume of the medium box is V_medium = (3l)(3w)(3h) = 27lwh = 27(216) cubic inches.

Therefore, the ratio of the volumes of the medium box to the small box is:

V_medium/V_small = 27(216)/216 = 27

The ratio of the areas of the bases of the medium box to the small box is:

A_medium/A_small = (3l)(3w)/(lw) = 9

The ratio of the areas of the sides of the medium box to the small box is:

S_medium/S_small = 2(3l)(3h) + 2(3w)(3h) + 2(3l)(3w)/(2lw + 2lh + 2wh) = 27/2

(b) For the large box, the height is tripled that of the small box, the length is doubled, and the width is quadrupled. Let's call the dimensions of the large box L, W, and H. Then, L = 2l, W = 4w, and H = 3h.

The volume of the large box is V_large = (2l)(4w)(3h) = 24lwh = 24(216) cubic inches.

Therefore, the volume of the large box is 24 times greater than the small box.

To know more about volume and area of rectangular prism, visit:

https://brainly.com/question/31542273

#SPJ1

Since magnesium has a larger volume than nickel, it will displace more water from an overflow can.

We need to compare their volumes.

We can use the formula:

Density = mass / volume

To solve for volume, we rearrange the formula:

Volume = mass / density

For nickel:

Volume = 130g / 8.90 g/cm³ = 14.61 cm³

For magnesium:

Volume = 60g / 1.78 g/cm³ = 33.71 cm³

Therefore, Since magnesium has a larger volume than nickel, it will displace more water from an overflow can.

Learn more about Density here : brainly.in/question/2786638

#SPJ1

The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

Given equation :

y=(x−2)2−8

y = 2x - 4 - 8

= 2x - 12

The final equation is y = 2x - 12.

Compare this equation with slope and y-intercept formula :

y = mx+c

So that c = -12

The value of y-intercept according to the solution is -12.

To find the vertex. Let's assume x=0; Substitute in the equation

y = 2(0) -12

y = -12

The first vertex will be (0, -12)

If x = 1; y = 2(1) -12

y = -10

Then the second vertex will be (1, -10).

Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

To know more about equation check the below link:

https://brainly.com/question/17145398

#SPJ1

If the sales amount doubles, the commission amount must also double.

The commission rate is 6%, which means that the salesperson earns 6 cents on every dollar of sales.

Therefore, for a sale of $44,000 worth of furnaces, the commission would be:

Commission = 0.06 * $44,000 = $2,640

If sales were to double, the commission would also double. This is because the commission is directly proportional to the amount of sales.

If the salesperson sells twice as many furnaces, they will earn twice the commission as they did before, assuming the commission rate remains the same.

This is true without using any calculations because the commission rate is a fixed percentage of the sales amount, regardless of the actual dollar value of the sales.

Read more about commission at

https://brainly.com/question/26283663

#SPJ1

The true statements are:

1. The radius of the circle is 3 units

2. The standard form of the equation is (x-1)^2+y^2=3

3. The center of the circle lies on X-axis

4. The radius of this circle is the same as the radius of the circle whose equation is x^2+y^2=9

The given equation is: x^2+y^2-2x-8=0

The equation in the standard form of the circle can be written as (x-h)^2+(y-k)^2=r^2, where h= center of the circle and r= radius of the circle

The given equation in standard form can be written as

(x^2-2x+1)+y^2-9=0

(x-1)^2+y^2=3^2

Hence from the above equation, the center of the circle is at (1,0) and the radius is 3 units.

To learn more about problems on the equation of a circle refer to:

https://brainly.com/question/23799314?referrer=searchResults

Since -4 is less than or equal to -2, we use the first part of the definition of f(x) which is f(x) = x + 4 if x ≤ -2. Therefore,

f(-4) = (-4) + 4 = 0.

So, the answer is D. 0.