Element X is a radioactive isotope such that every 11 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 70 grams, how long would it be until the mass of the sample reached 14 grams, to the nearest tenth of a year?

The simplified expression representing (−8x²−5x+8)−(−6x²+3x−3) is given as follows:

14x² - 8x + 11.

The expression for this problem is presented as follows:

(−8x²−5x+8) − (−6x²+3x−3).

The first step towards simplifying the expression is removing the negative signal from the expression, inverting the signal of each term inside the second parenthesis, hence:

(−8x²−5x+8) − (−6x²+3x−3) = 8x² - 5x + 8 + 6x² - 3x + 3.

(the first parenthesis can be removed with no changes as there is not any signal in front of it).

Then the like terms, which are the terms with the same variable and same exponent, are added, adding the coefficients and keeping the variables and exponents, as follows:

The simplified expression is obtained by these three additions of the like terms above, hence:

14x² - 8x + 11.

The problem is incomplete, and it asks for us to simplify the given expression.

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The square root of 92 lies between 9 and 10.

According to the question,

We have the following information:

Square root of 92

Now, we have to find the two integers between which its square root lie.

So, we will first find the perfect squares of positive integers to get an idea where the square root of 92 lies.

Perfect squares are given below:

1 = 1

2 = 4

3 = 9

4 = 16

5 = 25

6 = 36

7 = 49

8 = 64

9 = 81

10 = 100

Now, the square of 10 is greater than 92 and square of 9 is less than 92. So, it will lie between these two integers.

Hence, the square root of 92 lies between 9 and 10.

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Answer:3 1/2 hours

Step-by-step explanation: 5 2/5 - 1 1/4 -1 1/2= 3 1/2

The perimeter of the shaded region is 135 in.

Given, a triangle ABC in which K, L & M are the mid-points of the sides AB, BC, AC.

Also, the perimeter of the triangle ABC is 108 in.

Now, using the mid-point theorem, we get

KL = 1/2(AC)

LM = 1/2(AB)

KM = 1/2(BC)

Now, the perimeter of the shaded region is,

Perimeter of 3 small triangles + Perimeter of triangle KLM

Perimeter of 3 small triangles = (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4)

Perimeter of triangle KLM = AB/2 + BC/2 + AC/2

Perimeter of the shaded region = (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/2 + BC/2 + AC/2)

Perimeter of the shaded region = 5/4(AB + BC + AC)

As, we know that AB + BC + AC = 108 in

Perimeter of the shaded region = 5/4×108

Perimeter of the shaded region = 135 in

Hence, the perimeter of the shaded region is 135 in.

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The population size does not determine the sampling distribution.

In the give question we have to find which choice does not determine the sampling distribution.

We firstly learn more about sampling distribution

A sampling distribution is a probability distribution of a statistic that is derived from a bigger sample size of individuals chosen at random from a given population. The sampling distribution of a particular population is the distribution of frequencies of a variety of potential outcomes for a population statistic.

So, the population size does not determine the sampling distribution.

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The sample indicates that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

This given test is a test for single sample proportion

The test hypothesis are:

[tex]H_{o} :p=0.20[/tex], null hypothesis

[tex]H_{1} :p\neq 0.20[/tex], alternative hypothesis

The test statistic fallows a standard normal distribution and is given by:

[tex]Z=\frac{x-p}{{\sqrt{p(1-p)/n} } }[/tex]

p=0.20

X=47 plants

Sample size, n=500

x, is the sample mean:

x=X/n=47/500

x=0.094

So, test statistic is calculated as:

[tex]Z=\frac{0.094-0.20}{\sqrt{0.20(1-0.20)/500} }[/tex]

Z=-5.93

From the z-table, the p-value associated with Z=-5.93 is approximately 0

The decision rule based on p-vale, is to reject the null hypothesis if p-value is less than confidence level

In this case, the p-value is very small and less than confidence level of 0.20, we therefore reject the null hypothesis or the claim

So we conclude that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

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Answer:

Asymptote: x= -8
Two points: (-7,0) and (-6,-1)

Step-by-step explanation:

1. Convert log form to exponential form.
y = -2log_4(x+8)
-y/2=log_4(x+8)
4^(-y/2)=x+8
x=4^(-y/2)-8

Note: from here, you can choose to find the inverse of the graph, solve f(x)^-1, and then revert the x and y coordinates to find the f(x) (but I won't be going over that because the question is not asking for the inverse).

2. Make a table by plugging in points.
At this point, all you need to do is to plug in y-values into the equation: x=4^(-y/2)-8
If we plug in y as 0, we get x as -7, and plug in y as -1, we get x as -6, so (-7,0) and (-6,-1) will be your two points.

3. Find the asymptote

An asymptote is a line in which the log function will approach infinitely close to, but never touch. Same deal, we can try to plug in more numbers into our graph -- y as 1 and we will get x as -15/2 (-7.5); y as 3 and we will get x as -63/8 (-7.875); y as 5 and we will get x as-255/32 (-7.96875). At this point, it's pretty clear that our graph is approaching -8. Hence, x= -8
We use vertical asymptote (x=) when graphing log and we use horizontal asymptote (y=) when graphing exponential.

The vertical asymptote is x = -8.

One point on the graph is (-7, 0).

Another point on the graph is (-6, -1).

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To graph the function [tex]f(x) =-2 \log _{4}(x+8),[/tex]

we need to first find the vertical asymptote, which is the value of x that makes the argument of the logarithm equal to zero.

x + 8 = 0

x = -8

So the vertical asymptote is x = -8.

Next, we can choose two integer values of x and find their corresponding values of f(x).

Let's choose x = -7 and x = -6.

When x = -7:

[tex]f(-7) = -2 \log _{4}(-7+8) = -2 \log _{4}(1) = 0[/tex]

So one point on the graph is (-7, 0).

When x = -6:

[tex]f(-6) = -2 \log _{4}(-6+8) = -2 \log _{4}(2) = -2(1/2) = -1[/tex]

So another point on the graph is (-6, -1).

Now we can plot the points and draw the vertical asymptote at x = -8.

Thus,

The vertical asymptote is x = -8.

One point on the graph is (-7, 0).

Another point on the graph is (-6, -1).

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Answer: 21 tons/wk

Step-by-step explanation:

6000 lb/day = 3 tons/day

3 t/day * 7 = 21 t/wk

Answer:

For points earned (p), the button should be on the left, and for questions correct (q), its on the right.

Step-by-step explanation:

me not know how to speak English!

In the given equation p = 5q, p is the dependent variable and g is the independent variable.

Given that Tatiana earns 5 points for each question she answers.

So, the equation is p = 5q

The above equation explains that for every question she answers, she earns 5 points. That means answering questions which is "q" is an independent variable as it is not depending on any other factor.

The points earned which is "p", is completely depending on answering questions, so the "p" which is points earned is a dependent variable.

From the above explanation, we can conclude that p is dependent variable and q is independent variable.

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The statements that is true are "6 + 3 = 9 and 4 x 4 = 16" , the true statement is (2) .

In the question ,

four statements are given ,

we need to find which statement is true ,

Option(1) ,

if 6 > 10, then 8 x 3 = 24

we know , that 10 > 6 , but it is given that 6 > 10 ,

hence the statement is false  .

Option(2)

6 + 3 = 9 and 4 x 4 = 16

we know , that 6+3=9 and 4×4=16

so , the statement is true .

Option(3)

if 6 x 3 = 18 then 4+8=20

we know , that 4+8 = 12 , but it is given that 4+8=20

So , the statement is false ,

Option(4)

5x3=15 or 7+5 = 20

we know , that 7+5 = 12 , but it is given that 7+5=20

So , the statement is false .

Therefore , The statements that is true are "6 + 3 = 9 and 4 x 4 = 16" , the true statement is (2) .

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The area of the shaded portion of the circular disc is  112.255 cm².

A circle is a bounded object in which points from its center to its circumference is equidistant.

The area of the shaded portion is the difference between the area of the circular disc and the area of the circular hole.

Area of a circle = πr²

Where :

π = pi = 3.14

R = radius

Area of the circular disc = 3.14 x 6²

Area of the circular disc = 3.14 x 36

Area of the circular disc = 113.04 cm²

Area of the circular hole = 3.14 x 0.5²

Area of the circular hole = 3.14 x 0.25

Area of the circular hole = 0.785 cm²

Area of the shaded portion = area of the circular disc - area of the circular hole

Area of the shaded portion = 113.04 cm² -  0.785 cm²

Area of the shaded portion = 112.255 cm²

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An absolute value equation that can be used to find the maximum and minimum scores within one standard deviation of the mean is |x - 20.9| = 5.3.

The minimum score that is within one standard deviation of the mean is equal to 15.6.

In Mathematics, an absolute value function can be defined as a type of function that consist of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0).

Mathematically, an absolute value function can be represented by this mathematical expression:

Since the standard deviation is 5.3 and the mean is 20.9, an absolute value equation for the scores that is within one standard deviation of the mean is given by:

|x - 20.9| = 5.3.

x - 20.9 = ±5.3

Evaluating the absolute value function, the maximum score is given by:

x - 20.9 = 5.3

x = 20.9 + 5.3

x = 26.2.

Evaluating the absolute value function, the minimum score is given by:

x - 20.9 = -5.3

x = 20.9 - 5.3

x = 15.6.

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Complete Question:

The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the data are from the mean. For example, the mean score on the Wechsler IQ test is 100 and the standard deviation is 15. This means that people within one standard deviation of the mean have IQ scores that are 15 points higher or lower than the mean. One year, the mean mathematics score on the ACT test was 20.9 with a standard deviation of 5.3. Write an absolute value equation to find the maximum and minimum scores within one standard deviation of the mean. Use your equation to find the minimum score that is within one standard deviation of the mean

Answer:

Each interior angle of a regular polygon is 174°

To find The number of sides of the polygon.

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of sides of the polygon)

Now, the sum of an interior angle and an exterior angle of a regular polygon is always equal to 180°.

So, the exterior angle of the given regular polygon :

= (Sum of an interior angle and an exterior angle) - (An interior angle)

= 180° - 174°

= 6°

Let, the number of sides of the regular polygon = n

Now, the value of an exterior angle of a regular polygon = (360° / Number of sides)

So, the exterior angle of the given regular polygon :

= (360°/n)

By, comparing the two values of an exterior angle of the given regular polygon, we get :

360/n = 6

n × 6 = 360

n = 360/6

n = 60

Number of sides of the regular polygon = n = 60

(This will be considered the final result.)

Hence, the number of sides of the regular polygon is 60.

Answer:-9

Step-by-step explanation:

-(5+4)

-(9)

1(3x+9)/3 = -3x + 11,  3x/3 + 9/3, x + 3, 8 and 2 should be entered in each blank space respectively

Given: the algebraic equation, 4(3x+9)/12 = -3x + 11

4(3x+9)/12 = -3x + 11      

Divide the Right-Hand Side (RHS) by 4 to get:

1(3x+9)/3 = -3x + 11

Then, on the RHS divide 3x and 9 separately by 3:

3x/3 + 9/3  = -3x + 11

x + 3  = -3x + 11

Take -3x to the Left and take 3 to the right (Note that, this will change their signs):

x + 3 + 3x = 11

x+3x = 11-3

Add/subtract like terms:

4x = 8

Divide both sides by 4:

x = 8/4

x = 2

Therefore, 1(3x+9)/3 = -3x + 11,  3x/3 + 9/3, x + 3, 8 and 2 should be entered in each blank space accordingly. The solution of the equation is x =2

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The sun's angle of elevation when a 47-foot mast casts a 14-foot shadow 73.4127

At the foot of the mast, place the 90 degree (right) angle of a right triangle. When the sun hits the mast, it casts a 47-foot shadow. Consider the mask's height to be on the "opposite side" of the elevation angle, and this shadow to be on the "adjacent side."

The "tangent" trig function includes the following variables:

Tan = (opposite side) (elevation angle) (adjacent side).

In this case, tan (angle of elevation) equals opposing side / adj opposing side.

is used for

radians, or tan (angle of elevation)

= 47/14 = 3.3571

3.3571 is equal to 73.4127 degree.

The angle of elevation of the sun when a 47-ft mast casts a 14 ft

shadow 73.4127 degree

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Answer: decay

Step-by-step explanation: decay is when the input is less than 1 and greater than 0. 0.75 falls in between these numbers

the tell-tale factor is the value inside the parenthesis, if that's less than 1 is Decay, if more than 1 is Growth

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2.5\\ r=rate\to \text{\LARGE 28\%}\to \frac{28}{100}\dotfill &0.28\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=2.5(1 - 0.28)^{x} \implies A = 2.5(0.72)^x\hspace{5em}y= 2.5(0.72)^x[/tex]

Probability that first two babies born are boys is 0.23

Number of Mothers to be received ultrasound = 14

Number of mother giving birth to girl = 7

Number of mother giving birth to boy = 14 - 7 = 7

P(giving birth to girl) = P(G) = 7 / 14 = 0.5

P(giving birth to boy) = P(B) = 7 / 14 = 0.5

Probability that the first two babies that are born happen to be boys =

favorable outcome / total outcome

here, favorable outcome = ⁷C₂

Total outcome = ¹⁴C₂

Required probability = ⁷C₂ / ¹⁴C₂

= (7×6 / 2×1) / (14×13 / 2×1)

= 7×6/14×13

= 42 / 182

=0.23

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The remainder of the division of the given polynomial by (x - 3) is 966.

From the question, we have

f(x) = 4x^5 - x - 3

The remainder of the division is the f(x) at x= 3

f(3) = 4*3^5 - 3 - 3

=972-6

=966

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Answer: y=-0.5x-1

Step-by-step explanation:

                                              y=mx+b

Convert the given values f(-10) = 4, f (8) = -5 to coordinates (-10,4)  (8,-5)

Hence we use the formula for finding the slope m:

[tex]\displaystyle\\\boxed{m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=-1\ \ \ \ \ x_2=8\ \ \ \ \ \ y_1=4\ \ \ \ \ y_2=-5\\\\m=\frac{-5-4}{8-(-10)}\\\\m=\frac{-9}{8+10} \\\\m=\frac{-9}{18} \\\\m=-0.5\\\\Thus, y=-0.5x+b\ \ \ \ (1)\\\\[/tex]

We substitute the value of (-10,4) into equation (1):

[tex]4=-0.5(-10)+b\\\\4=5+b\\\\-1=b\\\\Thus, b=-1[/tex]

Hence, y=-0.5x-1

The coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)

The end points of the line segment = (-9, -10) and (1, 5)

The partition ratio = 2 : 3

According to the partition rule

The x coordinate of the point = [tex]x_1+\frac{A(x_2-x_1)}{A+B}[/tex]

A = 2

B = 3

Substitute the values in the equation

The x coordinate of the point = -9 + [2(1--9) / 2+3]

= -9 + [2×10 / 5]

= -9 + [20/5]

= -9 + 4

= -5

Similarly,

The y coordinate of the point = [tex]y_1+\frac{A(y_2-y_1)}{A+B}[/tex]

= -10+[2(5--10)/2+3]

= -10+[2×15/5]

= -10+[30/5]

= -10 + 6

= -4

Hence, the coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)

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The linear equations that can satisfy the values given in tabular form are

How to form line equation using values given in tabular form?

A line equation is of the form y = mx + b where x and y are the coordinate values, m is the slope of the line and b is the y intercept.

Follow these steps to find the line equation:

According to the given data:

Table I)

Standard form: t = md + b

Slope: m = [tex]\frac{16 - 11}{1 - 0}[/tex] = 5

y-intercept: t = 5d + b

Substituting (d, t) = (1, 16) as given in the table

16 = 5x(1) + b

∴ b = 11

Hence linear equation in terms of d and t is t = 5d +11

Similarly, for Table II)

Standard form: c = mr + b

Slope: m = [tex]\frac{2 - 1}{-0.6 + 2.1}[/tex] = [tex]\frac{2}{3}[/tex]

y-intercept: c =     (2/3)r + b

Substituting (r, c) = (-2.1, 1) as given in the table

1 = 2/3 x (-2.1) + b

∴ b = 2.4

Hence linear equation in terms of r and c is c =  [tex]\frac{2}{3}[/tex] r + 2.4

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if n decreases then the value of level of significance of each samples [tex]\alpha[/tex] decreases

1. Critical Value: The value of the statistic for which the test just rejects the null hypothesis at the given significance level.

2. Power of the Test: The probability that the test correctly rejects the null hypothesis when the alternative is true.

3. Significance Level: The prescribed rejection probability of a statistical hypothesis test when the null hypothesis is true.

4. Size of the test: The probability that the test incorrectly rejects the null hypothesis when it is true.

if n decreases then the value of level of significance of each samples [tex]\alpha[/tex] decreases and hence 1- [tex]\alpha[/tex] increases which are called the rejection of test sample increases

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The inequality is 45m + 14 n ≥ 250.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

He makes 45 for every lawn he mows

and an extra 15 for raking

His goal earning= at least 250 per week

let the number of lawn he mow is m and the number of lawn rakes is n.

Then the inequality is

45m + 14 n ≥ 250

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The cost of 10 sodas will be C(n) = 0.75n – 0.5; $7.00

Soda is on sale for $0.75 a can, and you have a coupon for $0.50 off your total purchase

Let n-----> the number of sodas

C(n) -----> the total cost

we know that

The total cost is equal to the number of sodas multiplied by the cost of one soda minus $0.50 of the coupon

so

C(n) = 0.75n – 0.5

For n=10 sodas

substitute the value of n in the equation

C(10) = 0.75(10) – 0.5

7.5 - 0.5

= 7

Therefore, the cost of 10 sodas will be C(n) = 0.75n – 0.5; $7.00

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Answer:

it is 20

Step-by-step explanation:

use the formula

hope i helped

From the graph the turning points are 4 i.e. (-1.467,17.765), (0,0),  (1.251,6.665), (2.616,-7.472), global maximum is (-1.467,17.765), global  minimum is (2.616,-7.472), local maximum is (0,0) and local maximum is (1.251,6.665).

In the given function, we have to  graph the function, then use the graph to determine the number of turning points, global maximums and minimums, and local maximums and minimums that are not global.

The given function is h(x) = x^2(x − 3)(x + 2) (x - 2).

The graph of the given function is below:

As we know that

A local minimum or maximum is represented by each turning point. A turning point may occasionally be the peak or trough of the entire graph. In these situations, we argue that a global maximum or global minimum marks the turning moment.

The output at the greatest or lowest point of the function is referred to as a global maximum or global minimum.

So the terning point of the given function is 4 i.e. (-1.467,17.765), (0,0),  (1.251,6.665), (2.616,-7.472).

Global Maximum = (-1.467,17.765)

Global Minimum = (2.616,-7.472)

Local Maximum = (0,0)

Local Maximum = (1.251,6.665)

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The radius of the cone is 16.33, the height of the cone is 11.55, and the maximum volume of the cone is 1,026.67[tex]\pi[/tex].

How to find volume of the cone?

Given

metal radius = R = 20

cone base radius = r

cone height = h

First, we can use Pythagoras theorem

R^2 = r^2 + h^2

r^2 = R^2 - h^2

r^2 = 400 - h^2

Then, we use volume of cone formula

V = 1/3[tex]\pi[/tex] * r^2 * h

V = 1/3[tex]\pi[/tex] * (400 - h^2) * h

V = 1/3[tex]\pi[/tex] * 400h - h^3

To get maximum volume of cone, V'(h) must be 0. So,

1/3[tex]\pi[/tex] * 400 - 3h^2 = 0

400 - 3h^2 = 0

3h^2 = 400

h^2 = 400/3

h = [tex]\frac{20}{\sqrt{3}}[/tex] or 11.55

Next, we find the r with substitution method. So,

r^2 = 400 -  ([tex]\frac{20}{\sqrt{3}}[/tex]    )^2

r^2 = 400 - [tex]\frac{400}{3}[/tex]

r^2 = [tex]\frac{800}{3}[/tex]

r = [tex]\frac{20\sqrt{2}}{\sqrt{3}}[/tex] or 16.33

Now, we can get maximum volume of cone.

V = 1/3[tex]\pi[/tex] *  16.33^2 * 11.55

V = 1,026.67[tex]\pi[/tex]

Thus, the radius of the cone is 16.33, the height of the cone is 11.55, and the maximum volume of the cone is 1,026.67[tex]\pi[/tex].

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Answer: No, the marketing manager was not correct in his claim.

We are given that in a survey of 1005 adult Americans, 46.6% indicated that they were somewhat interested or very interested in having web access in their cars.

Suppose that the marketing manager of a car manufacturer claims that the 46.6% is based only on a sample and that 46.6% is close to half, so there is no reason to believe that the proportion of all adult Americans who want car web access is less than 0.50.

Let p = population proportion of all adult Americans who want car web access.

SO, Null Hypothesis,  : p  50%   {means that the proportion of all adult Americans who want car web access is more than or equal to 0.50}

Alternate Hypothesis,  : p < 50%  {means that the proportion of all adult Americans who want car web access is less than 0.50}

The test statistics that will be used here are One-sample z-proportion statistics;

               T.S.  =    ~ N(0,1)

where = sample proportion of Americans who indicated that they were somewhat interested or very interested in having web access in their cars =  46.6%

           n = sample of Americans = 1005

So, test statistics  =  

                              =  -2.161

Since in the question we are not given the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives the critical value of -1.6449 for the left-tailed test. Since our test statistics are less than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Step-by-step explanation:

X= 1

First you subtract 6 from both sides to get

2x=2

Then you divide by 2 to get 1

x=1