how long will it take (in years) for the disintegration rate of this sample to drop to 809 disintegrations per minute?

Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.

Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.

Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.

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An item is regularly priced at, 1.98$ is discounted from the regular price.

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

Given that,

First, change the percentage into decimal:

Let us assume,

Sale of regular price = 1%

1% = 1/100 = 0.01

Assume, item regular price is = 2$

Multiply 2 with 0.01:

2 * 0.01 = 0.02

Note that this number 0.02 (0.01 of 2) is the amount off from the original price (2). Subtract 2 from 0.02

2 - 0.02 = 1.98

Therefore,

An item is regularly priced at, 1.98$ is discounted from the regular price.

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The pair (3, 6) is not a solution of the linear inequality y < -5x + 1.

What is linear inequality?

A linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

y < -5x + 1

Substitute the points and see if they are true

(3, 6)

6 < -5*(3) + 1

6 < -15 + 1

6 < -14  

Not true not a solution

Hence, the pair (3, 6) is not a solution of the linear inequality y < -5x + 1.

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4.

find slope;

3 - 0/-2 -(-3) = 3/1 = 3

y = 3x + b

0 = (3)(-3) + b

0 = -9 + b

b = 9

y = 3x + 9

Total coats should the store plan to sell this winter is 952.

Last winter, a store sold 408 coats in 3 months. This winter, the store plans to sell coats for 4 months.

What is sell?

Determine the total cost of all the purchased units. To find the cost price, divide the total cost by the quantity of units purchased. To get the final price, use the formula for selling price (SP), which is: SP = CP + Profit Margin. The cost of the commodity will then be increased by the margin to determine the proper pricing. Retail math describes the mathematical techniques or formulae utilised in the sales industry. It is earning money or receiving change in the most basic sense. Business owners, retailers, managers, and sales representatives all utilise retail math in their daily work.

3month = 408 coats

1 month = 408/3 =136 coats

Then, 4 months = 136*4 = 544 coats

Total coats should the store plan to sell this winter = 544+408 = 952.

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The equation that creases an inconsistent system when paired with y = 2x + 5 is given as follows:

2y - 4x = -10.

A system of equations is called inconsistent when the number of equations of the system is of zero.

The system in this problem is composed by linear equations, which have the following format:

y = mx + b.

In which:

For inconsistent system, we have that the equations:

The function in this problem is given as follows:

y = 2x + 5.

Hence the inconsistent system is formed with:

2y - 4x = -10.

Which is simplified by 2 as follows:

y - 2x = -5.

y = 2x - 5.

Having the same slope of 2, but a different intercept.

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Answer: 2y – 4x = –10

Step-by-step explanation: trust.

The solution of the given expression is equal to 2.17.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is [tex]2^{x+1} = 9[/tex]. The expression will be solved by using the logarithmic property below,

[tex]2^{x+1}=9[/tex]

Take logs on both sides,

(x+1) ln(2) = ln(9)

(x+1) = ln(9) / ln(2)

x + 1 = 3.17

x = 2.17

Hence, the expression will be solved by taking log on both sides.

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Answer:

Below

Step-by-step explanation:

Circumference of a circle = pi * diameter

                             circumference of ferris wheel = 3.14159 * 520=1633.6 ft

Answer:

Given: △ABC, m∠A=120°, AB=AC=1 Find: The radius of circumscribed circle

Step-by-step explanation:

:]

The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches

The quantity of surface contained within a semicircle's perimeter is known to as its area.

The formula for the Area of a half circle with a Radius (r) is given by  

            Area of Half circle = πr²/2

The formula for the perimeter of a half circle with a radius (r) is given by

           Perimeter of Half circle = πr

Here we have

A picture of a Rectangle with a half circle

Dimensions of Rectangle = 16 in × 12 in

=> Area of rectangle = 16 in × 12 in = 192 in²

=> Perimeter of rectangle shape = 12 + 16 + 12 = 40 inches

[ Here we only take one side of the rectangle since one of the sides is connected with a Half circle ]

The radius of half circle = 8 inch

=> Area of Half circle = π(8)² = (3.14)(64)/2 = 100.96 in²

=> Perimeter of Half circle = πr =(3.14)(8) = 25.12 in

Area of the composite shape

= Ractangle's Area + Half circle's Area

= 192 in² + 100.96 in²

= 292.96 in²

The perimeter of the composite shape

= Ractangle perimeter + Half circle perimeter

= 40 inches + 25.12 inches

= 65.12 inches

Therefore,

The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches

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Answer:

d.) 100

Step-by-step explanation:

To solve, first find the value of g(-2):

[tex]g(-2)=5(-2)\\g(-2)=-10[/tex]

Next, use this value to find f(-10):

[tex]f(-10)=(-10)^2\\f(-10)=100[/tex]

A study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. The study design being used is a randomized controlled trial (RCT).

Generally,  In an RCT, the study participants are randomly assigned to either the intervention group or the control group. This helps to ensure that any differences between the two groups are not due to preexisting differences between them, but rather are due to the intervention being tested.

In this case, the intervention is a daily exercise intervention, and the outcome being measured is blood pressure among people with pre-hypertension.

The control group serves as a comparison group, and any changes in blood pressure observed in the intervention group can be attributed to the intervention rather than other factors.

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For the given congruent triangles, the values of x = -1 and y = 3.

Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.

The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.

3y + x = y + 5 ...........(1)

y - x = x + 5 ..............(2)

Equation

1:3y + x = y + 5

3y - y = 5 - x

2y = 5 - x

x = 5 - 2y ..............(3)

Substitute this value of x in equation (2)

y - x = x + 5 y = x + x + 5y

= 2x + 5 y = 2(5 - 2y) + 5y

= 10 - 4y + 54y + y = 15

5y = 15 y = 15/ 5

y = 3

Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1

Therefore, x = -1 and y = 3

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Answer:

Step-by-step explanation:

a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.

To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.

Applying this rule to the expression 1/58^8, we get:

1/58^8 = 1/(58^8) = 58^-8

Therefore, the correct answer is 58^-8.

It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:

1/58^8 = (1/58)^8 = 58^-8

This simplification shows that the correct answer is still 58^-8.

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The formula to solve for height(h) is given as, if the volume of the cylinder is, V = π r² h, is h = V /  π r².

An object's volume is a measurement of the amount of space it occupies in three dimensions. This indicates that an elephant's volume is more than a mosquito's volume.

Given:

V = π r² h

Here, r is the radius of the cylinder, V is the volume, and h is the height of the cylinder. The value of π is 3.14.

Take the remaining term of the right side to the left as shown below,

V /  π r²  = h

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Answer:

  4.63%

Step-by-step explanation:

You want the interest rate that, compounded quarterly, will result in a balance of $216,000 for an investment of $90,000 after 19 years.

The formula for the balance of an account earning compound interest is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.

Filling in the given values, we can solve for r:

  216000 = 90000(1 +r/4)^(4·19)

  2.4 = (1 + r/4)^76 . . . . . divide by 90,000

  2.4^(1/76) = 1 +r/4 . . . . . . take the 76th root

  (2.4^(1/76) -1) = r/4 . . . . . . subtract 1

  r = 4(2.4^(1/76) -1) ≈ 0.0463437 ≈ 4.63%

The required interest rate is about 4.63%.

ANSWER : -1 , 3 , (-1 - 2i) , (-1 + 2i)

steps

find the zeros JUST MEANS SOLVE FOR X

x⁴-2x²-16x-15=0

break it up

let u = x²

x⁴ = (x²)² = u²

-16x+u²-2u-15=0

hold off on -16x

u²-2u-15=0

what 2 numbers when multiplied give you -15 & when added give you -2?

-5 and 3

(u-5) (u+3)

-16x + (u-5) (u+3) = 0

go back x

-16x + (x²-5) (x²+3) = 0

factor -1 out

( looks horrible so far lol )

-1 ((- x²+ 5) (x²+3) + 16x) = 0

multiply (- x²+ 5) with ( x² + 3 )

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0

-1 (( - x² * x² + -x² * 3 ) + 5x² + 15 ) + 16x ) = 0

-1 (( - x⁴ + -2x² + 15 ) + 16x ) = 0

The measure of ∠A is 29.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Given that,

m∠A = (2x−13)° and m∠B = (2x+ 7)° and ∠A and ∠B are complementary angles.

Therefore

m∠A + m∠B = 90°

(2x−13)° + (2x+ 7)° = 90°

4x + 6 =90

Subtract 6 from both sides:

4x = 84

Divide both sides by 4:

x = 21

Putting x = 21 in m∠A = (2x−13)°:

m∠A = (2 × 21−13)°

m∠A = 29°

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two thirds of a number b which is no more than 12, is b ≤ 18

What is inequality ?

In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.

According to question

two thirds of a number b = (2/3)b

Given two thirds of number b is no more than 12

⇒   (2/3)b ≤ 12

⇒   2b ≤ 12*3

⇒   b ≤ (12*3)/2

⇒   b ≤ 36/2

⇒   b ≤ 18

hence the number b whose 2/3 is no more than 12 is, b ≤ 18

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Answer:(x,y)=(1/3 , 4/3)

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

The y-intercept in the equation that is in slope-intercept form is the constant.

It will take 5 minutes before the stadium is half empty

Given that:

Over 92,000 fans pack the stadium to watch the Tigers play

The fans leave at a rate of 10% per minute

The number of fans that leave per minute will be:

10% of  92,000 = 10/100 × 92, 000 = 9,200

The stadium will be fully empty  in:

time = 92,000/9,200 = 10 minutes

The stadium will be half empty  in:

time = 10 minutes / 2 = 5 minutes

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2 points of inflection will f(x) = 3x5+2x4 - 5x - 12 have.

What is Inflection points definition?

An inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

If [tex]$f^{\prime \prime}(x) > 0$[/tex]then f(x) concave upwards.

If [tex]$f^{\prime \prime}(x) < 0$[/tex]then f(x) concave downwards.

[tex]$$f^{\prime \prime}(x)=126 x^5+40 x^3$$[/tex]

Show Steps

Find intervals: Concave Downward: [tex]-\infty < x < 0$, Concave Upward: $0 < x < \infty$[/tex]

Plug x=0 into [tex]$3 x^7+2 x^5-5 x-12: \quad-12$[/tex]

(0,-12)

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If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be 5.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Fatimah ate f treats. Satvinder ate six less than twice the number that Fatimah ate.

Let 's' be the number of cookies eaten by Satvinder. Then the equation is given as,

s = 2f - 6

If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be given as,

4 = 2f - 6

2f = 10

f = 5

On the off chance that Satvinder ate 4 treats, the number of treats that Fatimah ate will be 5.

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Answer:

Tabatha drives 1/6 mile more per minute than Horatio drives

Step-by-step explanation:

The translation rule that maps the preimage to the image is (x, y) ⇒ (x + 5, y + 1)

From the question, we have the following parameters that can be used in our computation:

Pre-image: L(-4,0), M(-2,0) and N(-3,-3)

Image: L'(1,1), M'(3,1) and N'(2,-2)

The translation rule is calculated as

(x, y) = L' - L

Substitute the known values in the above equation, so, we have the following representation

(x, y) ⇒ (x + 1 + 4, y + 1 - 0)

Evaluate

(x, y) ⇒ (x + 5, y + 1)

Hence, the translation is (x, y) ⇒ (x + 5, y + 1)

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Answer:2(8x-5)

Hope this helps!

The LCM of the given pairs are 10, 15,12,30,6,24,20,18, and 63 respectively.

The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers.

There are 9 pairs, so let's name them using the letters A to I.

The LCM of the first pair A (2, 5) is 10.

The LCM of the pair B (3, 15) is 1*3*5 = 15.

The LCM of the pair C (6, 12) is 3*2*1*2 = 12.

The LCM of the pair D (3, 15) is 2*3*1*5 = 30.

The LCM of the pair E (2, 3) is 1*3*2 = 6.

The LCM of the pair F (8, 24) is 2*2*2*1*3 = 24.

The LCM of the pair G (4, 10) is 2*2*5 = 20.

The LCM of the pair H (6, 9) is 3*2*3 = 18.

The LCM of the pair I (7, 9) is 7*9 = 63.

Hence, 10,15,12,30,6,24,20,18,63 are the LCM of the given pairs.

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