A radioactive sample has a half-life of 12 hours. after hours, 4 milligrams of the sample remain. what is the initial amount of the radio-active substance?

Answer:

Complementary angles have a sum of 90°.

(x - 22) + (x - 16) = 90

2x - 38 = 90

2x = 128

x = 64

Substitute x into angle A

A = 64 - 22 = 42°

Lower bound of 2.6 is 2.5

An element of K that is greater than or equal to each element of S is referred to as an upper bound or majorant in mathematics, notably in order theory. To determine a rounded number's upper and lower bounds: Determine the place value of the claimed level of accuracy. By two, multiply this place value. Find the upper bound by adding this amount to the provided value, and the lower bound by deducting this amount from the given value.

Given Data

2.6 to the lower bound

Bound of 2.6 is 2.5 to 2.7

Lower bound of 2.6 is 2.

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Answer:

The fraction of the shop’s T-shirts are blue T-shirts that are on sale and are size medium is 1/ 8

Step-by-step explanation:

Answer: $1.25x + $3.50 ≤ $45

Step-by-step explanation:

The total cost for a given number of miles is the initial cost number of miles multiplied by the cost per mile.

So, the expression for the cost is 1.25x+3.50.

Since she has $45 to spend, Jessica can spend no more than this, so the inequality is that in Option 3.

The information that a slope of 0.416 represents in the scatterplot is the crime index will increase 416 for every 1000 increment in the population.

The information that an intercept of -669.96 represents in the scatterplot is the value of the crime index when the population is zero.

A graph is a pictorial representation of data. It is used by as many fields that uses data. Graphs helps to make information that the data represents easier to understand the relationship existing within the variables

The graph plots the crime index against the population. The slope is the represents how the crime index will behave with respect to the population. While the intercept is the point where the graph intercept the y axis which represents the crime index

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Before a tax of 22 %, the product has an original price of $ 8032.79.

In this problem we find the case of a product that is sold including a given tax, that is, the price of the product before taxes. The original price can be found by means of the following equation, which is in terms of resulting price and tax rate:

C = C' / (1 + r / 100)

Where:

If we know that C' = $ 9800, r = 22 %, then the original price of the product is:

C = 9800 / (1 + 22 / 100)

C = 9800 / (122 / 100)

C = 9800 / 1.22

C = $ 8032.79

Therefore, the original price of the product, that is, the price before a tax of 22 %, is equal to $ 8032.79.

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The length of the side marked x is 10.2 cm.

We know that it is possible to solve the right angle triangle by the use of the Pythagoras theorem. Also, we could make use of the trigonometric ratios when we have to solve the right angled triangle.

The task here id to find the angle that has been marked x in the image that was shown above.

We are going to use the trigonometric ratios here;

Given that;

Cos θ = adjacent/ hypotenuse

θ = 40 degrees

Adjacent = x

Hypotenuse = 13.4 cm

adjacent = cos 40 * 13.4 cm

adjacent = 10.2 cm

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Answer:

91/8

Step-by-step explanation:

[tex]2\frac{4}{5} *4\frac{1}{6}[/tex]

→ Convert to improper fraction

14/5 × 65/16

→ Simplify

7 × 13/8 = 91/8

The amount of petrol consumed in one hour will be 200 liters.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

In 45 minutes, an automobile uses 150 gallons of gasoline.

Consequently, the rate of gasoline consumption in liters per minute will be

= 150 / 45

= 10 / 3  Liters per minute

We are aware that an hour is made up of 60 minutes.

The amount of gasoline that will be used in an hour will then be

= (10 / 3) x 60

= 10 x 20

= 200 liters

Thus, 200 liters of gasoline will be burned in an hour.

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Answer:

there the vehicle uses 250 litres

Step-by-step explanation:

[tex]150 = 45[/tex]

[tex]x = 75[/tex]

[tex]x = 75 \div 45 \times 150[/tex]

[tex]x = 250litres[/tex]

Answer:

Step-by-step explanation:

Take a look at the picture below to see how 3/4 looks when represented on a number line.

This is further explained below.

Generally, A image of a graded straight line is what is known as a number line, and its purpose is to provide a visual representation of the actual numbers.

It is generally accepted that a real number may be assigned to each point on a number line and that each real number can be assigned to a point.

In conclusion, consider the image below for the number line representation of 3/4

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From calculations, we can see that the number of smaller boxes to completely fill the larger one are; 250 boxes

The volume of a cuboid is given by the formula;

Volume = Length * Width * Height

Looking at the given dimensions of the larger box in the cuboid image attached, we can calculate the volume as;

Volume = 50 * 30 * 20

Volume = 30000 cm³

The length , width and height of smaller box are 10 cm, 3 cm and 4 cm respectively. Thus, the volume of smaller box is;

volume = 10 * 3 * 4

volume = 120 cm³

Thus, the number of smaller boxes to completely fill the larger one are;

n = 30000/120

n = 250 boxes

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Hey there!

6(2x - 6) + 2(13 - x) = 10
6(2x) + 6(-6) + 2(13) + 2(-x) = 10

12x - 36 + 26 - 2x = 10

10x - 10 = 10

ADD 10 to BOTH SIDES

10x - 10 + 10 = 10 + 10

SIMPLIFY IT

10x = 10 + 10

10x = 20

DIVIDE 10 to BOTH SIDES

10x/10 = 20/10
SIMPLIFY IT

x = 20/10

x = 2

Therefore, your answer should be:

Option D. x = 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

1. 82 2. 82 3. 82 4. 98 5. 123 6. 122 7. 119 8. 60 9. 60 10. 125 11. 35 12. 105

Answer:

x = 7

Step-by-step explanation:

To get rid of the x^2, do the opposite of x^2: radicals, or square roots.

x^2 = 121

x = √121

Think about what number can multiply by itself to get 121...

7 • 7 or 7^2 = 121

So, in x^2 = 121, x = 7.

x^2 = 121

x = √121

7 = √121

7 = 7 ✔

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The product of the rational numbers - 5/8 and - 2/15 will be 1 / 20.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction is referred to as the PEMDAS rule. To answer the problem properly and accurately, this rule is applied.

The rational numbers are given below.

- 5/8 and - 2/15

Then the product of the rational numbers - 5/8 and - 2/15 will be given by the multiplication of the rational numbers - 5/8 and - 2/15.

⇒ - 5/8 × - 2/15

⇒ 5/8 × 2/15

⇒ 1/20

The product of the rational numbers - 5/8 and - 2/15 will be 1 / 20.

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By the degfinition of a congruent triangle, the statement that was made that ∆JOL and ∆IOM are congruent triangles is false.

The two triangles are said to be congruent triangles based on the fact that all of their corresponding sides are the same and said to be equal. Then all of the corresponding sides of the angles would also have an equa; measure.

The definition that I have given above says that the congruent triangles are those that have the same shapes and also have the same sizes. The corresponding sides of the angles and the sides would also be the same.

In the diagram that we have here, we can see that IOM and JOL do not have the same size. Hence the congruent law is not correct. To be congruent it would have to be that the the corresponding sides are the same and there is the equality in the angles of the triangles.

Since this property is not in the shape we would have to conclyde that the statement is wrong. They are not congruent triangles.

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Answer:

10 times

Step-by-step explanation:

To figure this out, the first thing we will do is to find the LCM (Least Common Multiple). We will do this by making a list of the denominators that we have right now. Right now we have [tex]\frac{20}{4}[/tex] and [tex]\frac{3}{6}[/tex]. We will use 4 and 6 to make a list to find our multiple that is in both lists. (That comes up first)

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32...

Multiples of 6: 6, 12, 18, 24, 30, 36, 42...

Now, we just realized that we have 24 that are in common with both 4 and 6. Now we will multiply both the numerator and denominator by the same number to have the denominator equal 24.

[tex]\frac{20}{4} * \frac{6}{6}[/tex] = [tex]\frac{120}{24}[/tex] & [tex]\frac{3}{6} * \frac{4}{4}[/tex] = [tex]\frac{12}{24}[/tex]

Now that we have [tex]\frac{120}{24}[/tex] and [tex]\frac{12}{24}[/tex]. We will read the question again about how many [tex]\frac{3}{6}[/tex] equal to [tex]\frac{20}{4}[/tex]. Since we have our fractions, we will add [tex]\frac{12}{24}[/tex] multiple times until we get [tex]\frac{120}{24}[/tex].

[tex]\frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} = \frac{120}{24}[/tex]

Therefore, [tex]\frac{3}{6}[/tex] equals to [tex]\frac{20}{4}[/tex] 10 times.

Answer: 33.7lbs

Step-by-step explanation: One N equals 0.225lb so you do that times 150

Hope this helped!!!!

The angles are given below

What is an angle?

An angle is a symbol in Euclidean geometry created by two rays, called the flanks of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are placed in the plane having the rays. Angles are also generated when two planes overlap. These are termed as dihedral angles. An angle defined by two overlapping curves is the angle of both the rays falling tangent to the individual curves at their place of junction. Angle can also refer to the measurement of an angle or of a rotation. This measurement is the length of a circular arc divided by its radius.

(a) angle a = 112° (alternate angles)

angle b = angle a = 112° (vertically opposite angles)

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The most appropriate choice for perimeter of rectangle will be given by

It costs $76.16 to buy enough of the border to go around the room.

What is perimeter of a rectangle?

The total length of the outline of a rectangle is called perimeter of rectangle.

If the length of a rectangle is l units and breadth of a rectangle is b units, then perimeter of rectangle will be given by

                                      [tex]2 \times (l+b)[/tex] units

Here,

Length of room = 20 feet

Width of room = 12 feet

Perimeter of room = [tex]2 \times (20 + 12)[/tex]

                               = [tex]2 \times 32[/tex]

                               = [tex]64[/tex] feet

cost of 1 foot of border = $1.19

cost of 64 foot of border = $[tex]1.19 \times 64[/tex]

                                         = $[tex]76.16[/tex]

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The probability that the jury will make a wrong decision when it reaches a decision by majority rule is 0.033

To solve this, the number of jury that makes the wrong decision can be modeled as a binomial random with parameters n=7 and p=0.2. This jury as a whole will make wrong decision if 4, 5, 6, or 7 make the wrong decision.

We denote these events with A, B, C, D for 4, 5, 6, 7 respectively. The probability of this union is the sum of probabilities, so

P(Jury Error) = P(A)+P(B)+P(C)+P(D)

  = [tex]\left({{7} \atop {4}} \right.)(0.2)^{4} *0.8^{3} +(\left \({7} \atop {5}} \right)(0.2)^{5} *0.8^{2} +(\left{7} \atop {6}} \right.)(0.2)^{6} *0.8^{1} +(\left{7} \atop {7}} \right.)(0.2)^{7} *0.8^{0}[/tex]

   =0.033

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The additional money Ms. May must invest at rate of 4% to get the 5% interest on entire income is $16,000.

For the given question,

The money invested by Ms. May at 7% rate of interest is $8,000.

Let 'x' be the money invested at the rate of 4%.

The interest for the total annual income is 5%.

Thus,

7%of 8,000 + 4% of x = 5%(8,000 + x)

8,000×0.07 + 0.04×x = 0.05(8,000 + x)

On solving,

560 + 0.04x = 400 + 0.05x

0.01x = 160

x = 16,000

Thus, the additional money Ms. May must invest at rate of 4% to get the 5% interest on entire income is $16,000.

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From the figure the shaded parts are two: the quadrant part and the sector part. The solution shows that:

area of the shaded part of the quadrant = area of the shaded part of the sector = ( pi * r^2) / 4 - bh/2

given data

ACD is a sector of a circle

From the figure we deduce that arc AC with line O is a quadrant of a circle. Hence the area of the shaded part of the quadrant is:

= area of a circle /4 - area of the right angle triangle

where area of a circle = pi r^2

area of triangle =  1/2 * base * height = bh/2

Area of the shaded part of the quadrant

= ( pi * r^2) / 4 - bh/2

base AO = radius of the circle = height CO

this forms an isosceles triangle and base angles of an isosceles triangle are equal. < A = < C = x

< A + < C + 90 = 180

x = 45 degrees

area of sector

= ∅/360 * pi*r^2  

= (45 / 360) * (pi*r^2)

= (pi * r^2) / 4

area of the shaded part of the sector = area of sector - area of the right angle triangle

= (pi * r^2) / 4 - bh/2

Comparing both sides that shows that the tow shaded parts are equal hence the shaded part of the quadrant is equal to the shaded part of the sector

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The method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate is A. Use a rigid transformation to prove ∠NOP ≅ ∠NML.

The AA Similarity Postulate states that two angles in one triangle must be congruent with two angles in another triangle for the two triangles to be comparable. The AA Similarity Postulate is a shortcut for demonstrating the similarity of two triangles.

In this case, B is incorrect because angles NOP and ONP are not corresponding angles

Also, options (c) and (d) are incorrect, because they prove the similarities by lines segments.

In conclusion, the correct option is A.

The complete question is written below.

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Complete question

Which method and additional information would prove ΔONP and ΔMNL similar by the AA similarity postulate?

A. Use a rigid transformation to prove ∠NOP ≅ ∠NML.

B. Use a rigid transformation to prove ∠NOP ≅ ∠ONP.

C. Use rigid and nonrigid transformations to prove segment LN over segment ON = segment PN over segment MN.

D. Use rigid and nonrigid transformations to prove segment LM over segment ON = segment PN over segment MN

The height of the triangular prism is calculated as: 12 cm.

The volume of a right-triangular prism = 1/2(base of triangular face)(height of triangular face)(length of the triangular prism).

Given the following:

Plug in all the values into the volume formula for the triangular prism:

750 = 1/2(5)(h)(25)

750 = (1 × 5 × h × 25)/2

750 = (125h)/2

Multiply both sides by 2

750 × 2 = (125h)/2 × 2 [multiplication property of equality]

1,500 = 125h

Divide both sides by 125

1,500/125 = 125h/125 [division property of equality]

12 = h

h = 12 cm

Thus, the height of the prism that has a base of the triangle measuring 5cm, a prism length of 25 cm., and a volume of 750 cubic cm is determined as 12 cm.

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Zeroes of the equation are i3√3 and -i3√3.

A value (a number) at which the polynomial evaluates to zero is referred to as the "zero of a polynomial." For instance, the zeros of the polynomial x²-3x+2 are 1 and 2. A polynomial's zeros are frequently referred to as its "roots." Every polynomial has a unique multiset of zeros, which is an unordered list. The coefficients of a zero polynomial, which is a constant polynomial, are all equal to 0. The value of the variable that brings a polynomial to zero is referred to as its zero. As a result, any real integer is the zero of the zero polynomial.

Given Data

(x) = -x² - 27

To find zeroes,

m(x) = 0

0 = -x² - 27

x² = -27

As we know,

i² = -1

x² = i²(27)

x² = i (±3√3)

x = i3√3

x = -i3√3

Zeroes of the equation are i3√3 and -i3√3.

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