lodine-131, a radioactive substance that is effective in locating brain tumors, has a half-life of only eight days. A
hospital purchased 16 grams of the substance but had to wait six days before it could be used. How much of the
substance was left after six days?
...
The amount of substance left after six days was
9.

(Round the final answer to three decimal places as needed. Round all intermediate values to seven decimal places as
needed.)

The graph is a parabola, with a vertex at (4,-4), an axis of symmetry at x = 4, x-intercepts at x = 10 and x = -2, and a y-intercept at (0,-20).

A quadratic function is a type of polynomial function of degree 2. It can be defined as a function in which the highest power of the independent variable x is 2.

The quadratic function f(x) = x² - 8x - 20 has a graph that is a parabola with a vertical axis of symmetry.

Vertex: The vertex of the parabola can be found using the formula x = -b/2a, where a and b are the coefficients of x² and x respectively.

In this case, a = 1 and b = -8, so the x-coordinate of the vertex is x = -(-8)/(2×1) = 4.

To find the y-coordinate of the vertex, substitute x = 4 into the equation: f(4) = 4² - 8(4) - 20 = -4. Therefore, the vertex is located at (4,-4).

Axis of symmetry: The axis of symmetry of the parabola is a vertical line passing through the vertex.

In this case, the axis of symmetry is the line x = 4.

Intercepts: To find the x-intercepts set y = 0 and solve for x: x² - 8x - 20 =0.

this quadratic equation can be factored as (x - 10)(x + 2) = 0

so the x-intercepts are x = 10 and x = -2.

To find the y-intercept, set x = 0 and evaluate f(0) = 0² - 8(0) - 20 = -20. Therefore, the y-intercept is (0,-20).

Image is attached below.

The graph is a upward-facing parabola, with a vertex at (4,-4), an axis of symmetry at x = 4, x-intercepts at x = 10 and x = -2, and a y-intercept at (0,-20).

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Answer:

[tex]13 < \sqrt{181} < 14[/tex].

Step-by-step explanation:

We have been given an inequality ___[tex]< \sqrt{181} <[/tex]___. We are asked to fill in the blank with two consecutive integers to complete the given inequality.

We know that square root of 181 is not an integer. We can see that 181 is greater than square root 169 and and square root of 196.

[tex]\sqrt{169} < \sqrt{181} < \sqrt{196}[/tex]

We know that [tex]\sqrt{169}=13[/tex] and [tex]\sqrt{196}=14[/tex].

Therefore, our required inequality would be [tex]13 < \sqrt{181} < 14[/tex]

Answer:

-4y2 +y - 12

Step-by-step explanation:

-3y2 - y2= -4y2

-y+2y= y

-8 - 4= -12

-4y2 + y - 12

The number of gold balls in the given bag is determined as 25 gold balls.

Let's use the formula for calculating probability:

Probability of an event = Number of favorable outcomes / Total number of outcomes

The total number of possible ways to choose 2 balls from a bag of 40 is:

40C2 = (40 x 39) / (2 x 1) = 780

Now we need to find the number of ways to choose 2 gold balls from the bag.

Let's say there are "g" gold balls in the bag. Then the number of ways to choose 2 gold balls is:

gC2 = (g x (g-1)) / (2 x 1)

We want to find the probability that 2 gold balls are removed, so we use the formula above to get:

Probability of choosing 2 gold balls = Number of ways to choose 2 gold balls / Total number of ways to choose 2 balls

Therefore, we have:

Probability of choosing 2 gold balls = gC2 / 40C2

We are given that this probability is 12/95, so we can set up an equation:

(g x (g-1)) / (2 x 1) / (40 x 39) / (2 x 1) = 12/95

Simplifying, we get:

g x (g-1) = (12/95) x (40 x 39)

g x (g-1) = 624

Expanding and rearranging, we get a quadratic equation:

g² - g - 624 = 0

Solving this quadratic equation, we get:

g = 25 or g = -24

We discard the negative solution, as the number of gold balls must be a positive integer. Therefore, there are 25 gold balls in the bag.

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There is a 15.74% chance that a randomly chosen employee will earn between $450 and $550.

The study of random occurrences or phenomena falls under the umbrella of the mathematic discipline known as probability. It is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To find : the probability that a worker selected at random makes between $450 and $550

z = (x - μ) / б

where б is the standard deviation, μ is the mean, and x is the value we wish to normalize.

For $450, we have:

z₁ = (450 - 400) / 50 = 1

For $550, we have:

z₂ = (550 - 400) / 50 = 3

We can then use a standard normal distribution table or calculator to find the area under the standard normal curve between z₁and z₂:

P(z₁< z < z₂) = P(1 < z < 3) = 0.1574

This means that the probability that a worker selected at random makes between $450 and $550 is 15.74%.

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Answer:42

Step-by-step explanation:

Answer:

8 sides

Step-by-step explanation:

Let n be the number of sides

Then sum of internal angles [tex]=(n-2)180[/tex]

——-(1)

It is given that one internal angle [tex]=135[/tex]

So sum of n equal internal angles [tex]=135n[/tex] ————(2)

From(1) and(2)

[tex](n-2)180=135n[/tex]

[tex]180n-360=135n[/tex]

[tex]180n-135n=360[/tex]

[tex]45n=360[/tex]

[tex]n=360\div45=8[/tex]

[tex]\bold{So \ the \ number \ of \ sides=8}[/tex]

Step-by-step explanation:

5(2 + 1) can be simplified using the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Using this property, we get:

5(2 + 1) = 5(2) + 5(1)

Simplifying the expression further, we get:

5(2) + 5(1) = 10 + 5 = 15

Therefore, 5(2 + 1) is equivalent to 15.

Answer:

[tex]16-(6.25+2*2.25)[/tex]

Step-by-step explanation:

To find the amount of money she has left, you want to subtract the price of the ticket and the price of the two snacks from the amount of money she starts with.

So we want to subtract 6.25 once and subtract 2.25 twice (because she bought two snacks) from 16

16-6.25-2*2.25

Or you can also do this by adding up the monetary value of the ticket and the snacks and subtract that from the initial amount of money that Parvati has

16-(6.25+2*2.25)

(I am assuming that the "2.2.25" is supposed to say [tex]2*2.25[/tex])

Using the graph of the picewise function we can see that:

Here we have a piecewise function and we want to evaluate it in different values of x.

First we want to get:

i(-3)

Notice that at x = -3 we have a closed circle in the second line, the one constant at y = 2, so we need to use that value here:

i(-3) = 2

The closed dot means that the value belongs to that line, while a open one (like the one that is just above) means that the value does not belong.

For the second evaluation:

i(-4)

This time we just need to look at the line in the left, here we can see that: i(-4) = 3

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The possible present ages of each cockatoo, given the sum of the cockatoos would be Galah cockatoo is currently 10 years old and the white cockatoo would be 34 years old

Let's use variables to represent the present ages of the two cockatoos. Let W be the present age of the white cockatoo and G be the present age of the Galah cockatoo. We're given that the sum of their ages is 44 years:

W + G = 44 (1)

In n years, the white cockatoo will be W + n years old, and the Galah cockatoo will be G + n years old:

W + n = 4(G + n) (2)

Since n > 0, 5G - 44 must be positive. We can try different values of G to find possible integer values for n.

For G = 8:

44 - 5(8) = 4

4 = -3n

n is not an integer.

For G = 10:

44 - 5(10) = -6

-6 = -3n

n = 2

So one possibility is that the Galah cockatoo is currently 10 years old. In this case, the white cockatoo would be 34 years old (since W + G = 44).

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The coordinates of the point on the directed line segment are (-6, 0)

Coordinates of a point refer to a set of numbers that represent the location of the point in a particular coordinate system.

To find the coordinates of the point that partitions the line segment from (-7,3) to (3,-9) into a ratio of 3 to 1, we can use the following formula:

P = [tex]( (3/4)*x_1 + (1/4)*x_2 , (3/4)*y_1 + (1/4)*y_2 )[/tex]

where P is the point that partitions the line segment, (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints of the segment, and the coefficients 3/4 and 1/4 correspond to the ratio in which the segment is divided.

Plugging in the values, we get:

P = ( (3/4)*(-7) + (1/4)*3 ,  (3/4)3 + (1/4)(-9) )

= (-21/4 - 3/4 ,   9/4 - 9/4)

= (-6, 0)

Therefore, the coordinates of the point that partitions the line segment from (-7,3) to (3,-9) into a ratio of 3 to 1 are (-6, 0).

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Store A would be the better choice as the final price is lower than Store B even though the original price was also lower at Store B.

What is discount?

Discount means the amount which is deducted by sellers from the amount to be payable by buyers.

Part A:

Store A is selling the laptop for $900 and has a discount coupon for 15% off. To calculate the amount of the discount, we can multiply the original price by the discount percentage:

Discount amount = $900 x 15% = $135

Therefore, the amount of the discount at Store A is $135.

Part B:

Store B is selling the laptop for $950 and has a discount coupon for 10% off. To calculate the amount of the discount, we can multiply the original price by the discount percentage:

Discount amount = $950 x 10% = $95

Therefore, the amount of the discount at Store B is $95.

Part C:

At Store A, the final price would be:

Final price at Store A = $900 - $135 = $765

At Store B, the final price would be:

Final price at Store B = $950 - $95 = $855

Therefore, Store A would be the better choice as the final price is lower than Store B even though the original price was also lower at Store B.

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Answer:

Step-by-step explanation:

Solution:

We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).

The GCF of 305 and 60 is 5.

Divide both terms by 5.

305 ÷ 5 = 61

60 ÷ 5 = 12

Therefore:

305 : 60 = 61 : 12

The measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.

In the given diagram, we can see that angle ACD is a right angle, since it is formed by the radius AC and tangent CD at point C.

Therefore, angle BCD is equal to angle ACD, which is 90 degrees.

Since angle BCD is an exterior angle of triangle BCF, it is equal to the sum of the two remote interior angles, which are angles BFC and FCB.

Angle BFC is equal to angle ABC (since they are opposite angles), which is 60 degrees.

Similarly, angle FCB is equal to angle ACF, which is also 60 degrees.

Therefore, angle BCD is equal to angle BFC + angle FCB, which is 60 + 60 = 120 degrees.

Now, since arc CD is subtended by angle BCD, its measure is also equal to 120 degrees.

Hence, the measure of arc CD is 120 degrees.

Similarly, angles ACF and FCB are opposite angles in the cyclic quadrilateral AFCB, so they are supplementary. Therefore, angle FCB is equal to 180 - angle ACF,

Which is also 180 - 60 = 120 degrees.

Now we can apply the exterior angle theorem to find the measure of angle BCD. We have:

angle BCD = angle BFC + angle FCB

= 120 + 120

= 240 degrees

Finally, we can conclude that the measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.

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Answer:

Saanvi recorded the number of math problems she did for homework each night for 10 days.

Step-by-step explanation:

Answer:249.98

Step-by-step explanation: i had a question like this before.

Answer:

Step-by-step explanation:

the stabdard error is given with the se coefficient snf the y slope

Answer:

x =65°( being alternate angel)

The surface area of the rectangular prism graphed is given as follows:

10.12 ft³.

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

Converting the mixed numbers to decimal, the dimensions of the rectangular prism are given as follows:

1.3 ft, 1.4 ft and 1.2 ft.

Hence the surface area of the prism is given as follows:

S = 2 x (1.3 x 1.4 + 1.3 x 1.2 + 1.4 x 1.2)

S = 10.12 ft³.

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Answer:

a) There are four prime numbers between 1 and 10: 2, 3, 5, and 7. So the probability of drawing a prime number is 4/10 or 2/5, which is 20% and not 10%. Therefore, option (a) is not correct.

b) As we saw in part (a), the probability of drawing a prime number is 2/5 or 40% (since 2/5 is equivalent to 0.4). Therefore, option (b) is correct.

c) The probability of drawing a prime number is 2/5 or 40%, which is not 25%. Therefore, option (c) is not correct.

d) As we saw in part (a) and (b), the probability of drawing a prime number is 2/5 or 40%, which is not 50%. Therefore, option (d) is not correct.

So, the correct answer is (b) 25%.

Hope This Helps!

The correct column is (A), which correctly represents the responses as probability.

Probability is a measure of the likelihood or chance that a particular event will occur. It is usually expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

The sum of all the responses is 558 + 79 + 20 + 7 = 664.

To represent the responses as a probability model, we need to divide each response by the total number of respondents, 664.  

The correct column is (A), which correctly represents the responses as probabilities:

(A)Very important 558/664 = 0.841

Somewhat important 79/664 = 0.119

Not too important 20/664 = 0.030

Not at all important 7/664 = 0.011

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In a regular hexagon, where FGHIJK shares a common center with square ABCD on a coordinate plane. ||. It is Across any of the perpendicular bisectors of the sides of the square that the combined figure can reflect onto itself.

In Regular Hexagon FGHIJK, we have 6 lines of reflection across which the hexagon reflects onto itself. Those lines are:

3 perpendicular bisectors of sides i.e. perpendicular bisector of IJ , IH and GH

3 lines passing through vertices i.e. HK, IF and GJ.

While in Square, we have 4 line of reflection across which the square reflects onto itself. Those lines are:

2 perpendicular bisectors of sides AB and BC i.e. HK and perpendicular bisector of CD

2 diagonals of square i.e. AC and BD

Note as well that from figure we know that perpendicular bisector of CD and perpendicular bisector of IJ is the same line.

So, for combined figure we have to take common lines from both figures i.e. perpendicular of sides CD or IJ and line HK.

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Full Question:

Although part of your question is missing, you might be referring to this full question: See the attached image and the questions below.


In a regular hexagon, FGHIJK shares a common center with square ABCD on a coordinate plane. || . Across which lines can the combined figure reflect onto itself?
A. any of the perpendicular bisectors of the sides of the hexagon
B. either diagonal of the square
C. any of the perpendicular bisectors of the sides of the square
D. there are no lines across which this figure can reflect onto itself

Answer: x=6.5

Step-by-step explanation: 13 x 10=130

845/130= 6.5

The vertex is ( 6 , 1 ). The vertex of the graph of the equation maximum.

What is parabola in math?

Each point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line. All of the parabola-related ideas are discussed here since it is a crucial component of the conic section subject.

the equation  y = -x² + 6x + 1

  Use the formula: -b/2a

       = -6/-1

       = 6

The x-coordinate of the vertex is 6

Plug the x value back into the original equation to find the y-coordinate of the vertex

     y = -x² + 6x + 1

        = -(6)² + 6 * 6 + 1

        = -36 + 36 + 1

        = 1

The vertex is = ( 6 , 1 )

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Answer:

14

Step-by-step explanation:

Volume = height x width x length

6 x 10 = 60

480 divided by 60 = 14

The number of students who have both a cell phone and a tablet is 13. This corresponds to the intersection of the "Has Cell Phone" and "Has Tablet" sets.

What is meant by intersection?

In mathematics, the intersection of two sets A and B is a new set that contains all the elements that are common to both sets. In symbols, the intersection of A and B is denoted by A ∩ B, and it is defined as:

A ∩ B = {x : x ∈ A and x ∈ B}

Let A represent the set of students who have a cell phone, and B represent the set of students who have a tablet. The intersection of A and B, denoted by A ∩ B, represents the set of students who have both a cell phone and a tablet. Therefore, we want to find the cardinality (or size) of the set A ∩ B.

From the frequency table, we know that the total number of seventh graders surveyed is 100. We also know that there are 32 students who have a cell phone (i.e., |A| = 32) and 70 students who have a tablet (i.e., |B| = 70). We are given that 19 students who have a cell phone do not have a tablet, which means that there are 32 - 19 = 13 students who have both a cell phone and a tablet (i.e., |A ∩ B| = 13).

Therefore, the number of students who have both a cell phone and a tablet is 13. This corresponds to the intersection of the "Has Cell Phone" and "Has Tablet" sets.

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1.  36x+8- 3rd column;

2. (9·4x)+(9·1)=36x+9 - 1st column;

3. (3·12x)-(3·3)=36x+9 - 2nd column;

4. 9(4x+1)=36x+9 - 1st column;

5.  36x-9- 2nd column;

6. 4(9x+2)=36x+8 - 3rd column

In mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equals sign (=). Equations can contain one or more variables, which are quantities that can take on different values.

Start with expressions in blue boxes:

1st column) 36x+9;

2nd column) 9(4x-1)=36x-9;

3rd column) (4·9x)+(4·2)=36x+8.

You have 6 expressions. Consider all them:

1.  36x+8- 3rd column;

2. (9·4x)+(9·1)=36x+9 - 1st column;

3. (3·12x)-(3·3)=36x+9 - 2nd column;

4. 9(4x+1)=36x+9 - 1st column;

5.  36x-9- 2nd column;

6. 4(9x+2)=36x+8 - 3rd column

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The complete question is;

Drag each expression to show whether it is equivalent to 36x + 9, 9(4x – 1), or (4 • 9x) + (4 • 2).

We can cut 6 pieces of rope measuring 5/8 of a foot from a rope of 4 3/8 feet, with some rope left over.

Area is a measurement of the size of a surface or a region in a two-dimensional space. It is expressed in square units, such as square inches (in²), square meters (m²), or square feet (ft²). To find the area of a shape, you need to multiply its length by its width, or use an appropriate formula depending on the shape. For example, the formula for the area of a rectangle is A = l × w, where A is the area, l is the length, and w is the width.

To find the number of pieces of rope measuring 5/8 of a foot that can be cut from a rope of 4 3/8 feet, we need to divide the length of the rope by the length of each piece of rope:

4 3/8 feet = 4 + 3/8 feet = 4 feet + (3/8) x 12 inches = 4 feet + 3 inches = 51 inches

Each piece of rope measures 5/8 of a foot, which is equivalent to 5/8 x 12 inches = 7.5 inches.

Now we can divide the length of the rope (in inches) by the length of each piece of rope (in inches) to find the number of pieces:

51 inches ÷ 7.5 inches ≈ 6.8

Therefore, we can cut 6 pieces of rope measuring 5/8 of a foot from a rope of 4 3/8 feet, with some rope left over.

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