You have 544 grams of a radioactive kind of silver. If its half-life is 25 seconds, how much will
be left after 100 seconds?

Answer:

Step-by-step explanation:

Trapezium is a quadrilateral, and we know that the internal angles of a quadrilateral are equal to 360° .

SO:---

Angle A+Angle B+Angle C+Angle D=360°

(x²-105)+(x²-65)+(470-30x)+(510-30x)=360°

2x²+810-60x=360°

2x²+810-60x-360°=0

2x²+450-60x=0

2x²-60x+450=0

2(x²-30x+225)=0

2(x-15)²=0

(x-15)²=0/2

x-15=√0/√2

x-15=0

x=15

After putting the values, you will get the following:-

Angle A=x²-105=15²-105=120°

Angle B=x²-65=15²-65=160°

Angle C=470-30x=470-30×15=20°

Angle D=510-30x=510-30×15=60°

So, As we know that, the sum of internal angles of a quadrilateral is 360°

So, 120°+160°+20°+60°=360°

Hence, proved/verified that it a trapezium (quadrilateral).

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The measures of angles x, y and z are 40°, 50° and 130° and measures of the segments are AY = 16, IY = 9, FG = 30, AP = 24

Centroid is the point in a triangle where all the medians of the triangle intersects.

Given are two triangles, in first we have to find the missing angles and in the second one we need to find the asked segments,

1) We know that, in a right triangle, one angle is 90° and the sum of other two sides is 90°,

Therefore, 40°+y = 90°

y = 50°

x+y = 90°

x = 90°-50°

x = 40°

z = 180°-50° (linear pair)

z = 130°

2) we know that, the centroid divides the medians into 2:1

AY = 2YP

AY = 16

IY = TY/2

IY = 9

FG = GY+YF   (segment addition postulate)

GY = YF/2

GY = 10

FG = 10+20 = 30

PA = AY+YP  (segment addition postulate)

PA = 8+16

PA = 24

Hence. the measures are x, y and z are 40°, 50° and 130° and  AY = 16, IY = 9, FG = 30, AP = 24

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The height of the pile increasing when the pile is 16 feet high is 5/32 ft/min.

We are given dV/dt=10 cubic ft/min and we want to find dh/dt. Therefore, first we need to write a formula relating v and h.

V=pi*r^2*h/3  since d=h at any moment, we know that r=h/2 at any moment and if we substitute h/2 for r, we get

V=pi(h/2)^2*h/3 and if we simplify this,  we get

V=pi*(h^3)/12

Now we need to take the derivative of both sides with respect to t

dV/dt = pi * ( 3 * h^2 ) */12 * dh/dt

= pi * h^2 / 4 * dh/dt, substitute 40 for dV/dt and 16 for h and solve for dh/dt and we get

40 = pi * 16^2/4*dh/dt

dh/dt = 40 * 4 / ( 256 * pi )

= 40/(256*pi) ft/min,

= 10/64

= 5/32 ft/min

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Answer:

5x+x=90

Step-by-step explanation:

5 times the other = 5x

the other piece is x

Answer: the small pipe is 15 inches long

Step-by-step explanation: since the larger pipe is 5 times larger than the small pipe, the 90 inch pipe would have too be divided by 6 to make sure the 5 times of the large pipe and the 1 small pipe. so, you would do 90/6=15. so the small pipe is 15 inches long. the large pipe is 75 inches long.

Answer: Religion reinforces and promotes social inequality and social conflict. It helps convince the poor to accept their lot in life, and it leads to hostility and violence motivated by religious differences. This perspective focuses on the ways in which individuals interpret their religious experiences.

Step-by-step explanation:

The 3rd term of (4 - 5g) is -1050000g5

An arithmetic sequence is a set of integers that are ordered and have a common difference between each following word. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

It is simple to establish a series by starting with a number and repeatedly adding a fixed constant (d). An arithmetic sequence is this kind of sequence.

Given,

(4 - 5g)  simplifying

-1

So that is -1050000g5

The 3rd term of (4 - 5g) is -1050000g5

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Answer: 36.4

Step-by-step explanation:

Just convert the percentage to decimal and multiply.

70 x 0.52 = 36.4

The coterminal angle is 190°, the reference angle is 10°, and it lies on the third quadrant.

For any angle A written in degrees, the family of coterminal angles is written as:

B = A + n*360°

Where n can be any integer number different than zero.

Here we want to find a angle coterminal to -890° on the range [0°, 360°]

Then we need to find n such that:

B = -890°+ n*360°

is on the desired range.

If we take n = 3 we will get:

B = -890°+ 3*360°

B = 190°

That is coterminal angle, which is on the third quadrant, and it is 10° more than a 180° angle, so the reference angle (to the nearest axes) is 10°.

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The equation of the regression line is y = 4 + x and the regression analysis of the given data need not be done.

Straight line equation is y = a + bx.

The normal equations are

∑y = a·n + b ∑x ∑ xy = a ∑x + b∑x² Hence the regression analysis of the data :

The values are calculated using the following table

x y x²             x⋅y

58 62 3364 3596

47 51 2209 2397

84 88 7056 7392

62 66 3844 4092

57 61 3249 3477

72 76 5184 5472

69 73 4761 5037

hence :

∑x = 449

∑y = 477

∑x² = 29667

∑x⋅y = 31463

Substituting these values in the normal equations

7a+449b=477

449a+29667b=31463

Solving these two equations using Elimination method,

7a+449b=477

and 449a+29667b=31463

7a+449b=477→(1)

449a+29667b=31463→(2)

equation(1)×449

⇒3143a+201601b=214173

equation(2)×7

⇒3143a+207669b=220241

Substracting

⇒-6068b = -6068

⇒6068b = 6068

⇒b = 1

Putting b = 1 in equation (1), we have

7a+449(1) = 477

⇒7a = 477  - 449

⇒7a = 28 or a  = 4.

Now Estimate y for x=50

y = a + bx , we get

y = 4 + 1×50

y = 4 + 50

y = 54

At x equals 50 we get the value of y as 54 .

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A savings account with just an APR of 5.2% compounded quarterly on a balance of $2,000 will yield $16.61 more interest than a similar account with just an APR of 4.8% compounded monthly on the same balance.

Assume we had two different sorts of savings accounts, each with a deposit of $2,000 in it.

We must now determine the earnings for both accounts.

The following formula will be used to determine the earning:

Here,

Put the values for Account A now.

5.2 % in decimal form = 5.2/100= 0.052

v = 2000 x ( 1 + (0.052/4) )^(4*2)

v = 2217.71

Total earning for account A =  $ 2217.71.

For Account B:

4.8 % in decimal form = 4.8/100= 0.048

v = 2000*( 1 + (0.048/12) )^(12*2)

v = 2201.10

Total earning for account A = $ 2201.10

We will now deduct B's earnings from A's earnings to see how much more A earned than B.

2217.71 - 2201.10 = $16.61

Consequently, account A made $16.61 more so than account B.

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Answer: To simplify the expression (x - 4)(4x^2 + x - 6), you can use the distributive property, which states that you can multiply a number or expression by each term inside a set of parentheses.

Here is the process for simplifying the expression:

Multiply the first term, "x - 4", by the first term inside the second set of parentheses, "4x^2": (x - 4)(4x^2) = 4x^3 - 16x^2

Multiply the first term, "x - 4", by the second term inside the second set of parentheses, "x": (x - 4)(x) = x^2 - 4x

Multiply the first term, "x - 4", by the third term inside the second set of parentheses, "-6": (x - 4)(-6) = -6x + 24

Add the three products together: 4x^3 - 16x^2 + x^2 - 4x - 6x + 24 = 4x^3 - 16x^2 + x^2 - 10x + 24 = 4x^3 - 15x^2 - 10x + 24

The simplified expression is: 4x^3 - 15x^2 - 10x + 24

So, (x - 4)(4x^2 + x - 6) = 4x^3 - 15x^2 - 10x + 24.

Answer:

The slope of a line that is perpendicular to the graph of the equation x = 12 would be 0.

Step-by-step explanation:

To find the slope of a line that is perpendicular to the graph of the equation x = 12, follow these steps:

1. Remember that the slope of a line is a measure of how steep the line is. It is calculated by dividing the difference in the y-values of two points on the line by the difference in the x-values of those same two points.

2. Recall that a line with a slope of 0 is horizontal, meaning that it has no change in y-value as you move along it from left to right.

3. Since a line with a slope of 0 is horizontal and is therefore perpendicular to the vertical line represented by the equation x = 12, the slope of a line that is perpendicular to the graph of x = 12 would also be 0.

Note: In most mathematical contexts, an infinite slope is not considered a valid slope value and is typically not used in calculations. Instead, a line with an infinite slope is usually said to be parallel to the y-axis.

The reasons that complete the statements are:

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

Triangles = RST, and TUR

From the question, we have the following given parameters

∠SRT ≅ ∠UTR

This means that

Statement 2: ∠SRT ≅ ∠UTR ------ Given

At this point, we have

RS ≅ TU --- Congruent side (S)

∠SRT ≅ ∠UTR ------ Congruent angle (A)

RT ≅ TR --- Congruent side (S)

When these congruent sides and angles are combined, we have

SAS congruence property

The SAS congruent theorem implies that the corresponding sides of the triangles in question are congruent and the angles between the corresponding sides are also congruent

Hence, the additional information on the congruency of the triangles are Given and SAS congruence property

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Answer:

The sum will be an odd integer

Step-by-step explanation:

The even integers are divisible by 2 (as they are even) so we can write them as 2 times integer like this.

First even number = 2x

Second even number = 2y

An odd number is not divible by 2, but the number 1 smaller is even, so

The odd number = 2z + 1

Let's add them

2x + 2y + 2z + 1 = 2(x+y+z) + 1

So our sum is 1 more than another even number, so the sum is an odd number.

The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).

The distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by  

Here we have

A (-12, 2) and B(-6, 2)

B (-6, 2) and C(-6, -4)

C (-6, -4) and D(6, 2)

D (6, 2) and E(6, 4)

E (6, 4) and F(-12, 4)  

Here we will find the distance between given points to find the point which has 6 units between them.

As we know Distance = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]

For Option A

A (-12, 2) and B(-6, 2)

Distance = √(-6 + 12)² + (2 - 2)²

= √[(6)² + (0)²] = √36 = 6

For Option B

For  B (-6, 2) and C(-6, -4)

Distance = √(-6 - (-6))² + ( - 4 - 2)²

= √[(0)² + (-6)²] = √36 = 6  

For Option C

For C (-6, -4) and D(6, 2)

Distance =√(6 - (-6))² + (2 - (-4))²

= √(12)² + (6)² = √180 = 6√5

For Option D

For D (6, 2) and E(6, 4)

Distance = √(4 - 2)² + ( 6 - 6)²

= √[(2)² + (0)²] = √4 = 2      

For Option E

For E (6, 4) and F(-12, 4)  

Distance = √(-12 - 6)² + (4 - 4)²

= √[(18)² + (0)²] = √18² = 18

Therefore,

The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).

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The value of x in terms of y is,  x = y/2 + 1/2.

What is an equation?

Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

Consider, the given equation

y = 2x - 1

We have to find value of x from the given equation.

Let,

y = 2x - 1

Add 1 on both sides,

y + 1 = 2x - 1 + 1

y + 1 = 2x

Divide both sides by 2,

(y + 1)/2 = 2x/2

(y + 1)/2 = x

x = (y + 1)/2

x = y/2 + 1/2

Hence, the value of x in terms of y is,  x = y/2 + 1/2.

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There is a 90% probability that Abby and Bridget are seated adjacent to each other in the same row or the same column.

There are 10 total seating positions, and Abby and Bridget can be seated in any of these positions. There are two rows, and in each row there are 3 possible seating positions for Abby and 3 possible seating positions for Bridget, for a total of 6 possible seating arrangements in each row. There are also 3 possible seating positions for Abby and 3 possible seating positions for Bridget in the same column, for a total of 3 possible seating arrangements in the same column. Therefore, there are a total of 6+3=9 possible seating arrangements in which Abby and Bridget are seated adjacent to each other in the same row or the same column.

Out of all the possible seating arrangements, the probability that Abby and Bridget are seated adjacent to each other in the same row or the same column is therefore 9/10. This can be expressed as a fraction or as a decimal:

[tex]\frac{9}{10}[/tex] = 0.9

This means that there is a 90% probability that Abby and Bridget are seated adjacent to each other in the same row or the same column.

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The independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels is IV (  Interstate migration ) and DV ( State poverty level ) .

Given :

identify the independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels.

Independent variable :

An independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure.

Here in the given statement the independent variable is :

IV = Interstate migration

DV = State poverty level

Unit of Analysis = U.S. states

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Option a) 90% confidence interval for the population proportion of successes = 0.402

Option b) 90% confidence interval for the population proportion of failures = 0.598

According to the question given,

Critical values of Standard deviations are to be used to construct the proportions for the confidence interval.

The formula of a confidence interval that we will be using for the solution will be,

p = [tex]z_{a} * \sqrt{\frac{p(1-p)}{n} }[/tex]

In the above expression,

p = observed population.

n = sample size

[tex]z_{a}[/tex] = critical value of confidence interval

Now the given observations in question = 115

That result in success = 46

The resultant sample proportion = [tex]\frac{46}{115}[/tex]

⇒ 0.40 and it is for both success and failure

Here we can see that the answer for both parts will be identical.

The critical value of z at 90% confidence = 1.64

a) Lower bound = [tex]0.4 - 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]

⇒ 0.402

b) Upper bound = [tex]0.4 + 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]

⇒ 0.598

Confidence interval = 0.402 to 0.598

Therefore,

Option a) 90% confidence interval for the population proportion of successes = 0.402

Option b) 90% confidence interval for the population proportion of failures = 0.598

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The following conditions must be met in order to test hypotheses using proportions: np ≥ 5 and nq ≥ 5

To test hypotheses using proportions, the following requirements are necessary:

np ≥ 5 and nq ≥ 5: It is necessary to have a sufficient number of samples in each group being compared.

The rule of thumb is to have at least 5 observations in each group, where n is the sample size and p is the proportion in that group.

This ensures that the sampling distribution of the proportion is approximately normal, which is necessary for hypothesis testing.

Hence, the correct answer would be an option (A).

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The value of y is 21.3333. And from the options, 21.3333 is closest to 22.

So, the correct option is C. 22.

A term is composed of one mathematical expression. A single variable (a letter), a single integer (positive or negative), or a number of variables that have been multiplied but never added or subtracted are all examples of single variables. There is a number in front of certain words that are variables. When a phrase is used, a coefficient is given.

We have the expression,

y = 2 · 32 ÷ 3

Simplifying,

y = 2 x 32 ÷ 3

To solve for y:

Using PEMDAS,

the abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations.

P is for "parentheses,"

E is for "exponents,"

M is for "multiplication,"

D is for division,

A is for addition,

and S is for subtraction.

y = 2 x 32 ÷ 3

Firstly, we multiply the number,

y = 64 ÷ 3

Now, the division,

y = 21.3333

Therefore, the value of y is 21.3333.

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Eric typed 15 words more than Dae per minute.

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line. A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.

To find the amount of words typed in 1 minute for both;

Dae = 333/9

Dae = 27 words per minute

Eric = 252/6

Eric = 42 words per minute

Therefore 42 - 27 = 15 words per minute

Eric typed 15 more words per minute.

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Step-by-step explanation:

again, I just answered this question.

Answer: You must give more points for questions that are this long

sincerely,

A Friend

Step-by-step explanation:

The Statement is = TRUE

We can conclude from the statement given in the question that,

Some of the examples of the following pairs of algorithms could be seen below,

All these above pairs of algorithms are having some different ways of relationships between them eg, they might be having different parameters or their abilities to parameterize one another.

Therefore, in regard to the above explanations,

The Statement is = TRUE

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The number of hours it will take the student to complete the project is 5 / 6 hours.

A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate,  the time it will take the student to complete the project can be calculated as follows:

Therefore,

let

x = time it will take the student to complete the project

Hence

if 4 / 5 x = 2 / 3 hours

x = ? hours

cross multiply

Therefore,

number of hours to complete the whole math project = x × 2 / 3 ÷ 4 / 5 x

number of hours to complete the whole math project = 2 / 3 x × 5 / 4x

number of hours to complete the whole math project = 10x / 12x

number of hours to complete the whole math project = 10 / 12

number of hours to complete the whole math project = 5 / 6 hours

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The radius of the sphere B is 3 times greater than the radius of the sphere A or radius of the sphere A is 1/3 times greater than the radius of the sphere B.

A sphere is a three dimensional shape formed by the set of all points which are at equidistance from a point called the center of the sphere.

Volume of a sphere = [tex]\frac{4}{3}[/tex] π r³

Let the volume and radius of sphere A is V₁ and r₁ respectively and the volume and radius of sphere B be V₂ and r₂ respectively.

We have,

V₁ × 27 = V₂

[tex]\frac{4}{3}[/tex] π r₁³ × 27 = [tex]\frac{4}{3}[/tex] π r₂³

Common terms [tex]\frac{4}{3}[/tex] π get cancelled.

⇒ 27r₁³ = r₂³

⇒ r₁³ / r₂³ = 1 / 27

Taking cube root on both sides,

⇒ r₁ / r₂ = 1 / 3

⇒ 3r₁ =  r₂

⇒ r₁ = [tex]\frac{1}{3}[/tex] r₂

Hence the radius of the sphere A is 1/3 times greater than the radius of the sphere B.

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The equation of the line parallel to the line  7x - 4y = - 5 and passing through (16, - 4) is y = (7/4)x - 32.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know lines parallel to each other have the same slope which is

7x - 4y = - 5 ⇒ - 4y = - 7x - 5 ⇒ y = (7/4)x + (5/4) to our required line will also have the same slope passing through the point  (16, - 4).

Therefore, - 4 = 16(7/4) + b.

- 4 = 28 + b.

b = - 32.

Therefore, y = (7/4)x - 32 is the required line.

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