f(x) = ax^3 + bx^2 + cx + d In the polynomial above, a, b, c, and d are constants. If f(–5) = 3, which of the following must be true about f(x)? A x – 3 is a factor of f(x). B The remainder when f(x) is divided by x + 5 is 3. C x + 2 is a factor of f(x). D x + 5 is a factor of f(x).

5.8525 grams out of 25 grams of xenon will be left after 11 days.

The amount of time needed for an isotope's radioactivity to decrease to 50% of its initial value.

The given data is

T1/2=5.25 days.

No=25g

T=11 days

We'll have to find the disintegration constant first.

The formula for finding it is

T½ = In2 / λ

T½ = half-life

λ = disintegration constant

λ = In2 / T½

λ = 0.693 / 5.25

λ = 0.132

In(N / No) = -λt

where,

N = final mass of the radioactive sample

No = initial mass of the sample

λ = disintegration constant

t = time for the radioactive decay

In(N/No) = -λt

N / No = e^-λt

N = No(e^-λt)

N = 25 × e^-(0.132 × 11)

N=5.8525 g.

Therefore 5.8525 grams of Xe-133 will be left after 11 days.

To learn more about the half-life of isotopes refer to the link below:

https://brainly.com/question/25750315

#SPJ1

If the probability that the bug moves to its starting vertex on its tenth move is m/n , then the value of m+n is 683 .

In the question ,

it is given that ,

the bug starts from a vertex of an equilateral triangle , and

in each move , it randomly selects one of  two vertices where it is not currently located .

Let the probability that the bug is at its starting vertex after n moves is Pₙ .

If the bug is on its starting vertex after n moves, then it must be not on its starting vertex after n-1 moves .

At this point it will has (1/2) chance of reaching starting vertex in the next move.

Thus Pₙ =  (1/2)(1 - Pₙ₋₁) . P₀ =1 ,

So , the probabilities in each move can be written as

P₁ = 0 ,  P₂ = 1/2, P₃ = 1/4 , P₄ = 3/8 , P₅ = 5/16, P₆ = 11/32 , P₇ = 21/64 , P₈ = 43/128, P₉ = 85/256, P₁₀ = 171/512 ,

So , the tenth move P₁₀ is given as 171/512 , which is m/n .

So, m + n is = 171 + 512 = 683 .

Therefore , the value of m+n is = 683 .

Learn more about Probability here

https://brainly.com/question/28208934

#SPJ4

Answer:

AngleCAB = 44°

AngleHAB = 66°

Step-by-step explanation:

AngleEAF is a right angle, equal to 90°.

EH and DC are just two intersecting lines. They form a couple of pairs of vertical angles. Vertical angles are equal to each other. We'll use the vertical angles, AngleEAD and CAH.

Angle EAD and CAH are equal to each other.

EAD = CAH

90°+20° = 2x + 3x

Combine like terms.

110° = 5x

Divide by 5

110/5 = x

22 = x

Angle CAB

= 2x

= 2(22)

= 44

AngleCAB = 44°

AngleHAB

= 3x

= 3(22)

= 66

AngleHAB = 66°

Step-by-step explanation:

this is a structure of medians in the main triangle.

the center point X divides each median into parts in the ratio 2:1, with X being twice as far from the originating vertex than from the midpoint of the connected side.

so, RX is twice as long as XV.

RV = 54.

RX : XV = 2:1

that means RV consists of 2+1 = 3 equal parts. 2 of these parts are RX, and one part is XV.

how long is one part ?

54/3 = 18.

RX = 2×18, and XV = 1×18

XV = 18

The required measure of the XV in the triangle is 18.

The Median is defined as the line joining the vertex of a triangle to the midpoint of the facing side of the triangle.

Triangle RST is given, which consists of median RV, TU, and SW. All the median of the triangle intersects at X.

Now, the property triangle states that the point of intersection of the median(i.e centroid) X divides the median in the ratio of 2:1,

So,XV = 1 / 3 of RV and RX = 2/3 of RV,

Now,

XV = RV/3
XV = 54 / 3
XV = 18

Thus, XV = 18.

Learn more about the median of a triangle here,
https://brainly.com/question/2272632

#SPJ1

The older computer takes 8 minutes to send out the email on its own.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Let , the older computer works at the rate of x.

According to the condition,

then the rate of work of newer computer is x/2.

And the combined work of both the computer = x/2 + x = 3x/2

It means that  3x = 12

then x = 4

Hence, x =8of the job per minute.

It means the older computer will make the entire job in 84 minutes.

Therefore, the older computer takes 8 minutes to send out the email on its own.

To learn more about the addition;

https://brainly.com/question/29464370

#SPJ1

Answer:

C'(9,5)

Step-by-step explanation:

C(5,6)

Add or subtract how much you translate (move) left/right to the x-coordinate

Add or subtract how much you translate (move) up/down to the y-coordinate

C(5+x, 6+y) = C'

C(5+4, 6-1) = C'

C'(9,5)

please mark brainliest if this response helped you :)

$9.86 , Kendra donates to the charity.

Kendra worked 8 hours and 30 minutes last week

She earns $ 11.60 per hour

She will earn money if she works for 30 minutes = $(11.60÷2)

Therefore,

Total amount of money she earns last week = $((11.60×8) + (11.60÷2))

                                                                            = $(92.8+5.80))

                                                                            = $98.6

Kendra donates 1/10th of the total money she earns in a week

Therefore,

Amount she donate last week = total amount she earns last week * 1/10

= $(98.6*1/10)

= $9.86

To know more about calculations, follow link:

https://brainly.com/question/5759980

#SPJ1

Of the following, the option which is not a polynomial is 1/x+2. (Option D)

In mathematics, a polynomial refers to an expression consisting of indeterminates and coefficients, that only includes basic arithmetic operations of addition, subtraction, multiplication, and positive-integer powers of variables. In other words, it is a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power. The general form of a polynomial is a + bx + cx^2. Hence, it is identified by noting which expressions contain only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The non-polynomial expressions will be the expressions which contain other operations such as 1/x+2.

Note: The question is incomplete. The complete question probably is: Which of the following is not a polynomial (a) 3x+5 (b) 3y³-4y² +2y (c)x³-3 d) 1/x+2

Learn more about Polynomial:

https://brainly.com/question/4142886

#SPJ4

As per the given data, the correlation is 0.7.

Correlation:

in statistics, correlation refers the  association between two quantitative variables.

Given,

Here we have the table of data and now we need to find the correlation of the data.

As per the given data we have calculated the value of r as,

X Values

∑ = 132.38

Mean = 5.295

∑(X - Mx)² = SSₓ = 9.005

And the Y Values

∑ = 170.76

Mean = 6.83

∑(Y - My)² = SSₙ = 26.357

When the X and Y Combined

N = 25

∑(X - Mx)(Y - My) = 10.065

So, the R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSₓ)(SSₙ))

r = 10.065 / √((9.005)(26.357)) = 0.6533

Then the Meta Numeric (cross-check)

r = 0.6533

When we round of these value then we get the value of the correlation as 0.7.

To know more about Correlation here.

https://brainly.com/question/28898177

#SPJ4

The number of ice cubes that  Gregory could use in all is; 15

Algebraic word problems are defined as the questions that require translation of sentences into equations, and thereafter solving those equations. The variable in these usually represents an unknown quantity in a real-life scenario.

We are told that Greg gave a glass of water to each person at dinner. He put more than 2 ice cubes in each glass. Each glass had the same number of ice cubes.

More than 2 ice cubes tells us that there would be 3 cubes or 5 cubes especially when we consider the size of an ice cube.

Now from the given options, we see that only 15 is the number divided equally by 3 and 5.

Therefore, the total number of ice cubes will be 15.

Read more about Algebraic Word Problems at; https://brainly.com/question/13818690

#SPJ1

The missing options are;

A. 13

B. 15

C. 17

D. 19

MP = 16 ,, where NP = 13

therefore : MP - NP = MN <=> MN = 16 - 13 <=> MN = 3

MP = 16 ,, where MO = 9

therefore : MP - MO = OP <=> 16 - 9 = MO <=> MO = 7

MO = 7 & MN = 3

therefore : MO - MN = NO <=> NO = 7 - 3 <=> NO = 4

The expression  that could represent the cost of 7 t-shirts and a $6 tax is (a)  7n + 6

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

Number of shirts = 7

Tax = $6

Represent the cost of each shirt with n

So, we have the following equation

Total cost = Number of shirts * Cost of each shirt + Tax

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

Total cost = 7 * n + 6

Evaluate

Total cost = 7n + 6

Hence, the expression is (a) 7n + 6

Read more about expressions at

https://brainly.com/question/15775046

#SPJ1

The Probability of both Zack and Lucy missing the target will be 0.48

Let the probability of Lucy and Zack missing the target be = P(L) and  P(Z), respectively. So, If the probabilities of Zack and Lucy missing the target are as follows-

P(L) = 0.6 and

P(Z) = 0.8

then, the probability of both Lucy and Zack missing the target will be,

P(L) × P(Z) i.e.

0.6×0.8 = 0.48

Probability is basically a method to find out the possibility of likelihood of a certain outcome. In mathematics, it was introduced by Pierre and Cardano in the seventeenth century.

The complete question is-

The probabilities of Lucy and Zack hitting or missing the target are given in the following image. As per that, what will be the probability of both Lucy and Zack missing the target?

To know more about probability,

https://brainly.com/question/14210034?referrer=searchResults

https://brainly.com/question/30034780?referrer=searchResults

Based on the combination technique,

1. The position of wire 3

2. The magnitude and direction of current in wire 3

Combination method:

In statistics, the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter is know a combination method.

Given,

Here we have the three long wires hang vertically. The distance between wire 1 and wire 2 is 23.0 cm On the left, wire 1 carries an upward current of 1.50 A. To the right, wire 2 carries a downward current of 3.60 A. Wire 3 is to be located such that when it carries a certain current, each wire experiences no net force.

And now we need to find the position of wire 3 and the magnitude and direction of the current in wire 3.

As per the given question, we know that the

=> Current in wire 1, i1 =1.2A upward

=> Current in wire 2, i2=5A downward

And the distance between wire 1 and 2 is calculated is

=> 20cm = 0.2m

Here the current is calculated as

=> F/l = μo•i1•i3/2πx

So,

=> F/l=6×10⁻⁶N/m

=> 6×10⁻⁶ = μo•i1•i3/2πx

=> 6×10⁻⁶ =4π×10⁻⁷×1.2×i3/(2π×0.0632)

When we do Cross multiply,

=> 6×10⁻⁶×2π0.0632=4π×10⁻⁷×1.2×i3

=> 2.383×10⁻⁶=4π×10⁻⁷×1.2×i3

=> i3= (2.383×10⁻⁶)/(4π×10⁻⁷×1.2)

Therefore, i3= 1.58A and it's direction is downward.

To know more Combination method here.

https://brainly.com/question/28998705

#SPJ4

Answer:

$5809.17

Step-by-step explanation:

Using the formula for continuous compound interest [tex]P(t)=Pe^{rt}[/tex] We can plug in our values [tex]P(t)=5000e^{0.03*5}[/tex] and solve.

23

Step-by-step explanation:

The answer is 23 because it is closer to the 0

Answer: the answer is 141

Step-by-step explanation:

bro its not that hard the guy up top is a bum just add all the angles together thats the answer and remember the formula is (n-2)180 for INTERIOR i wrote it in caps cuz some of yall goofy fr

Using the fact that the two triangles are similar, we will see that the unknown side measures 50/3 units.

We know that the two triangles are similar, so if we take any two correspondent sides on the triangles and take the quotient, that will give a constant value. The base on the smaller triangle is 3, and the base in the larger one is 10, then the quotient gives:

Q = 10/3

If we make the quotient with the unknown we will get:Q = ?/5

The quotient is a constant, then these two quotients are equal:

10/3 = ?/5(10/3)*5 = ?50/3 = ?

In conclusion, the measure of the missing side is 50/3 units.

Learn more about similar triangles:

https://brainly.com/question/14285697

#SPJ1

72 mph = 105.6 ft/second

In order to convert any value from mph the following formula can be referred to:

speed in miles per hour x  5,280 = speed in foot per second

Therefore when 72 miles per hour is converted to foot per second would equal to the following value:

105.6 feet per second

The following can be referred to for a better understanding:

https://brainly.com/question/26689745

The graph of the piece-wise function in this problem is given by the image shown at the end of the answer.

A piece-wise function is a function that has different definitions, based on which interval the input value of the function belongs to.

In this problem, the function has three definitions, given as follows:

Hence the graph is defined as follows:

More can be learned about piece-wise functions at https//brainly.com/question/19358926

#SPJ1

The number of tickets that the band have to sell for each concert to meet the goal is 76 tickets

Based on the information given, the production costs, P , for a band to have a concert can be modeled by the equation P=850 + 5x.

x = the number of concert tickets sold.

Since the band earns $50 for each ticket sold. The band’s goal is for the amount earned on ticket sales minus production costs to equal $5,000 per concert.

This will be illustrated thus:

Revenue - Cost = Profit

50x - 850 + 5x = 5000

Collect like terms

55x = 5000 - 850

55x = 4150

Divide

x = 4150 / 55

x = 76

The tickets will be 76.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Based on the probability concept, the population is number of children in gymnastic class is 5 and the parameter is mean number of steps taken by the 5 children.

Probability:

In math probability  deals with the occurrence of a random event and the value is expressed from zero to one.

Given,

Suppose that there are 5 children in a gymnastics class.

One day, they count the number of steps each person takes while walking on their hands until they lose balance and come down.

The mean number of steps these children took while walking on their hands is 20 steps.

Here we need to find the the population and parameter.

Based on the given question,

We know that the parameters are descriptive measures of an entire population and their values are usually unknown because it is infeasible to measure an entire population.

Therefore, you can take a random sample from the population to obtain parameter estimates.

Similarly, for the population could simply be referred to as the total number or set of similar objects or subjects related to a certain study or research.

Here the given scenario described above, the area of interest is a particular gymnastic class, therefore all individuals or children belonging to this particular gymnastic class makes up the population.

And then the parameter on the other hand are statistical metrics, values or calculations derived from the population figure or information.

So, the mean value of steps obtained from the step counts of the population data is called the parameter.

And the parameter is a value that describes a characteristic of an entire population, such as the population mean.

Therefore, the population mean and standard deviation are two common parameters.

=> Population = number of children in gymnastic class = 5.

=> Parameter = mean number of steps taken by the 5 children.

To know more about Probability here.

https://brainly.com/question/11234923

#SPJ4

The height of the wall the brace reached is 8 feet.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Height of the wall the brace reached = x

Now,

10² = 6² + x²

100 = 36 + x²

x² = 100 - 36

x² = 64

x = 8

Thus,

The brace reached 8 feet of the wall.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ1

At 9 AM Bob could declare the pool was full of water, using given information about fill rate, discharge rate and time.

What is fill rate and discharge rate ?

The definition of fill rate is the percentage of customers orders you are able to meet without running out of stock at any given time.

The discharge rate is the amount of fluid that is passing through a given cross sectional area per unit time.

We need to divide it in 3 parts:

Part 1: When only 1 hose is filling the pool at 3 gal per hr.

Part 2 : When after 10 hours animals started drinking water .

Part 3: When 2nd hose also started at the rate 2 gal per hr.

Part 1:

For 10 hours it get started . So, pool get filled is 30gal.

Part 2:

After 10 hours, rate decreased by animals at 1 gal/hour.

So, rate = 3-1 = 2 gal/hour.

So, water filled for 5 hour = 10 gal.

So, total pool is filled = 10 + 30 = 40 gal.

Remaining = 60 - 40 = 20 gal.

Part 3:

2nd hose is added at the rate 2gal/hour.

Now, rate = 2+2 = 4 gal/hour.

Time taken for 20 gal = 5 hours.

So, total time taken = 10 + 5 +5

                                 = 20 hours.

We need to find the time ,

Time at which water is started = 1pm

1PM + 11hours = 12AM

For remaining , 9 hours

12AM + 9hours = 9AM.

Learn more from similar que using link:

https://brainly.com/question/11485594

#SPJ1

The commission rate is 20% and the base pay is $41,000.

The total pay is the sum of the base pay and the total commission earned.

Total pay = base pay + commission

Total pay = base pay + (percentage commission x sales)

The equations that represents the information in the question are:

a + 50,000b = 51,000 equation 1

a + 100,000b = 61,000 equation 2

The elimination method would be used to determine the required values:

Subtract equation 1 from equation 2:

50,000b = 10,000

b = 10,000 / 50,000

b = 0.2 = 20%

Substitute for b in equation 1:

a + (50,000 x 0.2) = 51,000

a + 10,000 = 51,000

a = 51,000 - 10,000

a = 41,000

To learn more about system of equations, please check: brainly.com/question/25875552

#SPJ1

In an acute triangle, the circumcenter of the triangle lies on the line O.

Acute triangle.

In geomentry, acute triangle is the type of triangle in which all the three internal angles of the triangle are acute

Given,

Here we need to prove that in the acute triangle ABC, the circumcenter of the triangle MNH lies on the line OH.

Let us consider T be the intersection of σ1 and σ1 other than W.

Now, the Lemma 1: T is on XY.

Now, the Proof is written as We have ∠XTW} = ∠YTW = 90 degres because they intercept semicircles.

Therefore, ∠XTY = ∠XTW + ∠YTW = 180 degrees,

Then XTY is a straight line.

Here we know that NHLB is cyclic because ∠BNH and ∠BLH, opposite and right angles, sum to 180 degree. Furthermore, we are given that NTWB is cyclic.

Therefore, the triangle MNH lies on the line OH.

To know more about Acute triangle here.

https://brainly.com/question/1311149

#SPJ4

No, Then the matrix has three columns and the eigenspaces' sum of dimensions is zero. The eigenspace's dimensions and the number of columns must add up to be equal.

A matrix is a rectangular arrangement of a collection of numbers into a fixed number of rows and columns. When the elements are arranged in a matrix horizontally, it forms the rows of a matrix. When the elements are arranged in a matrix vertically, it forms the columns of a matrix.

A matrix, also spelled "matrices," is a rectangular table, array, or set of letters, numbers, or phrases that are arranged in rows and columns to represent a mathematical object or a property of such an entity.

There are three eigen-spaces, since A has three eigen values, the dimension of each of the eigen value is at least one as there is at least one non-zero eigen vector in them.

Therefore,

No, Then the matrix has three columns and the eigenspaces' sum of dimensions is zero. The eigenspace's dimensions and the number of columns must add up to be equal.

To learn more about Matrix visit :

brainly.com/question/28180105

#SPJ4

Answer:

Step-by-step explanation:

Answer:

--------------------------

The linear functions will have same or equivalent equations in order to have infinitely many solutions.

Convert the given to slope-intercept form, y = mx + b, to make it equivalent: