induction can be used to prove the following is true for every nonnegitive integer n

Answer:

the portion of the x-axis that the straight line cuts is the interval [5r, -5r].

Step-by-step explanation:

To find the portion of the x-axis that the straight line cuts, we first need to solve the equation for θ. The sine function has a range of [-1, 1], so the value of r must be greater than or equal to 5 in order for the equation to have a solution.

To solve the equation, we can use the fact that sin(π/4 - θ) = cos(θ). Therefore, the equation can be rewritten as:

cos(θ) = 5

We can then use the fact that cos(θ) = x/r to solve for x:

x = 5r

Therefore, the portion of the x-axis that the straight line cuts is the interval [5r, -5r].

Note that this is only valid if r is greater than or equal to 5. If r is less than 5, there are no solutions to the equation and the straight line does not cut the x-axis.

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.

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The percentage of students that prefer biology only is; 60%

Percentage can simply be calculated by dividing the value by the total value, and then multiplying the result by 100.

Now, we are told that 29 of the students are girls. Thus;

Number of boys = 100 - 29 = 71 boys

Now, 9 of the girls like biology. Thus, this is;

9% of the total students

20 of the boys prefer physics and this in percentage is;

20% of the total students.

27 people prefer chemistry and this is;

27% of total students

Number of boys that prefer biology = 71 - (20 + 20) = 31

Thus;

Number of students that prefer biology = 29 + 31 = 60 students

This gives a percentage of 60% of the total students.

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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)

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A polynomial with two terms is called a binomial. For instance, the binomials x 2 x -2 x2 and x 6 x -6 x6 both exist.

A single-term expression is referred to as a monomial, a two-term expression as a binomial, and a three-term expression as a trinomial. An expression's name is just its number of terms if it has more than three terms.

Monomials have one term, binomials have two, trinomials have three, and polynomials have one or more terms.

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Step-by-step explanation:

200000000000+545-6678

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:

Answer:

 number one is 4.5

Step-by-step explanation:

The number of buttons A will be equal to 11. And the number of buttons B will be  equal to 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Given that container of buttons contains a similar number of each kind of button it contains 220g of buttons.

The weight of the button is given as follows;

Button A=8 grams

Button B = 12 Grams

Consider x be the number of each button. Then the equation is;

8x + 12x = 220

20x = 220

x = 11

The number of buttons A is 11. And the number of buttons B is 11.

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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 .

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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

Under ASA criterion, Δ ACB ≅ ΔDEF, as ∠C = ∠E, ∠B = ∠F, and the side CB = EF.

What is ASA Congruence Rule?

ASA Congruence rule stands for Angle-Side-Angle. Under this rule, two triangles are said to be congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. Look at the image given below to determine if the two given triangles, Δ ABC and ΔXYZ are congruent by the ASA rule.

Hence , Under ASA criterion, Δ ACB ≅ ΔDEF, as ∠C = ∠E, ∠B = ∠F, and the side CB = EF. Since Δ ACB ≅ ΔDEF, then the third angle ∠A and the other two sides of Δ ACB are bound to be equal to the corresponding angle ∠D and the sides of ΔDEF.

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Answer:

y=8

Step-by-step explanation:

9y-7y=20-4

2y=16

y=16/2

y=8

Answer:

slope = -1

Step-by-step explanation:

⭐What is the slope of a line?

⭐What is the slope of a line that is parallel to another line?

Therefore, we can just find the slope of the given line and put that as our answer.

Before we do that, we need to rewrite the equation in slope-intercept form. ([tex]y = mx + b[/tex])

x + y = -6

To do so, subtract x from the LHS (left-hand side) and RHS (right-hand side) to isolate "y"

x + y -x = -6 -x

y = -x + 6

The slope is the coefficient of the x-variable.

-1 is the coefficient of the x-variable.

Therefore, -1 is the slope of this line.

Parallel lines have the same slope of the line they are parallel to.

Therefore, -1 is the slope of the line parallel to this line.

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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.

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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°

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.

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Answer:

135%

Step-by-step explanation:

multiply 1.35 to 100 or move the decimal point to the right 2 places

The sample standard deviations of the data set 2, 3, 5, 6, 7 rounded up to 2 decimal spaces is 2.07.

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. Think about the following data: 2, 1, 3, 2, 4.

The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation. The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.

Number of data points (n)=5

Mean (x)= (2+3+5+6+7)/5= 4.6

Here x = 2, 3, 5, 6, 7

(x-x)  = -2.6, -1.6, 0.4, 1.4, 2.4

[tex](x-X)^{2}[/tex] = 6.76, 2.56, 0.16, 1.96, 5.76

∑[tex](x-X)^{2}[/tex] = 17.2

Sample standard deviation :

[tex]\sqrt{\frac{(x-X)^{2}}{n-1} } \\\\\sqrt{\frac{17.2}{4} } \\\\[/tex]

= 2.07

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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.

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The inequality that describes the problem is C. 8x ≤ 16

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since Kamari's Sweet Treats, cookies are packaged in boxes of 8 and the most a box can cost is $16. This will be:

8x ≤ 16

The correct option is C.

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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.

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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.

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m= 9.

[tex]0.4(20 - 10m) = 2.5 - 2m - 12.5[/tex]

[tex](0.4)(20)-(0.4)(10m)= 2.5 - 2m - 12.5\\ \\(8)-(4m)= 2.5 - 2m - 12.5\\ \\8-4m= 2.5 - 2m - 12.5[/tex]

[tex]8-4m-8= 2.5 - 2m - 12.5-8\\ \\-4m=2.5-2m-20.5\\ \\-4m=-2m-18[/tex]

[tex]-4m+2m=-2m-18+2m\\ \\-2m=-18[/tex]

[tex]\frac{-2m}{-2} =\frac{-18}{-2} \\ \\m=9[/tex]

[tex]0.4(20 - 10(9)) = 2.5 - 2(9) - 12.5\\\\0.4(20 - (90)) = 2.5 - (18) - 12.5\\ \\0.4(-70) = -28\\ \\-28=-28[/tex]

That's correct. Therefore, m= 9 is the correct answer!

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.

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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

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Using prime numbers and evaluating the factors of the given number, The prime factorization of 252 is 2 x 2 x 3 x 3 x 7. The prime factorization of 50 is 2 x 5 x 5. We can directly calculate the prime factorization using a calculator. Prime numbers for 52 is 2 and 13.

A natural number higher than 1 that is not the product of two smaller natural numbers is referred to as a prime number (or a prime).

Numbers that split an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal halves.

Prime factors of 252= 2 x 2 x 3 x 3 x 7

Prime factors of 50 =  2 x 5 x 5

Prime factors of 52 = 2 x 2 x 13

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If the 12 inch pizza is cut into 8 (equal) slices, the number of calories in one slice is 2440/8 = 305.

"Information available from the question"

In the question:

A 6 inch personal pizza has 610 calories, with 240 of those from fat. A 12 inch pizza is cut into 8 slices.

Estimate the number of calories in one slice of a 12 inch pizza.

Now, According to the question:

The 6 inches and 12 inches are  the diameters of the two pizzas.

Consider the two pizzas as similar figures with a ratio of similarity of 2:1. By a basic geometric principle, the ratio of the areas of the two pizzas is the square of that ratio. So the area of the 12 inch pizza is 2^2=4 times the area of the 6 inch pizza.

The number of calories in the 6 inch pizza is 610.

The number of calories in the 12 inch pizza is 610 x 4  = 2440.

Hence, If the 12 inch pizza is cut into 8 (equal) slices, the number of calories in one slice is 2440/8 = 305.

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Answer:

y = -x + 5

Step-by-step explanation:

2x+2y=10 slope intercept equation

2x+2y=10

subtract 2x from both sides:

2y = 10 - 2x

rearrange right side:

2y = - 2x + 10

divide all terms by 2:

y = -x + 5

Answer:

Step-by-step explanation:

5 over 2