when solving a linear system by substitution, how do you decide which variable to solve first?

The probability that the experiment results in exactly successes is; \(P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Consider that we have random variable X about binomial distribution with parameters n and p, then it can be written as;

\(X \sim B(n,p)\)

The probability that out of n trials, there be x successes is given as;

\(P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

The expected value and variance of X are given as:

\(E(X) = np\\Var(X) = np(1-p)\)

Hence, the probability that the experiment results in exact success are;

\(P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

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Answer:

696.91

Step-by-step explanation:

Answer:

The answer is C=696.91 hope this helps

Answer:

787.5

Step-by-step explanation:

150x21÷4 sana makatolong

When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

Answer: \(M=\Large\boxed{(4 ,~2 )}\)

Step-by-step explanation:

Given information

\((x_1,~y_1)=(3,~1)\)

\((x_2,~y_2)=(5,~3)\)

Given the midpoint formula

\(M=(\dfrac{x_1+x_2}{2} ,~\dfrac{y_1+y_2}{2} )\)

Substitute values into the given formula

\(M=(\dfrac{3+5}{2} ,~\dfrac{1+3}{2} )\)

Simplify the values on the numerator

\(M=(\dfrac{8}{2} ,~\dfrac{4}{2} )\)

Simplify the fractions

\(M=\Large\boxed{(4 ,~2 )}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x=120°

Step-by-step explanation:

angles on parallel lines ,there's an imaginary parallel line at x.

70 and 50 alternate respectively.

so x=50+70

x=120

Answer:

120 degrees

Step-by-step explanation:

I'm Big Brain

Answer:

1.0625 seconds

Step-by-step explanation:

Given that:

Initial velocity of Belinda, \(v_0=17\ ft/sec\)

Height in feet of Belinda above the trampoline is given as the formula:

\(d(t) = v_0t-16t^2\)

Where \(t\) is the time in seconds.

To find:

Time taken by Belinda to come back to trampoline = ?

Solution:

When Belinda will come back to trampoline, the height will be zero.

Putting \(d(t) =0\)

We have the equation as:

\(0 = 17t-16t^2\\\Rightarrow 16t^2-17t=0\\\because t\neq0\\\Rightarrow 16t=17\\\Rightarrow t=\dfrac{17}{16}\\\Rightarrow t =1.0625\ seconds\)

Therefore, the answer is: 1.0625 seconds

Answer:

First = 1251

Second = 1260

Third = 1268

Step-by-step explanation:

First: 9x

Second: 9(x+1)

Third: 9(x+2)

\({ \tt{first + second = 2511}} \\ { \tt{9x + 9(x + 1) = 2511}} \\ { \tt{9x + 9x + 9 = 2511}} \\ { \tt{18x = 2502}} \\ { \tt{x = 139}}\)

First = 9 × 139 = 1251

First = 9 × 139 = 1251Second = 9(139 + 1) = 1260

First = 9 × 139 = 1251Second = 9(139 + 1) = 1260Third = 9(139 + 2) = 1268

Answer:

16 rows, 8 seedlings left.

Step-by-step explanation:

Divide 200 by 12, since 200 seedlings are going to be split in 12 groups in order to fill the rows.

200 ÷ 12 = 16 with a remainder of 8.

The remainder is basically what is left.

Since 12 seedlings are planted in each row, 8 seedlings is not enough to completely fill the row. So, the answer is 16 rows with 8 seedlings left.

Hope this helped !

Using the given digits only once , the four 2 digit prime numbers are 23 , 41 , 59 , 67  and the the sum of the 4 prime numbers is 190 .

Prime Numbers can be defined as numbers that is greater than 1 and whose only factors are 1 and itself .

For Example : 2 is prime number , 11 is a prime number .

In the question ,

9 digits are given as 1, 2, 3, 4, 5, 6, 7, and 9  

we have to form 4 two - digit prime numbers , using each digit only once ,

So , the prime numbers using the given digits using the digits only once is

(i) 23

(ii) 41

(iii) 59

(iv) 67

and the sum of the 4 prime numbers is = 23 + 41 + 59 + 67

= 190

Therefore , the 4 prime numbers are 23 , 41 , 59 , 67 and their sum is 190 .

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The fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:

D = 1.24/4 = 0.31

Diffusiοn is the prοcess by which particles οf a substance mοve frοm an area οf high cοncentratiοn tο an area οf lοwer cοncentratiοn, resulting in a net mοvement οf particles dοwn their cοncentratiοn gradient.

This οccurs due tο the randοm mοtiοn οf individual particles, which leads tο a tendency fοr particles tο spread οut and becοme evenly distributed οver time.

Answer tο Questiοn 9:

The relatiοnship between average displacement squared (R²) and time (t) is linear.

Answer tο Questiοn 10:

The variable 'R2' in the diffusiοn equatiοn cοrrespοnds tο 'y' in the trendline equatiοn, and the variable 't' in the diffusiοn equatiοn cοrrespοnds tο 'x' in the trendline equatiοn.

Answer tο Questiοn 11:

We can sοlve fοr the diffusiοn cοnstant 'D' in terms οf the slοpe 'm' and a cοnstant 'c' by equating the diffusiοn equatiοn and the trendline equatiοn.

The diffusiοn equatiοn: R2 = 4Dt

The trendline equatiοn: y = mx + b

Substituting the cοrrespοnding variables, we get:

R2 = y, D = cοnstant, t = x, m = slοpe, b = cοnstant

Sο, we have:

R2 = 4Dt

y = mx + b

Equating the twο equatiοns, we get:

y = 4Dx + 0 (since b = 0)

Cοmparing this with the trendline equatiοn y = mx + b, we can see that:

m = 4D

Therefοre, we can sοlve fοr 'D' as:

D = m/4

Answer tο Questiοn 12:

Given the trendline equatiοn y = 1.24x + 5.63, we can see that the slοpe 'm' is 1.24.

Using the fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:

D = 1.24/4 = 0.31

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The area of the square is 1/4inches² in square inches

The area of a square is calculated by multiplying its two sides, that is area = s × s, where, 's' is one side of the square.

The square has side of length = 6/12

this can be simplified as 1/2

so

area of the square = (1/2 × 1/2) inches ²

area of the square = 1/4inches²

Thus, the area of the square is calculated using area = s × s, as 1/4inches²

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Answer:

-4

Step-by-step explanation:

The y-intercept of this graph is -4

Answer:

180-87 = 93

Step-by-step explanation:

supplementary angles add up to 180°

so (the other angle + 87)=180°

other angle =180-87=93°

Answer:

93 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees. Therefore, the equation for finding the supplementary angle to 87 would be:

\(87 + x = 180\\x=180-87\\x=93\)

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The boundary lines are y > -3x + 4: dotted line and  y <= 8x + 1: solid line

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

y > -3x + 4

y <= 8x + 1

The boundary line for the inequality "<" is a dotted line, which means that the endpoint is not included in the solution set.

The boundary line for the inequality ">=" is a solid line, which means that the endpoint is included in the solution set.

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There is not enough evidence to suggest that the percentage of students who smoke has changed over the last five years at a 5% level of significance.

To test whether there is a significant change in the percentage of students who smoke in the university, we can use a hypothesis test with the following hypotheses:

Null hypothesis (H0): The percentage of students who smoke has not changed over the last five years (p = 0.18).

Alternative hypothesis (Ha): The percentage of students who smoke has changed over the last five years (p ≠ 0.18).

We will use a two-tailed test with a significance level of 0.05. Using the sample data, we can calculate the sample proportion of smokers as 40/200 = 0.20.

Next, we can use the z-test statistic to calculate the p-value, which is the probability of observing a sample proportion as extreme as 0.20 or more extreme, assuming the null hypothesis is true. The z-test statistic is given by:

z = (p' - p) / √[p(1-p)/n]

where p' is the sample proportion, p is the hypothesized proportion under the null hypothesis, and n is the sample size.

Substituting the values, we get:

z = (0.20 - 0.18) / √[(0.18)(0.82)/200] = 1.13

Looking up the z-score in the standard normal table, we find that the corresponding two-tailed p-value is approximately 0.26.

Since the p-value (0.26) is greater than the significance level (0.05), we fail to reject the null hypothesis.

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Answer:

C. 4

Step-by-step explanation:

The initial value would be four because that's what the value is at the start of the graph.

The required order of solution for the given system equation,
1 No solution
2 Many solutions
3 One solution
4 No solution

Given a system of equations,
(1)

y = 5x + 7
3y -15x = 18

Since the slope of the equations are equal so this equation has no solution

(2)

x - 2y = 6
3x - 6y = 18
Since the slope of the equations is equal and also has an equal intercept so this equation has many solutions.

(3)

y=3x+6
y = -1/3x - 4
The slope of the equation of this line is the negative reciprocal of the other implying these lines are perpendicular to each other and have one solution.

(4)
y = 2/3x -1
y = 2/3x -2
Since the slope of the equations is equal so this equation has no solution.

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Answer:

i think light blue

Step-by-step explanation:

that or dark blue but you have to graph the answer to find where it lands.

Answer:

AB=BC

4X-1=1+2x so x=1 and both sides are 3

Step-by-step explanation:

since bd is a perpendicular bisector the two triangles formed are congruent so AB=BC

4X-1=1+2x so x=1 and both sides are 3

Freezing and thawing can cause significant damage to concrete. The repeated expansion and contraction of water within the concrete pores can lead to cracking, spalling, and reduced structural integrity.

When water freezes, it expands, exerting pressure on the surrounding materials. In the case of concrete, the water present in its pores expands upon freezing, creating internal stress. As the ice melts during thawing, the water contracts, causing the concrete to shrink. This cyclic process weakens the concrete's structure over time. The expansion and contraction of water can lead to various types of damage. Cracking occurs as a result of the tensile stress caused by ice formation and the subsequent contraction. These cracks can allow more water to penetrate, exacerbating the problem. Spalling refers to the flaking or chipping of the concrete surface due to the pressure exerted by the expanding ice. Freezing and thawing cycles can be detrimental to concrete, resulting in cracking, spalling, and reduced durability.

Proper precautions and construction techniques, such as using air-entrained concrete and adequate curing, can help mitigate these effects. Regular maintenance and timely repairs are also essential to prolong the lifespan of concrete structures in freezing climates.

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To build a concrete block wall, Kamila needs to determine the number of blocks required. The wall dimensions are 12 feet long, 6 feet high, and 8 inches thick. The task is to calculate number of blocks needed for wall.

To calculate the number of blocks needed, we first convert the wall dimensions to inches. The wall is 12 feet long, which is equivalent to 144 inches, and 6 feet high, equivalent to 72 inches. The thickness of the wall is 8 inches.

Next, we calculate the volume of each concrete block. The block measures 16 inches in length, 8 inches in width, and 8 inches in depth, resulting in a volume of 1024 cubic inches.

To determine the number of blocks needed, we divide the total volume of the wall by the volume of each block. The total volume of the wall is obtained by multiplying the length, height, and thickness, which gives 82,944 cubic inches.

Finally, by dividing the total wall volume by the block volume, we find that Kamila will need approximately 81 blocks to build the wall.

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The required answer is Kamila will need 81 concrete blocks to build the wall. To calculate the number of blocks Kamila will need to build the wall, we need to find the volume of the wall and divide it by the volume of each concrete block.

First, let's convert the measurements to a consistent unit. Since the dimensions of the concrete block are given in inches, we'll convert the length and height of the wall from feet to inches:

Length of the wall = 12 feet = 12 * 12 = 144 inches

Height of the wall = 6 feet = 6 * 12 = 72 inches

Thickness of the wall = 8 inches

Next, we'll calculate the volume of the wall:

Volume of the wall = Length * Height * Thickness

= 144 inches * 72 inches * 8 inches

= 82944 cubic inches

Now, let's calculate the volume of each concrete block:

Volume of each block = Length * Width * Depth

= 16 inches * 8 inches * 8 inches

= 1024 cubic inches

Finally, we'll divide the volume of the wall by the volume of each block to find the number of blocks needed:

Number of blocks = Volume of the wall / Volume of each block

= 82944 cubic inches / 1024 cubic inches

≈ 81 blocks

Therefore, Kamila will need approximately 81 concrete blocks to build the wall.

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The solution to the system is x = 2 and y = 6, represented as the ordered pair (2, 6). This corresponds to option (B) in the answer choices.

To solve the system using substitution, we'll substitute the value of one variable from one equation into the other equation and solve for the remaining variable.

Given the system:

x + y = 8

y = 3x

Substituting the value of y from the second equation into the first equation, we have:

x + (3x) = 8

4x = 8

x = 2

Now, substitute the value of x into the second equation to solve for y:

y = 3(2)

y = 6

Therefore, the solution to the system is (2, 6). Option (B) is the correct answer.

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Answer:

B

Step-by-step explanation:

Expanding the factors using FOIL

A

(x - 3)(x + 4)

= x² + 4x - 3x - 12

= x² + x - 12 ← a trinomial

B

(x + 3)(x - 3)

= x² - 3x + 3x - 9

= x² - 9 ← a binomial

C

(x - 3)² = (x - 3)(x - 3) = x² - 6x + 9 ← a trinomial

Answer:

"4" (and any subsequent words) was ignored because we limit queries to 32 words

35 is 78% of 45

Sure hope this helps you

Answer:

4096

Step-by-step explanation:

To get the highest answer, you must divide 128 by 2

128/2=64

Then you multiply it by each other.

64*64=4096

We know this is the largest because 128*1 is not the largest number as it is unbalanced. We need the most balanced answer. What is more balanced then 128/2?

Sorry if formatting is weird, first time answering questions

Given the expression

Use the facts that

So, the expression can be simplified as:

The number of hamburgers sold on Thursday is 106

Finding unknown quantity from Linear equation:

The Linear equation is a mathematical statement that is used to find an unknown quantity in a problem. Here to represent the Unknow qualities we use variables like x, y, z, etc.

Here we have,  

On Thursday, a local hamburger shop sold a combined total of 424 hamburgers and cheeseburgers.

Since we don't know the number of hamburgers and cheeseburgers.

Represent them with variables x and y  

Let x be the number of hamburgers

and y be the number of cheeseburgers

=> x + y = 424 ----(1)

Given that,

The number of cheeseburgers sold was three times the number of hamburgers sold  

=> y = 3x -----(2)

From (1) and (2)

=> x + 3x = 424  

=> 4x = 424

=> x = 106

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The complete question is

On Thursday, a local hamburger shop sold a combined total of 424 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Thursday?  

The present value of the annuity is $4,813.52.

To calculate the present value of the annuity, we can use the formula for the present value of an increasing annuity:

PV = C * (1 - (1 + r)^(-n)) / (r - g)

Where:

PV = Present Value

C = Payment amount at time t=1

r = Interest rate

n = Number of payments

g = Growth rate of payments

In this case:

C = $300

r = 8% or 0.08

n = Number of payments = Last payment amount - First payment amount / Growth rate + 1 = ($1000 - $300) / $50 + 1 = 14

g = Growth rate of payments = $50

Plugging in these values into the formula, we get:

PV = $300 * (1 - (1 + 0.08)^(-14)) / (0.08 - 0.05) = $4,813.52

Therefore, the present value of this annuity is $4,813.52. This means that if we were to invest $4,813.52 today at an interest rate of 8%, it would grow to match the future cash flows of the annuity.

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