In the figure below, line m is parallel to line n. If m∠3 = (12x + 5) degrees and m∠5 = (30x - 35) degrees:


a) Solve for x.


b)Find the angle measure of all eight angles below.

The value of the expression x² + 10x, when x = 2 is 24.

In the expression x² + 10x, x represents a variable, which is a placeholder for a value that can change. We are given that x = 2, which means we substitute 2 for x in the expression:

x² + 10x = 2² + 10(2)

Here, 2² means 2 raised to the power of 2, which is 2 multiplied by itself: 2² = 2 x 2 = 4.

10(2) means 10 multiplied by 2, which is 20.

So we can substitute these values in the expression:

x² + 10x = 2² + 10(2)

= 4 + 20

= 24

Therefore, when x is equal to 2, the value of the expression x² + 10x is 24.

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The complete question:

Evaluate the expression x² + 10x, when x = 2.

Answer:

only god knows

Step-by-step explanation:

because they didn't give us an answer on how many text messages anyone sent

Answer: 87.964594300514 feet3 or 87.96 feet3

Step-by-step explanation:

πr^2 h

=  π×2^2×7

=  28π

=  87.964594300514 feet3

The function which represents the graph is : D. y = 3sin(x)

"A function is an expression which assigns each element of X to exactly one element of Y from a set X to a set Y."

"The graph of a function f is the set of all points in the plane of the form (x, f(x))."

"The graph of y=sin(x) is like a wave that oscillates between -1 and 1, in a shape that repeats itself every 2π units.

Also, the graph of sine function passes though origin, as sin(0) = 0 ."

"The graph of y=cos(x) is like the graph of y=sin(x) but shifted horizontally by π units"

From given graph, we can observe that the graph must be of sine function.

Also, given graph represents the graph of y = sin(x) expanded 3 times.

So, the function which represents the graph is, y = 3sin(x).

Hence, the correct answer is option D. y = 3sin(x)

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x>23/5 is the answer

The friend makes a calculation error.

5x - 11 > 12

5x > 12 + 11

5x > 23

x > 23/5

A "mathematical error" when the calculation you entered makes mathematical sense, but the result cannot be calculated. If you try to divide by zero or the result is too large.

error, in applied mathematics, the difference between a true value and an estimate or approximation of that value. A common example in statistics is the difference between the mean of an entire population and the mean of a sample drawn from the population.

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Using the formula for the standard deviation and solving for x, we will get:

x = 7.6

To find the positive value of 'x' in the given set of numbers (3, 6, x, 7, 5) when the standard deviation is √2, we can use the formula for standard deviation.

The formula for calculating the sample standard deviation is as follows:

σ = √[(Σ(xi - m)²) / (n - 1)]

Where:

First, let's calculate the mean (m) of the given set of numbers:

Mean (m) = (3 + 6 + x + 7 + 5) / 5 = (21 + x) / 5

Next, let's substitute the values into the standard deviation formula:

√2 = √[( (3 - (21 + x) / 5)² + (6 - (21 + x) / 5)² + (x - (21 + x) / 5)² + (7 - (21 + x) / 5)² + (5 - (21 + x) / 5)² ) / 4]

Simplifying the equation:

2 = [( (3 - (21 + x) / 5)² + (6 - (21 + x) / 5)² + (x - (21 + x) / 5)² + (7 - (21 + x) / 5)² + (5 - (21 + x) / 5)² ) / 4]

Multiplying both sides of the equation by 4:

8 = (3 - (21 + x) / 5)² + (6 - (21 + x) / 5)² + (x - (21 + x) / 5)² + (7 - (21 + x) / 5)² + (5 - (21 + x) / 5)²

Expanding and simplifying:

8 = (15 - (21 + x) / 5)² + (30 - (21 + x) / 5)² + (5x/5)² + (35 - (21 + x) / 5)² + (25 - (21 + x) / 5)²

8 = (15 - (21 + x) / 5)² + (30 - (21 + x) / 5)² + x² + (35 - (21 + x) / 5)² + (25 - (21 + x) / 5)²

Expanding and simplifying further:

8 = (225 - 2(21 + x) + (21 + x)² / 25) + (900 - 2(21 + x) + (21 + x)² / 25) + x² + (1225 - 2(21 + x) + (21 + x)² / 25) + (625 - 2(21 + x) + (21 + x)² / 25)

Combining like terms:

8 = (225 + 900 + 1225 + 625) / 25 - 10(21 + x) + 5(21 + x)² / 25 + x²

8 = 2975 / 25 - 10(21 + x) + 5(21 + x)² / 25 + x²

Simplifying:

8 = 119 - 10(21 + x) + (21 + x)² / 5 + x²

Rearranging the terms:

8 - 119 = -10(21 + x) + (21 + x)² / 5 + x²

-111 = -10(21 + x) + (21 + x)² / 5 + x²

Multiplying through by 5 to eliminate the fraction:

-555 = -50(21 + x) + (21 + x)² + 5x²

Expanding and simplifying:

-555 = -1050 - 50x + x² + 441 + 42x + x² + 5x²

Combining like terms:

0 = 7x² - 8x - 114

Now, we can solve this quadratic equation to find the value of 'x'.

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 7, b = -8, and c = -114.

Plugging the values into the formula:

x = (-(-8) ± √((-8)² - 4(7)(-114))) / (2(7))

Simplifying:

x = (8 ± √(64 + 3192)) / 14

x = (8 ± 2√(814)) / 14

x = (4 ± √(814)) / 7

Therefore, the values of 'x' that satisfy the given equation are approximately:

x ≈ (4 + √(814)) / 7 ≈ 7.62

x ≈ (4 - √(814)) / 7 ≈ -0.29

Since we are looking for the positive value of 'x', the solution is:

x ≈ 7.6

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The surface area of given triangular prism = 24 ft².

For the given triangular prism

Base = 2 ft

height = 3 ft

side = 3ft

We know that,

Surface area of triangular prism

= side x base + 3x base x height

=  3 x 2  + 3x2x3

= 6 + 18

= 24 ft²

Thus,

Surface area = 24 ft²

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Answer:

0.9945 = 99.45% probability that the student answers at most four questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student answers correctly, or he/she does not. The probability of the student answering a question correctly is independent of any other question. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

A quiz consists of six multiple choice questions.

This means that \(n = 6\)

Each question has four choices. Student guesses randomly.

This means that \(p = \frac{1}{4}\)

What is the probability that the student answers at most four questions correctly?

This is:

\(P(X \leq 4) = 1 - P(X > 4)\)

In which

\(P(X > 4) = P(X = 5) + P(X = 6)\). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 5) = C_{6,5}.(0.25)^{5}.(0.75)^{1} = 0.0053\)

\(P(X = 6) = C_{6,6}.(0.25)^{6}.(0.75)^{0} = 0.0002\)

\(P(X > 4) = P(X = 5) + P(X = 6) = 0.0053 + 0.0002 = 0.0055\)

\(P(X \leq 4) = 1 - P(X > 4) = 1 - 0.0055 = 0.9945\)

0.9945 = 99.45% probability that the student answers at most four questions correctly

The volume of the cylinder is 623.17 cubic inches.

We have,

The volume of a cone is given by the formula V = (1/3)πr²h,

where r is the radius of the base and h is the height.

The volume of a cylinder is given by the formula V = πr²h,

where r is the radius of the base and h is the height.

Since the cone and cylinder have the same radius and height, we can set the equations for their volumes equal to each other:

(1/3)πr²h = πr²h

We can simplify this equation by multiplying both sides by 3:

πr²h = 3(1/3)πr²h

Simplifying further, we get:

πr²h = πr²(3h/3)

πr²h = πr²(3/1)

πr²h = 3πr²

Canceling the πr² from both sides, we get:

h = 3

We now know that the height of the cone and cylinder is 3.

We can use the given volume of the cone to solve for the radius:

V = (1/3)πr²h

162 = (1/3)πr²(3)

162 = πr²

r² = 162/π

r ≈ 6.4615

Now that we know the radius and height of the cylinder, we can use the formula for the volume of a cylinder to find its volume:

V = πr²h

V = π(6.4615)²(3)

V ≈ 623.17 cubic inches

Therefore,

The volume of the cylinder is 623.17 cubic inches.

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To find out how many flowers will be in each centerpiece, we can divide the total number of flowers by the number of centerpieces:

Total number of flowers: 1,064

Number of centerpieces: 28

Number of flowers in each centerpiece = Total number of flowers / Number of centerpieces

Number of flowers in each centerpiece = 1,064 / 28 = 38

Therefore, there will be 38 flowers in each centerpiece.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer: 38

Step-by-step explanation:

The question is asking you to divided.

1064 divided by 28 = 38

So there will be 38 flowers in each centerpiece

The Shorter route as per the bearing calculations is taken up by Julia.

What is a bearing?

Bearing calculations are illustrated below:

Route Taken up by Anna

360-330= 30°

First angle =90-30= 60°

Second angle= 60+(90-40) =110°

Third angle= 180-(110+30)= 40°

Route taken up by Julia:

First angle =20°

Second angle= 300-(180+20)=100°

Third angle=180-(20+100)=60°

Hence, the Shorter route as per the bearing calculations is taken up by Julia and bearing diagram is attached with the solution as an image.

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Answer:

-5

Step-by-step explanation:

The conclusion is option A, we cannot reject the null hypothesis.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

The null hypothesis cannot  be rejected for the entire population if your sample is not sufficiently incompatible with it, which can be determined if your P value is small enough.

Therefore, we can not reject the hypothesis.

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\(\huge\text{Hey there!}\)

\(\large\textsf{-12 + (-8) + 30}\\\\\large\textsf{= -12 - 8 + 30}\\\\\large\textsf{-12 - 8 = \bf -20}\\\\\large\textsf{= -20 + 30}\\\\\large\textsf{= \bf 10}\\\\\\\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf{10}}}}\huge\checkmark\\\\\\\\\huge\textsf{Good luck on your assignment \& enjoy your day!}\)

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we have drawn the graph of the inequality - 6 > t - ( - 13 ) which can also be written as t < - 19.

We are given an inequality:

- 6 > t - ( - 13 )

- 6 > t + 13

t + 13 < - 6

Subtract 13 from both the sides, we get that:

t + 13 - 13 < - 6 - 13

t < - 19

Now, we have to graph the inequality.

The line of the inequality will be t = - 19 which will be dotted as t is not equal to - 19.

The following graph is obtained.

Therefore, we have drawn the graph of the inequality - 6 > t - ( - 13 ) which can also be written as t < - 19.

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If the triple point of iodine is at 90 torr and 115°C , then the true statement about liquid I₂(l) is (d)I₂(l) cannot have a vapor pressure greater than 90 torr.

In the question ,

it is given that ,

Iodine substance exhibits three phases , solid , liquid and gases .

The iodine gas over solid l₂ is the molecule of iodine that has evaporated

, If the iodine pressure is low enough , it will resublime on cooling without going through the liquid phase .

So , the point in the gas phase that has temperature > 115°C ,

So , the curve move horizontally right ,

we can see that the pressure can be > 90 torr .

hence the statement (d) concerning liquid I₂(l) is True .

Therefore , the correct option is (d) .

The given question is incomplete , the complete question is

Iodine, like most substances, exhibits only three phases: solid, liquid, and vapor. The triple point of iodine is at 90 torr and 115 °C. Which of the following statements concerning liquid I₂(l) must be true?

a. I₂(l) is more dense than I₂(g).

b. I₂(l) cannot exist above 115°C.

c. I₂(l) cannot exist at 1 atmosphere pressure.

d. I₂(l) cannot have a vapor pressure greater than 90 torr.

e. I₂(l) cannot exist at a pressure of 10 torr.

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Answer:

C) 2.7 x 10-15

Step-by-step explanation:

Sorry if I'm wrong. hope you're having a great day

The computation shows that the value of (9 x 10−13) − (6.3 x 10−15) is C. 2.7 x 10−15

Simplify (9 x 10−13) − (6.3 x 10−15).

This will be solved as follows. It should be noted that one just have to subtract the values.rhat are given based on the information above.

Therefore, (9 x 10−13) − (6.3 x 10−15).

= 2.7 x 10−15

In conclusion, the correct option is C.

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Answer:

jordan caught 13 butterflies

Step-by-step explanation:

25-12=13

14

Step-by-step explanation:

start at 12 the count to 25 on your fingers

Answer:

the answer is 7, because x<8 means less than 8 so it's 7

Step-by-step explanation:

hope this helps!

Answer:

B is the right answer

Step-by-step explanation:

Try the first Point ( -2 ,1 )

1 = -2 x 2 + 5

Answer:

she will use 4.

Step-by-step explanation:

kajsbsbsjajaja

The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

The volume of the liquid in the bowl is given by the following integral:

\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)

where r = radius of the bowl and y = height of the liquid.

The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:

r = √{(4/(8-x)) - 1}² + 1²

The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:

h = (4/(8-x)) - 1

Substituting these equations into the volume integral:

\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)

Evaluate this integral using the following steps:

Expand the parentheses in the integrand.

Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.

Integrate each part separately.

The integral of the square root term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)

The integral of the linear term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)

Substituting these formulas into the integral:

V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h

Evaluating this integral:

V = π { 16/27 (8-h)³ - 16/18 (8-h)² }

The rate of change of the volume of the liquid is given by:

dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }

The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.

Substituting these values into the equation for dV/dt:

dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π

Solving this equation for the rate of change of the depth of the liquid:

dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹

Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

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What are you trying to solve for?

\(824381 + 1654 = - 121\)

Answer:

216.00 = 134.22

Step-by-step explanation:

216.1 =134.22

Answer:

5 hours

Step-by-step explanation:

120/60= 2

120/40= 3

3+2=5

Answer:

Option A

Step-by-step explanation:

Option A is an arithmetic sequence.

Each week, the salary goes up by a fixed $50.

To verify this, subtract any two consecutive weeks' salaries.

For example: $250 - $200 = $50; $350 - $300 = $50, etc.

The common difference in 50.

We have an arithmetic sequence with 20 terms. The first term is $200. We need to find the sum of the 20 terms.

The sum of an arithmetic sequence is given by the formula:

\( S_n = \dfrac{n}{2} \times [2a_1 + (n - 1)d] \)

S_n = sum of first n terms

n = number of terms = 20

a_1 = first term = 200

d = common difference = 50

\( S_{20} = \dfrac{20}{2} \times [2(200) + (20 - 1)(50)] \)

\( S_{20} = 10 \times [400 + 19(50)] \)

\( S_{20} = 10 \times [400 + 19(50)] \)

\( S_{20} = 13500 \)

Option A gives a total of $13,500 for the first 20 weeks.

Option B is a geometric sequence in which the salary goes up by 10% each week. To verify this, divide any salary by the previous week's salary.

For example: $220/$200 = 1.10; $266.20/$242 = 1.10; in each case, each salary is 1.1 times the previous week's salary which means a 10% increase. The common ratio of the geometric sequence is 1.1.

We need the formula for the sum of the first n terms of a geometric sequence.

\( S_n = \dfrac{a_1(1 - r^n)}{1 - r} \)

\( S_{20} = \dfrac{200(1 - 1.1^{20})}{1 - 1.1} \)

\( S_{20} = \dfrac{200(1 - 6.7274999)}{-0.1} \)

\( S_{20} = 11455 \)

Option B gives a total of $11,455 for the first 20 weeks.

Answer: Option A

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

534.07cm² * 0.35=186.9245 dollar

Answer: y=-3/4x

Step-by-step explanation:

The slope intercept form is when you use the equation y=mx+b (m is the slope and b is the y-intercept). First, let's find the y intercept. The y intercept is what y would be if x is 0. here, you can see that this particular line passes through the origin. So, the y-intercept is zero because when x passes through zero, y is also zero. Next, let's find the slope. The formula for slope is change in y/change in x. Let's randomly choose 2 points off this line. To make this a thousand times easier for us, let's choose the points (-4, 3) and (4, -3). Now, to find the change in y, let's find the difference between the 2 y coordinates we have chosen. To do this we just need to do -3-3, which gives us -6. Now let's find the change in x. To do this we will do the same thing we did to find the change in y but this time we'll use the x coordinates. We will do 4-(-4), which simplifies to 8. Now, we're almost done. Just divide the change in y by the change in x. You will get -6/8. This can be simplified to -3/4. So now we know our slope is -3/4 and our y-intercept is 0. Let's insert them into the equation. y=-3/4x+0. We know that we can just get rid of that 0 because 0 literally means nothing. So our final answer is y=-3/4x. Hope this helps!