Solve the following system of equations using the method of substitution: 3x+2x=11 y=x+3

Answer:

143°

When solving angle problems, make sure to label the other angles (even the ones that are not asked) and use them to relate to each other to find the answer.

Answer:

B. Isosceles right triangle

C. Quadrilateral

D. Parallelogram

Step-by-step explanation:

Answer:

The geometric figures that could describe how the garden might look are B. Isosceles right triangle and C. Quadrilateral.

Answer:

27.18

Step-by-step explanation:

Firstly, you must label the triangle.

r- opposite

13.85- adjacent

We know that tan θ = opposite/ adjacent so we substitute our numbers into the equation.

tan (63) = r/13.85

Then, times 13.85 on both sides so we only have our unknown on one side.

(x13.85)  tan(63)= r/13.85   (x13.85)

r= tan (63) x 13.85

r=27.18

:)

Answer:

B

Step-by-step explanation

After running the given code, Karel will be at Street 2 and Avenue 2, facing North.

Here is a step-by-step explanation of what the code does:

   move(); - Karel moves one block east, to Street 1 and Avenue 2.

   turnLeft(); - Karel turns left to face north.

   putBall(); - Karel puts a ball at Street 1 and Avenue 2.

   turnLeft(); turnLeft(); turnLeft(); - Karel turns left three times to face south.

   move(); - Karel moves one block south to Street 2 and Avenue 2.

   turnLeft(); - Karel turns left to face east.

So after executing this code, Karel will be at Street 2 and Avenue 2, facing North.

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The percent error from the real and estimated values is 16%.

The difference between a precise value and an approximation to it is the approximation error in a data value. Either an absolute mistake or a relative error can be used to describe this error. It is possible for measurement mistake or computing machine precision to produce an approximation error. The percent error is the distinction between the estimated value and the real value in relation to the actual value. In other terms, the relative error is multiplied by 100 to calculate the percent error.

The estimated value= 170

the real value= 147

Percent error ={ (170-147)/147}*100= 0.1564*100

Percent error = 15.64% ≈ 16%

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The value of lim f(x)g(x) as x approaches infinity is 0.

L'Hopital's rule is a mathematical tool used to evaluate limits of functions that are in an indeterminate form.

To find the limit of f(x)g(x) as x approaches infinity, we can use L'Hopital's rule since it is an indeterminate form of infinity times zero. We have:

lim x→[infinity] f(x)g(x) = lim x→[infinity] [(3x + 2e^(-3x))(1/x + 4)]

= lim x→[infinity] [(3 + 2e^(-3x)/x)/(1/x + 4)^(-1)]

Applying L'Hopital's rule to the fraction in the numerator, we get:

lim x→[infinity] [(2e^(-3x)(-3)/x^2)/(1/x + 4)^(-1)]

= lim x→[infinity] [(6e^(-3x)/x^2)/(1/x + 4)]

= lim x→[infinity] [(6e^(-3x)/(x + 4x^2))]

= 0

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The probability that a randomly selected component is shorter than 7 inches long is approximately 25.14%.

We are given that the lengths of components produced by the automatic press are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches.

We need to find the probability that a randomly selected component is shorter than 7 inches long.

We can use the standard normal distribution to find this probability. We first need to convert the length of 7 inches to a z-score:

z = (7 - 8) / 1.5 = -0.67

Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the probability that a randomly selected component is shorter than 7 inches long:

P(z < -0.67) = 0.2514

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Answer:

To factor 30b³-54b², we can factor out the greatest common factor of 6b² to get:

30b³-54b² = 6b²(5b-9)

To factor 35-48y³, we can notice that it is a difference of cubes:

35-48y³ = (5)³ - (4y)³ = (5-4y)(25+20y+16y²)

To factor x³+8, we can use the sum of cubes formula:

x³+8 = (x+2)(x²-2x+4)

To factor 3-64, we can use the difference of squares formula:

3-64 = (1)² - (8)² = (1+8)(1-8) = -7(-9) = 63

To factor 8c³+343, we can use the sum of cubes formula:

8c³+343 = (2c)^3 + 7³ = (2c+7)(4c²-14c+49)

To add or subtract complex polynomials, we simply combine like terms. For example:

(3x²+2x-5) + (4x²-3x+7) = 7x²-x+2

To multiply complex polynomials, we can use the distributive property and FOIL method. For example:

(2x+1)(3x-4) = 6x²-5x-4

To factor complex polynomials, we can use various methods such as factoring out the greatest common factor, using the difference of squares formula, using the sum or difference of cubes formula, or factoring by grouping.

The formulas provided are for factoring the sum or difference of cubes:

These formulas can be useful for factoring complex polynomials that have a cube term or a constant term in addition to the quadratic and linear terms.

Answer:

x/8 + 6 = 4

Step-by-step explanation:

x / 8 + 6 = 4

x/8 = -2

x = 8*-2 = -16.

The maximum possible number of handshakes that can happen at the party with 23 people with at most 22 other people is 253. This is calculated by combination.

Twenty-three people attend a party. each person shakes hands with at most 22 other people.

To find the maximum possible number of handshakes, assuming that any two people can shake hands at most once, we need to use Combination by finding the number of unique pairs of people in the party.

nCr (combination) to find the number of unique pairs of people.

Therefore,[tex]^nC_r = \frac{n!}{(n-r)!  r!}[/tex]

where n is the total number of people and r is the number of people in a handshake at a time.

Therefore, the number of unique pairs of people that can shake hands at most once is:

[tex]^{23}C_2 = \frac{23!}{(23-2)!  (2!)}[/tex] [tex]=\frac{23 X22}{2} = 253[/tex]

Hence, the maximum possible number of handshakes that can happen at the party is 253.

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Answer: -109

Step-by-step explanation:

Concept : First take note of what operations are in play and how they relate to y. In this case, -10 is being multiplied to y and then 19 is subtracted from the product of -10 and y.

Steps:

Plug 9 in for y (parentheses just mean multiply):

-10(9)-19

Simplify using correct order of operations:

-90-19

-109

Hope this helps :)

To find:-

Answer:-

To find out the equation of the line , we need to find out the slope first. It can be calculated as ,

[tex]\implies m =\dfrac{\Delta y}{\Delta x }=\dfrac{y_2-y_1}{x_2-x_1} \\[/tex]

And here ,

On substituting the respective values, we have;

[tex]\implies m =\dfrac{25-20}{8-3} \\[/tex]

[tex]\implies m=\dfrac{5}{5}\\[/tex]

[tex]\implies m=\boxed{1} \\[/tex]

Hence the slope of the line is 1 . Now we may use point slope form of the line to find out the equation of the line. Point slope form of the line is,

[tex]\implies y - y_1 = m(x-x_1) \\[/tex]

Take any of the given two points. Here i am taking (3,20) . So here we have;

On substituting the respective values, we have;

[tex]\implies y - 20 = 1(x - 3) \\[/tex]

[tex]\implies y -20 = x - 3 \\[/tex]

[tex]\implies x - 3 - y +20 = 0 \\[/tex]

[tex]\implies \underline{\underline{\green{ x - y +17=0}}}\\[/tex]

Hence the equation of the line in standard form is x - y + 17 = 0 .

and we are done!

The Shalane should keep her shop open all year round to maximize her sales and revenue.

The scatter plot with a line of best fit that was generated with technology reveals that when the temperature outside is higher, more snow cones are sold in Panama City, Florida. Since the line has a positive slope, it means that as the temperature outside increases, the number of snow cones sold also increases. As a result, if Shalane were to keep her shop open all year round, she might generate more revenue by providing snow cones during the warmer months, when more people are inclined to purchase them.Therefore, based on the scatter plot with a line of best fit that was generated with technology, Shalane should keep her shop open all year round to maximize her sales and revenue.

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Answer:

We can use the formula for the area of a triangle which is given by:

Area = (1/2) x base x height

Where the base and height are the two sides that form the right angle.

Looking at the given triangle, we can see that the sides 3 in. and 5 in. form the right angle, so the base is 3 in. and the height is 5 in.

Therefore, the area of the triangle is:

Area = (1/2) x 3 in. x 5 in.

Area = 7.5 in²

Alternatively, we could also use the sides 2.5 in. and 6 in. to find the area of the triangle. In this case, the base would be 2.5 in. and the height would be 5 in. (since the 6 in. side is not perpendicular to the 2.5 in. side). So the area of the triangle would still be:

Area = (1/2) x 2.5 in. x 5 in.

Area = 6.25 in²

Either way, the area of the triangle is approximately 7.5 in² or 6.25 in², depending on which set of sides we use.

Step-by-step explanation:

The required correct answers are [tex]$$H_0: p = 0.08$$[/tex] , [tex]$$H_a: p < 0.08$$[/tex].

Let p be the proportion of residents in the town who are unemployed. The null hypothesis [tex]$H_0$[/tex] is that the proportion of unemployed residents in the town is the same as the national unemployment rate of 8%. The alternative hypothesis [tex]$H_a$[/tex] is that the proportion of unemployed residents in the town is significantly lower than the national unemployment rate.

Using the appropriate notation, the hypotheses can be expressed as:

$H_0: p = 0.08$

$H_a: p < 0.08$

Therefore, the appropriate set of hypotheses for the mayor's significance test are:

[tex]$$H_0: p = 0.08$$[/tex]

[tex]$$H_a: p < 0.08$$[/tex]

Note that this is a one-tailed test since the alternative hypothesis is only considering the possibility of the proportion being lower than the national unemployment rate

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Option a. (All of the above (1, 2, and 3)) is the right answer to the question regarding the key ingredients of a confidence interval based on the Central Limit Theorem.

A confidence interval is a statistical estimate of a population parameter with a level of confidence or certainty.

The Central Limit Theorem states that the distribution of the means of a sufficiently large sample size from a population with a finite variance will be approximately normal, regardless of the population's actual distribution.

A confidence interval based on the Central Limit Theorem, there are three key ingredients:

1. A summary statistic (e.g. a mean) from your sample

2. A multiple z, based on a tail area from the normal distribution.

3. A formula for the standard error of your summary statistic.

For a given level of confidence, the z-score corresponds to the number of standard deviations from the mean. The standard error of a summary statistic is a measure of the variability of the estimate that is dependent on the size of the sample, the variability of the population, and the type of summary statistic. The standard error of a sample mean is given by the formula σ/√n, where σ is the population standard deviation and n is the sample size.

Thus, all the above points (1, 2, and 3) are the key ingredients of a confidence interval based on the Central Limit Theorem.

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Answer:

Step-by-step explanation:

The predicted fuel efficiency for a speed of 30 miles per hour is given as follows:

26.50 mpg.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is defined as follows:

In(Fuel Efficiency) = 1.437 + 0.541 In(Speed).

The speed is of 30 miles per hour, hence the predicted fuel efficiency is given as follows:

In(Fuel Efficiency) = 1.437 + 0.541 x In(30).

In(Fuel Efficiency) = 3.277.

The exponential is the inverse of the ln, hence:

Fuel Efficiency = e^3.277

Fuel Efficiency = 26.50 mpg.

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An appropriate theorem to show that the given set, W, is a vector space. A specific example can be

[tex]\left[\begin{array}{ccc}p\\q\\r\end{array}\right][/tex] , -p- -3q = s  and 3p = -2s - 3r

Sets represent values ​​that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.

The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.

The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.

The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.

Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is

S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties

u +v =y+ u and (u + v)+w=u + (v +W).

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The answer is: C. 1.5%

Answer:

Step-by-step explanation:

Calculate fraction of boys

If girls =3/5, then boys = 1 - 3/5 = 2/5.

Calculate fraction of students absent

Girls - 2/5 of 3/5 = 6/25

Boys - 1/3 of 2/5 = 2/15

6/25+2/15=28/75

Calculate total number of students

If 28/75 = 280

280/28=10

10x75=750

Total number of students = 750

Answer:

m = -3/4

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0, -2) (-3,2)

We see the y increase by 4 and the x decrease by 3, so the slope is

m = -3/4

Answer:

x = 8500

y = 15000

Step-by-step explanation:

small vans: x

large vans: y

A: 5x + 2y = 72500

B: 2x + 6y = 107000

5x + 2y = 72500 => y = (72500 - 5x)/2

2x + 6(72500 - 5x)/2 = 107000

2x + 217500 - 15x = 107000

15x - 2x = 217500 - 107000

13x = 110500

x = 110500/13 = 8500

y = (72500 - 5x)/2 = y = (72500 - 5x8500)/2 = 15000

The solution to the system of equations is (15, 30).

A group of two or more equations that must be solved all at once is known as a system of equations. The system's equations each show how two or more variables relate to one another. The variables' values that satisfy every equation in the system can be discovered using algebraic techniques.

Algebraic systems of equations can be solved using a variety of techniques, such as substitution, elimination, and graphing. The substitution approach involves solving one equation for one variable in terms of the other variable, and then substituting the result for that variable's expression into the other equation.

The given system of equations are y=x + 15, y= 2x.

Substitute the value of y from equation 2 in equation 1:

x + 15 = 2x

15 = x

Substitute the value of x to get the value of y:

y = 2x = 2(15) = 30

Hence, the solution to the system of equations is (15, 30).

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Answer:

you need to show the numbers

Step-by-step explanation:

Answer:

[tex]\textsf{$\boxed{\checkmark}\;\;y$-value\;of\;vertex\;is\;$-1$}[/tex]

[tex]\textsf{$\boxed{\checkmark}$\;\;Minimum\;value\;occurs\;at\;$y = -1$}[/tex]

Step-by-step explanation:

Given equation:

[tex]y=x^2+8x+15[/tex]

As the given equation is quadratic with a positive leading coefficient, it is a parabola that opens upwards. Therefore, its vertex is its minimum point. This means that the minimum value of the range is the y-value of the vertex.

The x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a. Therefore, the x-value of the vertex of the given equation is:

[tex]\implies x=\dfrac{-8}{2(1)}=-4[/tex]

To find the y-value of the vertex, substitute x = -4 into the equation:

[tex]\begin{aligned}\implies y&=(-4)^2+8(-4)+15\\&=16-32+15\\&=-16+15\\&=-1\end{aligned}[/tex]

Therefore, the minimum y-value of the function is y = -1, so the range is y ≥ -1.

Therefore, the following are true statement about the given equation:

Answer:

b ≈ 12.1

Step-by-step explanation:

using the tangent ratio in the right triangle

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{7}[/tex] ( multiply both sides by 7 )

7 × tan60° = b , then

b ≈ 12.1 ( to the nearest tenth )

The nth term of the sequence is 2^n.

(a) 3, 3, 3, 3, ... is a sequence that has 0 for both its first and second differences. That is, every term in the sequence is the same.(b) The sequence is the series of natural numbers. It has 0 for its first and second differences, and 6 for its third differences. The nth term of the sequence is n.(c) The sequence has 0 for its first 99 differences and 100! for its 100th difference. The nth term of the sequence is 2^n.

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