Direct variation: if y = 4, when x = -2, find x when y = 6

Given that value of y exceeds a, then value of a must be smaller than -8.2.

The provided equation is-

(13-20- A* 13y)= 168* 13-22

We get,

By 260, divide both sides.

Y has a value of -8.265.

Thus, provided that y exceeds a, then value of a must be smaller than -8.2

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The correct question is-

What is the value of (a,y) in (13-20- A* 13y)= 168* 13-22?

Answer:

Step-by-step explanation:

what i do not undersante

The number that is divisible by both 2 and 4 is option c. 2,836.

To determine which number is divisible by both 2 and 4, we need to identify the number that is divisible by the prime factorization of both 2 and 4.

To be divisible by 2, a number must be even, meaning it should end with 0, 2, 4, 6, or 8. Looking at the given options, we can eliminate options a. 1,022 and d. 2,918 because they end with 2 and 8 respectively.

To be divisible by 4, a number must be divisible by 2 twice. In other words, the last two digits of the number should form a multiple of 4. Examining the remaining options b. 1,974 and c. 2,836, we find that only option c. 2,836 satisfies this condition. The last two digits of 2,836, 36, form a multiple of 4 (9 times 4 is 36).

Therefore, the number 2,836 is divisible by both 2 and 4, hence the correct answer is: c.2,836

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Answer:

The factors are,

x + 12 and x - 2

Step-by-step explanation:

x^2 + 10x - 24,

Here, we note that,

12 - 2 = 10,

and (12)(-2) = 24,

so, we  can re-write 10x as 10x = 12x - 2x

so,

\(x^2 + 12x - 2x - 24 = 0\)

Taking x common from the 1st two terms (x^2 and 12x),

and taking -2 common from the last two tems (-2x and -24), we get,

\(x^2 + 12x - 2x - 24 \\x(x+12)-2(x+12)\\taking \ (x+12) \ common,we \ get,\\(x+12)(x-2)\)

So, The factors are,

x + 12 and x - 2

The correct angle for a ladder is about 75 degrees from the ground, and you have a 15-foot ladder.

You need to determine how far from the house you should position the ladder's base if you know these fact.
Step 1: It is crucial to keep in mind that the height of the ladder is the same as the vertical distance between the base and the wall.
Step 2: Consider the height of the ladder to be the "opposite" side of the triangle, and the distance you want to find as the "adjacent" side of the triangle. In this scenario, we're looking for the distance from the house (the base of the ladder) to the wall, which will be the adjacent side.
Step 3: To figure out the length of the adjacent side, we'll need to use the tangent of the angle, which is given by the following formula:tan(θ) = opposite/adjacent
Step 4: The angle is 75 degrees, and the opposite side's length is 15 feet, so we can solve for the adjacent side as follows: tan(75) = 15/adjacent
Step 5: Rearranging the equation: adjacent = 15/tan(75)Step 6: Using a calculator, tan(75) is approximately 3.732, so: adjacent = 15/3.732 ≈ 4.01

Therefore, the base of the ladder should be approximately 4.01 feet from the wall (rounded to the hundredths place).

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Answer: cosφ=-3/5

Step-by-step explanation:

\(\displaystyle\\sin\phi=\frac{4}{5} \ \ \ \ \ 90^0 < \phi < 180^0\\\\sin^2\phi+cos^2\phi=1\\\\\cos^2\phi=1-sin^2\phi\\\\cos^2\phi=1-(\frac{4}{5})^2\\\\ cos^2\phi=1-\frac{16}{25} \\\\cos^2\phi=\frac{1(25)-16}{25}\\\\ cos^2\phi=\frac{25-16}{25} \\\\cos^2\phi=\frac{9}{25} \\\\cos\phi=б\sqrt{\frac{9}{25} } \\\\cos\phi=б\sqrt{\frac{3^2}{5^2} }\\\\cos\phi=б\sqrt{(\frac{3}{5})^2} \\\\cos\phi=б\frac{3}{5} \\\\90^0 < \phi < 180^0\\\\Hence,\ \\\\cos\phi=-\frac{3}{5}\)

The 40th percentile for these test results is 74,  the 40th percentile is a score equal to or greater than the 12th score in the ordered list. Counting from the top of the list, the 12th result is 74.

To discover the 40th percentile of these test scores, we to begin with have to arrange them from least to most elevated. 

44 56 58 62 64 64 70 72 72 72 74 74 75 78 78 79 80 82 82 84 86 87 88 90 92 95 96 96 98 100

This list has 30 items. To find the 40th percentile, we need to find scores that are at least 40% of the scores.

To do this, first, calculate how many scores are below the 40th percentile.

0.40 × 30 = 12

This means that the 40th percentile is a score equal to or greater than the 12th score in the ordered list. Counting from the top of the list, the 12th result is 74.

Therefore, the 40th percentile for these test results is 74. 

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Step-by-step explanation:

- The distance traveled to get to the top of the hill will be equal to the distance traveled to get to the bottom of the hill. Distance down the hill = Distance up the hill = 187.5 meters.

- Only the speed of going up the hill and down the hill will be different.

Given:

What is 8/9 of 3/8?

So, we will multiply 8/9 by 3/8

So, the answer will be 1/3

A number line goes from 0 to 16. A line divides the box at 10. The range of the data is 10.

The range of the data is the difference between the maximum and minimum values in the data set. In a box plot, the whiskers represent the range of the data, so the minimum value is the left end of the left whisker and the maximum value is the right end of the right whisker.

From the given information, we know that the left end of the left whisker is at 5 and the right end of the right whisker is at 15. Therefore, the range of the data is:

range = maximum value - minimum value

range = 15 - 5

range = 10

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Answer:

D. 10

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

multiply both sides by -5/2

Answer:

B. 55

Step-by-step explanation:

-2/5y = -22

y = -22 : -2/5

y = -22 x 5/-2

y = 11 x 5/1

y = 11 x 5

y = 55

Answer:

x/5+9

Step-by-step explanation:

The expression "9 more than the quotient of x and 5" in the mathematical form will be 9 + x / 5.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression "9 more than the quotient of x and 5" that is converted into mathematical form is written as,

⇒ 9 + x / 5

The expression "9 more than the quotient of x and 5" in the mathematical form will be 9 + x / 5.

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By answering the question the answer is Therefore, landscapers should equation use 35 gallons of an 80% pesticide solution.

In mathematics, an equation is a statement that two expressions are equal. The equation consists of her two sides divided by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of solving an equation is to find the values ​​of the variables to make the equation true. Simple or complex equations, regular or nonlinear, and equations involving one or more factors are all possible. For example, the expression "\(x2 + 2x - 3 = 0\\\)" squares the variable x. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.  

Let's say a landscaper needs to use x gallons of an 80% pesticide solution.

The amount of pesticide for an 80% solution is 0.8 x gallons and the amount of pesticide for a 30% solution is 0.3 (35) = 10.5 gallons.

After mixing the two solutions, the total amount of pesticides in the mixture is 0.8 x + 10.5 gallons and the total volume of the mixture is x + 35 gallons.

Since we need a 55% pesticide solution, we can set the following formula:

\(0.8x10.5 0.55(x+35)0.8x10.5 0.55x+19.250.25x = 8.75x = 35\)

Therefore, landscapers should use 35 gallons of an 80% pesticide solution.

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The probability that neither smoke alarm will sound in the presence of smoke is 0.04.

When two events operate independently, the probability of both events occurring is the product of their individual probabilities. In this case, the probability of one smoke alarm functioning properly and sounding an alarm in the presence of smoke is 0.8. Therefore, the probability of one smoke alarm not sounding in the presence of smoke is 1 - 0.8 = 0.2.

Since the two smoke alarms operate independently, the probability of both smoke alarms not sounding in the presence of smoke is the product of their individual probabilities. Thus, the probability that neither alarm will sound is 0.2 × 0.2 = 0.04.

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The first three nonzero terms of the Maclaurin series for f is f(x) = x^2 + 0x^3/3! + 0x^4/4!

We can use the formula for the Maclaurin series of a function to find the first few nonzero terms of the series for f:

f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

Since f(0) = 0, the first term of the series is 0. We can find the higher order derivatives of f as follows:

f'(x) = 2x cos(x^2)

f''(x) = 2 cos(x^2) - 4x^2 sin(x^2)

f'''(x) = -12x cos(x^2) - 8x^3 cos(x^2)

Evaluating these derivatives at x = 0 gives:

f'(0) = 0

f''(0) = 2

f'''(0) = 0

Substituting these values into the formula for the Maclaurin series, we get:

f(x) = 0 + 0 + 2x^2/2! + 0 + ...

Simplifying, we get:

f(x) = x^2

So the first three nonzero terms of the Maclaurin series for f are:

f(x) = x^2 + 0x^3/3! + 0x^4/4! + ...

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Correct option is E, The slope of a line perpendicular to y = -10/4 x + 5 is 4/10

The slope of the parallel line is undefined and the slope of the perpendicular line is 0.

Yes, the slope of a line perpendicular to the line 10x + 4y = 20 is indeed -4.

To find the slope of a perpendicular line, we can find the negative reciprocal of the slope of the original line.

The slope of line 10x + 4y = 20 can be found by solving for y and writing the line in slope-intercept form (y = mx + b), where m is the slope.

By solving for y in the equation 10x + 4y = 20:

10x + 4y = 20

4y = -10x + 20

y = -10/4 x + 20/4

y = -10/4 x + 5

So the line is in the form y = -10/4 x + 5, which is the slope-intercept form of a line where the slope (m) is -10/4 and the y-intercept (b) is 5.

Now, to find the slope of a line perpendicular to this line, we need to find the negative reciprocal of the slope of this line. The negative reciprocal of -10/4 is 4/10.

hence,. the slope of a line perpendicular to y = -10/4 x + 5 is 4/10

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Answer:

10%.

Step-by-step explanation:

There are a total of 40 numbers.

Number of permutations of 3 numbers from 40

= 40 P 3

= 40! / (40-3)!

= 59,280.

The total of even numbers is (38 - 2) / 2 + 1 = 19.

Number of permutations of 3

=  19P 3

=  5814

So Prob(all even) = 5814/59280

= 0.098077

= 9.8%

= 10% to nearest whole number.

To set up the equation system in matrix format, we can rewrite the given system of equations using matrix notation.

Let's define the following matrices and vectors:

- Y: Output vector (Y = [Y1, Y2, Y3]ᵀ)

- Q: Endowment vector (Q = [Q1, Q2, Q3]ᵀ)

- S: Input-output matrix (S = [sij])

Now, let's expand and rewrite the equation system using matrix notation:

∑(j) sij Yj = Qi

Expanding this equation for each i, we get:

s11Y1 + s12Y2 + s13Y3 = Q1

s21Y1 + s22Y2 + s23Y3 = Q2

s31Y1 + s32Y2 + s33Y3 = Q3

We can rewrite the above system of equations in matrix format as:

S * Y = Q

where S is the input-output matrix, Y is the output vector, and Q is the endowment vector.

In matrix format, the equation system can be written as:

⎡ s11  s12  s13 ⎤  ⎡ Y1 ⎤   ⎡ Q1 ⎤

⎢ s21  s22  s23 ⎥  ⎢ Y2 ⎥ = ⎢ Q2 ⎥

⎣ s31  s32  s33 ⎦  ⎣ Y3 ⎦   ⎣ Q3 ⎦

This is the equation system represented in matrix format.

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Answer:

132 cm squared

Step-by-step explanation:

for the two triangles 8 times 3 divided by 2 is 12 times 2 for two triangles equals 24

the two side rectangles easy just do 5 times 6 and it equals 30 times two because there is 2 and you get 60

the bottom rectangle do the same thing except 6 times 8 and there is only one so 48

add all areas together to get 132

The polynomial is x²  + 5x + 4 = 0 which has the least degree two with roots -1 and -4.

Polynomial is an algebraic expression that has more than two terms. In other words, it is a combination of different variables with mathematical operations.

Given that,

The roots of the polynomial are -1 and -4,

And leading coefficient of the polynomial is 1.

There are, two roots of the polynomial, so the maximum degree can be equal to 2 or grater than 2.

Let the standard equation of the polynomial is,

ax² + bx + 1 = 0        (1)

Substitute x = -1 in equation (1),

a(-1)²  + b(-1) + 1 = 0

a - b + 1 = 0     (2)

Again substitute x = -4 in the equation (1),

a(-4)² b(-4) + 1 = 0

16a - 4b + 1 = 0    (3)

By solving equation (2) and (3),

The value of a is 1/4 and the value of b is 5/4.

So, the required polynomial,

1/4x²  + 5/4 x + 1 = 0

x²  + 5x + 4 = 0

Hence, x²  + 5x + 4 = 0 is the required polynomial.

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The total cost of the 12 movie tickets purchased by the group of friends is $ 108 .

The formula to find out the total amount spent by the group of friends if they bought 12 tickets would be :

= Number of tickets purchased x Cost per ticket

Number of tickets purchased :

= 12 tickets

Cost per ticket :

= $ 9. 00

The total amount spent by the group of friends is therefore :

= 12 tickets  x 9 per ticket

= $ 108

In conclusion, the group of friends spent $ 108.

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Question is:

How much did the group spend in total ?

The alternating harmonic series is convergent, while the second alternating series is not convergent.

To show that an alternating series is convergent, we need to use the Alternating Series Test. This test states that if the terms of an alternating series satisfy two conditions:
1) The terms are positive and non-increasing, meaning an−1 ≤ an for all n.
2) The limit of the terms as n approaches infinity is 0, lim(n→∞) an = 0.

Let's apply this test to the given examples:

1) For the alternating harmonic series ∑(-1)^(n-1)/n, we can see that the terms are positive (as the numerator alternates between -1 and 1) and non-increasing (as 1/n is always greater than or equal to 1/(n+1)). Also, as n approaches infinity, the limit of 1/n is 0. Therefore, all the conditions of the Alternating Series Test are satisfied, and we can conclude that the alternating harmonic series is convergent.

2) For the alternating series ∑(n^2+5)(-1)^(n-1)/n^2, we can see that the terms are positive and non-increasing (as n^2+5 is always positive, and 1/n^2 is always less than or equal to 1/(n+1)^2). Additionally, as n approaches infinity, the limit of (n^2+5)/n^2 is 1. Since 1 is not equal to 0, the conditions of the Alternating Series Test are not satisfied, and we cannot conclude that this series is convergent.

In summary, the alternating harmonic series is convergent, while the second alternating series is not convergent.

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The regular expression is ^(a(aa)*b)$.

To create a regular expression for the language L = {w = {a,b}* | w has an odd number of 'a's and ends with 'b'}, we can use the following expression:

^(b|(a(aa)*b))$

Breaking it down:

^ indicates the start of the string.

(b|(a(aa)*b)) matches either 'b' or a sequence of 'a's followed by an odd number of 'a's and 'b'.

(aa)* matches zero or more pairs of 'a's.

$ indicates the end of the string.

This regular expression ensures that the string starts with 'b' or a sequence of 'a's, followed by an odd number of 'a's, and ends with 'b'. Any additional characters or sequences in between are not allowed.

Please note that regular expressions can have different notations and conventions depending on the context or programming language you're using. The expression provided here follows a general pattern that should work in most cases.

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Answer:

 P(x) = 3x - 150  

The weight of the melted ice cream would be the same as the weight of the original ice cream, which is 5 ounces.

a quantity or thing weighing a fixed and usually specified amount. : a heavy object (such as a metal ball) thrown, put, or lifted as an athletic exercise or contest. 3. : a unit of weight or mass see Metric System Table.

When the ice cream melts, it undergoes a change in state from solid to liquid, but the total mass or weight remains unchanged. Therefore, the weight of the melted ice cream is still 5 ounces.

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The expression used to find the amount of fencing needed for your yard is 2(xy² + 2y + 3x - 10).

We have,

To find the amount of fencing needed for your yard, we need to calculate the perimeter of the yard, which is the sum of all four sides.

Given that the length of the yard is 3xy² + 2y - 8 and the width is

-2xy² + 3x - 2

The perimeter can be calculated as follows:

Perimeter = 2 x (Length + Width)

Substituting the given expressions for length and width:

Perimeter = 2 x (3xy² + 2y - 8 + (-2xy² + 3x - 2))

Simplifying:

Perimeter = 2 x (3xy² - 2xy² + 2y + 3x - 8 - 2)

Perimeter = 2 x (xy² + 2y + 3x - 10)

Thus,

The expression used to find the amount of fencing needed for your yard is 2(xy² + 2y + 3x - 10).

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To solve the initial value problem (IVP) y" - 2y + y = 3tet + 4, y(0) = 1, y'(0) = 1, we are given the complementary homogeneous solution yc = C₁et + C₂tet and the particular solution yp = 4 + t³et.

We can find the values of C₁ and C₂ by applying the initial conditions to the IVP. Applying the initial condition y(0) = 1: y(0) = yc(0) + yp(0); 1 = C₁e^0 + C₂te^0 + 4; 1 = C₁ + 4; C₁ = -3. Applying the initial condition y'(0) = 1: y'(0) = yc'(0) + yp'(0); 1 = C₁e^0 + C₂(te^0 + e^0) + 0 + 3te^0; 1 = -3 + C₂ + 3t C₂ = 4 - 3t. Therefore, the values of C₁ and C₂ are C₁ = -3 and C₂ = 4 - 3t.

The value of C₂ depends on the variable t, so it is not a constant. It is determined by the specific value of t in the IVP.

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In 2.63  hours the prices of the two stocks be the​ same

Two or more expressions with an Equal sign is called as Equation.

Given,

The price of Stock A at 9 A.M. was $12.71.

Price has been increasing at the rate of $0.08 each hour

Price of Stock B was $13.21

The price has been decrease at the rate of $0.11 each hour.

We can write in the form of equation , to find how many hours will the prices of the two stocks be the​ same

12.71+0.08h=13.21-0.11h

0.11h+0.08h=13.21-12.71

0.19h=0.5

Divide both sides by 0.19

h=0.5/0.19

h=2.63

Hence, in 2.63  hours the prices of the two stocks be the​ same

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Answer:

2 Pi

Step-by-step explanation:

Notice that the shape is made of:

● 1 square with a side of 1 meter length

● 4 half-circles wich means 2 cicles with a diameter lf 1 meter.

■■■■■■■■■■■■■■■■■■■■■■■■■■

The square is inside so it isn't necessary to calculate the perimeter.

The perimeter of a circle is:

P' = d × Pi

We have 4 half-squares wich means two circles

So the total perimeter is:

● P = 2×P'

● P = 2 × d × Pi

● P = 2 × 1 × Pi

● P = 2Pi