LAST QUESTION ON TEST, DESPERATELY NEED HELP
Solve the following: -4x - 2 = -2(1 - 4x)

Answer:

183.26cm

Step-by-step explanation:

Radius of the Circle = 50cm

Let the point be at A

It turns forward 210 degrees to B.

Therefore, the central angle subtended by the arc AB = 210 degrees

The movement of the point from A to B will be the length of the arc AB.

\(\text{Length of an arc }=\dfrac{\theta}{360} \times 2\pi r \\$Therefore, the distance moved forward$\\=\dfrac{210}{360} \times 2\times\pi \times 50\\\\=183.26$ cm\)

Answer:

Functions: Second Graph

The other two are not. Use the vertical line test. I'm pretty sure but not 100%

Step-by-step explanation:

Answer:

base=24

Step-by-step explanation:

2*4=8

192/8=24

Answer:

y+2=1/2(x+3)

Why?

Point slope form is written as (y-y1) = m(x-x1) with y1 being the value of y at a certain point, x1 being the value of x at a certain point, and m being slope. y1 and x1 are given to us by the point (-3, -2) letting us know that y1=-2 and x1=-3. The only thing left to find is slope. Parallel lines have the same slope. If the line we are trying to find is parallel to the one given in the question, we just need to find the slope of the equation given. That equation is given in slope-intercept form which is y = mx + b. m is still slope so we can see that the slope is 1/2. Now we can plug m, x1 and y1 into the point slope form equation to get y + 2 = 1/2(x + 3)

(a) To determine how fast the population is growing when it reaches 5 million people, we can substitute P(t) = 5 into the differential equation P'(t) = 0.06P(t). This gives us P'(t) = 0.06(5) = 0.3 million people per year. Therefore, the population is growing at a rate of 0.3 million people per year when it reaches 5 million people.

(b) To determine the population size when it is growing at a rate of 700,000 people per year, we can set P'(t) = 700,000 and solve for P(t). From the given differential equation, we have 0.06P(t) = 700,000, which implies P(t) = 700,000/0.06 = 11,666,666.67 million people. Therefore, the population size is approximately 11.67 million people when it is growing at a rate of 700,000 people per year.

(c) To find a formula for P(t), we can solve the differential equation P'(t) = 0.06P(t). This is a separable differential equation, and integrating both sides gives us ln(P(t)) = 0.06t + C, where C is the constant of integration. By exponentiating both sides, we get P(t) = e^(0.06t+C). Using the initial condition P(0) = 3, we can find the value of C. Substituting t = 0 and P(0) = 3 into the equation, we have 3 = e^C. Therefore, the formula for P(t) is P(t) = 3e^(0.06t).

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Answer:

8x-2=-9+7x equals X=-7

Answer:

x = -7

Step-by-step explanation:

Answer:

The side with 64 units cannot be the height of the parallelogram and the side with 8 units can be the side of the parallelogram.

Step-by-step explanation:

Area of parallelogram= 40 sq units

One side of the parallelogram= 64 units

∴ the dimension with 64 units cannot be the height of the parallelogram because the side is more than area. When multiplying with the other side, the area will be more than 40.

Other side of the parallelogram= 8

∴ the dimension with 8 units is possible and it can be the height of the parallelogram because the side is less than area. When multiplying with the other side, the area will be 40.

Answer:

- 7

Step-by-step explanation:

Given

t < - 6

Then t = - 7 is less than - 6 and is a solution

To sketch the curve with polar equation θ = −π/6, we need to plot all the points (r, θ) that satisfy the equation for various values of r. Since θ is fixed at −π/6, all the points will lie on a line at an angle of −π/6 to the positive x-axis.

The value of r can be positive or negative, so we will plot points both above and below the x-axis.

Since r can be any value, we will just choose a few values for illustration purposes. Let's choose r = 1, 2, −1, and −2. Then the corresponding points are:

(1, −π/6), (2, −π/6), (−1, −π/6), and (−2, −π/6)

We can plot these points on a polar coordinate system as follows:

These points lie on a line at an angle of −π/6 to the positive x-axis, as expected. Note that the sign of r determines whether the point lies above or below the x-axis.

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Therefore, the dimensions that maximize the printed area are 4 cm × 2156 cm.

Let's first find the dimensions of the printable region of the poster.

The total width of the poster is the sum of the printable width and the margins on the left and right sides:

Total width = Printable width + Left margin + Right margin

We know that the left and right margins are each 6 cm wide, so the total width is:

Total width = Printable width + 6 cm + 6 cm = Printable width + 12 cm

Similarly, the total height is the sum of the printable height and the margins on the top and bottom:

Total height = Printable height + Top margin + Bottom margin

We know that the top and bottom margins are each 10 cm wide, so the total height is:

Total height = Printable height + 10 cm + 10 cm = Printable height + 20 cm

The area of the printable region is:

Printable area = Printable width × Printable height

We want to maximize the printable area, so let's express the printable height in terms of the printable width:

Printable height = Total height - Top margin - Bottom margin

Printable height = (Printable width + 12 cm) - 10 cm - 10 cm

Printable height = Printable width - 8 cm

Substituting into the equation for printable area, we get:

Printable area = Printable width × (Printable width - 8 cm)

Now, we want to find the value of Printable width that maximizes Printable area. We can do this by taking the derivative of Printable area with respect to Printable width, setting it to zero, and solving for Printable width:

d(Printable area)/d(Printable width) = 2Printable width - 8 cm

2Printable width - 8 cm = 0

Printable width = 4 cm

So, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

This is not a valid solution, since the height cannot be negative. Therefore, we made an error somewhere.

Printable width = -b/2a

where a = 1 and b = -8

Printable width = -(-8)/(2×1) = 4

Therefore, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:

Printable height = Printable width - 8 cm

Printable height = 4 cm - 8 cm

Printable height = -4 cm

Again, this is not a valid solution, since the height cannot be negative. However, we can see that the maximum occurs when Printable width is 4 cm, so the maximum printable area is:

Printable area = Printable width × Printable height

Printable area = 4 cm × (8640 cm / 4 cm - 16 cm)

Printable area = 4 cm × 2156 cm

Printable area = 8624 cm

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\(40 \times 0.80 = 32\)

\(32 \times 12 = 384\)

He gains £384

\(40 - 32 = 8\)

\(8 \div 2 = 4\)

\(2(12) + 2(6) = 36\)

He gains £36

//

\( - 130 + 384 + 36 = 290\)

Ryan made £290

//

I'm not too sure about this...

Anyway if he sold 80% of the jumpers at a normal price, he would earn £384.

There are 8 left and he managed to sell half of those but there is a promo where you can buy one at full price and get one for half the price so only two of the four can be bought at full price while the other two gets bought at half price. He earns £36 from this.

If you take in account the starting cost and add the profits, he made a total of £290 selling jumpers.

But again, I'm not too sure.

Answer:

I think it's consistent

Step-by-step explanation:

The expected number of times that a cyan napkin would be drawn if she performs the experiment a total of 189 times is given as follows:

A. 60.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of trials is given as follows:

7 + 20 + 11 + 3 + 22 = 63.

Hence the probability of drawing a cyan napkin is given as follows:

p = 20/63.

Meaning that the expected number of times that a cyan napkin would be drawn if she performs the experiment a total of 189 times is obtained as follows:

E(X) = 189 x 20/63

E(X) = 60.

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Answer:

2.5x100÷340000=

5x340000/1000

Answer:

300

Step-by-step explanation:

25% of 240 is 60.

Answer: 42.57

Step-by-step explanation:

To solve this equation, you will first need to add the numbers inside the first parenthesis.

12.9 (12.05 - 30.4 + 21.65)

Then, you will need to add the numbers inside the second parenthesis.

12.9 x 3.3

Multiply the two numbers together, and then you will get 42.57. Therefore, that will be the answer to your equation!

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Answer:

Ordered Pair An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension. The numeric values in an ordered pair can be integers or fractions.

Step-by-step explanation:

i hope this helped! :)

Answer:

An ordered pair contains the coordinates of one point in the coordinate system. A point is named by its ordered pair of the form of (x, y). The first number corresponds to the x-coordinate and the second to the y-coordinate. To graph a point, you draw a dot at the coordinates that corresponds to the ordered pair.

Step-by-step explanation:

After 10 years, the voter percentages would be approximately 50.3% for LEFT and 49.7% for RIGHT.

The Markov assumption in this context is that the probability of a voter's next vote depends only on their current vote and not on their past voting history. In other words, the Markov assumption states that the future behavior of a voter is independent of their past behavior, given their current state.

Transition diagram:

        LEFT      RIGHT

    |--------->--------|

LEFT |   0.8        0.2   |

    |                   |

RIGHT|   0.1        0.9   |

    |--------->--------|

The diagram represents the two possible states: LEFT and RIGHT. The arrows indicate the transition probabilities between the states. For example, if a voter is currently in the LEFT state, there is a 0.8 probability of transitioning to the LEFT state again and a 0.2 probability of transitioning to the RIGHT state.

Transition matrix:

     |  LEFT   |  RIGHT  |

---------------------------

LEFT  |   0.8   |   0.2   |

---------------------------

RIGHT |   0.1   |   0.9   |

---------------------------

The transition matrix represents the transition probabilities between the states. Each element of the matrix represents the probability of transitioning from the row state to the column state.

If 55% of the electorate votes RIGHT one year, we can use the transition matrix to find the percentage of voters who vote RIGHT the next year.

Let's assume an initial distribution of [0.45, 0.55] for LEFT and RIGHT respectively (based on 55% voting RIGHT and 45% voting LEFT).

To find the percentage of voters who vote RIGHT the next year, we multiply the initial distribution by the transition matrix:

[0.45, 0.55] * [0.2, 0.9; 0.8, 0.1] = [0.62, 0.38]

Therefore, the percentage of voters who vote RIGHT the next year would be approximately 38%.

To find the voter percentages in 10 years' time, we can repeatedly multiply the transition matrix by itself:

[0.45, 0.55] * [0.2, 0.9; 0.8, 0.1]^10 ≈ [0.503, 0.497]

After 10 years, the voter percentages would be approximately 50.3% for LEFT and 49.7% for RIGHT.

Interpretation: The results suggest that over time, the voter percentages will tend to approach an equilibrium point where the percentages stabilize. In this case, the percentages stabilize around 50% for both LEFT and RIGHT parties.

No, there will not be a steady state where the party percentages don't waiver. This is because the transition probabilities in the transition matrix are not symmetric. The probabilities of transitioning between the parties are different depending on the current state. This indicates that there is an inherent bias or preference in the voting behavior that prevents a steady state from being reached.

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Answer:

to 1dp = -2.6

to 2 dp= -2.64

as fraction = 29/-11

Step-by-step explanation:

x+1 = 6(2x+5) - you multiply each side by 2x + 5

x+1 =12x+30 - expanding the brackets

x-12x+1=30 - subtract 12x from both sides

x -12x = 30-1 - subtract one from both sides

-11x = 29 - you just work each side out to get these answers

29/-11 =x - divide -11 from both sides

-2.63636363636 =x - using a calculator ( if finding whole number ) you do 29/-11

to 1dp = -2.6

to 2 dp= -2.64

Answer:

51 notes

Step-by-step explanation:

Firstly we need to get the value of the 200 pounds in koruna

From the question, 1 pound is 25.82

200 pounds will be;

200 * 25.82

= 5,164 koruna

So to know the number of possible 100 koruna bills, we simply need to divide what we have by 100

We have this as :

5,164/100

= 51.64

So the number of notes she would be is 51 100 koruna notes

The test static value is 1.44 and its associated p-value is 0.1335.

Given that the problem deals with the concept of test for single proportion. The parameter of the interest is the population proportion of graduates with GPA of 3.00 or below is less than 0.09.

Let the population proportion be p=0.09.

Let the number of graduates in a sample be n=260.

Let the number of students have a GPA of 3.00 or below be x=20.

Based on the known data, the null and alternative hypothesis are,

H₀:p≥0.09

H₁:p<0.09

The sample proportion of students have a GPA of 3.00 or below is,

\(\begin{aligned}\hat{p}&=\frac{x}{n}\\ &=\frac{20}{260}\\ &=0.07\end\)

Under the null hypothesis, the test static value is,

\(\begin{aligned}z&=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\ &=\frac{0.07-0.09}{\sqrt{\frac{0.09(1-0.09)}{260}}}\\ &=\frac{-0.02}{0.018}\\ &=-1.11\end\)

The p-value for the left-tailed test is

p-value=p(z<-1.11)

p-value=0.1335

Hence, the value of the test statistic and its associated p-value for the proportion of graduates with a GPA of 3.00 or below is less than 0.09. are 1.44 and 0.1335.

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Answer

the answer is (3×16^x×y)/(8-3^x )

Step-by-step explanation:

The missing side of the triangle, B, is approximately 13.86 units long.

Let's denote the missing side as B. According to the Pythagorean Theorem, the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, which is the hypotenuse. Mathematically, this can be represented as:

A² + B² = C²

In our case, we are given the lengths of sides A and C, which are 8 and 16 respectively. Substituting these values into the equation, we get:

8² + B² = 16²

Simplifying this equation gives:

64 + B² = 256

To isolate B², we subtract 64 from both sides of the equation:

B² = 256 - 64

B² = 192

Now, to find the value of B, we take the square root of both sides of the equation:

√(B²) = √192

B = √192

B ≈ 13.86 (rounded to two decimal places)

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Complete Question:

How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures: A= 8, C= 16?

The perimeter can be calculated using the formulas 22x+23 and 2x+3x+17x+7+16.

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The surface of a shape's area is measured.

The total length of the four sides makes up the perimeter (P) of a rectangle. A rectangle has two equal lengths and two equal widths since its opposite sides are equal. The following is the formula for calculating a rectangle's perimeter: The formula for perimeter is length + length + width + width. P = l + l + w + w.

you want to add the variables of the same kind in this case

2x        

3x         7

17x       16

_________

22x  +     23

Therefore Two expressions for the perimeter would be 22x+23 and 2x+3x+17x+7+16

The complete question is : Write two expressions for the perimeter of the figure.

2x

7

3x

172

16

Note: The figure is not drawn to scale.

(a) Use all five side lengths.

perimeter - ] + + + +

(b) Simplify the expression from part (a).

perimeter =

Х

$ ?

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Answer:

Step-by-step explanation: D. (24, 12), (36, 0)

The ordered pair lie on the inverse of the function is (62,−3).

Option A is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -(x - 1)³ - 2

The inverse of f(x).

y = -(x - 1)³ - 2

interchange x and y and solve for y.

x = -(y - 1)3 - 2

(y - 1)³ = -2 - x

(y - 1)³ = -(2 + x)

Cuberoot on both sides.

y - 1 = ∛-(2 + x)

y = ∛-(2 + x) + 1

Now,

Substitute in the inverse of g(x).

(62, -3) = (x, y)

(−4, 123) = (x, y)

(3, 1) = (x, y)

(3,−6) = (x, y)

So,

y = ∛-(2 + x) + 1

y = ∛-(2 + 62) + 1

∛-1 = -1

y = -1∛64 + 1

y = -1 x 4 + 1

y = -4 + 1

y = -3

So,

(62, -3) ______(1)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 - 4) + 1

∛-1 = -1

y = ∛(-2 + 4) + 1

y = ∛2 + 1

y =  1.26 + 1

y = 2.26

So,

(-4, 2.26) _______(2)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) _______(3)

And,

y = ∛-(2 + x) + 1

y = ∛-(2 + 3) + 1

∛-1 = -1

y = -1∛5 + 1

y = -1 x 1.71 + 1

y = -1.71 + 1

y = -0.71

So,

(3, -0.71) ______(4)

Thus,

From (1), (2), (3), (4) we see that,

(62, -3) is the solution to the inverse of g(x).

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In equation A, the values of x =-1 and y = 3

In equation B, the values of x = 12 and y = 16.

Given that :

Equation A :

(x+ yi)+(4-7i) = 3-4i

Simplify it.

x + 4 = 3

⇒ x = 3 - 4 = -1

Also :

y - 7 = -4

⇒ y = 3

Equation B :

(x+yi)-(-6+14i) = 18+2i

x - -6 = 18

⇒ x = 18 - 6 = 12

y - 14 = 2

y = 2 + 14 = 16

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The ratio of the volume of the figure is 3:1.

The term called volume in math is defined as the space occupied within the boundaries of any three-dimensional solid

Here we know that the cylinder and a cone are having equal radii of their bases and heights.

Then let us consider that radius of the cone is equal to radius of the cylinder is defined as r and Height of the cone and height of the cylinder is defined as h.

Then their volume is written as,

=> Volume of cylinder /volume of cone

=> πr²h/ (1/3)πr²h

When we simplified this on, then we get the fraction as,

=> 3/1

Then the resulting ratio is 3:1.

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