4. Determine whether the figures are similar. If so, what is the scale factor of the right figure to the left figure.

Answer:

mabey dis will help

Step-by-step explanation:

A =l X w

52.2 = 12 X w

w = 52.2 */* 12

It will take 2.32 years for Michael to reach USD 25000.

The interest one earns on interest is known as compound interest. In other words, the process of adding interest to a loan's or deposit's principal is known as compound interest.

The formula for compound interest calculation is given as,

[tex]A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]

Where,

Here, the compound interest (A) is USD 25000, r is 9.6%, n is 12 months (1 year), and P is USD 20000. Using these we have to find t,

[tex]\begin{aligned}20000\left(1+\frac{0.096}{12}\right)^{12t}&=25000\\20000(1.008)^{12t}&=25000\\1.008^{12t}&=1.25\\12t \ln{(1.008)} &=\ln{(1.25)}\\12t\times0.008&=0.223\\t&=\mathrm{2.32\;years}\end{aligned}[/tex]

Therefore, the answer is 2.32 years.

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Answer:

10x^2 + 26x - 56

Step-by-step explanation:

10 x^2 -14x + 40x - 56 =

= 10x^2 + 26x - 56

Answer: 5x -2x = 8 +7, 3x = 15 x = 15/3) X= 5

If If the measure of an angle is not 180, then it is not a straight angle" relate to the conditional statement "If an angle is a straight angle, then its measure is 180." This is a A. counterexample.

Contraposition in logic and mathematics refers to the inference of going from a conditional statement to its logically equivalent contrapositive, as well as the associated proof method known as proof by contraposition. A statement's contrapositive has its antecedent and consequent inverted and flipped.

Any exception to a generalization is a counterexample. A counterexample disproves the generalization in logic, and it does so rigorously in mathematics and philosophy.

Find a case where P is true but Q is false to provide a counterexample to a conditional statement P Q. Here is the equivalent rule for negating a conditional: (P Q) (P Q) Once again, the "if-part" P must be true and the "then-part" Q must be false (that is, Q must be true).

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Answer:

(top to bottom)104.04...6800...272...3

Step-by-step explanation:

68 can go into 7075, 104 times.

68 goes into 275 4 times.

275-272=3

Of the following statements regarding time-series methods, the statement that is false is a simple moving average of three periods is identical to exponential smoothing with an alpha equal to 0.33. (Option D)

In mathematics, a time series refers to a series of data points indexed or listed or graphed based on the time order. Generally, a time series is a sequence captured at successive equally spaced points in time and hence is a sequence of discrete-time data. Time-series methods are used in forecasting. It comprises of analytical methods in order to obtain meaningful statistics and other characteristics of the data. Time series forecasting is a model used to predict future values based on previously observed values. From the given options, the time-series methods that is false is is a simple moving average of three periods is identical to exponential smoothing with an alpha equal to 0.33.

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Answer:

512 ÷ 64 = 8 is the correct representation.

113 crates are needed for the company to mail an order of 8927 watermelon, if one crate can hold 79 watermelon.

A single or unique unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.

Given,

There are 8927 watermelon and each watermelon can hold 79. We have to divided the number  of watermelon by the number of watermelon each crate can hold, to get the how many crate is needed to mail the order.

8927/79

=113

Therefore, 113 crates will be needed by the company.

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33% is the increasing percentage in the size of the graduating class.

The formula for percentage increase = Final number - Initial number x 100

                                                                              Initial number

Or, it can be also written as

Percentage increase =   Increase       x 100

                                       Initial number

Given that:

The final number of students = 266

The initial number of students = 200

Therefore, putting the value in the formula. We get,

Percentage increase = 266 - 200   x 100

                                           200

Percentage increase = 66   x 100

                                      200

Percentage increase = 33 %

Hence, the increase percentage from the previous year to this year of the students of the class graduating is 33%.

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The average temperature last Sunday is 1.08T or (1 + 8/100)T.

Temperature simply means the hotness and coldness of a body.

In this case, last Sunday, the average temperature was 8 percent higher than the average temperature two Sundays ago.

This will be expressed as:

= T + (8% × T)

= T + (0.08 × T)

= T + 0.08T

= 1.08T

The temperature is 1.08T.

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The area of rectangle ABCD is 23.5 cm² with vertices A(-1,11) B( 7,9) C(10,13) and D(2,7).

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies. The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

Given,

A(-1,11) B( 7,9) C(10,13) and D(2,7)

Calculate the length of the sides using the distance formula:

AB = √(7+1)² + (9 - 11)²

AB = √8² + 2²

AB = √16 + 4

AB = √20

AB = 4.47

BC = √(10-7)² + (13-9)²

BC = √3² + 4²

BC = √9 + 16

BC = √25

BC = 5

For area of rectangle:

Length × Width

5 × 4.47

23.5

The area of rectangle ABCD is 23.5 cm².

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The slope of the line is B.

In mathematics, the slope of a line is the change in y-coordinate with respect to the change in x-coordinate.

The net change in the y coordinate is denoted by Δy and the net change in the x coordinate is denoted by Δx.

So the change in the y coordinate for a change in the x coordinate is:

The slope of a straight line can also be expressed as:

In general, the slope of a line is a measure of its steepness and direction. The slope of the line between two points (x1,y1) and (x2,y2) can be easily determined by finding the difference in the coordinates of the points.

If the x-coordinate of each point on a line is 5 more than half the y-coordinate, then x= y2+5.

To find the slope of the line, solve for y and put the equation in slope-intercept form (y = mx + b, where m is the slope).

To do so, first subtract 5 from both sides, then multiply the entire equation by 2 to get y = 2x − 10.

The slope is 2.

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Answer:

6, 8

Step-by-step explanation:

just replace x with the number

2(2)+2

4+2

6

2(3)+2

6+2

8

Hopes this helps please mark brainliest

Answer:  [tex]h = \frac{3}{4}y[/tex] is the cone's height.

==================================================

Work Shown:

Let's set up each volume equation.

[tex]\text{VL} = \text{volume of cylinder}\\\\\text{VL} = \pi*r^2*h\\\\\text{VL} = \pi*x^2*y\\\\[/tex]

[tex]\text{VC} = \text{volume of cone}\\\\\text{VC} = \frac{1}{3}*\pi*r^2*h\\\\\text{VC} = \frac{1}{3}*\pi*(2x)^2*h\\\\\text{VC} = \frac{4}{3}\pi x^2*h\\\\[/tex]

Then we're told that VL and VC are the same value. Let's equate the right hand sides and solve for h.

[tex]\text{VL} = \text{VC}\\\\\pi x^2y = \frac{4}{3}\pi x^2 h\\\\x^2y = \frac{4}{3}x^2 h\\\\3x^2y = 4x^2 h\\\\h = \frac{3x^2y}{4x^2}\\\\h = \frac{3y}{4}\\\\h = \frac{3}{4}y\\\\[/tex]

Answer:

3y

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $(r)$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]   [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $(r)$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Given dimensions of the cylinder:

Therefore, the equation for the volume of the cylinder is:

[tex]\implies V_{\sf cylinder}=\pi x^2y[/tex]

Given dimensions of the cone:

Therefore, the equation for the volume of the cone is:

[tex]\implies V_{\sf cone}=\dfrac{1}{3} \pi x^2 h[/tex]

As the cylinder and the cone have the same volume, substitute the equation for the volume of the cylinder into the equation for the volume of the cone an solve for h:

[tex]\begin{aligned}V_{\sf cylinder}&=V_{\sf cone}\\\implies \pi x^2 y&=\dfrac{1}{3} \pi x^2 h\\y&=\dfrac{1}{3} h\\3y&=h\\h&=3y\end{aligned}[/tex]

Therefore, the height of the cone is 3y.

The sidelength of the square is 6 units, with that we can find that the perimeter is 24 units.

For a square of side length S, the perimeter is give by the formula:

P = 4*S

In this case, the vertices of the square are given, and I and J are consecutive vertices, where:

I = (8, - 10)

J = (2, - 10)

Notice that the y-component is the same, then the side length of the square is:

S = 8 - 2= 6

Using the formula for the perimeter we get:

P = 4*S = 4*6 = 24

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The number of fidget spinners that had not sold yet is; 9,455.

The quantities given in the problem are the total number of fidget spinners shipped each weeks and the number of them sold.

It follows from the task content that the total number of fidget spinners that had not sold yet be determined from the information given.

According to the task content;

1st week;

12,875 fidget spinners were shipped and 9,843 of them were sold.

The number of fidget spinners that had not sold yet is therefore; = 12875 - 9843 = 3,032.

2nd week;

19,175 fidget spinners were shipped and 12,752 of them were sold.

The number of fidget spinners that had not sold yet is therefore; = 19,175 - 12,752 = 6,423.

Ultimately, the total number of fidget spinners that had not sold yet is; 3,032 + 6,423 = 9,455.

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Answer:

2x

Step-by-step explanation:

The size of the union according to the given data is 37.

The study of sets, which are collections of objects, is a topic covered by the mathematical field known as set theory. A set is a clearly defined group of unique items, sometimes referred to as its elements or members, in set theory.

Let's use the inclusion-exclusion principle to compute the number of elements in the union of four sets:

First, we add up the sizes of the individual sets:

4 x 15 = 60

Next, we subtract the sizes of the pair-wise intersections:

6 x 5 = 30

We have to multiply by 6 because there are 6 pairs of sets.

Now we need to add back the sizes of the three-way intersections:

4 x 2 = 8

We have to multiply by 4 because there are 4 triples of sets.

Finally, we need to subtract the size of the intersection of all four sets:

-1

Putting it all together, we have:

60 - 30 + 8 - 1 = 37

Therefore, the size of the union is 37.

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After solving the value of r = (-1 - t / 5).

Given equation:

6r + t = r - 1

6r - r + t = -1

5r + t = -1

5r = -1 - t

divide by 5 on both sides

5r/5 = -1 - t / 5

r = (-1 - t / 5)

Therefore r = (-1 - t / 5)

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Answer: y = 4

Step-by-step explanation:

First, we have to look at the triangle and understand which sides match each other. The side measure of EF matches the side of KH. Since we know these are congruent sides, we can set them equal to each other in an equation. So,

7y - 11 = 17.00

Now we add 11 to both sides, isolating the variable.

7y = 28.00

Now, we divide by 7 on both sides.

7y/7 = 28/7

y = 4

Randomly selecting a white golf ball first and then a white golf ball second are independent events.

What do you mean by dependent events?

Events that are dependent upon prior events are called dependent events. The results of earlier events have an impact on these current ones. For example, two or more events that are interdependent are referred to as dependent events.

It is given that in the beginning we have 3 white balss and 2 yellow balls

Total number of balls = 3 + 2 = 5

Probability of first selecting a white ball = 3/5

Now remaining white balls = 3 - 2 = 1

Remaining total balls = 5 - 1 = 4

Probability of selecting second white ball = 2/4

Probability of selecting a white golf ball first and then a white golf ball second = 3/5 × 2/4 = 3/10

Both the events are dependent as if we select first white ball, then it will change the number of white balls for selecting second time.

Therefore,  randomly selecting a white golf ball first and then a white golf ball second are independent events.

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Step-by-step explanation:

6+7=13,13+7=20,20+7=27,27+7=(34)!

Joe has $120 after all the trades, which is the entire amount.

Given that,

With $80, Joe opened a bank account. Then he took out $35, put in $115, and took out another $40.

To know how much balance left in his account after all the transactions in dollars;

Assume that,

Amount when account opened (x) = $80

Amount withdrawn (y) = $35

Amount deposited again (z) = $115

Amount withdrawn again (p) = $40

The total amount left after all the above transactions is;

A = x - y + z - p

  = 80 - 35 + 115 - 40

  = 195 - 75

A = $120

Therefore, the total amount left with Joe after all the transactions is $120.

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The slope of the line y = -3x is  -3.

The slope of a line is the measure of the steepness and the direction of the line. It is defined as the change in y coordinate with respect to the change in x coordinate of that line.

The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. Then the slope

m = Δy/Δx = dy/dx

Here the line is y = -3x

Differentiating the equation of line with respect to x, we get

   dy /dx = -3

⇒ dy /dx = m = -3.

Therefore, the slope of the line y = -3x was found to be -3.

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Answer:

£5,900 in taxes

Step-by-step explanation:

How much Income Tax would be paid by someone earning £41,000 in a tax year when the basic rate of Income Tax is 20% and the annual tax-free personal allowance is £11,500?

41,000 - 11,500 = 29,500 taxable

20% = 0.2

29,500 * 0.2 = £5,900 in taxes

Answer:

14

Step-by-step explanation:

first add inside the parentheses 4+7=11

then add three 11+3=14

Answer: 3 + 11 = 14

Step-by-step explanation: Follow PEMDAS (Parentheses, exponent, multi, divi, add, subtract.)

The measure of angle B is 78°.

∠A = (2x - 9)°

∠B = (2x + 4)°

∠C = x°

In triangle ABC,

      ∠A + ∠B + ∠C = 180°

2x - 9 + 2x + 4 + x = 180

                   5x - 5 = 180

                        5x = 180 + 5

                        5x = 185

                          x = 185/5

                          x = 37

∠B = 2x + 4

     = 2*37 + 4

     = 74 + 4

     = 78

Hence, ∠B is 78°.

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Answer:

8 1/3

Step-by-step explanation:

We want to find a number, x, that when divided by 10/3 equals 2.5.  We can write that as:

  x/(10/3) = 2.5

x = (2.5)*(10/3)    [MULTIPLY BOTH SIDES BY (10/3)

x = 25/3

x = 8 1/3             [

Answer:

  (2, 8)

Step-by-step explanation:

You want the image coordinates of (8,-2) after 90 degree counterclockwise rotation.

The transformation of (x, y) coordinates that does a 90° CCW rotation about the origin is ...

  (x, y) ⇒ (-y, x)

Applying this transformation to the given point, we have ...

  (8, -2) ⇒ (2, 8)

The rotated point is (2, 8).

The required equation is y = 14.85x + 110.25.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

Given that, Jake collects $311.95 after receiving 21 texts.

Therefore, he collected $311.95/21 per text.

$311.95/21 = $14.85

The collection balance was $422.20, therefore, Jake already has $422.20-$311.95 = $110.25.

Let Jake receives x texts, then he will get $14.85x, and Jake already has $110.25, therefore, the total collection after receiving x texts is:

y = 14.85x + 110.25

Hence, The required equation is y = 14.85x + 110.25.

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