What decimal does the model represent?
The model below is shaded to represent 2
A 25.6
2.056
2.56
0.256

The ratio of the areas of two similar polygons can be found by using the ratio of their perimeters or the ratio of similarity and squaring it which is true.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

Similar polygons are those whose perimeter ratios are identical to their respective scale factors. The common fraction of the sizes of two matching sides of two identical polygons is known as a scale factor.

The given statement is true.

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Answer:

210

Step-by-step explanation:

First off, the tenth's place is 0 in 206, so the number after that will determine the value. If the number past the tenths place is more than five, you round up, so you would raise the tenths place by 1, so you would get 210. Instead if it was the hundreds place needed rounding, it would be 200, since 206 is closer to 200 than 300. I hope this helps you.

Answer:  210.

Step-by-step explanation:

To round a number to the nearest tenth, we look at the digit in the hundredths place. If that digit is 5 or greater, we round the number in the tenths place up. If the digit is less than 5, we round the number in the tenths place down.

In this case, 206 rounded to the nearest tenth is 210.

The gravitational force varies directly with mass of the objects and

inversely with the square of the distance between them, therefore,

doubling the mass doubles the gravitational force while halving the

distance between the masses quadruples the gravitational force. The

option that create the greatest increase in the gravitational force is;

Halving the distance between the masses.

Reasons:

The known parameters are;

m₁ = 200 kg

m₂ = 400 kg

The distance between the centers of the masses = 8 meters

Required:

Change in variable that produces the greatest increase in the gravitational

force.

Solution;

The equation for the gravitational force is \(F = \mathbf{G \cdot \dfrac{m_{1} \cdot m_{2}}{r^{2}}}\)

The gravitational force between the masses is therefore;

\(F =6.67408 \times 10^{-11} \times \dfrac{200 \times 400}{8^{2}} = 8.3426 \times 10^{-8}\)

F = 8.3426 × 10⁻⁸ N

Doubling the mass of m₂ gives;

\(F_{2 \cdot m } = G \cdot \dfrac{m_{1} \cdot 2 \times m_{2}}{r^{2}} = \mathbf{2 \times G \cdot \dfrac{m_{1} \cdot m_{2}}{r^{2}}}\)

Doubling the mass of m₂, doubles the gravitational force.

\(F_{2 \cdot m }\) = 2 × F = 2 × 8.3426 × 10⁻⁸ N = 1.66852 × 10⁻⁷ N

Halving the distance between the masses gives;

\(F_{\frac{r}{2} } =G \cdot \dfrac{m_{1} \cdot m_{2}}{\left(\dfrac{r}{2} \right) ^{2}} = 4 \times G \cdot \dfrac{m_{1} \cdot m_{2}}{r^{2}}\)

\(F_{\frac{r}{2} }\) = 4 × F = 4 × 8.3426 × 10⁻⁸ N = 3.33704 × 10⁻⁷ N

Therefore, halving the distance between the masses quadruples (multiplies

by 4) the gravitational force between the masses.

Halving the distance between the masses creates the greatest

increase in the gravitational force because the gravitational force varies

with inverse of the square of the distance between the masses, and,

halving the distance between the masses has the effect of quadrupling the

gravitational force.

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Answer:

The gravitational force varies directly with mass of the objects and

inversely with the square of the distance between them, therefore,

doubling the mass doubles the gravitational force while halving the

distance between the masses quadruples the gravitational force. The

option that crate the greatest increase in the gravitational force is halving

the distance between the masses.

Step-by-step explanation:

Answer:

80 questions

Step-by-step explanation:

If 16 questions is 20%, then 16 comprises of 1/5 of the total questions. This means that 16 times 5 makes 100%, so 80 is correct.

The option II "The interval is narrower than a 98% confidence interval would be" and III "95% of all samples would show mean commercial length between 23 and 27 seconds" is the true about the question. So the option d is correct.

If all possible samples are taken and confidence intervals are calculated, 95% of them will include the true population mean somewhere within their range.

Because of the large margin of error, a 98 percent confidence interval would be wider than a 95 percent confidence interval. So, here we are. The confidence interval is narrower than a 98% confidence interval.

Furthermore, 95% of all samples would have a mean commercial length of 23 to 27 seconds. As a result, the correct answer is II and III (d).

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THe value of the expression using BODMAS rule is 26

The abbreviation BODMAS, which stands for "Brackets, Order of powers or roots, Division, and Multiplication," is followed by the BODMAS rule. A stands for addition and S for subtraction. According to the BODMAS rule, multi-step mathematical statements must be solved in the BODMAS order from left to right.

The order of operations, or BODMAS, is a method for carrying out operations in an arithmetic statement. Math is all about logic, and there are several established laws that help us with our calculations. BODMAS is one of the established rules for consolidating multiple operator expressions.

An expression or equation in mathematics has two parts:

A character known as an operator joins two integers to form an expression or equation. The four most often used operators in mathematics are addition (+), subtraction (-), multiplication (*), and division (*/*). Finding the solution to mathematical statements or equations with just one operator is usually rather easy.

The expression is 14 + 2 + 3(4) - (6-1-3) = 14 + 2 + 12 - 2 = 26

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Given the figure of the functions f(x) and g(x)

The graph of the function is the shown lines

The equation of f(x):

As shown the line of f(x) passes through the points: (-2, 0) and (0, -1)

The slope of the line will be:

The y-intercept = -1

so, the equation of f(x) =

The equation of g(x):

As shown the line of g(x) passes through the points: (-2, 0) and (0, 1)

The slope of the line will be:

The y-intercept = 1

So, the equation of g(x) will be:

Identify the reflection that transforms the graph of f(x) to the graph of g(x).

As shown, the functions are symmetric around the x-axis

And as we can see for the same value of x: g(x) = -f(x)

So, the type of transformation is: Reflection over the x-axis

The mean, median, range, and standard deviation  for the new data set must all be 7 greater than for the original data set.

The mean is the sum of all the values divided by the number of values. Adding the number 6 to the original data set of 30 positive integers increases the sum of all the values by 6, which means the mean for the new data set must be 7 greater than the mean for the original data set.

The formula for the mean is: Mean = (Sum of Values)/(Number of Values)

For the original data set: Mean = (Sum of Values)/30

For the new data set: Mean = (Sum of Values + 6)/31

Therefore, the mean for the new data set must be 7 greater than the mean for the original data set.

The median is the middle value in a set of data. Adding the number 6 to the original data set of 30 positive integers increases the total number of values to 31, which means the median is calculated differently for the new data set than the original data set. The median for the new data set must be 7 greater than the median for the original data set.

The formula for the median is: Median = (n+1)/2

For the original data set: Median = (30+1)/2 = 15.5

For the new data set: Median = (31+1)/2 = 16.5

Therefore, the median for the new data set must be 7 greater than the median for the original data set.

The range is calculated by subtracting the smallest value from the largest value in a data set. Adding the number 6 to the original data set of 30 positive integers increases the largest value by 6, which means the range for the new data set must be 7 greater than the range for the original data set.

The formula for the range is: Range = (Largest Value) - (Smallest Value)

For the original data set: Range = (Largest Value) - 13

For the new data set: Range = (Largest Value + 6) - 13

Therefore, the range for the new data set must be 7 greater than the range for the original data set.

The standard deviation is a measure of how spread out the values in a data set are. Adding the number 6 to the original data set of 30 positive integers increases the total number of values by 1, which means the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.

The formula for the standard deviation is: Standard Deviation = √ (Sum of (Values - Mean)2 / Number of Values)

For the original data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 30)

For the new data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 31)

Therefore, the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.

The mean, median, range, and standard deviation for the new data set must all be 7 greater than for the original data set

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Answer:

Y=-4/5x+3/5y

Step-by-step explanation: first get the gradient

3--1/-3-2

=4/-5

y-3/x+3=4/-5

-5y+15=4x+12

-5y=4x-3

y=4/-5x+3/5

Answer:

6.4 or 6 2/5 or 32/5

Step-by-step explanation:

Answer:

5%

Step-by-step explanation:

33/650=0.0507

0.0507*100=5.07

\(3x=x+10\)

We tripple something and get 10 more than something.

Put the x-es on the left and non x-es to the right,

\(2x=10\)

Divide both sides by 2,

\(x=5\)

Et Viòla.

Hope this helps :)

When a number is tripled, its value increases by 10 then the original number is 5.

Let's call the original number "x". According to the problem, when this number is tripled, its value increases by 10. Mathematically, we can represent this as an equation:

3x = x + 10

Now, we can solve for "x" step by step:

1. Subtract "x" from both sides of the equation:

  3x - x = 10

2. Simplify the left side:

  2x = 10

3. Divide both sides by 2 to solve for "x":

  x = 10 / 2

  x = 5

So, the original number "x" is 5.

In other words, if you take a number, triple it (multiply by 3), and then increase the result by 10, you would end up with the value 5. This can be verified by checking:

3 * 5 = 15

15 + 10 = 25

The equation 3x = x + 10 represents the relationship between the original number and its tripled value with an increase of 10. Solving this equation helps us find the original value that satisfies the given condition.

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Answer:

T=71 degrees

Step-by-step explanation:

180- 82º-27º=71º

you got this! lmk if you need any more help! <33

Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

(8,-43)

(4,-22)

Step-by-step explanation:

In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.

For example:

(4,-22)

x=4 ; y=-22

Plug y into the inequality

y≤0

-22≤0

Since the statement is true, I know that (4,-22) must be a solution to the inequality.

Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.

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Answer:

Step-by-step explanation:

To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.

Let's check each ordered pair:

(8, -43):

The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(4, -22):

The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(-3, 25):

The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

(-7, 45):

The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

So, the solutions to the inequality y ≤ 0 are:

(8, -43) and (4, -22).

The solution to the the given system of equation are x = 11/33 and y = -4/3.

Hence, (2,3) is not a solution to the system of equation.

Given the system of equation;

-x + 4y = -9 ------ equ 1

y = -2x + 6 --------equ 2

Replace the occurrence of y in equation 1 with equation 1.

-x + 4y = -9

-x + 4( -2x + 6 ) = -9

Now, we simplify

-x - 8x + 24 = -9

Collect like terms

-x - 8x = - 9 - 24

-9x = -33

Divide both sides by -9

x = -33/-9

x = 11/33

Next, substitute x = 11/33 into equation 2

y = -2(11/33) + 6

y = -22/33 + 6

y = -4/3

The solution to the the given system of equation are x = 11/33 and y = -4/3.

Hence, (2,3) is not a solution to the system of equation.

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Answer:

15/8

Step-by-step explanation:

2-(7/8-3/4)=

2-(1/8)=

15/8

Answer:

4

Step-by-step explanation:

Any angle you know on one side, it will be the same to the other no matter what it is. That is unless the arms are tilted unnaturally and unevenly.

Answer:

Step-by-step explanation:

The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.

To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.

So, the growth rate of the investment is:

1.035 - 1 = 0.035

0.035 * 100 = 3.5%

Therefore, the growth rate of the investment is 3.5%.

\(1/2 * 2 * 1 = 1\) square unit.

Step-by-step explanation:

To find the maximum area of the triangle, we need to locate the vertex of the parabola. This occurs when x=1. The y-coordinate at x=1 is 1. We can then use this as the height of the triangle. The base of the triangle is the distance between x=0 and x=2, which is 2. Therefore, the maximum area of the triangle is 1/2 * 2 * 1 = 1 square unit.

Answer:

5

Step-by-step explanation:

The given two triangles are similar , therefore ,

⇒ 5x /20 = 45/36

⇒ x/4 = 5/4

⇒ x = 5/4 × 4

⇒ x = 5

Hence the value of x is 5.

The reflection of the point (–4, 6) across both axes is (b) (4, -6)

From the question, we have the following parameters that can be used in our computation:

Point = (-4, 6)

The rule of reflections across both axes is

(x, y) = (-x, -y)

Using the above as a guide, we have the following:

Image = (4, -6)

Hence, the reflection of the point (–4, 6) across both axes is (b) (4, -6)

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Answer:

Tails Tails Heads

Heads Tails Heads

Tails Heads Tails

Heads Heads Tails

Tails Tails Tails

Heads Heads Heads

Tails Tails heads

Heads Tails Tails

------------------------------------------------——------------------------------------------------------

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Answer: -6

Step-by-step explanation:

     The initial value is the value of y when x is equal to 0.

-> In this case, and many with the equation in slope-intercept form, the initial value will be the y-intercept

y = -5x -6

y = -5(0) -6

y = -6

         The initial value in y = -5x -6 is -6.

Answer:

BC = 21 cm

Step-by-step explanation:

In similar triangles the corresponding sides are in same proportion.

Its given in the sum that AC = 12 cm; DF = 20 cm and EF = 35 cm.

      \(\sf \dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}\\\\\\\dfrac{AC}{DF}=\dfrac{BC}{EF}\\\\\dfrac{12}{20}=\dfrac{BC}{35}\)

     \(\sf \dfrac{12}{20}*35=BC\\\\\\\dfrac{12}{4}*7=BC\\\\\\3*7=BC\\\\ \boxed{BC = 21 cm}\)

Answer:

the 4 gallon jug of 24$ is cheaper

Answer:

The company that sells 4 gallon jug of lemonade for $24 is cheaper

Step-by-step explanation:

The second company sells 8 packs of 1 quart bottles for $16 which basically means 8 quarts for $16.

There are 4 quarts in a gallon so if there are 8 quarts,  it would equal 2 gallons.

Now we know that the second company sells 2 gallons of lemonade for $16. So to find how much they will sell for 4 gallons, we just need to multiply by 2 for gallons and the price.

The second company sells 4 gallons of lemonade for $32.

This means that the first company is cheaper.

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Answer:

w<13

Step-by-step explanation:

Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.

Answer:

w < 1`3

Step-by-step explanation:

Isolate the variable w on one side of the inequality sign.

w+7<20

w<20 - 7

w<13.