Figure 1 and figure 2 are right triangles. two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 5 units long What scale factor was used to produce Figure 2 from Figure 1? 3 over 5 5 over 3 3 5

By using Taylor series, the limit does not exist, since the third term does not converge as x approaches 0.

To evaluate the limit using series, we can use the Taylor series expansion of each term in the limit as x approaches 0. A Taylor series is an infinite sum of terms that are expressed in terms of the derivatives of a function at a single point.

Starting with the first term:

lim x→0 (1/3) * x^3 = 0

Next, for the second term, we have:

lim x→0 ((x^3 - 1)/(2x^2)) = lim x→0 (x^3/2x^2) = lim x→0 (x/2) = 0

For the third term, we have:

lim x→0 (x - ln(1 + x))/x^4

= lim x→0 [(x - (x - x^2/2 + x^3/3 - ...))/x^4] (using the Taylor series expansion of ln(1+x))

= lim x→0 [x^2/2 - x^3/3 + ...]/x^4

= lim x→0 [1/2x^2 - 1/3x^3 + ...]

= ∞

Therefore, the limit does not exist, since the third term does not converge as x approaches 0.

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Answer:

x > -9.5

Step-by-step explanation:

2x - 6 > -25

2x > -19

x > -19/2

x > -9.5

Answer: x= 5/2, y= 11, z= 3/2

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point form:

(5/2, 11, 3/2)

The rate of the canoe in still water is 5 miles per hour, and the rate of the current is 1 mile per hour.

Let's use the letters "c" for the canoe's speed in still water and "r" for the current's speed. The formula is as follows:

Rate times distance

establishing two equations, one for the upstream trip and one for the downstream trip.

Trip downstream:

12 miles is the distance.

rate = c plus r. (since the current is helping them)

t = two hours

We thus have:

12 = (c + r) × 2

When we simplify this equation, we obtain:

6 = c + r

Trip upstream:

12 miles is the distance.

rate equals c-r (since they are now going against the current)

three hours.

We thus have:

12 = (c - r) × 3

When we simplify this equation, we obtain:

4 = c - r

There are now two equations:

6 = c + r

4 = c - r

By combining the two equations, we may find the value of one of the variables:

6 + 4 = 2c

If we simplify, we get:

10 = 2c

When you divide both sides by 2, you get:

c = 5

To solve for the other variable, we may now re-insert this value into one of the equations. Let's apply the formula:

6 = c + r

With c = 5, we obtain:

6 = 5 + r

5 is subtracted from both sides to yield:

r = 1

In still water, the canoe moves at a rate of 5 miles per hour, while the current moves at a rate of 1 mile per hour.

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The domain of the given function in the graph will be x ≤ -1.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, a function as we can see in the graph,

Since The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values.

The y-axis on a graph represents the possible output values or range.

thus, in the given graph the domain of the function will be All real values smaller than -1.

therefore, the domain of the given function in the graph will be x ≤-1.

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Homogeneity of variance assumption assumes that the two populations have equal variances, so the correct answer is option c, "The two populations have equal variances.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The homogeneity of variance assumption assumes that the two populations have equal variances. Therefore, the correct answer is option c, "The two populations have equal variances."

This assumption is often made in statistical tests that compare the means of two groups, such as the t-test.

When the variances of the two populations are equal, it allows for more precise estimates of the standard error and can improve the accuracy of the test results.

However, if the variances are not equal, it can lead to biased and unreliable results.

In such cases, alternative methods, such as Welch's t-test or the Brown-Forsythe test, can be used to adjust for unequal variances.

Hence, homogeneity of variance assumption assumes that the two populations have equal variances, so the correct answer is option c, "The two populations have equal variances.

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The conversion of 5 million Yen to USD results in 37000 US Dollars .

We can convert the amount 5 million Japanese Yen to US Dollars by using the currency exchange rate .

The exchange rate can vary due to the fluctuations in the global financial markets , the current currency exchange rate from "Japanese Yen" to US Dollar is ;

⇒ 1 Yen is = 0.0074 US Dollar ;

The amount 5 million dollar can be numerically written as 5000000 ;

On multiplying the amount by 0.0074 , we get ;

⇒ 5000000 × 0.0074 = 37000 US Dollar .

Therefore , 5000000 Yen is equivalent to $37000 .

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Answer:

1 cake

Step-by-step explanation:

12 slices = 2 cakes

6 slices = 1 cake

The most likely mean for the sample distribution is option c. negatively skewed.

Based on the given information, we know that the mean (M) is less than both the median and the mode. This suggests that the distribution is skewed to the left (negatively skewed), with a long tail on the left side of the distribution.

The mean of a sample distribution is the average value of all the observations or measurements in the sample. It is calculated by adding up all the values in the sample and dividing the sum by the total number of observations in the sample.

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The line of best fit can be used to make predictions about the response variable based on the predictor variables. It can also be used to identify correlations between variables, as well as to estimate the strength of those correlations.

A. Line of Best Fit

A regression line is a statistical tool used to predict the value of a response variable based on the value of one or more predictor variables. It is also known as a line of best fit because it is used to show the best fit of a given data set. The line of best fit is a straight line that best represents the data by minimizing the sum of the squared distances between the observed data points and the line. The line of best fit can be used to make predictions about the response variable based on the predictor variables. It can also be used to identify correlations between variables, as well as to estimate the strength of those correlations.

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In linear equation,the number of customers who will pay by debit card will be 88.97.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                    The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Known as a linear equation, this type of equation has a highest power of one for each variable.

Last week there were

87 + 24 + 7 = 118 customers.

That means that the fraction of the customers, who paid by debit card, was

7/118  

In situations like that, when we use historical data and try to predict future behaviour, we use that past experience and extrapolate to a predicted result.

we simply say that we expect the same fraction, 7/118 if customers use credit cards

for the absolute number of predicted debit  card customers we multiply the predicted number of customers by the expected fraction

1500  × 7 / 118 = 88.97

Therefore the number of customers who will pay by debit card will be 88.97.

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Commutative property of addition is the property that we used to get the answer for 27+29+31 = 87.

The commutative property of addition says that changing the order of addends does not change the sum. As the first civilization to study fractions, the Egyptians used fractions to address a variety of mathematical problems, including the division of food and supplies and the absence of a bullion currency.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).

In the properties used for this question use the properties of the Commutative property of addition

If counted then the final result

31 + 27 + 29

= (30 +1) + (30 - 3) + (30 - 1)

= 3(30) + 1 - 3 - 1

= 90 - 3

= 87

Hence, 27+29+31 = 87

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The value of the expression -13x-7y is -8.

What is the system of equations?

Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.

Given system of equations are

-9x + y = 2   .....(i)

-4x - 8y = -10 ....(ii)

Solve the equation by using system of equations.

Multiply equation (i) by 8 and add with equation (ii)

-72x + 8y = 16

-4x - 8y = -10

___________

-76x = 6

x = 6/-76

x = - (3/38)

Putting x = - (3/38) in equation (i):

-9[- (3/38)] + y = 2

27/38 + y = 2

y = 2 - 27/38

y = 49/38

Putting x = - (3/38) and y = 49/38 in -13x-7y:

-13(-3/38)-7(49/38)

= 39/38 - 343/38

= -304/38

= -8

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Answer:

D.  (39.6) or 39.0

Step-by-step explanation:

See the attached worksheet.

Two right triangles are formed in the diagram.  Use the pythagorean theorem on both, starting with the lower triangle, since two of the sides are known and the third (d) may be calculated.  

1.  From the first (bottom) triangle, we find that d is 36.66.

2.  Using this value of d in the upper triangle provided a length for x of 39.6, closest to answer option D at 39.0

The value of x to 3 significant figures is approximately 18.9 cm.

Area of circle can be defined as the product of pi and square of radius of circle.

The area of a circle is given by the formula[tex]A = πr^2[/tex], where r is the radius of the circle.

Since the area of the circle is 56^2 cm, we can set up the equation:

[tex]πr^2 = 56^2[/tex]

Solving for r, we get:

[tex]r = √(56^2/π) ≈ 13.37 cm[/tex]

Since the square fits exactly inside the circle, its diagonal is equal to the diameter of the circle, which is 2r. Therefore:

x√2 = 2r

Substituting the value of r, we get:

[tex]x√2 = 2(√(56^2/π))[/tex]

x√2 ≈ 26.74

Dividing both sides by √2, we get:

x ≈ 18.94

Therefore, the value of x to 3 significant figures is approximately 18.9 cm.

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Ascending order of the numbers are,

⇒ - 2 1/4, - 1 1/4, | 1 1/4| , | - 1 3/4|, | - 2 1/4 |

The numbers which are arrange in order to least to greatest number is called Ascending order.

We have to given that;

All the numbers are,

⇒ |-2 1/4| , -1 1/4,  3/4,  -2 1/4,  |1 1/4|,  |-1 3/4|

Now, We can simplify each number as;

⇒ | - 2 1/4 | = 2 1/4

                 = 9/4

                 = 2.15

⇒ - 1 1/4 = - 5/4

            = - 1.25

⇒ 3/4 = 0.75

⇒ - 2 1/4 = - 9/4

             = - 2.25

⇒ | 1 1/4| = 5/4

              = 1.25

⇒ | - 1 3/4| = 7/4

                = 1.75

Thus, Ascending order of the numbers are,

⇒ - 2.25, - 1.25, 1.25, 1.75, 2.15

⇒ - 2 1/4, - 1 1/4, | 1 1/4| , | - 1 3/4|, | - 2 1/4 |

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The table of values for y = -128x + 3840 is:

x y

0 3840

5 3200

8 2816

10 2560

30 0

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

Y= -128x + 3840

Then, we have

x = 0,5,8,10,30​

To find the values of y, we substitute each value of x into the equation and simplify:

This means that the above is the table of values for y = -128x + 3840 when x takes on the values 0, 5, 8, 10, and 30

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The spherical tanks of Eindhoven can hold a maximum of approximately 14,137 cubic meters of water.

The maximum amount of water that one of the spherical tanks of Eindhoven will hold can be found using the formula for the volume of a sphere:

V = (4/3) * π * [tex]r^3[/tex]

where V is the volume of the sphere, r is the radius of the sphere, and π is a constant equal to approximately 3.14159.

According to the Eindhoven website, the diameter of each spherical tank is 30 meters. The radius, therefore, is half of the diameter, which is:

r = 30/2 = 15 meters

Substituting this value into the formula for the volume of a sphere, we get:

V = (4/3) * π * [tex](15)^3[/tex]

V ≈ 14,137 cubic meters

When we round this to the closest integer, we obtain:

Maximum amount of water = 14,137 cubic meters

Therefore, one of the spherical tanks of Eindhoven can hold a maximum of approximately 14,137 cubic meters of water.

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Answer:

210 students

Step-by-step explanation:

We want to find 75% of 280, which means we want to find 75 out of every 100 students who voted. We can do this by multiplying 280 by 75% (or 0.75).

280 x 0.75 = 210

So, 210 students voted for the Chiefs to win the Super Bowl.

I hope this helps! And if you could label my answer brainliest that would be awesome.

- Dante

Answer:

Step-by-step explanation:

75% = .75

280 x .75 =210

Answer = 210

The metric system is defined as the decimal system of units based on the meters, kilograms, and second as the units of length, mass, and time respectively. The imperial system is defined as the measurement system used in countries like the UK, Liberia, Myanmar, etc. that uses units like an inch, pound, ton etc.

The Metric and Imperial systems are both systems of measurement. That is, they are not just one unit of measure, but are correlated systems of many units of measure – measuring length and area, weight and mass, volume, force, temperature etc.

The imperial system of measurement is defined as a system that originated in Britain and came to formal use in the early 19th century with the Weights and Measures Act of 1824 and 1878. It uses some of the commonly used units there like an inch, ton, pound, gallon, pint, etc.

Most countries use the metric system which uses the measuring units such as meters and grams, and adds prefixes like kilo, milli, and centi to count orders of magnitude.

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Answer:(-2,-3)

Step-by-step explanation: We are using elimination to solve this system of equations. They've already done the balancing so let's use their given equation. It states

[tex]4y+3x=-6[/tex]  and  [tex]3y-3x=-15[/tex]

Combine the equations which will eliminate the x term and you get :

[tex]7y = -21[/tex]

which means

[tex]y=-3[/tex]

plug it back in to solve for x and you get the x-value to be -2.

The conversion of 1.70 meters to feet gives the value which is equal to 5.5774 feet ( approximately ) .

Meters to feet can be converted by the following relation ,

1 meter = 3.28084 feet

Now Substitute the given value to convert meters  into feet.

Here, convert 1.70 meters into feet we get,

⇒ 1.70 meters =  ( 1.70 ) × ( 3.28084 ) feet

⇒ 1.70 meters =  5.577428 feet

Rewrite upto four decimal places we get,

⇒ 1.70meters =  5.5774 feet ( approximately )

Therefore, after converting unit of 1.77 meters into feet it is equal to 5.5774 feet ( approximately ) .

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For someone working 24 hours daily, the equivalent hourly wage for a $48,000 yearly salary would be $5.48 per hour.

Assuming that someone works 24 hours a day, 365 days a year, their total number of working hours in a year would be 8,760 hours. To calculate how much an hourly rate would be for a $48,000 yearly salary if someone works 24 hours daily, you can divide the annual salary by the total number of working hours.

Dividing $48,000 by 8,760 hours gives an hourly wage of $5.48. This means that if someone works 24 hours daily, their equivalent hourly wage for a $48,000 yearly salary would be $5.48 per hour.

Additionally, laws and regulations related to working hours vary by country and industry, and many limit the maximum number of working hours per day or week.

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The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The manager of the shop gathered data from several donut shops in the city for the total cost, y, for different amounts of donuts, x.

Now, Let two point on the line are (3, 3) and (8, 7).

Hence, The value of slope is,

Slope = (7 - 3) / (8 - 3)

Slope = 4/5

Thus, We get;

The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80.

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Answer:

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases in quadrant 1. It goes through (0, 1), (2, 4), and (3, 8).

Step-by-step explanation:

Answer:

graph 2

Step-by-step explanation:

I did the assignment

A probability mass function is a function that describes the probability of a discrete random variable taking on each possible value in its sample space.

A probability mass function (PMF) is a function that assigns a probability to each possible value of a discrete random variable. The PMF maps each value to the probability of that value occurring in the random variable's sample space. The probabilities assigned by the PMF must sum to 1, since the random variable must take on one of the possible values in its sample space.

The PMF is used to calculate the expected value, variance, and other statistical properties of the random variable. It is also used to create probability distributions and generate simulations of the random variable. Probability mass functions are commonly used in probability theory, statistics, and other fields that involve discrete random variables.

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A pile of 6 boards is 2 timed the volume of a pile of 3 boards with the given dimensions. Option D is the correct answer.

The dimension of an item in mathematics is, approximately speaking, the quantity of degrees of freedom of a moving point on the object. To put it another way, a dimension is indeed the amount of distinct factors or coordinates required to define the location of a point that must be on an object. For instance, a point has a dimension of zero; a line has a size of one since a point can only move along a line in one direction (or its opposite); a plane has a dimension of two; etc.

The volume of the wooden board is given by the formula:

V = (l)(b)(h)

V = (2)(6)(14)

V = 168 cubic inches.

The volume of pile of 3 boards has dimensions:

l = 14

b = 6

h = 3(2)

V = 3(168) = 504 cubic inches.

Similarly, piling the boards and changing the height.

The volume of pile of four boards = 4(168).

The volume of pile of 5 boards = 5(168)

The volume of pile of 6 boards = 6(168) = 2(3(168))  = 2(Volume of pile of 3 boards)

Hence, a pile of 6 boards is 2 timed the volume of a pile of 3 boards with the given dimensions.

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[tex]\frac{1}{10}[/tex] of electricity is made up of other resources and it can be found by addition and subtraction of fractions.

Examine the fractions' denominators. Find the LCM of the denominators and rationalise them to make the denominators of the fractions the same. Add the fraction numerators while keeping the denominator constant. To get the final sum, simplify the fraction.

To subtract fractions, first calculate the denominator's LCM. Step 2: Multiply the numerator and denominator by the same number to get the LCM value. Step 3: When the denominator and numerator are equal, subtract the numerator. Step 4: If necessary, simplify the resulting fraction.

[tex]\frac{5}{10} + \frac{2}{10} + \frac{2}{10} + x = 1.\\\frac{9}{10} + x = 1.\\\frac{10x+ 9}{10} = 1\\10x + 9= 10\\x= \frac{1}{10}[/tex]

hence, 1/10 of the electricity is made up of other resources.

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The value of the exponent 'x' in  5ˣ⁻⁵⁵ = 125⁵ is 70.

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, An equation in exponents 5ˣ⁻⁵⁵ = 125⁵.

5ˣ⁻⁵⁵ = 5³ˣ⁵.     (as 5³ is 125)

Therefore, x - 55 = 15.

x = 70.

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