Whats the rate of change (1, 9.5), (2, 12), (3, 14.5), (4, 17)

(1,2,4)

Range describes the y-values of a graph.

Range

Range is the y-values that a graph covers. Remember that the y-values are found on the vertical axis. If the graph is not continuous, then the values between the points are not included in the range. Similar to the range, the domain of a graph is the x-values that a graph covers. If there is a coordinate point with a y-value, then that y-value should be included in the range.

Finding Range

In order to find the range, we need to find all the unique y-values of the graph. Additionally, the range is given in numerical order. This means starting from the least value and going up to the greatest. The lowest y-value is 1, then 2, and finally 4. Even though there are two points where y = 2, we are only looking for unique values. This means that the range is (1,2,4).

Answer:

g=28

Step-by-step explanation:

g+6=3=31

3+4=31

g+3-3=31-3

g=31-3

g=28

Answer:

28

Step-by-step explanation:

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

The expression y³x⁵ in terms of u and v is \(e^{3u} e^{5v}\)

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x.  The equation being \(e^{\ln x}=x\)

Given here, the polynomial expression y³x⁵ where \({\ln x}=u\) and  \({\ln y}=v\)   thus, \(e^{v} =y\) and \(e^{u} =x\)

∴ , y³x⁵=\(e^{3u}e^{5v}\)

Hence, The expression y³x⁵ in terms of u and v is \(e^{3u} e^{5v}\)

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Answer:

c

Step-by-step explanation:

x=1 g(x)=-10

x=2 g(x)=-12

x=3 g(x)=-14

f(x)=x+4

=＞ g(x)=-2·(x+4)

Hey there! :)

Domain is the set of all x-values while Range is the set of all y-values!

When we want to find the domain of functiom through graph, we can do by finding the left point first and then the right point in x-plane or horizontal line.

The left point is (-4,0) and the right point is (4,0)

Since both points are opened, we use ( and ) instead.

Hence, the domain is (-4,4)

Next is finding range. Range is similar to Domain but y-value. You can find the range by finding the minimum point first then maximum point in y-plane or vertical line.

From the graph, minimum point is (-1,-3) and maximum point is (-4,0),(1,0) and (4,0)

Remember that we use the y-coordinate point for range! The minimum point and maximum point (1,0) both are closed dot. Since they are closed dot, we use [ or ].

Therefore, the range is [-3,0]

In conclusion, the answer is first choice.

Let me know if you have any questions!

Topic: Functions / Domain & Range

The number of the boys in the class will be equal to 18.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that In math class, the girl-to-boy ratio is 8 to 6. If there are 24 girls in the class.

The number of the boys in the class will be calculated as,

Let, 8x = 24

x = 24 / 8

x = 3

The number of boys,

6x = 6x 3 = 18

Therefore, the number of the boys in the class will be equal to 18.

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Answer:

y=x+2

y=x+4

slope intercept form is y=mx+b

The average annual return on this investment from 2011 to 2015 is approximately 0.8%.

To calculate the value of a $1 investment made at the beginning of 2011 and its average annual return by the end of 2015, we need to multiply the successive annual returns and calculate the cumulative value.

The successive annual returns on small U.S. stocks from 2011 to 2015 are:

-3.80%, 19.15%, 45.91%, 3.26%, and -3.80%.

To calculate the cumulative value, we multiply the successive returns by the initial investment value of $1:

(1 + (-3.80%/100)) * (1 + (19.15%/100)) * (1 + (45.91%/100)) * (1 + (3.26%/100)) * (1 + (-3.80%/100))

Calculating this expression, we find that the cumulative value is approximately $1.044, rounded to three decimal places.

Therefore, a $1 investment made at the beginning of 2011 would have been worth approximately $1.044 at the end of 2015.

To calculate the average annual return, we need to find the geometric mean of the annual returns. We can use the following formula:

Average annual return = (Cumulative value)^(1/number of years) - 1

In this case, the number of years is 5 (from 2011 to 2015).

Average annual return = (1.044)^(1/5) - 1

Calculating this expression, we find that the average annual return is approximately 0.008 or 0.8% per year, rounded to two decimal places.

Therefore, the average annual return on this investment from 2011 to 2015 is approximately 0.8%.

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The area of the given shape is 78.5 unit²

Given,

The shape is 1/4th part of circle.

The radius is given as 10 units

We have to find the area of the shape.

Here,

The area of a circle is pi times the radius squared (A = π r²).

Area of circle = π × r²

Then

Area of 1/4th part of circle = π × r² / 4

That is,

Area of 1/4th part of circle = 3.14 × 10² / 4

Area of 1/4th part of circle  = 314 / 4

Area of 1/4th part of circle = 78.5 unit²

That is,

The area of the given shape is 78.5 unit²

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Answer:

x>8

Step-by-step explanation:

make the equation equal to -22 and get 8 and see if if it is less than or greater than

The negative correlation coefficient of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer suggests that as vitamin A consumption increases, the cancer rate tends to decrease.

A correlation coefficient measures the strength and direction of the linear relationship between two variables.

In this case, a correlation coefficient of -0.73 indicates a negative correlation between consumption of vitamin A and the cancer rate.

Interpreting this correlation, it can be inferred that there is an inverse relationship between the two variables. As consumption of vitamin A increases, the cancer rate tends to decrease.

However, it is important to note that correlation does not imply causation.

It would be incorrect to conclude that consuming more vitamin A causes this type of cancer. Correlation does not provide information about the direction of causality.

Other factors and confounding variables may be involved in the relationship between vitamin A consumption and cancer rate.

To establish a causal relationship, further research, such as experimental studies or controlled trials, would be necessary. These types of studies can help determine whether there is a causal link between vitamin A consumption and the occurrence of this particular cancer.

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the expression x + (x - 5) can be used to determine how many apples Martin and Omar used in total. It helps us understand that Martin used more apples than Omar and that the number of apples in total is greater than 10.

a. Let x represent the number of apples that Martin used.

The expression is x + (x - 5).

b. We can substitute 10 for x in the expression to see if it is possible for Martin to have used 10 apples: 10 + (10 - 5). The answer is 15, which is greater than 10, so it is not possible for Martin to have used 10 apples.

Martin and Omar both used apples in their recipes, but Omar used 5 fewer apples than half as many as Martin used. To represent the number of apples that they used altogether, we can use an expression that includes a variable x, which represents the number of apples that Martin used. The expression is x + (x - 5). To check if Martin could have used 10 apples, we can substitute 10 for x in the expression: 10 + (10 - 5). The answer is 15, which is greater than 10, so it is not possible for Martin to have used 10 apples. Therefore, the expression x + (x - 5) can be used to determine how many apples Martin and Omar used in total. It helps us understand that Martin used more apples than Omar and that the number of apples in total is greater than 10.

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The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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Answer:

-7 1/7

Step-by-step explanation:

Hope that helps!

The binary representations of the given decimal numbers are: (a) 8 = 1000, (b) 35 = 100011, (c) 108 = 1101100, and (d) 176 = 10110000.

(a) To convert 8 to binary, we repeatedly divide the number by 2 and keep track of the remainders. The remainders, read in reverse order, give the binary representation.

Starting with 8, the division process yields: 8/2 = 4 with a remainder of 0, 4/2 = 2 with a remainder of 0, and 2/2 = 1 with a remainder of 0. The binary representation of 8 is 1000.

(b) To convert 35 to binary, we follow the same process. The division steps are as follows: 35/2 = 17 with a remainder of 1, 17/2 = 8 with a remainder of 1, 8/2 = 4 with a remainder of 0, 4/2 = 2 with a remainder of 0, and 2/2 = 1 with a remainder of 0. The binary representation of 35 is 100011.

(c) For 108, the division steps are: 108/2 = 54 with a remainder of 0, 54/2 = 27 with a remainder of 0, 27/2 = 13 with a remainder of 1, 13/2 = 6 with a remainder of 1, 6/2 = 3 with a remainder of 0, 3/2 = 1 with a remainder of 1. The binary representation of 108 is 1101100.

(d) Finally, for 176, the division steps are: 176/2 = 88 with a remainder of 0, 88/2 = 44 with a remainder of 0, 44/2 = 22 with a remainder of 0, 22/2 = 11 with a remainder of 0, 11/2 = 5 with a remainder of 1, 5/2 = 2 with a remainder of 1, and 2/2 = 1 with a remainder of 0. The binary representation of 176 is 10110000.

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It should be noted that the numbers that are less than -8/3 include -2.76 and -11/4.

It should be noted that the information is to find the numbers that are less than -8/3. It should be noted that -8/3 simply implies 2.67

It should be noted that - 2 1/4 implies -2.25.

It should be noted that -11/4 implies -2.75.

Therefore, it should be noted that the numbers that are less than -8/3 include -2.76 and -11/4.

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Which numbers are less than –8/3? the options are -2.6 (with a line over the 6 meaning it repeats), -2.76, -2 1/4, -11/4, and -2

As per the side splitter theorem, the segment length would complete the proportion is GJ

In math, the side splitter theorem states that "if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally".

Here we have to find the segment length that would complete the proportion by using the side splitter theorem.

According to this theorem and by using the following diagram, we can elaborate the following proportion

=> GH/HE = GJ/JF

Here we have identifies that the segment that completes the proportion is GJ, because it must be used according to the theorem.

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A graph of the function f(x) = sin(2πx + π/2) is shown in the image attached below.

In Mathematics and Geometry, a sine wave is also referred to as a sinusoidal wave, or just sinusoid and it can be defined as a fundamental waveform that is typically used for the representation of periodic oscillations, in which the amplitude of displacement at each interval is directly proportional to the sine of the displacement's phase angle.

In this exercise, we would use an online graphing calculator to plot the given sine wave function f(x) = sin(2πx + π/2) with its minima, midline, and maxima as shown in the graph attached below.

In conclusion, we can logically deduce that the midline of this sine wave function y = 1/2sin(3x/2) + 2 is represented by y = 0.

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\(\dfrac{10}{1+2i}\\\\\\=\dfrac{10(1-2i)}{(1+2i)(1-2i)}\\\\\\=\dfrac{10-20i}{1 - (2i)^2}\\\\\\=\dfrac{10-20i}{1+4}~~~~~;[i^2 =-1]\\\\\\=\dfrac{10-20i}5\\\\=\dfrac{10}5 - \dfrac{20i}5\\\\=2-4i\)

Answer:

becuase it is evil

Step-by-step explanation:

the will be evil and will become bad :)

15 hours.

(please mark me as brainlest.)

Answer:

15 hours

Step-by-step explanation:

I'll assume "1 2" is 1/2 and "7 1 2" is 7 1/2.

We can make this into an equation by using x for hours and 1/2 as the rate and set it equal to 7 1/2 to find x.

1/2x=7 1/2

Divide each side of the equation by 1/2.

x=15

SO it took 15 hours for 7 1/2 inches of snow to fall

We need to show that the span of v2 is a subset of the \($\text{span}\{v_2\} \subseteq \text{span}\{v_1, v_2\}$\) and \($\text{span}\{v_2\} \subseteq \text{span}\{v_2, v_3\}$\).

To prove \($\text{span}\{v_2\} \subseteq \text{span}\{v_1, v_2\}$\), consider an arbitrary vector x in \($\text{span}\{v_2\}$\). This means that x can be written as \($x = a v_2$\) for some scalar a. Since \($v_1$\) is linearly independent of \($v_2$\), we know that \($v_2$\) cannot be expressed as a linear combination of \(v_1$ and $v_2$\). Therefore, x cannot be expressed as a linear combination of \(v_1$ and $v_2$\) either, implying \($x \notin \text{span}\{v_1, v_2\}$\). Hence, \($\text{span}\{v_2\} \subseteq \text{span}\{v_1, v_2\}$\).

Similarly, to prove \($\text{span}\{v_2\} \subseteq \text{span}\{v_2, v_3\}$\), consider an arbitrary vector y in \($\text{span}\{v_2\}$\). This means that y can be written as \($y = b v_2$\) for some scalar b. Since \($v_3$\) is linearly independent of \($v_2$\), we know that \($v_2$\) cannot be expressed as a linear combination of \(v_2$ and $v_3$\). Therefore, y cannot be expressed as a linear combination of \(v_2$ and $v_3$\) either, implying \($y \notin \text{span}\{v_2, v_3\}$\). Hence, \($\text{span}\{v_2\} \subseteq \text{span}\{v_2, v_3\}$\).

(b) We need to find the intersection of \($\text{span}\{v_1, v_2\}$\) and \($\text{span}\{v_2, v_3\}$\).

Notice that \($\text{span}\{v_1, v_2\}$\) is a subspace of \($\mathbb{R}^n$\) that contains both \(v_1$ and $v_2$\). Similarly, \($\text{span}\{v_2, v_3\}$\) is a subspace of \($\mathbb{R}^n$\) that contains both \(v_2\,\, and \,\,v_3\). Since \($v_2$\) is common to both spans, any vector in the intersection of these spans must contain \($v_2$\) as well.

Therefore, the intersection \($\text{span}\{v_1, v_2\} \cap \text{span}\{v_2, v_3\}$\) is equal to \($\text{span}\{v_2\}$\).

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60+90+ angle U = 180 {sum of angle of triangle}

or, 150+ U= 180

or, angle U = 30°

From here we got that ,

angle U is smallest.

We know that, side opposite to the shortest angle is shortest side. So , short leg is side PM

In right angled triangle PMU,

hypotenuse(h) = 10

angle theta = 60°

perpendicular (PM)= ?

NOW,

sin theta = Perpendicular/ hypotenuse

or, sin 60° = P/10

\( \\or \frac{ \sqrt{3} }{2} = p \div 10\)

\( or\frac{10 \sqrt{3} }{2} = p\)

\(or \: 5 \sqrt{3 } = p\)

Therefore,

\(short \: leg = 5 \sqrt{3} \)

In order to solve for the measure of angle P, the equation x + y + z + w = 360° can be used.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians and are used to describe the direction of two intersecting lines in a plane. Angles are also used to measure the central angle of a circle and the angle between two curves.

This equation is known as the Angle Sum Theorem, which states that the sum of the measures of the angles of a triangle or a quadrilateral equals 360°. The measure of each angle of the quadrilateral can be used in the equation to solve for the measure of angle P, which is labeled as y. This equation can be written as x + y + z + w = 360° and then solved for the measure of angle P by subtracting x + z + w from both sides of the equation. This would result in y = 360° - (x + z + w). By substituting the measure of each angle into the equation, the measure of angle P can be found.

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According to the conversion factor, 10 grams is equal to 0.0220462 pounds and 0.3527392 ounces.

Converting units can be a tricky task, but it's important to be able to do it correctly in order to make accurate measurements. In this case, we will be converting grams to pounds and ounces.

To begin the conversion, we need to know the conversion factor between grams and pounds. The conversion factor is 0.00220462, which means that one gram is equal to 0.00220462 pounds.

Now, to convert 10 grams to pounds, we simply multiply 10 by the conversion factor:

10 grams * 0.00220462 pounds/gram = 0.0220462 pounds

So 10 grams is equivalent to 0.0220462 pounds.

Next, we need to convert the remaining decimal to ounces. There are 16 ounces in a pound, so we can use the conversion factor of 1 pound equals 16 ounces to find out how many ounces are in 0.0220462 pounds.

0.0220462 pounds * 16 ounces/pound = 0.3527392 ounces

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Complete Question:

Find the equivalent value for 10 grams in pounds and ounces.

The equation for the number of restaurants per capita in the town can be derived by dividing the number of restaurants by the population. The equation is given by R/P = (4t + 25)/(600t + 4000).

To determine the number of restaurants per capita in the town, we divide the number of restaurants (R) by the population (P). Given the equations for population growth (P = 600t + 4000) and restaurant growth (R = 4t + 25), we can create an equation for the number of restaurants per capita.

The number of restaurants per capita is expressed as R/P. Substituting the equations for R and P, we have (4t + 25)/(600t + 4000). This equation represents the ratio of the number of restaurants to the population at any given year (t) after 2010.

The equation indicates that as time (t) increases, both the numerator (number of restaurants) and the denominator (population) increase. However, the rate at which the population grows (600t) is much higher compared to the rate at which the number of restaurants increases (4t). This implies that the number of restaurants per person gradually decreases over time.

By utilizing this equation, we can analyze the changing ratio of restaurants to population and gain insights into the dining options available to individuals in the town as it experiences population growth.

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Answer:

2 and 4 are true.

Step-by-step explanation:

1. False. Centi (100) times smaller than a meter, gram, or liter. Deci (10) times smaller than a meter, gram, or liter.

2. True. Hecto (100) times larger. Kilo (1000) times larger.

3. False. Deka (10) times larger. Kilo (1000) times larger.

4. True. Deka (10) times larger than a gram, which is a base unit.

Answer:

The answer is:

1*28

2*14

4*7

Factors are 1,2,4,7,14,28

The Jackson family averaged 22.71 miles per gallon on their trip.

To find out the average miles per gallon used by the Jackson family on their trip, the distance they covered and the amount of fuel they consumed are both necessary information.

They started their trip with an odometer reading of 18,649.3 miles, and the odometer reading at the end of the trip was 20,630.5.

The distance covered, therefore, is:20,630.5 - 18,649.3 = 1,981.2 miles

Next, to determine the average miles per gallon, divide the total distance covered by the amount of fuel consumed:1,981.2 miles ÷ 87.3 gallons

= 22.71 miles per gallon.

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