Write down the size of angle ABC. Give a reason for your answer.

Answer:

c = 56°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

120° is an exterior angle of the triangle , then

c + 64° = 120° ( subtract 64° from both sides )

c = 56°

The polynomials that are equivalent to  (x-3y+72)2 are

A polynomial is described as an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

A polynomial equation in two variables is an equation of the form

p(x, y) = q(x, y) where both p(x, y) and q(x, y) are polynomials in two variables.

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If you are trying to predict Y scores from X scores, X is referred to as the a. predictor variable. Therefore, option a. predictor variable is correct.

The predictor variable, also known as the independent variable or explanatory variable, is a variable that is used to explain the changes or variations in another variable. In this case, the predictor variable (X) is used to predict the value of the dependent variable (Y).

For example, if you are trying to predict the score of a student on a test (Y) based on the number of hours they study (X), then the number of hours studied is the predictor variable. The predictor variable is what you manipulate or control to see its effect on the dependent variable. In other words, the predictor variable is what you believe influences the outcome variable.

It is important to note that the predictor variable does not necessarily cause changes in the dependent variable. There may be other variables at play that can affect the outcome variable. Therefore, it is important to consider other potential confounding variables in your analysis.

In summary, when trying to predict Y scores from X scores, X is referred to as the predictor variable. It is the variable that is manipulated to explain the changes in the dependent variable, Y.

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Answer:

Step-by-step explanation:

4x - 3 ≤ -7

Add 3 to both sides of the inequality to isolate the term with x on one side:

4x - 3 + 3 ≤ -7 + 3

4x ≤ -4

Divide both sides of the inequality by 4 to solve for x:

4x/4 ≤ -4/4

x ≤ -1

So, the solution to the inequality is x ≤ -1. The largest integer value of x that satisfies this inequality is -1.

Answer:

18.62π square inches

Step-by-step explanation:

To find the surface area of the cylinder, we need to find the area of each of its components and add them together. We can use the net of the cylinder to visualize its components and dimensions.

First, let's find the area of the top and bottom circles. We know the diameter of each circle is 3.8 inches, so the radius is half of that, or 1.9 inches. The formula for the area of a circle is A = πr^2, so:

A(top and bottom circles) = 2π(1.9 in)^2

= 2π(3.61 in^2)

= 7.22π in^2

Next, let's find the area of the curved surface of the cylinder. The height of the cylinder is labeled as 3 inches, which is also the height of the rectangle in the net. The length of the rectangle is the circumference of one of the circles, which is πd (where d is the diameter). So:

length of rectangle = π(3.8 in) = 11.96 in

The formula for the area of the curved surface of a cylinder is A = 2πrh, where r is the radius and h is the height. We can use the radius we found earlier and the height of 3 inches to calculate the area of the curved surface:

A(curved surface) = 2π(1.9 in)(3 in)

= 11.4π in^2

Finally, we can add the areas of the top and bottom circles and the curved surface to get the total surface area of the cylinder:

Total surface area = A(top and bottom circles) + A(curved surface)

= 7.22π in^2 + 11.4π in^2

= 18.62π in^2

Therefore, the surface area of the cylinder in terms of π is 18.62π square inches.

The correct statement regarding the best measure of center for the data-set in this problem is given as follows:

The mean is the best measure of center because there are no outliers present.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The dot plot shows the number of times that each observation appears, hence the data-set is given as follows:

2, 3, 3, 3, 4, 6, 6, 7, 7, 8, 9.

We can see that the data-set is clustered, meaning that there are no outliers, hence the mean can be used instead of the median.

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The statement that is not necessarily correct is ΔTRS ≅ ΔVUW. So, correct option is D.

The given information states that two triangles are congruent based on the corresponding parts, RS ≅ UV, RT ≅ UW and ∠R ≅ ∠U.

To determine which statement is not necessarily correct, we need to use the congruence criteria that are sufficient to prove the congruence of triangles. These criteria are:

SSS (Side-Side-Side): If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

SAS (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

ASA (Angle-Side-Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Using the given information, we can apply the SAS criterion to show that ΔRST ≅ ΔUVW. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (a) ΔRST ≅ ΔUVW is correct.

Now, we can use the SAS criterion again to show that ΔSTR ≅ ΔVWU. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (b) ΔSTR ≅ ΔVWU is also correct.

We can also use the SAS criterion to show that ΔTRS ≅ ΔVWU. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (c) ΔTRS ≅ ΔVWU is correct.

However, we cannot use any of the above criteria to show that ΔTRS ≅ ΔVUW. This is because we do not know that TU ≅ VW. Therefore, the statement (d) ΔTRS ≅ ΔVUW is not necessarily correct.

So, correct option is D.

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The exponential function f(x) = 2^x is given by the blue graph on the given graph.

The horizontal asymptote of a function is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

The function in this problem is defined as follows:

y = 2^x.

Two relevant numeric values are given as follows:

Hence the function is represented by the blue graph.

The horizontal asymptote is of y = 0, as when x goes to negative infinity, y goes to zero.

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Step-by-step explanation:

DECREASING 3.8% means  96.2 % is left each year   ( .962 in decimal)

1800 (.962) ^6  =~ 1427 population

Answer:

1389.6

explamation

1500 of 3.8% is 68.4

68.4*6=410.4

1800-410.4=139.6

The error in the proportion is the second line should be 2x + 18 = 3x making the final answer 18 = x

The error in the solution of the proportion shown can be calculated as follows:

Therefore, let's solve the equation to know the error made.

2 / 3 = x / x + 9

cross multiply

2(x + 9) = 3x

open the brackets

2x + 18 = 3x

subtract 2x from both sides of the equation

2x + 18 = 3x

2x - 2x + 18 = 3x - 2x

x = 18

Therefore, he made mistake in the second line, it should be  2x + 18 = 3x making the final answer 18 = x

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the direction angle of w=8j is 90.0 degrees. The direction angle of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.

what is direction angle ?

The direction angle, also known as the argument or phase angle, of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.

In the given question,

The direction angle of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.

In this case, the complex number is w=8j, which has an imaginary part of 8 and a real part of 0. Therefore, the vector representing w points directly upwards in the complex plane, and the angle between this vector and the positive real axis is 90 degrees.

Rounding this to the nearest tenth of a degree gives 90.0 degrees.

So the direction angle of w=8j is 90.0 degrees.

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The function best models the data in the table is y=-0.6x+132 (option a).

The table shows the minimum target heart rates by age, which implies that as a person ages, their heart rate should be maintained within a certain range during exercise to achieve optimal cardiovascular benefits. In order to determine the target heart rate for a given age, we need a mathematical function that can accurately model the data in the table.

This is a linear function, which means that it assumes a constant rate of change in the target heart rate as age increases.

However, the data in the table shows that the target heart rate decreases gradually with age. Therefore, this function does  accurately model the data and is a suitable option.

Hence (a) is the right one.

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Complete Question:

Age x (year)                           Minimum Target Heart Rates by Age

30                                                                114

35                                                                 111

40                                                                108

45                                                                105

50                                                                102

Which function best models the data in the table?

a) y=-0.6x+132

b) y=(x-30)²+114

c) y= 19/30x

Well, a diameter is double the radius. The radius is given in the image.

So, 2+2 = 4

The polynomial equation with roots -26, -2, and 4.39 is:

x³ + 15.22x² - 239.44x + 1049.44 = 0

The given root of 0.11 is not a root of this equation.

Any equation with a sum of terms that includes constant coefficients multiplied by one or more variables raised to a non-negative integer power constitutes a polynomial equation.

If the roots of a polynomial equation are -26, -2, and 4.39, then the factored form of the polynomial equation can be written as:

(x + 26)(x + 2)(x - 4.39) = 0

Expanding this equation gives us:

(x + 26)(x² - 2x - 8.78x + 8.78×2) = 0

Simplifying further, we get:

(x + 26)(x² - 10.78x + 38.44) = 0

Multiplying out the second factor, we get:

x³ - 10.78x² + 38.44x + 26x² - 277.88x + 1049.44 = 0

Combining like terms, we get:

x³ + 15.22x² - 239.44x + 1049.44 = 0

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Answer: 23 1/2

Step-by-step explanation:

you need to include the number of roses in the mean calculation (Ex: 22, 22, 23, 23, 23, 23, etc.)

The triangular prism therefore has a  123.5 cubic unit volume as by dividing its base area by its height.

what is prism ?

A prism is indeed a three-dimensional solid object in geometry made up of two bases that are parallel and congruent and are joined by a collection of rectangular faces. The kind of prism depends on the form of the bases. The prism is referred to as an n-sided prism, for instance, if the basis are triangles with n sides.

Although parallelograms and squares are also possible, a prism's faces are typically rectangular. A prism's height is determined by the mean line between its bases, and its lateral edges are those that link the corresponding base vertices.

given

The volume of a triangular prism can be calculated by multiplying the base area by the height and dividing by 2, as it is essentially a triangular pyramid extruded in the height direction. The formula for calculating the volume of a triangular prism is:

Volume = (Base Area × Height) / 2

Given that the base area is 38 units^2 and the height is 6.5 units, we can substitute these values into the formula to calculate the volume:

Volume = (38 × 6.5) / 2

Volume = 247 / 2

Volume = 123.5 units^3

So, the volume of the triangular prism is 123.5 units^3.

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The series is not geometric.

What is geometric series?

In mathematics, the geometric series means the sum of the terms that have a common ratio between every adjacent two terms of them. There can be two types of geometric series: finite and infinite.

The given series is

3 , 3z, 6z², 9z³

The given series is either geometric or not.

The initial term or the first term is 3 which also can be written as 3z⁰

Ratio between successive terms can be determined by

second term/ first term

Here second term is 3z and first term is 3

So the ratio is 3z/3

                     = z

If the series is geometric then

it must be equal to 6z²/ 3z= 2z and 9z³/ 6z² = (3/2)z

The ratios are not equal to each other.

Hence, the series is not geometric.

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The inequality for "number t​ divided by 32 is at most 4. 25" is t/32 ≤ 4.25 and the solution is t ≤ 136

To write the word sentence as an inequality, we need to translate the words into mathematical symbols.

The phrase "a number t divided by 32" can be written as t/32. The word "is" can be translated as an equals sign, and "at most" can be translated as less than or equal to. Therefore, the word sentence "A number t divided by 32 is at most 4.25" can be written as:

t/32 ≤ 4.25

To solve the inequality, we can isolate the variable t by multiplying both sides by 32:

t ≤ 4.25 * 32

t ≤ 136

Therefore, the solution to the inequality is t is less than or equal to 136. This means that any value of t that is less than or equal to 136 will make the original inequality true. If t is greater than 136, then the inequality will be false.

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The volume of the bookshelf is 1/4 cubic units.

The amount of space a three-dimensional object occupies is measured by its volume.

A cubic unit, such as a cubic foot, cubic metre, or cubic metre is typically used to express it.

An object's volume can be calculated by figuring out how much space is contained within its boundaries. Depending on the shape of the object, different mathematical formulas can be used to accomplish this.

To calculate the volume of the bookshelf, we need to add the volumes of the two cubes together.

The length of one side cubed determines a cube's volume.

Since each cube has a side of (1/2), the volume of each cube can be calculated as:

(1/2)³ = 1/8

To get the total volume of the bookshelf, we can add the volumes of the two cubes:

1/8 x 2 = 1/4

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Answer:

12

Step by step explanation

radius of a cone= square root of 3v

πh

r= square root of 3×2712.96

3.14×18

r= square root of 8138.88

56.52

r= square root of 144

r=12

length: 33, width: 9

write it out as 4x-3(2) + 2x. simplify that and you gey 84= 10x-6. add the 6 over and you get x=9, this is your width. know you just do 4(9) - 3 to find length, which equals 33

The solution to the system of equations is:

x = -1/42

y = -11/6

In mathematics, a variable is a symbol that represents a value that can vary or change. It is often represented by a letter, such as x, y, or z. Variables are used to write algebraic expressions and equations that can be solved to find unknown quantities. The value of a variable can be determined by solving an equation that involves the variable, or by assigning a specific value to the variable. In algebra,

To solve this system of equations by the method of elimination, we need to eliminate one of the variables by adding the two equations together. We can do this by multiplying the first equation by 3, which will make the y terms cancel out when we add the equations:

7x - y = 2 (multiply by 3)

-21x - 3y = 5

21x - 3y = 6 (first equation multiplied by 3)

-21x - 3y = 5

Now we can add the two equations together:

(21x - 3y) + (-21x - 3y) = 6 + 5

0x - 6y = 11

Simplifying, we get:

-6y = 11

Dividing both sides by -6, we get:

y = -11/6

Now that we have solved for y, we can substitute this value back into either equation to solve for x. Let's use the first equation:

7x - y = 2

7x - (-11/6) = 2

Multiplying both sides by 6 to eliminate the fraction, we get:

42x + 11 = 12

Subtracting 11 from both sides, we get:

42x = -1

Dividing both sides by 42, we get:

x = -1/42

Therefore, the solution to the system of equations is:

x = -1/42

y = -11/6

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The amount that the Jones family would pay in the 18th month would be $1,233.45

Prior to determining the required payment for the 18th month, it is paramount to calculate the collective minimum payments by the Jones family during the course of seventeen months.

First, find the amount that had been paid in total by the Jones in 17 months to be :

= Monthly payment x minimum monthly payment

= 17 x 25

= $ 425

The balance after 17 months is :

= $ 1 , 658. 45 - $ 425

= $ 1, 233. 45

The remaining balance of $ 1, 233. 45 would have to be paid in the 18th month.

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The unknown number in the statement is 64/3.

The problem can be translated into an algebraic equation as follows:

(3/4)x - 6 = 10

where x is the unknown number we are trying to find.

To solve for x, we need to isolate it on one side of the equation. We can start by adding 6 to both sides:

(3/4)x = 16

Next, we can multiply both sides by the reciprocal of 3/4, which is 4/3:

x = (4/3) * 16

x = 64/3

Therefore, the solution to the equation is x = 64/3, which means that the unknown number is 64/3.

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If cash is  54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills, the total deposit is $454.00.

To find the total deposit, we need to add up the amounts from the checks and cash, and then subtract the cash received.

First, let's add up the amounts from the checks:

$152.54 + $147.46 = $300.00

Next, let's add up the amounts from the cash:

54 one-dollar bills = $54.00

12 five-dollar bills = $60.00

6 ten-dollar bills = $60.00

Total cash = $174.00

Finally, we need to subtract the cash received:

$174.00 - $20.00 = $154.00

Therefore, the total deposit is $300.00 + $154.00 = $454.00.

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Complete question is:

Find the total deposit if you have: Checks: $152.54 and $147.46: cash: 54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills; less $20.00 as cash received.

The true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.

In hypothesis testing, the power of a test refers to the probability of correctly rejecting a false null hypothesis.

To calculate the power of a test, we need to know the significance level of the test, the sample size, the effect size, and the variance of the population.

Additionally, we need to know the specific hypothesis being tested, as the decision rule and power calculation depend on the null and alternative hypotheses.

A hypothesis test for the population mean amount of mercury in a certain type of fish.

Test whether the mean amount of mercury is different from 11.5 micrograms per ounce, using a two-tailed test at a significance level of 0.05.

If the sample size is 100, the effect size is 0.5, and the population variance is 4, then the power of the test is approximately 0.7629.

This means that if the true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.

The hypothesis test, it is impossible to calculate the power.

It is essential to know the specific hypothesis being tested, as well as the details of the test, such as the sample size, effect size, and variance.

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The model of local restaurant which sends a 20% off coupon to its email subscribers, based on past data is an example of supervised model.

Supervised model is defined by its use of labeled datasets to train algorithms based on classification of data or predict outcomes accurately. While the accuracy of supervised learning models is more than unsupervised learning models. Supervised, as we are using past data. Classification, as we are trying to classify the customers into categories to study which ones will use the coupons. We have a local restaurant which send

a 20% off on a coupon to its email subscribers. It is based on past data. Using the above definition the predicted model for the provide example is supervised model.

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Therefore,  The length of the hollow cylindrical pipe is approximately 55.48 meters.

To solve this problem, we will first find the volume of the solid iron rectangular block and then use it to find the length of the hollow cylindrical pipe. Here are the steps:

1. Find the volume of the rectangular block:
  Volume = Length × Width × Height
  Volume = 3.5m × 2.4m × 2m = 16.8 m³
2. Convert the internal radius and thickness to meters:
  Internal radius = 27 cm = 0.27 m
  Thickness = 4 cm = 0.04 m
3. Calculate the external radius of the pipe:
  External radius = Internal radius + Thickness
  External radius = 0.27m + 0.04m = 0.31m
4. Let L be the length of the pipe. We can write the volume of the hollow pipe as:
  Volume = π × (External radius² - Internal radius²) × Length
  16.8 m³ = π × (0.31² - 0.27²) × L
5. Solve for L:
  L = 16.8 m³ / [π × (0.31² - 0.27²)]
  L ≈ 55.48 meters
Therefore,  The length of the hollow cylindrical pipe is approximately 55.48 meters.

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