Triangle ABC has angle A = 31 degrees and angle B = 87 degrees.  What is the measure of angle C ?
​

Probability that that sum of the two dice outcomes is 6 is 5/36

What is probability?

We know,

Probability = Number of events / Total no. of favourable outcomes

If we through two dice then ,

Total number of favourable outcomes = 36

Here, we need the sum of the two outcomes is 6 is

(1, 5) , (2, 4), (3, 3), (4, 2), (5, 1)

So, the number of events = 5

P(of getting sum 6) = 5/ 36

Hence, Probability that that sum of the two dice outcomes is 6 is 5/36

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Answer:

Line C

Step-by-step explanation:

Given:

Create the equation for the line using the given information:

[tex]\implies y=\dfrac{1}{2}(x-4)[/tex]

Distribute:

[tex]\implies y=\dfrac{1}{2}x-2[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Compare the found equation with the slope-intercept formula:

The y-intercept is the y-value of the point at which the line crosses the y-axis.  Therefore, the line crosses the y-axis at y = -2.

The slope tells us how much y increases as x increases.  Given the slope is ¹/₂, the line increases by one y-value for every two x-values.

Therefore, the line that represents the given information is line C.

The relationship between the variable is the direction, strength, and linearity .

Scatterplots can be used when one continuous variable is under the control of the experimenter and the other is dependent on it, or when both continuous variables are independent. When one parameter is systematically increased and/or decreased by the other, it is called the control parameter or independent variable and is usually plotted along the horizontal axis. Measured or dependent variables are usually plotted along the vertical axis. In the absence of a dependent variable, any type of variable can be plotted on any axis and the scatter plot he only shows the degree of correlation (not causality) between the two variables.

Scatterplots can suggest different types of correlations between variables with specific confidence intervals. If the dot pattern slopes downwards from the lower left to the upper right, this indicates a positive correlation between the investigated variables. If the dot pattern slopes from top left to bottom right, it indicates a negative correlation. You can draw a line of best fit (also called a "trend line") to explore the relationship between variables. The formula for correlation between variables can be determined by established best-fit methods. For linear correlation, the optimal procedure is called linear regression, which guarantees a correct solution in finite time. There is no one-size-fits-all procedure that guarantees the correct resolution in any relationship. Scatterplots are also very useful for seeing how two comparable data sets match up to show non-linear relationships between variables.

Desired Weight:

A standardized table of desirable (or ideal) weight for adult height is based on life expectancy. Both malnutrition and obesity are associated with an increased risk of early death. A desirable weight corresponds to a body mass index (ratio of weight in kg/height in m2) between 20 and 25. Ideal weight charts based on actuarial data were first published in 1942 by the Metropolitan Life Assurance Company of New York and were replaced in 1959 by charts of average and desirable weights.

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Answer: -108y^2 + 84y

Step-by-step explanation:

y^2 is y squared

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The required simplified solution of the given expression is -108y² + 84y.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

Given expression,
= −12y(9y − 7).

Simplify,
Applying distributive property,
= -12y×9y - 12y(-7)
= -108y² + 84y

Thus, the required simplified solution of the given expression is -108y² + 84y.

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The required probabilities of the given parts are a) 56%, b) 6% , c) 94%.

The probability is the proportion of the probability of an occasion to occur. It estimates the conviction of the occasion. The recipe for probability is given by; P(E) = Number of Good Results/Number of absolute results.

a) These two occasions are autonomous, consequently, the probability of both is the increase of the probabilities of every, accordingly:

0.56 = 56% probability that the two offers are fruitful.

b) E1 has a 1 - 0.7 = 0.3 probability of being ineffective, while E2 has a 0.2

likelihood, thus:

0.06 = 6% probability that neither one of the bids is effective.

c) 1 - 0.06 = 0.94

0.94 = 94% probability that the firm is effective in no less than one of the two bids.

Thus, required probabilities are a) 56%, b) 6% , c) 94% .

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The real part of Z₁+Z₂ is 8 and imaginary part of Z₁+Z₂ is -2, when Z₁ and Z₂ are added together and the result moves Z₁ 6 units right and 3 units down

A complex number is of the structure a + bi, a, b are real numbers, and I = √(- 1). Deciding the upsides of square underlying foundations of negative numbers is utilized. It is addressed in the direction plane with the real part on the x-hub and imaginary part b on the y-pivot, the arranged pair being (a, b).

In the inquiry, we are given two complex numbers,

Z₁ = 2 + i

Z₂ = 6 - 3i

These focuses are addressed on the direction plane as a circle and a triangle separately. We ascertain their total, z3.

To add Complex Numbers, the real parts are added to the genuine parts and the nonexistent to the imaginary.

∴ Z₃ =Z₁+Z₂ = (2 + i) + (6 - 3i) = (2+6) + (1-3)i = 8 - 2i.

This point is addressed as a square on the Direction plane.

Hence, we can say that real part is 8, and its imaginary part is - 2.

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The strategy to catch the spider is elaborated out here.

The best strategy for catching the spider after infinitely many steps is to start at one point in the grid and then move in a clockwise spiral, expanding your search area every time you move. As you move, you can use a combination of visual and physical cues, such as vibrations and sound, to detect the spider's presence. This method will ensure that the spider will eventually be caught in a finite amount of time. Additionally, if the spider changes directions, your search will be able to adjust to that change, as you will be able to detect it in the spiral pattern.

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Answer:

Step-by-step explanation:

12.33(4)+24= 73.32

then add the extra 30$ that was spent

73.32+30= $103.32

In order to calculate the slope ratio of a ramp, divide the difference between the elevations of two points by the distance between them, then multiply the quotient by 100, the resultant figure is the slope ratio.

What is the slope of a line?

The slope or gradient of a line in mathematics is a number that defines both the direction and the steepness of the line. The tangent relation or the height-to-distance ratio helps to determine the slope of the line.

The difference between the elevations is also called as the rise. And the distance between the points is known as the run.

Thus, we can also say that,

Slope ratio= rise / run x 100.

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Answer: A. 16.7%

The probability of the letter C being chosen is 16.7% because there are 6 options and the probability will always be out of 100%. If you divide 100 by those 6 choices you will get 16.66 and rounded it is 16.7

Answer:

the answer is option B. 20%

The scale factor tells at what ratio a figure has been changed from other figures

Shapes in various dimensions can be scaled using the Scale Factor.

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

K is the scaling factor for x in the equation y = Kx. This expression can also be visualised in terms of proportionality:

y ∝ x

K can therefore be regarded as a proportionality constant in this context.

The scale factor tells a particular percentage increment or to calculate the percentage of an amount.

Also , To compare 2 Similar geometric figures: When we compare two similar geometric figures by the scale factor, it gives the ratio of the lengths of the corresponding sides.

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Answer:

1

Step-by-step explanation:

there's no common factor between them

95% of the given number is 285 if 75% of that number is 225 and 20% of the same number is 60.

In mathematics, a percentage is defined as a number or ratio that can be expressed as a fraction of 100.

Let assume the number is x

So, according to first statement, we are given that 75 percentage of x=225,it means

=>(75/100) × x=225

=>(3/4) × x=225

=>x=(225 × 4) /3

=>x = (75 × 4)

=>x = 300

Now, check for same number whether 20% is 60 or not

=>20% of x=60

=>(20/100) × x=60

=>(1/5) × x =60

=>x= 60 × 5

=>x = 300

So, our assumption is correct.

Now,95% of the same number is 95% of x

=(95/100) ×300

=95 × 3

=285

Hence,95% of 300 is 285.

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Answer: 1.06 cm

Step-by-step explanation:

Take 2.7 divided by 2.54 = 1.062cm

Rounded the nearest hundredth, so it will be 1.06 cm

The value of b is 3.

The value of c is 1/8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 5 = 9 is an equation.

We have,

Two equations given are:

b = 24c ____(1)

(1/4)b + 4c = 5/4 _____(2)

Putting (1) in (2) we get,

(1/4)24c + 4c = 5/4

6c + 4c = 5/4

10c = 5/4

c = 5/40

c = 1/8

Putting c = 1/8 in (1) we get,

b = 24/8

b = 3

Thus,

b = 3.

c = 1/8.

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Raw score can be computed by using arithmetical operations such as addition, subtraction, multiplication, and division.

This can be done by hand or by using a calculator or a computer program. Additionally, statistical methods such as mean, median, mode, and standard deviation can be used to compute raw data. Raw data can also be influenced in many ways.

For example, data can be organized, filtered, and sorted into categories or hierarchies. Data can also be visualized in graphs, charts, and diagrams to make patterns and trends feasible to understand. Statistical methods such as correlation and regression can also be used to analyze and interpret raw data. Additionally, data can be combined with other data sets to create new insights and relationships. Finally, machine learning and predictive analytics can be used to make predictions about future outcomes based on existing data.

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The speed of the each train = 63

Speed is defined as : The rate of change of position of an object in any direction.

Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

There are four types of speed and they are:

1. Uniform speed

2. Variable speed

3. Average speed

4. Instantaneous speed

Given that

The passenger train travels23mphr faster than the coal train

In 4 hours the two trains are 412 miles apart

Let the speed of  train = x

4*x+4*(x+23)=412

4x + 4x + 92 = 412

8x = 320

x = 40

the speed of the each train = x + 23 = 40 + 23 = 63

Given that

The passenger train travels 23mphr faster than the coal train

In 4 hours the two trains are 412 miles apart

let the speed of  train = x

4*x+4*(x+23)=412

4x + 4x + 92 = 412

8x = 320

x = 40

the speed of the each train = x + 23 = 40 + 23 = 63

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By using percentage, it can be calculated that

Percentage reduction on the portable cd player  [tex]= 18.76 \%[/tex]

What is Percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 9% means [tex]\frac{9}{100}[/tex]. Here, 9 is expressed as a fraction of 100.

Original price of the CD player = $79.95

Selling price = $64.95

Reduction in price = $(79.95 - 64.95) = $15

Percentage reduction on the portable cd player = [tex]\frac{15}{79.95} \times 100 = 18.76 \%[/tex]

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Greater than 0.05 is the p-value, which indicates that it is greater than the significance level.

When determining whether the available data are sufficient to support a given hypothesis, one method of statistical inference is known as a statistical hypothesis test. Making probabilistic claims about a population parameter is possible through hypothesis testing.

given

a 95% confidence interval with bounds for the inference's outcome (-0.0509,0.04273).

As the value p1-p2=0 is included in the interval and is one of the possible values of the genuine difference between the proportions, this confidence interval indicates that the difference (p1-p2) is not substantially positive at the level of significance utilized in the study.

The null hypothesis would then not be rejected by a test of hypothesis performed with the same data and level of significance because the proportional difference is not significant.

In this example, the P-value is more than 0.05, which indicates that it is greater than the significance level.

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if they work together it takes 12/7 hours to mow one lawn

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

jake can mow a lawn in 3 hours.

kellie can mow a lawn in 4 hours.

1/3 lawns can be cut per hour by Jake.

kellie has a 1/4 hour cutting rate for lawns.

They can cut 7/12 lawns per hour by working together at a rate of 1/3 + 1/4.

One lawn can be mowed in 12/7 hours at a rate of 7/12 lawns per hour.

Hence if they work together it takes 12/7 hours to mow one lawn.

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Answer:

Step-by-step explanation:

o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...

Answer:

7.9

Step-by-step explanation:

7.06<7.9

Answer:

6.48%

Step-by-step explanation:

The measures of x are obtained with the Pythagorean Theorem, as follows:

1. x = 10.2.

2. x = 7.2.

3. x = 13.7.

4. x = 36.2.

5. x = 10.7.

The Pythagorean Theorem is a geometry axiom which states that for a right triangle, the length of the hypotenuse squared is equals to the sum  of the lengths of the sides squared.

Hence, for item 1, we have that:

x² + 16² = 19²

x = square root(19² - 16²)

x = 10.2.

For item 2, we have that:

x² + 12² = 14²

x = square root(14² - 12²)

x = 7.2.

For item 3, we have that:

x² + 9.2² = 16.5²

x = square root(16.5² - 9.2²)

x = 13.7.

For item 4, we have that:

x² = 15² + 33²

x = square root(15² + 33²)

x = 36.2.

For item 5, first we find the side of the top right triangle, hence:

h² + 16² = 25²

h = square root(25² - 16²)

h = 19.2.

Then the value of x is obtained as follows:

x² + 19.2² = 22²

x = square root(22² - 19.2²)

x = 10.7.

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The area of a plane figure is the region enclosed by the figure's boundary . Here the area is measured in square units of length such as a square meter   or square centimeter

The area of plane figures is a mathematical concept that is used to measure the size of two-dimensional shapes. It is the amount of space inside the figure and can be calculated by multiplying the length and width of the figure. The measurement of the area is usually measured in square units, such as inches, centimeters, or meters. The area is a fundamental concept in geometry and is used in many areas of mathematics, such as calculus and trigonometry.

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Hence, a temperature increase of  

9

5

​

 degree Fahrenheit is equivalent to a temperature increase of  

81

25

​

 degree Celsius.

The length of one side of square garden that Sam built in Area 4x² + 28x + 49 is (2x+7) feet.

Area is the region enclosed by the shape of an object. The space covered by a figure or any two-dimensional geometric shape in the plane is called the area of the shape. Area is measured in square units (m², cm², inch², etc.)

Example: The area of a rectangular floor is equal to its length times its width

We have given that,

The shape of garden is Square.

The area of garden , A = 4x² + 28x + 49

We know that , Area of square= Side × Side --(*)

where side is dimension of square. We have to find out the side of the square garden.

A = 4² + 28x + 49

Factorize the middle term such that sum of factors is 28x and multiply of factors is 196x².

A = 4x² + 14 x + 14x + 49

=> A = 2x( 2x + 7 ) + 7(2x + 7)

=> A = (2x+7)(2x+7)

comparing this Area with equation(*) we get,

Side = 2x+7

Hence, the required side is (2x+7) feet.

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Answer:

v < 2.2

Step-by-step explanation:

0.5v < 1.14 – 0.04

0.5v < 1.1

v < 1.1/0.5

v < 2.2

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The slope of the line passing through points (3, -3) and (0, -3) is equal to zero.

If we look at the general meaning of slope then we find out that Slope is nothing but the elevation or the steepness of any curve plotted on a graph paper. Now, the formula for finding the slope between two points (x₁, y₁) and (x₂, y₂) is expressed as

m = (y₂ - y₁)/(x₂ - x₁)

where m is the slope between the points, (y₂ - y₁) is difference between the y coordinates and (x₂ - x₁) is the difference between the x coordinates.

We have the values as (x₁, y₁) = (3, -3) and (x₂, y₂) = (0, -3)

So, the slope will be expressed as

m = (-3 + 3)/(0 - 3)

m = 0/-3

m = 0 which is the required slope.

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Complete Question:

What is the slope of the line that passes through (3, -3) and (0, -3).