The four triangles at right are placed in a bag. If you reach into the bag without looking and pull out one triangle at random, what is the probability that: Homework Help ✎

The triangle is scalene?

The triangle is isosceles?

At least one side of the triangle is 6 cm?

The equation of the best-fit model is given as follows:

y = 5.33x + 67.78.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

The points for this problem are given as follows:

(10, 120), (15, 150), and (25, 200).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 5.33x + 67.78.

Meaning that the correct option is given by the first option.

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Answer:The graph of x = -4 is a vertical line located 4 units to the left of the y-axis.

The domain of x = -4 is the set of all real numbers, since any real number can be plugged into x = -4 and the equation will be true. This is because x = -4 is a vertical line and not a function, it cuts the y-axis at one point, so it doesn't matter what value you put on x it will always be -4.

The range of x = -4 is a single point on the y-axis, y = -4.

Step-by-step explanation:

Using the interactive ruler, we can determine that there are 4 Units between the dilation's center and the image and pre-image.

This digital instrument, which appears on the computer screen and is often referred to as an Interactive Teaching Program ruler, is used to measure the lines and sides of a shape.

In units,

how far is it between points C and A?

With the help of the interactive ruler, we can calculate that the separation between points C and A is 2 units.

Additionally, the distance is 1.5 units between point C and point A'.

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Answer:

34.5 square units.

Step-by-step explanation:

We can construct a 7 x 7 square around the polygon. Then, we measure the two right triangles that together, along with the polygon, make up the 7x7 square. The total measure of the two triangles is 15/2+7=14.5. Now we subtract that from the area of the square to get the area of the polygon. 49-14.5=34.5, so 34.5 square units is the answer.

The line's x value at the x-axis intersection is referred to as the x intercept, and the line's y value at the y axis junction as the y intercept.

Because they are located on the horizontal and vertical axes, respectively, the x and y-intercepts are also known as the horizontal intercept and vertical intercepts.

The equation is a non-function

solve f(x)=6^x

Here are some points we can plug in. We should try to use full numbers:

(-2,1/36)

(-1,1/6)

(0,1)

(1,6)

This is the graph:

graph{6^x [-10, 10, -2, 40]}

Make sure the line approaches, but never touches, the x-axis. Even though the line sweeps up until it reaches infinity, it will never be vertical because that would render the equation useless.

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The width of the parallelogram can be any value greater than or equal to 14 feet.

What is parallelogram ?

A parallelogram is a four-sided polygon with opposite sides that are parallel. It has opposite angles that are equal and opposite sides that are equal in length. A special cases of parallelograms are rectangles, which have four right angles, and squares, which have four right angles and all sides are equal in length.

P = 2l + 2w >= 40

where P is the perimeter, l is the length and w is the width.

Substituting the given value for the length, we get ,

2(6) + 2w >= 40

Simplifying and solving for w ,

12 + 2w >= 40

2w >= 28

w >= 14

Therefore, the width of the parallelogram can be any value greater than or equal to 14 feet.

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Answer: Well you have to see on the number that is close to the decimal point

Step-by-step explanation:

0.2438

0.4485

0.8641

3.2527

17.9926

$156.78 is the total cost of material for the bunny costumes.

Given a specified quantity of goods produced, a cost function is a mathematical formula that may be used to determine the overall cost of production. 

Given that,

Total required bunny costumes = 6

Total faux fur requirements for each bunny costume =  2.6 square yards

Cost of faux fur = $10.05 per square yard

The costume budget for the bunny costumes = $200

The total cost of material for the bunny costumes = 2.6 *10.05 *6 = $156.78.

Thus, $156.78 is the total cost of material for the bunny costumes.

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The approximate number of years for which the species is extinct is 7.7 years.

Zeros of an equation is defined as the value of the independent variable where the equation or function gives zero.

Here,
The population of a species is modeled by the equation,
p(t) = -t⁴ + 56t² + 240,

Where t is the number of years.

The approximate number of years until the species is extinct, is given by determining the zero of the equation,
-t⁴ + 56t² + 240 = 0

So, zeros is given as,
t = 2i, -2i, 2√15, -2√15

Now,
We only consider the positive real value of t,
t = 2√15
t = 7.7 years

Thus, the approximate number of years for which the species is extinct is 7.7 years.

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Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

When the equals sign (=) is used to denote equality, an algebraic theorem resembles a rule joining two statements. An algebraic equation is a factual assertion that shows the equivalence of multiple numerical variables. The values ob d + 6 and 12 are separated by an equal sign in the calculation data logger + 6 = 12. The number of syllables that correspond to each side of each letter can be expressed numerically. The message of a symbol is frequently its complete opposite.

Here,

Given :

After a few weeks, you create and calculate an equation

so determine how much money is in your bank account.

M equals -36, as you discover.

Thus,

It mean that you owe 36 amount of money to bank.

Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

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Answer: The Area of Shaded Region is 576  [tex]cm^{2}[/tex] and the perimeter is 24 (2 + [tex]\pi[/tex]) cm

Step-by-step explanation: Given, the length of the line segment BC is 24 cm.

     First, The area of the Semi Circle AD : We know that area of a circle is [tex]\pi[/tex][tex]r^{2}[/tex]  where r=radius of the circle. Since the shape ABCD is a sqaure, BC=AD=24cm. We can see from the figure that AD is the diameter for the semi circle AD. And diameter = 2 x Radius. Therefore radius of the semi circle is 12cm.

Therefore, area of the first Semi circle AD will be :

⇒ [tex]\pi \frac{r}{2}cm ^{2}[/tex]

⇒([tex]\pi[/tex]*12*12)/2

⇒72[tex]\pi[/tex] [tex]cm^{2}[/tex]

Now, perimeter of semi circle AD : We know perimeter of a Semi circle is [tex]\pi[/tex]r + length of the base.

Therefore, perimeter of Semi circle AD is :

⇒[tex]\pi[/tex]*12 + 24 cm

⇒12 (2 + [tex]\pi[/tex])

Now, Area of the Shape ABCD, As we can see from the figure, The area will be Area of square ABCD - Area of the semi circle BC. Therefore,

Area of Square = [tex]side^{2}[/tex]

⇒24 x 24 [tex]cm^{2}[/tex]

Area of semi circle BC :

⇒(12 x 12 x [tex]\pi[/tex])/2 [tex]cm^{2}[/tex]

∴ Area of shape ABCD = [(24 x 24) - (12 x 12 x [tex]\pi[/tex])/2] [tex]cm^{2}[/tex]

⇒576 - 72[tex]\pi cm^{2}[/tex]

Now, Perimeter of Shape ABCD :

We can see from figure, the perimeter will be Sum of 3 sides of the square and the circumference of the semi circle BC.

Therefore,

⇒72 + 12[tex]\pi[/tex] cm

Now, Finally The Area of the shaded region :

⇒ Area of Shape ABCD + Area of Semi circle AD

⇒[576 - 72[tex]\pi cm^{2}[/tex]] + [72[tex]\pi[/tex] [tex]cm^{2}[/tex]]

⇒576 [tex]cm^{2}[/tex]

Perimeter of the shaded region :

⇒ Sum of 2 sides of the square ABCD + 2 Times the Circumference of the semi circle

⇒[24 + 24] + [2 x 12[tex]\pi[/tex]]cm

⇒ 24 (2 + [tex]\pi[/tex]) cm, Final Answer  

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A total of 96 pots can be made in one eight-hour day.

The result of two numbers being multiplied is known as the product. The multiplier is the number of such equal groups, and the multiplicand is the number of items in each group. In this instance, the multiplicand is, the multiplier is, and the product is 6.

Speed of coffee machine = 12 pots of coffee per hour.

Amount received after selling each pot of coffee = $10

For finding the total pots of coffee made by the coffee machine in 8 Hr, we will simply multiply the total number of hours which is 8 Hr to the efficiency of the machine which is 12 pots per hour.

So, the total pot made by the machine will be 12*8 = 96 pots

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The four types of data in excel are text type, number type, logical and error type.

Excel data types are the four different kinds of values in Microsoft Excel. The four types of data are text, number, logical and error.

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Plug in t = 0, in the given equation to get d=32-5t² = 32

Plug in t = 0.5, in the given equation to get d= 30.75

Plug in t = 1 , in the given equation to get d= 27

Plug in t = 1.5, in the given equation to get d= 20.75

Plug in t = 2 , in the given equation to get d= 12

Below is the completed table and the data on the coordinate plane.

The study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. Vertices (also known as nodes or points) make up a graph in this sense, which are connected by edges (also called links or lines).

Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics of study in discrete mathematics is graphs.

In physical, biological, social, and information systems, graphs can be used to model a wide variety of linkages and processes. Graphs can be used to represent a variety of real-world issues.

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The manager of a garden shop wants to make a mixture that contains 74% rye grass. The weight of the 60% mixture used in this composition is 30 lb.

Percentage is used to denote a fraction of a hundred.

Suppose q represents the weight of the mix that contains 60% rye grass, then the weight of rye grass in this mix is:

w1 = 60% q = 0.6 q

Mix 2: 70 lb grass seed that contains 80% rye grass. The weight of rye grass in the second mix is:

w1 = 80% x 70 = 56 lb

The final mixture has 74% rye grass. Total weight of rye grass in the final mixture:

weight of rye grass = w1 + w2

                                = 0.6 q + 56

Total weight of the final mixture = (q + 70) lb

74% = 0.74 = (0.6 q + 56) / (q + 70)

0.6 q + 56 = 0.74 (q + 70)

0.74 q - 0.6 q = 56 - 0.74 x 70

0.14 q = 4.2

q = 4.2/0.14 = 30

Hence, the weight of 60% mixture is 30 lb.

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The scientist that made histogram of the data of amount of rainfall he collected each day for a year to study rainfall has performed descriptive statistics.

Descriptive statistics involves organizing, summarizing, and presenting data in a way that makes it easy to understand. Histograms are a common tool used in descriptive statistics. They are used to visualize the distribution of a dataset, by showing the frequency of data points within different ranges or bins. In this case, the scientist has organized the data by showing the frequency of days with different amounts of rainfall over the course of a year.

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462 ways are there to distribute all five hats among all eleven people so that no one gets more than one hat

given that

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally, a k-combination of a set S is a subset of k distinct elements of S. So, two combinations are identical if and only if each combination has the same members. (The arrangement of the members in each set does not matter.) If the set has n elements, the number of k-combinations, denoted as nck

there are 5 hats

there are 11 people

now , we need to distribute all five hats among all eleven people so that no one gets more than one hat = 11 [tex]C_{5}[/tex]

= [tex]\frac{11!}{5!(11-5)!}[/tex]

=462 combinations

462 ways are there to distribute all five hats among all eleven people so that no one gets more than one hat

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The angle measure of triangle DEF in order of smallest to largest is m∠E = 36.03°, m∠F = 70.72° and m∠D = 73.25°.

The answer is: m∠E < m∠F < m∠D

The angle of a triangle can be found given its 3 sides using the cosine rule.

The formula is: cos(C) = (a² + b² -c²) / 2ab  

where c is the length of the side opposite angle C, a and b are the lengths of the other two sides, and cos(C) is the cosine of angle C.

DE = f = 69 miles, EF = d = 70 miles and DF = e = 43 miles

cos (F) = (d² + e² -f²) / 2de  

cos (F) = (70² + 43² -69²) / (2*70*43)

cos (F) = 71/215

F = cos⁻¹(71/215)

F = 70.72°

cos (E) = (d² + f² -e²) / 2df

cos (E) = (70² + 69² -43²) / (2*70*69)

cos (E) = 93/115

E = cos⁻¹(93/115)

E = 36.03°

DE = f = 69 miles, EF = d = 70 miles and DF = e = 43 miles

cos (D) = (e² + f² - d²) / 2ef

cos (D) = (43² + 69² - 70²) / (2*43*69)

cos (D) = 285/989

D = cos⁻¹(285/989)

D = 73.25°

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Answer: II Only

Step-by-step explanation:

Let's see.

The given inequality is -2<=-8-x

Therefore, we can add 8 to both sides and get

6<=-x

Now we need to multiply -1 to both sides to get

x<=-6, which means that x is less than or equal to -6.

Now the only choice that satisfies this inequality is -6.

So II only is the answer.

The rate of change of the volume at that particular instant is - 62.8 m^3/h.

How to get the rate of change of the volume?

First, we can write the dimensions as:

radius = R = (5m + 1m/h*t)

height = H = (8m - 4 m/h*t)

Where t is the time in hours.

Then the volume of the cylinder will be:

V = pi*R^2*H = 3.14*(5m + 1m/h*t)^2*(8m - 4 m/h*t)

To get the rate of change, we need to differentiate it with respect to t, we will get:

V' = 3.14*(2*(5m + 1m/h*t)*(1m/h)*(8m - 4 m/h*t) + (5m + 1m/h*t)^2*(-4m/h))

V' = 3.14*( (2 m/h)*(5m + 1m/h*t)*(8m - 4 m/h*t) - (4m/h)*(5m + 1m/h*t)^2)

V' = 3.14*(2m/h)*( (5m + 1m/h*t)*(8m - 4 m/h*t) - 2*(5m + 1m/h*t)^2)

As you can see the rate of change depends on t, but we want the rate of change at this instant, then we use t = 0, replacing that on the above equation we get:

V'(0) = 3.14*(2m/h)*( (5m + 1m/h*0)*(8m - 4 m/h*0) - 2*(5m + 1m/h*0)^2)

V'(0) = 3.14*(2m/h)*( (5m)*(8m ) - 2*(5m)^2)=  -62.8 m^3/h

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The given condition can be modeled by the compound inequality:

x < -3 or x > 3.

We want to find an inequality that describes the next condition:

"All real numbers X with an absolute value of greater than three"

So our variable will be X, and the absolute value of X is written as:

|X|

We want to have an absolute value larger than 3, so we can write the inequality:

|X| > 3.

The absolute value part can be separated into two, such that we will get two inequalities:

x > 3

x < -3

So the inequality that illustrates the given condition is the compound inequality:

x < -3 or x > 3.

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Paying a bill amount through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.

1. Paying a bill amount through the mail without check is a convenient and secure way of making payments.

2. It allows for payment to be made without having to visit a physical location to do so.

3. It also allows for payment to be made without having to use a credit or debit card.

4. Therefore, an advantage of paying a bill through the mail without check is that it is convenient and secure.

Paying a bill through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.

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A. Johnny's biweekly gross pay is $2,595.23.

B. Johnny's Social Security deduction is 6.2% of his gross pay is $160.90.

C. Johnny's Medicare deduction is 1.45% of his gross pay, which is $37.63.

D. Johnny's new annual salary with a 14.5% raise is $71,179.93.

A. Johnny's biweekly gross pay is $62,285.50 / 24

= $2,595.23.

B. Johnny's Social Security deduction is 6.2% of his gross pay, which is $2,595.23 * 6.2% = $160.90.

C. Johnny's Medicare deduction is 1.45% of his gross pay, which is $2,595.23 * 1.45% = $37.63.

D. Johnny's new annual salary with a 14.5% raise is $62,285.50 * 1.145 = $71,179.93.

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Answer:

yes, but not less than zero.

Step-by-step explanation:

The absolute value is only greater than or equal to zero.

[tex] | - x| \geqslant 0[/tex]

where x is real number

The values of a and b are 1 and 12 respectively.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Different Types of Equations

Linear Equation.

Radical Equation.

Exponential Equation.

Rational Equation

In the given question:-

y = ax² + bx

dy/dx=2ax+b

If x=3 and dy/dx=18

the solution becomes

18=6a+b

If x=5 and dy/dx=22

The solution becomes

22=10a+b

Solving the equation we get a=1 and b=12

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The present ages of the teachers are 25 and 29 years old.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that sum of the present ages of two teachers is 54 years. If the age of one teacher is 4 years more than the other, then;

Let the ages of teachers are x and y

x + y = 54

x = 4 + y

So, 4 + y + y = 54

4 + 2y = 54

y = 25

x = 29

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The expression 81x⁴y⁸ rewritten as a power of a product is (3xy²)⁴.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

1) 3³·3⁶ =3⁹

3³⁺⁶ =3⁹

[tex]3^{(6\times3)}=3^{18}[/tex]

3⁶·3³=3⁹

2) 5⁻¹/(-9)⁰

= 5⁻¹/1

= 1/5

3) 3x⁻⁵y⁰/5⁻³z⁻¹⁰

= 3×5³/x⁵z¹⁰

= 375/x⁵z¹⁰

4) (4s⁵t⁻⁷/-2s⁻²t⁴)³

= (4s⁵s²/-2t⁴t⁷)³

= (-2s⁷/t¹¹)³

= -8s²¹/t³³

5) 81x⁴y⁸

= 3⁴x⁴y⁸

= (3xy²)⁴

Hence, the expression 81x⁴y⁸ rewritten as a power of a product is (3xy²)⁴.

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