2) Simplify |-5| + |6|. A) -30 B) -1 C) 1 D) 11

Answer:

Step-by-step explanation:

Correct order to prove BD bisects ∠ABC is,

              Statements                              Reasons

1). AB ≅ BC                                1). Given

   D is the midpoint of AC                

2). AD ≅ DC                              2). A midpoint divides a segment into two

                                                       congruent segments.

3). BD ≅ BD                              3). Reflexive property

4). ΔABD ≅ ΔCBD                    4). SSS property

5). ∠ABD ≅ ∠CBD                    5). Corresponding parts of congruent

                                                      triangles are congruent (CPCTC)

Answer:

7x + 2y = -6

Step-by-step explanation:

Multiply the equation with 2

2 ( y = -7x/2 - 3 )

2y = -7x - 6

7x + 2y = -6

In a sampling distribution of means, the distribution will approximate the normal distribution, the mean of the sampling distribution will equal the mean of the population and the standard deviation of the sampling distribution is based on Central Limit Theorem, option A.

The central limit theorem (CLT) of probability theory states that, under the assumption that all samples are of equal size and regardless of the population's actual distribution shape, the distribution of a sample variable approaches a normal distribution (i.e., a "bell curve") as the sample size increases.

In other words, the central limit theorem (CLT) is a statistical assumption that, given a sufficiently enough sample size from a population with a limited degree of variance, the mean of all sampled variables from the same population will be roughly equal to the mean of the entire population. According to the law of large numbers, these samples also resemble a normal distribution, with their variances almost equaling the variation of the population as the sample size increases.

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Complete question:

In a sampling distribution of means... 1. the distribution will approximate the normal distribution (bell curve). 2. the mean of the sampling distribution will equal the mean of the population 3. the standard deviation of the sampling distribution is called the standard error. This is based on the...

Central Limit Theorem

Standardization of Transformation

Z-Score Distribution Table

Relative Frequency of Probability

Answer:

40

Step-by-step explanation:

Total number of toffees = 975

Total number of children = 23

Estimate the numbers of toffees that each child will get in nearest tens.

Number of toffees each child get = Total number of toffees / Total number of children

= 975 / 23

= 42.391304347826

Approximately,

Number of toffees each child get = 40 to the nearest tens

The measurement that is closest to the value of x, in centimeters, is given as follows:

14.3.

In this problem, we have a right triangle, in which the legs, which are the sides between the angle of 90º, are of 11.9 cm and 7.9 cm.

Then the hypotenuse x, which is the segment connecting both legs, is obtained using the Pythagorean Theorem.

The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.

Then the length of x is calculated as follows:

x² = 11.9² + 7.9²

x = square root of (11.9² + 7.9²)

x = 14.28.

Closest to 14.3, rounding to the nearest tenth, meaning that the third option is correct.  

We suppose that 11.9 cm and 7.9 cm are the measures of the legs.

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The Aztec Empire was much larger than the state of Ohio, with an estimated area of around 80,000 square miles at its peak.

This vast empire encompassed much of central Mexico and included cities such as Tenochtitlan, the capital of the Aztec Empire. The area of Ohio is approximately 44,825 square miles, not 4,000 square miles. At its peak, the Aztec Empire covered an area of about 80,000 square miles. To compare the two:

1. Note the area of Ohio: 44,825 square miles
2. Note the area of the Aztec Empire at its peak: 80,000 square miles
3. Compare: The Aztec Empire was larger, covering nearly 1.78 times the area of Ohio.

In conclusion, the Aztec Empire was significantly larger than the state of Ohio at its peak, with an area estimate of around 80,000 square miles.

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Answer:

A= b×h

b=12

h=9

12×9= 108

A=108m

Hope this helps.

543 cubic centimeters has 0.543 L approximate displacement

Engine displacement means the displacement of the piston inside cylinder from Bottom Dead Center into Top Dead Center in one cycle.

Basic formula to calculate engine displacement is

V = π/4 x \(D^{2}\) x H x N

Where :

D = Bore Diameter

H = Length of Stroke

N = Number of Cylinder

Since the question has already stated cubic centimeter, it has already show the displacement. So, we can ignore above formula and the 4 cylinder engine information.

First, we state what is known. It is the displacement at cubic centimeter

Cubic centimeter = 543 cc

Next, we change the unit of cubic centimeter ( cc ) into liter ( L )

Displacement = cc / 1000 L

                       = 543 / 1000 L = 0.543 L

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y/x is equivalent to a constant and is equal to [m].

The general equation of a straight line is -

y = mx + c

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Other possible equations of lines are -

(y - y₁) = m(x - x₁)                                {Point - slope form}

(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁)      {Two point - slope form}

x/a + y/b = 1                                        {intercept form}

x cos(β) + y sin(β) = L                          {Normal form}

We have a relationship that is proportional when the ratio of [y] over [x].

The equation of a straight line -

y = mx + c

can be used to represent proportional relationship when [c] = 0. Now -]

y = mx

m = y/x

Now, y/x is equivalent to a constant and is equal to [m].

Therefore, y/x is equivalent to a constant and is equal to [m].

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Answer: x = 12, ∠B = 45°

Step-by-step explanation:

Angle A and Angle B are alternate exterior angles meaning that they are equal

5x - 15 = 2x + 21

3x - 15 = 21

3x = 36

x = 12

B = 2(12) + 21

B = 24 + 21

B = 45

The quotient when \(\frac{5-x}{x^2+3x-4} /\frac{x^2-2x - 15}{x^2+5x+4}\) in simplified form is \(\frac{-(x+1)}{(x-1)(x+3)}\)

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that equation:

\(\frac{5-x}{x^2+3x-4} /\frac{x^2-2x - 15}{x^2+5x+4}\)

\(=\frac{5-x}{(x+4)(x-1)} /\frac{(x-5)(x+3)}{(x+4)(x+1)} \\\\=\frac{5-x}{(x+4)(x-1)} * \frac{(x+4)(x+1)}{(x-5)(x+3)}\\\\\frac{-(x-5)}{(x+4)(x-1)} * \frac{(x+4)(x+1)}{(x-5)(x+3)}\\\\=\frac{-(x+1)}{(x-1)(x+3)}\)

The quotient when \(\frac{5-x}{x^2+3x-4} /\frac{x^2-2x - 15}{x^2+5x+4}\) in simplified form is \(\frac{-(x+1)}{(x-1)(x+3)}\)

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Answer:

The quotient when \(5-x/x^2+3x-4/x^2-2x-15/x^2+5x+4\) in simplified form is \(-(x+1)/(x-1)(x+3)\)

The expressions x + x + x + x and 4x are equivalent.

We can see this by simplifying the first expression:

x + x + x + x = 4x

So we can see that both expressions represent the same quantity, which is the total of adding x four times.

To explain this using a diagram, we can draw four boxes, each labeled with an "x".

x   x   x   x

Then, we can count the total number of "x" in the diagram, which is 4x.

Alternatively, we can also think of distributing the coefficient 4 to each term in the second expression:

4x = 4 * x

= x + x + x + x

This gives us the same expression as the first one, so they are equivalent.

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Answer:c

Step-by-step explanation:

Answer:

\(98m^{2}\)

Step-by-step explanation:

(find the unshaded triangle first)

length of unshaded triangle—> 13m-9m=4m

Breadth of unshaded triangle—> 8m-5m=3m

Area of unshaded triangle—> 0.5 x 4m x 3m = 0.5 x 12m = 6\(m^{2}\)

Area of whole rectangle—> 8mx13m=104\(m^{2}\)

area of shaded part is whole rectangle minus the unshaded triangle.

Thus, area of shaded part—> 104\(m^{2}\) - 6\(m^{2}\) = 98\(m^{2}\)

The SI unit for density is kilogram per cubic meter (kg/m³)/

The density of liquid is 0.17 × 10⁸.

Kilogram Per Cubic Meter:

The SI unit for density is the kilogram per cubic meter (kg/m3). For many situations, however, this as an inconvenient unit, and we often use grams per cubic centimeter (g/cm3) for the densities of solids and liquids, and grams per liter (g/L) for gases.

According to the question:

Firstly, have to change your units to kilograms and cubic meters. Since there are a thousand grams in a kilogram,

                        170g = 1.70 x 10⁻¹ kg.

Since there are a thousand milliliters in a liter and a thousand liters in a cubic meter

               100ml = 1.00 x 10⁸ cubic meters

Therefore, Density= mass/volume

Density = 1.7 x 10⁻¹/ 1.00 x 10⁸ kg/m³

             = 0.17 x 10⁸ kg/m³.

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A group should consist of 13 people in order to ensure that at least two of the group members have birthdays that are in the same month.

Given:

This problem is an example of pigeonhole principle which states that If n+ 1 objects are placed into n boxes, then some box contains at least 2 objects.

Here no. of months in a year are boxes n = 12.

Therefore number of objects( people) = n+1= 13.

Then, at least two people  in the group whose birthdays fall in the same month.

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If the average salary of several of the groups was close to $51,000 then least likely to be the average salary of another one of the groups are equal to $41,000.

Random groups of teachers are = 30

If the average salary of several of the groups was close to equal to = $51,000

The mean, or average, salary is the amount derived by adding two or more salary values and dividing the sum by the number of values.

So we can write,

The average wage is known to be close to $41,000

$41,000 < $51,000

Therefore,

The average salary of another one of the groups are equal to $41,000.

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Answer:

Step-by-step explanation:

Assume that the number is x. Angle #1: 7x - 5. Angle #2: 7x + 8.

Answer:

91.1 cm

Step-by-step explanation:

the formula to find circumferences is pi times diameter

29pi

91.1

Hopes this helps please mark brainliest

Step-by-step explanation:

= 3a+3b

or, 3×4+3×3

or, 12+9

or, 21

again,

= 3(a+b)

or, 3×(4+3)

or, 3×7

or, 21

hence 3a+3b is equivalent to 3(a+b) is proven

Answer:

∴ m∠KIJ = 18°  and   m∠HIJ = 50°

Thus, option a is correct.

Step-by-step explanation:

From the figure, it is clear that:

m∠KIH = m∠HIJ + m∠KIJ

Given

now substituting m∠KIH = 68°, m∠KIJ = (2x + 6)° and m∠HIJ = (9x - 4)° in the equation

m∠KIH = m∠HIJ + m∠KIJ

68° = (2x + 6)° + (9x - 4)°

switch sides

\(\left(2x+6\right)+\left(9x-4\right)=68\)

Group like terms

\(2x+9x+6-4=68\)

\(11x+2=68\)

Subtract 2 from both sides

\(11x+2-2=68-2\)

Simplify

\(11x=66\)

Divide both sides by 11

\(\frac{11x}{11}=\frac{66}{11}\)

Simplify

\(x=6\)

Hence, the value of x = 6

Therefore,

m∠KIJ = (2x + 6)° = 2(6) + 6 = 12 + 6 = 18°

m∠HIJ = (9x - 4)° = 9(6) - 4 = 54 - 4 = 50°

∴ m∠KIJ = 18°  and   m∠HIJ = 50°

Thus, option a is correct.

Step-by-step explanation:

Let P be price after t year . From the formula of compounding

P = 9 (1.015)^t

Taking log to the base e on both sides

ln P = ln 9 + t ln 1.015

= (2.197 + .0149t )

P = e^{(2.197+.0149t)}

the range of the frequency is 0 to 5

so the answer is option A that is 5

The required answer is the y = 80

The best fit line equation in a scatter plot represents the relationship between two variables. It is also known as the regression line or the line of best fit. The equation of the best fit line is typically represented as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

To find the best fit line equation in a scatter plot,

1. Plot the data points on a scatter plot.
2. Visualize the trend or pattern in the data points.
3. Determine whether the relationship between the variables is linear, meaning that the data points roughly form a straight line pattern.
4. Use a statistical method, such as the least squares method, to find the line that minimizes the distance between the data points and the line.
5. Calculate the slope (m) and the y-intercept (b) of the best fit line.
6. Write the equation of the line using the values of m and b.

Using the least squares method, determine that the slope of the best fit line is 2 and the y-intercept is 70.

Therefore, the equation of the best fit line would be:

y = 2x + 70

This equation represents the expected test score (y) based on the number of hours studied (x). For example, if a student studies for 5 hours, estimate their test score by substituting x = 5 into the equation:

y = 2(5) + 70
y = 10 + 70
y = 80

So, according to the best fit line equation, if a student studies for 5 hours,  expect their test score to be around 80.

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Answer:

y=5×+2

Step-by-step explanation:

5(1)+2=7

5(2)+2=12

5(3)+2=17

5(4)+2=22

\( \\ \tt \longmapsto 2 \frac{1}{3} \div 4\frac{1}{3} = \frac{7}{x} \\ \\ \tt \longmapsto \frac{7}{3} \div \frac{13}{3} = \frac{7}{x} \\ \\ \tt \longmapsto \frac{7}{3} \times \frac{3}{13} = \frac{7}{x} \\ \\ \tt \longmapsto \frac{7}{13} = \frac{7}{x} \\ \\ \tt \longmapsto 7x = 7 \times 13 \\ \\ \tt \longmapsto 7x = 91 \\ \\ \tt \longmapsto x = \frac{91}{7} \\ \\ \tt \longmapsto x = 13\)

Answer:

\(x = 13\)

Step-by-step explanation:

\( \frac{2 \frac{1}{3} }{4 \frac{1}{3} } = \frac{7}{x} \\ \frac{7}{3} \div \frac{13}{3} = \frac{7}{x} \\ \frac{7}{ 3} \times \frac{3}{13} = \frac{7}{x} \\ \frac{7}{13} = \frac{7}{x} \\ 7x = 13 \times 7 \\ x = \frac{13 \times 7}{7} \\ x = 13\)

Answer:y=4/3x-18/3

Step-by-step explanation:

4x-3y=18

3y=4x-18

y=4/3x-18/3

Answer:

Hi, there your answer is     \(y=\frac{4}{3} x -6\)

Step-by-step explanation:

Let's solve for y.

8x−6y=36

Step 1: Add -8x to both sides.

8x−6y+−8x=36+−8x

−6y=−8x+36

Step 2: Divide both sides by -6.

\(\frac{-6y}{-6} =\frac{-8x+36}{-6}\)

\(y=\frac{4}{3} x-6\)

Hope This Helps :)

Answer:

y = ±2i

Step-by-step explanation:

6y^2 + 24 = 0

Divide both sides by 6

y^2 + 4 = 0

Subtract 4 from both sides

y^2 = -4

Take the square root of both sides

y = ±√-4

y = ±2√-1

y = ±2i

Answer:

Step-by-step explanation:

6y^2+24=0

/6

y^2+4=0

y^2=-4

y=±\(\sqrt{-4}\)

y=±\(\sqrt{4}\) i