What is the formula for finding the area of an isosceles triangle?

Marcus has had 107 at-bats in total.

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

To calculate Marcus's total number of at-bats, we need to sum up the number of times he reached base for each type of hit.

A single count as one at-bat, so Marcus has had 18 at-bats for his singles.

A double counts as one at-bat, so Marcus has had 33 at-bats for his doubles.

A triple counts as one at-bat, so Marcus has had 2 at-bats for his triples.

A home run counts as one at-bat, so Marcus has had 54 at-bats for his home runs.

Therefore, Marcus has had 18 + 33 + 2 + 54 = 107 at-bats in total.

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To construct a confidence interval for the population variance σ² and the population standard deviation σ, we use the chi-square distribution.

In this case, we have a sample of 12 computer software engineers with a sample standard deviation of $3720. We want to calculate a 99% confidence interval for the population variance σ².

To construct the confidence interval for the population variance σ², we use the chi-square distribution with n-1 degrees of freedom, where n is the sample size. Since we have a sample size of 12, we will use the chi-square distribution with 11 degrees of freedom.

First, we need to find the chi-square values corresponding to the lower and upper critical values for a 99% confidence level. The lower critical value is obtained from the chi-square distribution table or a calculator using a significance level of 0.01 and 11 degrees of freedom. The upper critical value is obtained using a significance level of 0.99 and 11 degrees of freedom.

Next, we calculate the confidence interval for the population variance σ² using the formula (n-1) * (s²) / χ², where n-1 is the degrees of freedom, s² is the sample variance, and χ² is the chi-square critical value.

Interpreting the results, we can say with 99% confidence that the true population variance σ² lies within the calculated confidence interval. The confidence interval provides a range of plausible values for the population variance based on the sample data.

The confidence interval for the population variance σ² is reported as a range, rounded to the nearest integer, and can be used for further statistical analysis or decision-making regarding the variability of the population.

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Answer:

7 is D and 8 is D

Step-by-step explanation:

I'm assuming you were asked for the volume of both of these.

7. The area of the trapezoid is 18 then multiply by the length of 8 to get 144 units cubed.

8. The area of the trapezoid is 28 then multiply by the length of 14 to get 392 units cubed.

Answer:

0.97 cents

Step-by-step explanation:

4/3.88=0.97

price per pound=0.97 cents

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26 square feet is the exact surface area of the composed figure with two cones.

The composed figure has two cones.

The formula to find the surface area of cone is A=πr(r+√h²+r²))

Where r is radius and h is height of the cone.

Both the cones have radius of 1 ft and height of 2ft and 4 ft.

Area of cone 1=3.14×1(1+√4+1)

=3.14(1+√5)

=10.16 square fee

Area of cone 2=3.14×1(1+√16+1)

=3.14(1+√17)

=16.01square feet.

Total surface area = 10.16+16.01

=26.17 square feet.

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Developers determine the specifics of how to build a system in the design phase. b

The design phase and its importance:
Define Objectives:

The design phase begins after the completion of the analysis phase, where developers have gathered and evaluated requirements.

The main objective of the design phase is to create a blueprint for the system that addresses all identified requirements.
Create Architectural Design:

During this step, developers establish the overall structure of the system, including its components, their relationships, and the interactions between them.

This architectural design provides a high-level view of the system's organization.
Design System Components:

With the architectural design in place, developers focus on designing individual components or modules of the system. They create detailed specifications, which include the functionality, inputs, outputs, and processes for each component.
Design User Interface:

The user interface design involves creating a user-friendly and efficient way for end-users to interact with the system. This can include designing screen layouts, menus, buttons, and other interface elements.
Validate Design:

The final step in the design phase is to ensure that the proposed design meets all the requirements identified during the analysis phase.

Developers may use various methods, such as reviews and simulations, to validate their design before proceeding to the implementation phase.
The design phase is a crucial part of the system development process, as it defines how the system will be built, ensuring it meets the needs of its users and the project's objectives.

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The equation of the line that passes through the point (2,-3) and is parallel to the line 2x + 5y = 10 is y = - 2 / 5 x - 11 / 5

The equation of a line can be represented in various form such as point slope form, slope intercept form and standard form.

Therefore, let's find the equation of the line that passes through the point (2, -3) and is parallel to the line 2x + 5y = 10.

Hence, parallel lines have the same slope.

5y = -2x + 10

y = - 2 / 5 x + 2

Therefore, the slope of the line is - 2 / 5.

Let's find the y-intercept using the slope intercept equation.

y = mx + b

where

Hence, (2, -3)

-3 = - 2 / 5(2) + b

-3 = - 4 / 5 + b

b = - 3 + 4  /5

b = - 11 /  5

Therefore, the equation of the line is y = - 2 / 5 x - 11 / 5

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The required equation of the line y = - (2/5)x - 11/5 passes through the point (2,-3) and is parallel to the line 2x + 5y = 10.

We have to determine the line that passes through the point (2,-3) and is parallel to the line 2x+5y=10

Parallel lines are known to have the same slope.

Firstly, we have to find its slope by the given line

⇒ 5y = -2x + 10

⇒ y = - (2/5)x + 2

Thus, the slope of the line is - 2/5.

Let the required equation of the line is y - y₁ = m(x -x₁ )

Here x₁ = 3, y₁ = 1 and m = -2/5

y - 1 = (-2/5)(x - 3)

y - 1 = (-2/5)x + 3(-2/5)

y = - (2/5)x - 6/5 +1

y = - (2/5)x - 11/5

Therefore, the required equation of the line is y = - (2/5)x - 11/5.

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Answer:

that is a quadratic function so yes it is a function

Step-by-step explanation:

it is a function becausr you can write an equation with it. Hope I could help!

The measure of <1 is 147 degree.

Given:

m∠2 = 12x - 15

m∠7 = 3x + 21

Since angles 2 and 7 are alternate Exterior angles, they are congruent.

So, 12x - 15 = 3x + 21

12x - 3x = 21 + 15

9x = 36

x = 4

So, <2 = 12x - 15= 48 - 15 = 33

Now, <1 + <2 = 180 (Linear Pair)

<1 + 33 = 180

<1 = 147 degree

Thus, the measure of <1 is 147 degree.

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For different types of triangle, The circumcenter has different properties. The properties varies for acute, obtuse and right angle triangles.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

The spot where the three perpendicular bisectors of a triangle's sides meet and which is equally spaced from the triangle's three vertices.

Properties of circumcenter of triangle are:

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The statement is false and a counterexample is {u, v, w} such that w is a linear combination of u and v. Therefore, it means that the statement is true if w is not a linear combination of u and v and false otherwise.

A linear combination is the sum of scalar products between an array of values and a corresponding array of variables, plus a bias term. Linear combinations are important in linear algebra because they provide a way to describe one vector in terms of others. A linear combination of vectors is the sum of the scalar multiples of those vectors. What are Linearly Independent Vectors? When no vector in the set can be represented as a linear combination of other vectors in the set, the set is said to be linearly independent. A set of vectors that spans a space but does not have a linearly independent subset that spans the same space is called a linearly dependent set of vectors.

So, {u,v,w} is linearly independent if w is not a linear combination of u and v. The statement is false if w is a linear combination of u and v. Constructing a Counterexample: A counterexample to this statement would be if w can be expressed as a linear combination of u and v in such a way that the three vectors are linearly dependent. For example, suppose that u = [1, 0, 0], v = [0, 1, 0], and w = [1, 1, 0]. The following vector equations are obtained from this: u + 0v + w = [2, 1, 0]2u + 2v + 2w = [4, 2, 0]u, v, and w are linearly dependent, as seen by the second equation since one of the vectors can be represented as a linear combination of the others.

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Answer:

−2 0 2 + 8

Step-by-step explanation:

The function is expanding to the right of x = 3.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must have at least one second-degree term. It performs algebraic operations.

Given graph of a quadratic function,

to find where function is increasing,

The maximum value or minimum value of a quadratic function are located at its vertex, which is shaped like a U. The quadratic function's axis of symmetry crosses the function (a parabola) at its vertex.

here vertex  is at x = 3,

the increasing and decreasing of graph is shown by vertex,

the shape of curve is parabola so,

In parabolas, the rate of increase (the slope or rate of change) isn't consistent. If the parabola opens up, it will increase as you move towards the right; if the parabola opens down, it will decrease.

The function is increasing to the right side of 3

The parabola's apex can be found at (3, 2) Therefore, all real numbers make up the domain, and the range is y ≥  2. As can be seen in the figure, the function is expanding to the right of x = 3 and contracting to the left of x = 3

Hence the function is increasing to right at x = 3.

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Answer:

the mean is $80

Step-by-step explanation:

The scores of three students, who were randomly selected from a class, are 72, 70, and 63. We are to find the sample mean, sample variance and sample standard deviation.

1. Sample mean: The sample mean is defined as the sum of all the observations divided by the total number of observations. Hence, the sample mean of the given data is:

$\bar{x} = \frac{72+70+63}{3} = \frac{205}{3}$

2. Sample variance: The sample variance is defined as the sum of the squares of deviations from the mean divided by one less than the number of observations. Hence, the sample variance of the given data is:

$s^2 = \frac{(72 - \frac{205}{3})^2 + (70 - \frac{205}{3})^2 + (63 - \frac{205}{3})^2}{3-1} = \frac{214}{3}$

3. Sample standard deviation: The sample standard deviation is defined as the square root of sample variance. Hence, the sample standard deviation of the given data is: $s = \sqrt{\frac{214}{3}} = 6.54$

Therefore, the sample mean is 68.33, the sample variance is 71.33 and the sample standard deviation is 6.54.

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Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 nickels

1 nickel = 5 cents

4x5=20

20 cents from 4 Nickels

10 quarters

1 quarter = 25 cents

10x25=250

250 cents from Nickels

250 ⇒ $2.50

$2.50 dollars from 10 quarters

$2.50+0.20=$2.70

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If you see someone without a smile, give them one of yours!

Thanks!

Have a great night!

:D

Answer:

3. Distributive

Step-by-step explanation:

In the equation 3(x - 2y) if you distribute the 3 to the x and the -2 you would get 3x-6y.

The property illustrated in the equation is 3)Distributive

Distributive law, also called distributive property, in mathematics, the law relating the operations of multiplication and addition, stated symbolically as a(b + c) = ab + ac; that is, the monomial factor a is distributed, or separately applied, to each term of the binomial factor b + c, resulting in the product ab + ac.

Given here, 3x-6y=3(x-2y)

Thus clearly 3 is distributed over x and 2y

Hence, The property illustrated in the equation is 3)Distributive

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Answer: $68.33

Step-by-step explanation:

15% = 10.25

100%  = 100/15 X 10.25 = 1025/15 = $68.33 ANSWER

Answer:

$68.33

Step-by-step explanation:

.15x = 10.25

10.25/.15 = 68.33

x = 68.33

An Endure chosen randomly the likelihood of any battery lasting longer than 550 hours is 10.56%.

These steps are used to determine the Z score:

z = (x - μ)/σ

As mentioned in question-

x > 550 and μ = 500, σ = 40:

z = 550 - 500 / 40

z = 1.25

Obtain the p-value from normal distribution chart,

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Thus, an Endure chosen at random the likelihood of any battery lasting longer than 550 hours is 10.56%.

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Answer:

three billion eight hundred million

Step-by-step explanation:

The least integer value that satisfies the inequality   \(2^{x-7} - 3\) ≥ y is 7.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round.

Here, In the given function

            Least possible value of 2ˣ⁻⁷ is 1

                     2ˣ⁻⁷ = 2⁰

    On comparing both sides, we get

                 x-7 = 0

                  x = 7

Thus, The least integer value that satisfies the inequality   2ˣ⁻⁷-3≥ y is 7.

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Answer:

7

Step-by-step explanation:

edg 2022

815,000 in 10 years

To find the population of a city after a certain number of years, we can use the following formula:

Population after n years = Population after 0 years × (1 + growth rate)^n

In this case, the population at year 0 (current population) is 500,000, the growth rate is 50/1000 = 0.05 (because the rate is given as 50 per 1000 people), and n is the number of years (10 in this case). Substituting these values ​​into the formula gives:

Population in 10 years = 500,000 × (1 + 0.05)^10 = 500,000 × 1.63 = 815,000

So, if the population of the city continues to grow at a rate of 50 people per 1000 people per year, it will be about 815,000 in 10 years.

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Answer:

x = ± √15

Step-by-step explanation:

x 2 - 15 + 15 = 0 + 15

√ x 2 = ± √15

x = ± √15

The die was rolled 7 times in there 60 times if it is landed on one-11 times, two-9 times, four-12 times, five-12 times, and six - 8 times.

Probabilities are mathematical explanations of the probability of an event occurring or of a proposition being true. The probability of an event is expressed as a number between 0 and 1, where 0 often indicates impossibility and 1 generally indicates certainty.

Given,

Number of times a die rolled=60

And also given that it landed on,

One --- 11 times

Two -----9 times

Four -----12 times

Five -----12 times

Six -------8 times

Total number of times the die was landed on is 52 times.

Therefore, total number of times a die was rolled=60

S0, 52+x=60

x=7

Therefore, the die was rolled 7 times in there 60 times.

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The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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