Write two expressions for the perimeter of the figure.
2
8
4x
4
7x
Note: The figure is not drawn to scale.
(a) Use all five side lengths.
perimeter = 0+0+0+0+0
(b) Simplify the expression from part (a).
perimeter =

Answer:

Distributive property

Step-by-step explanation:

This is a property that lets you rewrite expressions in simplier ways.

HOPE IT HELPED

Answer: She had left 54% of the money which is $1620.

Step-by-step explanation:

40% of $3000 = $1200

15% of $1200 = $180

$3000 - ($1200 + $180)

$3000 - $1380 = $1620

$1620 is the money she had left.

$1620 is 54% of $3000

She had 54% left of the money.

Hope that helped~!

Answer:

{ 0, 3, - 3 }

Step-by-step explanation:

f(x) = x(2x - 3)(x + 3)

to find the zeros let f(x) = 0 , that is

x(2x - 3)(x + 3) = 0

equate each factor to zero and solve for x

x = 0

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = \(\frac{3}{2}\)

x + 3 = 0 ⇒ x = - 3

zeros are { 0, \(\frac{3}{2}\) , - 3 }

By conducting a comprehensive SI, engineers and designers can make informed decisions and implement suitable measures to address any potential challenges or risks associated with the proposed structures.

To gather the necessary information for an SI, the following types of data are typically required:

1. Geological information: This includes the composition and characteristics of the soil and rock formations on the site. This information helps determine the stability of the ground and potential risks such as landslides or sinkholes.

2. Geotechnical data: Geotechnical investigations involve soil and rock testing to assess their strength, density, and permeability. This data is vital for designing foundations and determining the bearing capacity of the ground.

3. Groundwater information: Understanding the groundwater levels and flow patterns is essential for designing drainage systems and preventing water-related issues like flooding or excessive moisture.

4. Environmental data: This includes information about the presence of pollutants, contaminants, or protected species in the area. It helps ensure compliance with environmental regulations and enables appropriate mitigation measures.

5. Archaeological data: If the site has historical significance, an archaeological investigation may be necessary to identify and preserve any cultural artifacts or structures.

By conducting a comprehensive SI, engineers and designers can make informed decisions and implement suitable measures to address any potential challenges or risks associated with the proposed structures.

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Answer:

After two years in the computing pool, Mary Jackson received an offer to work for engineer Kazimierz Czarnecki in the 4-foot by 4-foot Supersonic Pressure Tunnel, a 60,000 horsepower wind tunnel capable of blasting models with winds approaching twice the speed of sound.

SO this answer would be C.

Step-by-step explanation:

hope its helps u

Explanation

Answer:

120⁰

Step-by-step explanation:

180⁰- 60⁰= 120⁰

a straight line is 180⁰

Answer:

i need more information

Step-by-step explanation:

need more information

Answer: 19 apples

Step-by-step explanation:

1 pound = 16 ounces

We find the price of an ounce by taking 12 divided by 16 = $0.75

Then we find the total ounces we can buy by taking 72 divided by 0.75 = 96 ounces.

Then we take 96 divided by 5 ounces = 19.2

So we can buy 19 apples.

Using inequalities we know that x=68 and x=66 respectively.

A mathematical phrase in which the sides are not equal is referred to as being unequal.

In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

So, solve the inequalities as follows:

x+3>70

x>70-3

x>67

Then, it will be x = 68.

Then,

x+3<70

x<70-3

x<67

Then, it will be s = 66.

Therefore, using inequalities we know that x=68 and x=66 respectively.

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Answer: (5,7)

Step-by-step explanation:

Answer:

The radical approximations of 7.07, 7.21, and 7.93 to the nearest whole number are:

2.65

2.68

2.82

Step-by-step explanation:

Sure, here's a step-by-step explanation of finding the approximate square root of 7.07, 7.21, and 7.93 to the nearest whole number:

Start by finding an approximate square root by making an educated guess or by using a calculator.

Use the initial guess to determine if the number is closer to the actual square root or to a smaller or larger value.

Refine the estimate by averaging the guess and the number divided by the guess.

Repeat the process of refining the estimate until a satisfactory level of accuracy is reached.

Here's an example for 7.07:

An educated guess for the square root of 7.07 could be 2.7

Dividing 7.07 by 2.7 gives an estimated value of 2.61, which is closer to the actual value.

To get a more accurate estimate, the average of 2.7 and 2.61 (2.655) is taken as the new estimate.

Repeat steps 2 and 3 until the desired level of accuracy is achieved.

After several iterations, the square root of 7.07 is approximately equal to 2.65.

Similarly, you can find the approximate square roots of 7.21 and 7.93.

To determine the probability mass function (PMF) and cumulative distribution function (CDF) of the carbon dioxide atmosphere for the trees, we can use the given percentages and corresponding carbon dioxide levels and it found that, the probability mass function of the carbon dioxide atmosphere is not represented by any of the given options, the cumulative distribution function of the carbon dioxide atmosphere is 565 ppm (option b), the mean of the carbon dioxide atmosphere for these trees is 565 ppm (option b).

a. Probability Mass Function (PMF):

The PMF gives the probability of each possible value of the random variable. In this case, the random variable is the carbon dioxide atmosphere (in ppm). We can determine the PMF by assigning the probabilities to each carbon dioxide level.

The PMF for the carbon dioxide atmosphere is as follows:

P(350 ppm) = 0.06

P(450 ppm) = 0.10

P(550 ppm) = 0.47

P(650 ppm) = 0.37

b. Cumulative Distribution Function (CDF):

The CDF gives the cumulative probability up to a certain value of the random variable. We can calculate the CDF by adding up the probabilities from the PMF up to each carbon dioxide level.

The CDF for the carbon dioxide atmosphere is as follows:

CDF(350 ppm) = P(350 ppm) = 0.06

CDF(450 ppm) = P(350 ppm) + P(450 ppm) = 0.06 + 0.10 = 0.16

CDF(550 ppm) = P(350 ppm) + P(450 ppm) + P(550 ppm) = 0.06 + 0.10 + 0.47 = 0.63

CDF(650 ppm) = P(350 ppm) + P(450 ppm) + P(550 ppm) + P(650 ppm) = 0.06 + 0.10 + 0.47 + 0.37 = 1.00

c. Mean of the carbon dioxide atmosphere:

To calculate the mean of the carbon dioxide atmosphere, we multiply each carbon dioxide level by its corresponding probability and sum them up.

Mean = (350 ppm * 0.06) + (450 ppm * 0.10) + (550 ppm * 0.47) + (650 ppm * 0.37)

= 21 + 45 + 258.5 + 240.5

= 565

Therefore in summary:

a. The probability mass function of the carbon dioxide atmosphere is not represented by any of the given options.

b. The cumulative distribution function of the carbon dioxide atmosphere is 565 ppm (option b).

c. The mean of the carbon dioxide atmosphere for these trees is 565 ppm (option b).

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The standard deviation of the data set {28, 34, 27, 42, 52, 15} is approximately 11.73.

To calculate the standard deviation of the data set {28, 34, 27, 42, 52, 15}, we can follow these steps:

Find the mean (average) of the data set by summing all the numbers and dividing by the total count:

Mean = (28 + 34 + 27 + 42 + 52 + 15) / 6 = 198 / 6 = 33.

Calculate the difference between each data point and the mean:

Subtract the mean from each data point: {28 - 33, 34 - 33, 27 - 33, 42 - 33, 52 - 33, 15 - 33} = {-5, 1, -6, 9, 19, -18}.

Square each of the differences obtained in step 2:

Square each value: \({(-5)^2, 1^2, (-6)^2, 9^2, 19^2, (-18)^2} = {25, 1, 36, 81, 361, 324}.\)

Find the mean of the squared differences:

Sum the squared differences: 25 + 1 + 36 + 81 + 361 + 324 = 828.

Divide by the total count (6): 828 / 6 = 138.

Calculate the square root of the mean of squared differences:

Standard deviation = √138 ≈ 11.73 (rounded to two decimal places).

Therefore, the standard deviation of the given data set {28, 34, 27, 42, 52, 15} is approximately 11.73.

The standard deviation measures the spread or variability of the data points from the mean, indicating the average distance of each data point from the mean.

In this case, the standard deviation of 11.73 suggests that the data points are relatively spread out from the mean value of 33.

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There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

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There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

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(0, -5) and (2, -8.75)

Given the function expressed as:

We are to find two other coordinates other than the vertex and x-intercept. Note that the equation of a parabola in vertex form is expressed as:

Another coordinate point is the y-intercept of the graph. The y-intercept occurs at the point where x = 0.

Substitute x = 0 into the given function;

Hence the y-intercept of the graph is (0, -5)

The other coordinate of the function we can determine is the FOCUS.

The coordinates for the focus of the parabola is given as (h, k+1/4a).

where:

• a is the intercept

• (h, k) is the vertex

Comparing the given function with the general function, we can see that:

a = 1

h = 2

k = -9

Substitute these values into the coordinate of the focus will give:

Therefore the other two points on the graph are (0, -5) and (2, -8.75)

Based on the above, the capacity of a 5-liter tin is about  500 cm³.

To be able to convert the capacity of a 5-liter tin to its volume in cm³, One need to use the conversion factor that is, 1 liter is equivalent to 100 cm³.

So, to be able to calculate the volume of a 5-liter tin in cm³, one have to multiply the capacity (5 liters) by the conversion factor (100 cm³/liter):

Volume in cm³ = 5 liters x 1000 cm³/liter

                           = 500 cm³

Therefore, the capacity of a 5-liter tin is about  500 cm³.

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See full text below

Convert the capacity of a 5 litre tin to its volume in cm³.1litre is equivalent to 100cm³

Answer:

7

Step-by-step explanation:

Answer:

Step-by-step explanation:6

Answer:

x = - 18

Step-by-step explanation:

Let certain number = x

The difference between half of a certain number and seven

x/2 - 7

is the same as

=

with adding two to that number

x + 2

Find the number

x/2 - 7 = x + 2

x - x/2 = - 7 - 2

( 2x - x ) / 2 = -9

2x - x = -18

x = - 18

Answer:

Step-by-step explanation:

The required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system. which is the correct answer would be an option (A).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The video game system will cost at least $450.

He earns $6 per hour babysitting and $10 per hour tutoring.

Let x be the number of hours babysitting and y be the number of hours of tutoring.

According to the given situation, we can write the inequality would be as:

⇒ 6x + 10y ≥ 450

Rearrange the terms of variables in the above inequality,

⇒ 10y ≥ 450 - 6x

Divided by 10 into both sides of the above inequality,

⇒ 10y/10 ≥ 450/10 - 6x/10

⇒ y ≥ 45 - 0.6x or

⇒ y ≥ - 0.6x + 45

Thus, the required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system.

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The general solution of the differential equation y''(x) + y(x) = sec(x) tan(x) is y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x); here c₁ and c₂ are constants.

To solve the differential equation y''(x) + y(x) = sec(x) tan(x) using variation of parameters, we first need to find the solutions to the homogeneous equation y''(x) + y(x) = 0.

The auxiliary equation for the homogeneous equation is r² + 1 = 0, which has complex roots r = ±i.

The corresponding solutions to the homogeneous equation are y₁(x) = cos(x) and y₂(x) = sin(x).

Next, we need to find the particular solution using the method of variation of parameters. Let's assume the particular solution has the form y_p(x) = u(x)cos(x) + v(x)sin(x).

Now, we need to find u(x) and v(x) by substituting this form into the original differential equation and solving for u'(x) and v'(x).

Differentiating y_p(x), we get y_p'(x) = u'(x)cos(x) - u(x)sin(x) + v'(x)sin(x) + v(x)cos(x).

Taking the second derivative, y_p''(x) = -u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x).

Substituting these derivatives into the original differential equation, we have:

(-u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x)) + (u(x)cos(x) + v(x)sin(x)) = sec(x)tan(x).

Simplifying, we get:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x).

To find u'(x) and v'(x), we solve the following system of equations:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x),

u(x)cos(x) + v(x)sin(x) = 0.

We can solve this system using various methods such as substitution or elimination.

Solving the system, we find:

u'(x) = sin(x)sec(x),

v'(x) = -cos(x)sec(x).

Integrating these expressions, we obtain:

u(x) = -ln|sec(x) + tan(x)| + C₁,

v(x) = -ln|sec(x) + tan(x)| + C₂.

Finally, the particular solution is given by:

y_p(x) = (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

The general solution to the differential equation is the sum of the homogeneous and particular solutions:

y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

Here, c₁ and c₂ are constants.

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Answer:

y=3x-2

Step-by-step explanation:

y = 3x+ 2 ; y= 3x - 2 is a system of equations with no solution.

The given fraction and decimals have been plotted on a number line as shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.

Additionally, a number line typically decreases in numerical value towards the left from zero (0) and increases in numerical value towards the right from zero (0).

In order to place the given numbers on a number line, we would convert the fraction into a decimal number as follows:

1/3 = 0.3

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The derivative of H(z) is H'(z) = -2zd^2/[(d^2-z^2)(d^2+z^2)].

To differentiate the function H(z) = ln[(d^2-z^2)/(d^2+z^2)]^(1/2), we will use the chain rule and the power rule of differentiation.

First, we can simplify the expression inside the natural logarithm using the laws of exponents:

[(d^2-z^2)/(d^2+z^2)]^(1/2) = [(d^2-z^2)^(1/2)/(d^2+z^2)^(1/2)]

Now we can differentiate H(z) as follows:

H'(z) = d/dz [ln[(d^2-z^2)/(d^2+z^2)]^(1/2)]

= (1/2)[(d^2+z^2)^(1/2)/(d^2-z^2)^(1/2)] * d/dz [(d^2-z^2)/(d^2+z^2)]

Using the quotient rule, we can simplify the derivative:

d/dz [(d^2-z^2)/(d^2+z^2)] = [(2z)(d^2+z^2) - (d^2-z^2)(2z)]/(d^2+z^2)^2

= -4zd^2/(d^2+z^2)^2

Substituting this back into H'(z), we get:

H'(z) = (1/2)[(d^2+z^2)^(1/2)/(d^2-z^2)^(1/2)] * (-4zd^2/(d^2+z^2)^2)

= -2zd^2/[(d^2-z^2)(d^2+z^2)]

Therefore, the derivative of H(z) is:

H'(z) = -2zd^2/[(d^2-z^2)(d^2+z^2)]

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Answer:

Corresponding angles :)

Answer:

the third line

Step-by-step explanation:

i just need points

Answer: X = -12

Step-by-step explanation:  1)  12 + x/4 = 9

                                              2)  12 + x/ 2^2 = 9

                                              3)   x/ 2^2  + 12 = 9  

The distance between two complex numbers z and v is given by |z - v|, where |.| denotes the modulus or absolute value.

Therefore, we have:

|z - v| = √26

Substituting z = 5 + ai and v = 2a - 3i, we get:

|5 + ai - (2a - 3i)| = √26

Simplifying the expression inside the modulus, we get:

|5 - 2a + (a + 3i)| = √26

|3 - a + 3i| = √26

Taking the modulus of the complex number on the left side, we get:

√((3-a)² + 3²) = √26

Squaring both sides, we get:

(3-a)² + 9 = 26

Expanding the left side and simplifying, we get:

a² - 6a - 14 = 0

We can solve this quadratic equation using the quadratic formula:

a = [6 ± √(6² + 4(14))]/2

a = [6 ± √52]/2

a = 3 ± √13

Therefore, the value(s) of a that satisfy the given condition are

a = 3 + √13 and a = 3 - √13.

Answer:

$330.03

Step-by-step explanation:

You start by adding all of the pairs of pants: 57. Then, you multiply 57 by $5.79: 330.03