16=4+3(t-2) fast someone​

Answer:

YX is congruent to XZ - given

WX bisects angle YXZ - given

angle YXW is congruent to angle ZXW - definition of an angle bisector

WX is congruent to WX - reflexive theorem of congruency

triangle WYX is congruent to triangle WZX - SAS

Answer:

The answers are:

Step-by-step explanation:

1)Adjacent

2)Vertical

3)Corresponding

4)None of these

5)1,7  3,5  4,6  2,8 (<--angle numbers)

6)4,5  2,7 (<--angle numbers)

7)1=85, 2=95, 3=85, 4=85

8)1=60, 2=120, 3=60, 4=120

9)1=90, 2=90, 3=90, 4=90

10) No, they are not parallel. A protractor would show that the intersection angles are different, meaning the lines aren't parallel.

SORRY it took so long hope this helps!!

Answer:

1.

adjacent

2.

vertical

3.

corresponding

4.

none (just regular interior and thats not an option)

5.

(<5,<7) (<6,<8) (<1,<3) (<2,<4)

6.

(<2,<7) (<6,<3)

7.

<1= 85

<2= 95

<3= 85

<4= 85

8.

<1= 60

<2= 120

<3= 60

<4= 120

9.

<1= 90

<2= 90

<3= 90

<4= 90

10. No, its not parallel because the corresponding angles 1 and 7 aren't equal. You can use a protractor to figure this out by finding the measurement of angles 1 and 7. Because they aren't equal degrees, the lines will cross at some point

Answer:

x = 19

Step-by-step explanation:

Since DF is an angle bisector then it divides the opposite sides into segments that are proportional to the other 2 sides, that is

\(\frac{DE}{DG}\) = \(\frac{EF}{GF}\) , substitute values

\(\frac{25}{22.5}\) = \(\frac{x-9}{9}\) ( cross- multiply )

22.5(x - 9) = 225 ( divide both sides by 22.5 )

x - 9 = 10 ( add 9 to both sides )

x = 19

A) enable a project to have sufficient technical support for projects with challenging and complex technology.

Internal integration tools refer to software or other technologies that facilitate collaboration and communication within a project team. These tools can include project management software, communication platforms, and other applications that help project teams work together more effectively.

One of the main benefits of internal integration tools is that they can provide technical support for projects with challenging and complex technology. For example, project management software can help teams manage complex schedules and resource allocations, while collaboration platforms can facilitate communication and information sharing among team members.

While internal integration tools may support documentation and monitoring of project plans (B), portraying a project as a network diagram (C) is more commonly associated with project scheduling software, and linking the work of the implementation team with users (D) and enabling end-user communication with system developers (E) are more closely associated with user engagement and support tools.

The actual area of the football field is 5,333 ¹/₃ square yards.

The length of the football field is 100 yards.

The width of the field is 53 ¹/₃ yards.

The formula for the area of a rectangle is;

Area = length × width

Area = length * width

Thus, plugging in the relevant values gives;

Area = 100 yd. * 53 ¹/₃ yd.

= 5333 ¹/₃ sq. yd.

The area of the football field is 5,333 ¹/₃ square yards.

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Complete question is;

Lewis directs the school marching band. He uses scale drawings of the football field to design marching formations for the band. The football field is 100 yards long and yards wide. Lewis always uses a scale of 1 inch to 10 yards for his drawings.

Complete the steps below to find the length and width of the football field as it appears in one of Lewis’s scale drawings.

Part A

What is the actual area of the football field? Assume that the field is shaped like a rectangle.

The code from solving the expressions is MGWMGWW

1. 7b

2. 6y - 1

3. -m + 0.5

4. 9x - 2y

5. 4j

6. -12x + 22

7. 6m - 8

Algebraic expressions are expressions that are composed of coefficients, variables, terms, factors and constants.

They also consist of mathematical operations, such as;

Given the expression;

b + b + b + b + 3b

collect the like terms

7b

2(4y-  3) - 2x + 5

collect like terms

6y - 1

Hence, the code is MGWMGWW

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Timmy needs to exert approximately 85.5 pounds of force to hold the piano in place on the ramp.

To determine the amount of force Timmy needs to exert to hold the piano in place on the ramp, we can consider the forces acting on the piano.

When the piano is on an inclined ramp, there are two main forces at play: the gravitational force pulling the piano downward and the normal force exerted by the ramp perpendicular to the surface. The normal force acts in the direction perpendicular to the ramp and helps counteract the gravitational force.

To find the force exerted by Timmy, we need to consider the component of the gravitational force acting parallel to the ramp. This force is given by:

Force parallel = Weight × sin(angle)

where Weight is the weight of the piano, and angle is the angle of inclination of the ramp.

In this case, the weight of the piano is 250 pounds, and the angle of inclination is 20 degrees. Plugging in these values into the equation, we get:

Force parallel ≈ 250 × 0.3420 ≈ 85.5 pounds

Therefore, Timmy needs to exert approximately 85.5 pounds of force to hold the piano in place on the ramp.

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Where is the question ???

Answer:

1. b ∈ B 2. ∀ a ∈ N; 2a ∈ Z 3. N ⊂ Z ⊂ Q ⊂ R 4. J ≤ J⁻¹ : J ∈ Z⁻

Step-by-step explanation:

1. Let b be the number and B be the set, so mathematically, it is written as

b ∈ B.

2. Let  a be an element of natural number N and 2a be an even number. Since 2a is in the set of integers Z, we write

∀ a ∈ N; 2a ∈ Z

3. Let N represent the set of natural numbers, Z represent the set of integers, Q represent the set of rational numbers, and R represent the set of rational numbers.

Since each set is a subset of the latter set, we write

N ⊂ Z ⊂ Q ⊂ R .

4. Let J be the negative integer which is an element if negative integers. Let the set of negative integers be represented by Z⁻. Since J is less than or equal to its inverse, we write

J ≤ J⁻¹ : J ∈ Z⁻

The wage of 2001 in terms of wage in 2012 is option A $14.97

Given,

Mack's wages in 2001 = $7 per hour

Mack's wages in 2012 = $12 per hour

The CPI in 2001 = 94

The CPI in 2012 = 201

We have to fins the wage of 2001 in terms of wage in 2012;

CPI;- Consumer Price Index

The CPI is calculated by the Bureau of Labor Statistics each month using a sample of 94,000 prices. To determine the overall change in prices, the index for each good or service is weighted according to its share of recent consumer spending.

Here,

The wage of 2001 in terms of wage in 2012 = (CPI in present year / CPI in past year) x Wage of earlier year

= (201 / 94) x 7

= 14.97

That is,

The wage of 2001 in terms of wage in 2012 is option A $14.97

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Answer:

The x-intercept is (-9,0). The y-intercept is (0,27).

Step-by-step explanation:

9x - 3y = -81

-9x         -9x                  Subtract 9x from both sides

-3y = -9x - 81                Divide both sides by -3

y = 3x + 27

I graphed the equation below.

Step-by-step explanation:

9x-0=-81

divide all through with 9x to get

x=-2

0-3y=-81

divide all through with 3y to get

y=27

The given double integral is ∫ ∫ (x² + y²)dx dy, and we need to evaluate it over the region in the positive quadrant where x+y≤1.

To evaluate this double integral, we can first determine the limits of integration for both x and y based on the given region. In the positive quadrant, x and y both range from 0 to 1.

Now, integrating the inner integral with respect to x, we get:

∫ (x² + y²)dx = (1/3)x³ + y²x + C1,

where C1 is the constant of integration.

Next, we integrate the resulting expression with respect to y:

∫ [(1/3)x³ + y²x + C1] dy = (1/3)x³y + (1/3)y³x + C1y + C2,

where C2 is another constant of integration.

Finally, we evaluate this double integral over the given region by substituting the limits of integration:

∫∫ (x² + y²)dx dy = ∫[0 to 1] ∫[0 to 1-x] (x² + y²)dy dx.

Performing the integration, we can find the numerical value of the double integral within the given region.

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Thus, the value of x for the given bottom isosceles triangle is found to be x = 88°.

Additional angles are two angles that add up to 180 degrees. The situation when they happen to be on the identical side of a straight line is a typical one.

For the top isosceles triangle:

Base angle = ?

Using the property of supplementary angles:

base angle + 113 = 180

base angle = 180 - 113

base angle = 67

Now, using the Triangle sum Theorem:

Vertex angle = ?

Vertex angle + 67 + 67 = 180

Vertex angle = 180 - 134

Vertex angle = 46

For the bottom isosceles triangle:

base angle  = Vertex angle of top triangle (vertically opposite angles)

base angle  = 46

Now,

For the values of x, use Triangle sum Theorem:

x + 46 + 46 = 180

x = 180 - 92

x = 88

Thus, the value of x for the given bottom isosceles triangle is found to be x = 88°.

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The Laplace transform of the given function \((t)-{: 01277 1, 0\)is given by:

\(L{(t)-{: 01277 1, 0} = L{(t - 1)e^(-2t) u(t - 1)} + L{e^(-2t) u(t)}\) where u(t) is the unit step function.

Step-by-step solution is given below: Given function is (t)-{: 01277 1, 0Laplace transform of the given function is \(L{(t)-{: 01277 1, 0}=L{(t-1)e^-2t u(t-1)}+L{e^-2t u(t)}\) Where u(t) is the unit step function.

We have to find the Laplace transform of the given function.\((t)-{: 01277 1, 0 = (t-1)e^-2t u(t-1) + e^-2t u(t)\)Laplace Transform of \((t-1)e^-2t u(t-1) = L{(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)} = e^{-as} * F(s)So, (t-1)e^-2t u(t-1) = 1(t-1)e^-2t u(t-1)\)

Taking Laplace transform on both sides,\(L{(t-1)e^-2t u(t-1)} = L{1(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\)(On substituting a = 2)

Now, Let's solve \(L{e^-2t u(t)}\)

Taking Laplace transform on both sides,\(L{e^-2t u(t)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\) (On substituting a = 2) Laplace transform of the given function L{(t)-{: 01277 1, 0}= L{(t-1)e^-2t u(t-1)} + L{e^-2t u(t)}= F(s+2) + F(s+2)= 2F(s+2)= 2L{e^-2t} = 2 / (s+2)

Hence, the Laplace transform of the given function is 2 / (s+2) which is a transfer function of a system with a first-order differential equation.

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The angle relations in a cyclic quadrilateral are discussed above.

Given is that ABCD is a cyclic quadrilateral.

A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.

Each vertex of the quadrilateral lies on the circumference of the circle and is connected by four chords.

The opposite angles of a cyclic quadrilateral have a total of 180°.

For a cyclic quadrilateral with successive sides a, b, c, d, semi - perimeter s, and angle A between sides a and d, the angle relations for a cyclic quadrilateral as -

        \($\tan {\frac {\theta }{2}}={\sqrt {\frac {(s-b)(s-d)}{(s-a)(s-c)}}}.\)

       \(${\displaystyle \cos {\frac {\varphi }{2}}={\sqrt {\frac {(s-b)(s-d)(b+d)^{2}}{(ab+cd)(ad+bc)}}}}\)

Therefore, the angle relations in a cyclic quadrilateral are discussed above.

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Answer:

a is correct ................

The diameter of the aperture in a 35-mm lens set to a stop of f/2 is 17.5mm.

In this question, we are asked to determine the size of the aperture or we can say Diameter of aperture

Given the focal length of lens (f) = 35 mm

The lens is set to a stop f/2

We need to find the size of the aperture

Let d be the diameter of the aperture.

So, d = f/2   --(1)

Putting the value of f = 35 mm in equation (1). We get,

d = (35 mm)/2

d = 17.5 mm

Hence, the Size (diameter) of the aperture is 17.5 mm

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All the evaluations of f(x) and g(x) are:

We have the functions:

f(x) = 2x² + x - 3

g(x) = (2x - 1)/3

Let's evaluate the functions in the given values, to do so, just replace the x by the correspondent value.

a) f(0):

f(x) = 2x² + x - 3

f(0) = 2(0)² + (0) - 3

f(0) = 0 + 0 - 3

f(0) = -3

b) g(0):

g(x) = (2x - 1)/3

g(0) = (2(0) - 1)/3

g(0) = (0 - 1)/3

g(0) = -1/3

c) f(-2):

f(x) = 2x² + x - 3

f(-2) = 2(-2)² + (-2) - 3

f(-2) = 2(4) - 2 - 3

f(-2) = 8 - 2 - 3

f(-2) = 3

d) g(5):

g(x) = (2x - 1)/3

g(5) = (2(5) - 1)/3

g(5) = (10 - 1)/3

g(5) = 9/3

g(5) = 3

e) f(-(2/3)):

f(x) = 2x² + x - 3

f(-(2/3)) = 2(-(2/3))² + (-(2/3)) - 3

f(-(2/3)) = 2(4/9) - 2/3 - 3

f(-(2/3)) = 8/9 - 2/3 - 3

f(-(2/3)) = 8/9 - 6/9 - 27/9

f(-(2/3)) = (8 - 6 - 27)/9

f(-(2/3)) = -25/9

f) g(7/2):

g(x) = (2x - 1)/3

g(7/2) = (2(7/2) - 1)/3

g(7/2) = (14/2 - 1)/3

g(7/2) = (13/2)/3

g(7/2) = 13/6

g) f(3):

f(x) = 2x² + x - 3

f(3) = 2(3)² + 3 - 3

f(3) = 2(9) + 3 - 3

f(3) = 18 + 3 - 3

f(3) = 18

h) g(-7):

g(x) = (2x - 1)/3

g(-7) = (2(-7) - 1)/3

g(-7) = (-14 - 1)/3

g(-7) = -15/3

g(-7) = -5

i) f(1/2):

f(x) = 2x² + x - 3

f(1/2) = 2(1/2)² + (1/2) - 3

f(1/2) = 2(1/4) + 1/2 - 3

f(1/2) = 1/2 + 1/2 - 3

f(1/2) = 1 - 3

f(1/2) = -2

j) g(-1/2):

g(-1/2) = (2*(-1/2) - 1)/3

g(-1/2)  = (-1 - 1)/3 = -2/3

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43.75 divided by 7 is 6.25, thus your answer is 6.25 hours

Answer:

Inequality: 4g + 70 < 90

Step-by-step explanation:

Given that:

Flat cost per month = $70

Cost per gigabyte = $4

Budget amount = under $90

As she wants to keep the budget under 90, then we will use less than sign to form the inequality.

Let,

g be the number of gigabytes.

4g + 70 < 90

Hence,

Inequality: 4g + 70 < 90

Answer:

g<5

Step-by-step explanation:

Have a good day :)

The annual effective interest rate is 8%, the present value of the annuity is option C: $1,381.63

To calculate the present value of the annuity, we can use the formula for the present value of a series of periodic payments:

\(\[ PV = PMT \times \left(1 - (1 + r)^{-n}\right) / r \]\)

Where:

- PV is the present value of the annuity,

- PMT is the payment amount,

- r is the interest rate per compounding period, and

- n is the total number of compounding periods.

In this case, Mildred will receive payments of $50 every three months for 10 years, which is a total of 40 payments (since there are 4 quarters in a year and 10 years equals 40 quarters).

The interest rate is 8% per year, so we need to adjust it for the compounding period. Since the payments are made every three months, the interest rate per quarter is 8% divided by 4, which is 2%.

Substituting the values into the formula, we have:

\(\[ PV = 50 \times \left(1 - (1 + 0.02)^{-40}\right) / 0.02 \]\)

Using a calculator, we find that the present value of the annuity is approximately $1,381.63.

Therefore, the correct answer is option C: $1,381.63.

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The amount that Bert should deposit to earn $192 interest is $4,000 (option C).

When an account earns a simple interest, the account increases linearly. It means that the value of the account increases at a constant rate.

The rate of increase is determined by the amount deposited, the interest rate and the number of years the money was deposited for.

Amount to be deposited = simple interest / (years x interest rate)

$192 / (0.016 x 3) $192 / 0.048 = $4,000

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The corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

To perform u-substitution with indefinite integrals, follow these steps:

Identify a suitable substitution: Look for a part of the integrand that resembles the derivative of a function. Choose a variable u to substitute for that part.

Calculate du: Take the derivative of u with respect to the original variable. This will help us express du in terms of the original variable.

Rewrite the integral: Substitute the chosen variable and du in the original integral, replacing the part to be substituted with u and the corresponding differential element du.

Integrate with respect to u: Treat the integral as a new integral with respect to u. Evaluate the integral using the rules of integration.

Replace u with the original variable: Rewrite the result of the integration in terms of the original variable.

Simplify and solve: If necessary, simplify the expression further or perform additional algebraic manipulations to obtain the final result.

Let's illustrate these steps with an example:

Consider the integral ∫(2x + 3)² dx.

Identify a suitable substitution: Let u = 2x + 3.

Calculate du: Take the derivative of u with respect to x: du/dx = 2. Rearrange the equation to solve for du: du = 2 dx.

Rewrite the integral: In terms of u and du, the integral becomes ∫u² (du/2).

Integrate with respect to u: Treat the integral as a new integral with respect to u: (1/2) ∫u² du = (1/2) * (u³/3) + C, where C is the constant of integration.

Replace u with the original variable: Substitute back u = 2x + 3 in the result: (1/2) * ((2x + 3)³/3) + C.

Simplify and solve: Further simplify the expression if necessary to obtain the final result.

In summary, to perform u-substitution with indefinite integrals, identify a suitable substitution, calculate the corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

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The value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

Given that a researcher measures the relationship between two variables, X and Y.

If SS(XY) = 340 and SS(X)SS(Y) = 320,000, then we need to calculate the value of the correlation coefficient.

Correlation coefficient:

The correlation coefficient is a statistical measure that determines the degree of association between two variables.

It is denoted by the symbol ‘r’.

The value of the correlation coefficient lies between -1 and +1, where -1 indicates a negative correlation, +1 indicates a positive correlation, and 0 indicates no correlation.

How to calculate correlation coefficient?

The formula to calculate the correlation coefficient is as follows:

r = SS(XY)/√[SS(X)SS(Y)]

Now, substitute the given values, we get:

r = 340/√[320000]r = 0.34

Therefore, the value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

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Use formula to calculate area increase in rectangle when length and width increase by percentages, resulting in a 32% increase.

To find the percent by which the area of a rectangle increases when the length and width are increased by certain percentages, we can use the formula:
\(${Percent increase in area} = (\text{Percent increase in length} + \text{Percent increase in width}) + (\text{Percent increase in length} \times \text{Percent increase in width})$\)
In this case, the percent increase in length is 20% and the percent increase in width is 10\%. Plugging these values into the formula, we get:

\($\text{Percent increase in area} = (20\% + 10\%) + (20\% \times 10\%)$\)
\($\text{Percent increase in area} = 30\% + 2\%$\)
\($\text{Percent increase in area} = 32\%$\)
Therefore, the area of the rectangle increases by 32%.

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The Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

To investigate whether the span of a person's dominant hand is greater than that of their non-dominant hand, the most appropriate statistical technique would be the Paired samples t-test.

The Paired samples t-test is used when comparing the means of two related groups or conditions. In this case, the dominant and non-dominant hands are related because they belong to the same individuals in the study. By comparing the means of the dominant and non-dominant hand spans, we can determine if there is a significant difference between the two.

The other options listed, ANOVA (Analysis of Variance), Independent samples t-test, Wilcoxon's matched-pairs signed rank test, and Mann-Whitney U test, are not suitable for this scenario because they are designed for different types of comparisons:

- ANOVA is used when comparing the means of three or more independent groups, which is not the case here.

- Independent samples t-test is used when comparing the means of two independent groups, which is not the case here as the measurements are paired.

- Wilcoxon's matched-pairs signed rank test and Mann-Whitney U test are non-parametric tests that are used when the data do not meet the assumptions of parametric tests. However, in this case, we have paired measurements, and the paired samples t-test is the appropriate parametric test.

Therefore, the Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

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Answer:

6 miles per hour

Step-by-step explanation:

1 mile is 1760 yards (5280 feet);

10560/1760=6

so we know that Kelly rowed 6 miles per hour!

say we're going to add "x" gallons of water, now how many gallons of alcohol is in pure water? well 0%, and 0% of "x" is (0/100) * x = 0.

the 3 gallons we know are 100% alcohol, how many gallons of alcohol is in it?  well (100/100) * 3 = 3.

the resulting mix will have x + 3 gallons total and it's going to be 15% alcohol, how many gallons of alcohol is that? (15/100) * (x+3).

now, the amount of alcohol never increased, so the original 3 gallons of only alcohol will remain even after the water has been added, so.

\(\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{amount}\\ \cline{2-4}&\\ \textit{pure water}&x&0.00&0\\ \textit{pure alcohol}&3&1.00&3\\ \cline{2-4}&\\ mixture&x+3&0.15&0.15(x+3) \end{array} \begin{array}{llll} \\[3em] \leftarrow \textit{this amount}\\\\ \leftarrow \textit{must be equal to this one} \end{array} \\\\\\ 3 = 0.15(x+3)\implies 3=0.15x+0.45\implies 2.55=0.15x \\\\\\ \cfrac{2.55}{0.15}=x\implies 17=x\)