EFG, e = 9.8 cm, f = 3 cm and ∠G=167°. Find the length of g, to the nearest 10th of a centimeter.

Answer: [tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]

Step-by-step explanation:

By inspection, we know the equation of the parabola is [tex]y=x^2 +4[/tex] and the equation of the line is [tex]y=-x+4[/tex].

Since there is an open hole at x=3 for the parabola and a closed hole at x=3 for the line, the function is

[tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]

The exact distance and direction that Patrick is from Johnny is; 177.81 ft and 215.52°

Let the distance of Johnny to Patrick be x.

The angle opposite x would be; (90 - 50) + 90 + 30 = 160°

We will therefore use the cosine rule to find x;

X² = A² + B² - 2ABcosx

Where;

A and B are the distance of Johnny to Rob and Rob to Patrick respectively. Thus;

X² = 130² + 50² - 2(130)(50)cos160

X²= 16900 + 2500 + 12216.004

X² = 31616.004

X = 177.81 ft

To get the direction "y" we will use sine rule;

50/siny = 177.809/sin160

50/siny = 177.809/0.342

50/siny = 519.9094

Siny = 50/519.904

Siny = 0.09617

y = sin⁻¹(0.09617)

y = 5.52°

The bearing of Patrick from Johnny is;

5.52 + 30 + 180 = 215.52°

Read more about Trigonometric Ratios at; https://brainly.com/question/24349828

#SPJ1

Using the z-distribution, the z-statistic would be given as follows:

c) z = -2.63.

At the null hypothesis we test if the means are equal, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, it is tested if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

For each sample, they are given as follows:

Hence, for the distribution of differences, they are given by:

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

[tex]z = \frac{-2 - 0}{0.76}[/tex]

z = -2.63.

Hence option B is correct.

More can be learned about the z-distribution at brainly.com/question/13873630

#SPJ1

The area of the poster is  28.75 feet square.

Note that the area of a rectangle is given as;

Area = length × width

Length = 11. 5 feet

Width = 2. 5 feet

Area = 11. 5 × 2. 5

Area = 28. 75 feet square

Thus, the area of the poster is  28.75 feet square.

Learn more about area of a rectangle here:

https://brainly.com/question/14137384

#SPJ1

The given coordinates are actually a rectangle

The coordinates are given as:

A (3, 1), B (1, 5), C (9, 9), and D (11, 5).

Calculate the distance between the coordinates using:

[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(3 -1)^2 +(1-5)^2} =\sqrt {20[/tex]

[tex]BC = \sqrt{(1 -9)^2 +(5-9)^2} =\sqrt {80[/tex]

[tex]CD = \sqrt{(9 -11)^2 +(9-5)^2} =\sqrt {20[/tex]

[tex]DA = \sqrt{(11 -3)^2 +(5-1)^2} =\sqrt {80[/tex]

The above shows that the opposite sides are congruent

Next, we calculate the slopes using:

m = (y2- y1)/(x2- x1)

So, we have:

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

BC = (5- 9)/(1-9) = 1/2

CD = (9- 5)/(9-11) = -2

DA = (5- 1)/(11-3) = 1/2

The slopes of adjacent sides are opposite reciprocals.

This means that the sides are perpendicular

Hence, the given coordinates are actually a rectangle

Read more about quadrilateral at:

https://brainly.com/question/16691874

#SPJ1

Answer: 5

Step-by-step explanation:

Because there are 35 when you add yourself so u subtract 30 to get 5

There would be 4 people left in the garden.

34 - 30 = 4.

Subtraction is a mathematical operation that involves taking away one number from another to find the difference between them. For the question, At first, there were 34 people in the garden and later 30 people were no longer alive in the garden, so the difference between 30 people and 34 people is 4.

Subtraction is the opposite of addition, and it is used to measure the distance between two values on the number line.

Subtraction is represented by minus Sign (-). For example, subtracting 5 from 10 gives you a difference of 5 (10 - 5 = 5).

Learn more about subtraction of Numbers here

https://brainly.com/question/28467694

#SPJ3

The probability that the mean fill is more than 84.8 ounces is 0.39358

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (84.8 - 84.5)/1.1

Evaluate the difference of 84.8 and 84.5

z = 0.3/1.1

Evaluate the quotient of 0.3 and 1.1

z = 0.27

The probability that the mean fill is more than 84.8 ounces is then calculated as:

P(x > 84.8) = P(z > 0.27)

From the z table of probabilities, we have;

P(x > 84.8) = 0.39358

Hence, the probability that the mean fill is more than 84.8 ounces is 0.39358

Read more about probability at:

https://brainly.com/question/25870256

#SPJ1

Answer:

y = 2x + 6

Step-by-step explanation:

We are given the line R, which is y=2x+5, and we want to find the equation of the line that is parallel to this line, and that also passes through the point (-2, 2).

Parallel lines have the same slope, yet different y-intercepts.

So, we should first find the slope of y=2x+5.

The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.

As 2 is in the place of where m (the slope) should be, 2 is the slope of the line.

It is also the slope of the line parallel to it.

We can write the equation of the new line in slope-intercept form as well; here is the equation so far, with what we know:

y = 2x + b

We need to find b.

As the equation passes through the point (-2, 2), we can use its values to help solve for b.

Substitute -2 as x and 2 as y.

2 = 2(-2) + b

Multiply.

2 = -4 + b

Add 4 to both sides.

6 = b

Substitute 6 as b.

y = 2x + 6

Answer:

y = 2

Step-by-step explanation:

Algebraic Equation is an equation where alphabets are used to represent numbers.

Solving the above question,

Let the number = y

Therefore,

Sum of the number = y + 3

If it's subtracted from 10 it becomes

10 - ( y + 3 )

The result : 10 - y - 3 = 5

- y = 5 - 10 + 3

- y = -2

Therefore,

y = 2

Answer:

11

Step-by-step explanation:

The focal length is 14, and thus the sum of the lengths of the blue and red segments is also 14.

Based on the equation of the function of the height of the building, it takes the man 44.7 seconds to fall from the top

The function of the height where the man falls is a quadratic function, and the equation of the function is given as:

d = t^2 * 0.25

The height of the building is 500

This means that the value of d is 500.

So, we have;

d = 500

Substitute 500 for d in the equation d = t^2 * 0.25

500 = t^2 * 0.25

Divide both sides of the above equation by 0.25

500/0.25 = t^2 * 0.25/0.25

Evaluate the quotient in the above equation

t^2 = 2000

Take the square root of both sides in the above equation

√t^2 = √2000

Evaluate the exponent

t = 44.7

Hence, it takes the man 44.7 seconds to fall

Read more about quadratic functions at:

https://brainly.com/question/12446886

#SPJ1

The sample should include 2702 men and 2702 women.

Given that you want to be 99% sure your error doesn't exceed 0.035.

A sample is a group of people selected from a larger population to provide data to researchers. The number of members of the population included in the sample is called the sample size.

The significance level is the probability that the test statistic is in the critical range if the null hypothesis is actually true. The confidence interval is 99% or 0.99.

The level of significance α = 1-0.99 = 0.01

the margin of error, ME = 0.035

The Z-critical value at the 99% confidence level or at the significance level of 0.01 is 2.575 (from standard normal tables).

We will now use the formula:[tex]n=\frac{Z^2_{critical}}{2(ME)^2}[/tex].

Substitute the values ​​in the above formula, we get

n = (2.575) ² / (2 × (0.035) ²)

n = 6.630625 / (2 × 0.001225)

n = 6.630625 / 0.00245

n = 2701.966

Therefore, the sample should include 2702 males and 2702 females with a 99% certainty that the error does not exceed 0.035

Learn more about significance level from here brainly.com/question/4599596

#SPJ1

Andy needs to subtract cost from the service revenue.

Revenue is the total income earned before any deductions are made. Net income is the total revenue less total expenses or cost.

Net income = total revenue - cost

For example, if a company sold 100 loaves of bread for $100 dollars. The cost of making the bread is $50. The revenue is $100 and the net income is $50 (100 - 50).

To learn more about net income, please check: https://brainly.com/question/10207673

#SPJ1

Answer:

y = 6

Step-by-step explanation:

   3x + y = 9 ---------------(I)

          y = -4x + 10 -----------------(II)

Substitute y = -4x + 10 in equation (I)

  3x - 4x + 10 = 9

Combine like terms,

        -x + 10  = 9

Subtract 10 from both sides. (subtraction property of equality)

               -x  = 9 - 10

              -x = -1

Divide both sides by (-1).  {Division property of equality}

              [tex]\sf \dfrac{-x}{-1}=\dfrac{-1}{-1}\\\\ \boxed{x = 1}[/tex]

Now, substitute x = 1 in equation (II) and find the value of y.

        y = -4*1 + 10

          = -4 + 10

       [tex]\sf \boxed{\bf y = 6}[/tex]

The graph shows the comparison of the human welfare and ecological footprints.

A graph simply means a diagram that shows the relationship between variables.

From the graph, it can be seen that countries such as Norway, Canada, USA, and Australia meet the minimum criteria for sustainability.

The graph also shows that Sierra Leone is the least developed country among the countries compared as it has the lowest human development index.

The threshold for high human development as given as 0.8. Most African countries had a human development index of 0.5 and below.

Learn more about graphs on:

brainly.com/question/19040584

#SPJ1

SOLUTION :

YES as well as NO , two equilateral ∆s can be congruent if any of their side matched to one another,

& CANNOT be congruent if any of their side didn't matched in terms of length (magnitude).

________________________________

MARK BRAINLIEST!

Answer:

Domain [-4 , +∞)

Range [0 , +∞)

Step-by-step explanation:

the function g such that g(x)=√(x+4) ,is defined

for the values of x that verify :

x + 4 ≥ 0

⇔ x ≥ -4

Then

The domain of g is [-4 , +∞)

………………………………………………

Let  x ∈ [-4 , +∞)  

then x ≥ -4

then x + 4 ≥ 0

then g(x) = √(x+4) ≥ 0

Therefore, we can affirm that the range of g is [0 , +∞)

[tex]\textbf{Heya !}[/tex]

✏[tex]\bigstar\textsf{Given:-}[/tex]✏

✏[tex]\bigstar\textsf{To\quad find:-}[/tex]

✏[tex]\bigstar\textsf{Solution \quad steps:-}[/tex] ✏

first use the distributive property

[tex]\sf{\longmapsto{ 5x+5=5x}[/tex]

subtract both sides  by 5x

[tex]\sf{\longmapsto{0x+5=0}[/tex] (strange expression right)

[tex]\sf{\longmapsto 0=-5}[/tex] (whattt ?!)

the above statement's false, so the equation has no solutions

`hope that was helpful to u ~

Step-by-step explanation:

OK, let's assume it this way:

Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!

Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+

Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+...+(n+1)!-n!=(n+1)!-1!=(n+1)!-1

and boom problem solved

Answer:

t >= [tex]\frac{25}{3}[/tex] or 8.33333333333

Step-by-step explanation:

We need to set up an inequality where demand is less than or equal to 0. The inequality looks like this:

50 - 6t <= 0

50 <= 6t

t >= [tex]\frac{25}{3}[/tex] or 8.33333333333

Savings after 6 years would be $ 1992.

Savings is the money that remains after expenses and other commitments have been subtracted from income.

Savings are the sum of money that would otherwise be lying about, not being risked on investments or used for consumption.

Savings and investing can be compared because the latter includes putting money at risk in an effort to try to increase wealth.

Indicators of household debt or a negative net worth include negative savings.

According to the question,

Amount contributed(P)= $1200

Rate(R)= 11%

Time(T)= 6 years

Interest(SI)=P*R*T/100

                   = 1200*11*6/100

                   = 792

Savings after 6 years = P+ SI

                                      = 1200 + 792

                                      = $ 1992

Learn more about savings here:

https://brainly.com/question/738615

#SPJ1

The point of intersection for the pair of linear equations is (-5.5, -4.8)

Linear equations are equations that have constant average rates of change, slope or gradient

The pair of linear equations is given as:

x + y = 0.7

y = 3x + 11.7

Substitute y = 3x + 11.7 in x + y = 0.7

x + 3x + 11.7 = 0.7

Evaluate the like terms

2x = -11

Divide both sides by 2

x = -5.5

Substitute x = -5.5 in y = 3x + 11.7

y = 3*-5.5 + 11.7

Evaluate

y = -4.8

So, we have

x = -5.5 and y = -4.8

Express the above points as an ordered pair, to determine the point of intersection

(x, y) = (-5.5, -4.8)

Hence, the point of intersection for the pair of linear equations is (-5.5, -4.8)

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

Answer: The function is odd because f(–x) = –f(x).

Step-by-step explanation:

[tex]f(x)=6x^7\\\\f(-x)=6(-x)^7 = -6x^7\\\\\therefore f(x)=-f(-x)[/tex]

The function is odd because f(–x) = –f(x).

The function is given as:

f(x) = 6x^7

A function is odd if the following is true

f(-x) = -f(x)

Calculate f(-x)

f(-x) = 6(-x)^7

f(-x) = -6x^7

Calculate -f(x)

-f(x) = -6x^7

By comparison;

f(-x) = -f(x) = -6x^7

Hence, the function is odd because f(–x) = –f(x).

Read more about odd function at:

https://brainly.com/question/14264818

#SPJ1

The probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The given parameters are:

Mean = 0.8

Variance = 0.0004

Calculate Standard deviation using

σ = √σ²

This gives

σ = √0.0004

Evaluate

σ = 0.02

Calculate the z-score at x = 0.84 using

z = (x - [tex]\bar x[/tex])/σ

This gives

z = (0.84 - 0.8)/0.02

Evaluate

z = 2

The probability is then represented as:

P(x > 0.84) = P(z > 2)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.84) = 0.977

Hence, the probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

Read more about probability at:

https://brainly.com/question/11234923

#SPJ1

Answer:

y = (-3/4)x + 2

Step-by-step explanation:

y = m * x + b   where m is the slope and b is the y-intercept

y = (-3/4)x + b       substituting the slope

4 = 6 + b     =>         b = 2        substituting the point given

y = (-3/4)x + 2

Answer:

B. ABCD is a trapezoid because it has at least

one pair of parallel sides.  

Step-by-step explanation:

the two points A(-3,-1) and D(5,-1) have the same y-coordinates

Then

The line AD is parallel to the x-axis

On the other hand,

the two points B(1,5) and C(5,5) have the same y-coordinates

Then

The line BC is parallel to the x-axis.

We obtain :

• AD is parallel to the x-axis

• BC is parallel to the x-axis.

Therefore

AD // BC

Conclusion:

ABCD is a trapezoid because it has at least

one pair of parallel sides. 

Answer:

b

Step-by-step explanation:

plato

Considering the probability of success of 0.8 in the Bernoulli trial, the probability of failure is of 0.2.

The probability of failure in a Bernoulli trial is one subtracted by the probability of a success.

In this problem, the probability of a success is of 0.8, hence the probability of failure is:

pF = 1 - 0.8 = 0.2.

More can be learned about Bernoulli trials at https://brainly.com/question/16931609

#SPJ1