Refer to the figure. Find the indicated values to the nearest hundredth of a centimeter or hundredth of a degree. Round all intermediate values to four decimal
places.
150
Part 1 of 2
D
Part 2 of 2
36
60°
C
78
31°
B
20 cm
(a) Find the lengths of BC, AC, DB, DC, ED, EC, and EA.
BC
cm, AC
cm, DC
cm, ED
DBN
(b) Find the measures of ZAEC and CAE.
ZAEC
and CAE.
cm, EC
my
cm, and EA
cm.

The local maximum of f is at (-5/3, 128/27), and the local minimum is at (4/3, -64/27).

To find the neighborhood maxima and minima of the capability f(x) = (x-3)(x+1)(x+4), we really want to take its subordinate:

f'(x) = (x+1)(x+4) + (x-3)(x+4) + (x-3)(x+1)

f'(x) = [tex]3x^2 + 6x - 20[/tex]

Setting f'(x) equivalent to nothing and settling for x, we get:

[tex]3x^2 + 6x - 20 = 0x^2 + 2x - 20/3 = 0(x+5/3)(x-4/3) = 0[/tex]

Thusly, the basic focuses are x=-5/3 and x=4/3.

To decide the time periods and diminishing, we can utilize the principal subsidiary test. Since f'(x) is a quadratic capability with a positive driving coefficient, it is dependably certain for x < - 5/3 and x > 4/3, and consistently negative for - 5/3 < x < 4/3.

Thusly, f(x) is expanding on the spans (- ∞, - 5/3) and (4/3, ∞), and diminishing on the stretch (- 5/3, 4/3).

To find the nearby maxima and minima, we can utilize the subsequent subsidiary test. Taking the subordinate of f'(x), we get:

f''(x) = 6x + 6

Subbing x=-5/3 and x=4/3, we get:

f''(- 5/3) = - 2 < 0, so f has a neighborhood greatest at x=-5/3.

f''(4/3) = 10 > 0, so f has a neighborhood least at x=4/3.

Thusly, the neighborhood limit of f is at (- 5/3, 128/27), and the nearby least is at (4/3, - 64/27).

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If you choose the baseball workshop, you will need to know the kind of beverage that would be better for the participants after playing baseball, and if we ask participants it is likely they choose water or soda.

Information about the workshop is limited; however, it is likely the participants have to play baseball and they will need to drink and eat something after this.

We want to know the beverage and snack that would be better for hydration. Moreover, it can be expected the participants choose common options such as soda or water.

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Answer:

its 15.5 m

Step-by-step explanation:

A function f(x) = (x⁴ - 5x² + 4) / (x² + x - 2) is discontinuous at  x = 1 and x = -2. And it is a removable discontinuity.

Consider function f(x) = (x⁴ - 5x² + 4) / (x² + x - 2)

We factorise denominator as,

x² + x - 2

= x² + 2x - x - 2

= x(x + 2) - 1(x  + 2)

= (x  + 2)(x - 1)

So, the function f(x) becomes,

f(x) = (x⁴ - 5x² + 4) / ((x  + 2)(x - 1))

A function f(x) is discontinuous when the denominator of f(x) is zero.

i.e.,  (x  + 2)(x - 1) = 0

i.e., x = 1 or x = -2

Also, the factors of the polynomial x⁴ - 5x² + 4 are (x - 2), (x  + 2), (x - 1) and (x + 1)

We can write function f(x) as,

f(x) = (x⁴ - 5x² + 4) / (x² + x - 2)

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

f(x) = (x - 2)(x + 1)

Now, the function f(x) is continuous.

Therefore, the type of discontinuity is removable discontinuity.

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Answer:

The new shape has a base of 35 cm and a height of 20 cm.

Step-by-step explanation:

Since the shape is five times larger than the shape it is similar to, we can simply multiply everything by 5.

7×5=35

4x5=20

The new shape has a base of 35 cm and a height of 20 cm.

Hope this helps (and is correct)! Good luck on your homework!

The probability by the given data is 1%.

We are given that;

set α=0.01

Now,

The probability of making a type I error is the significance level, or alpha (α), which is the threshold we set for rejecting the null hypothesis124. It is also known as the false positive rate3.

If we set α=0.01, it means that we are willing to accept a 1% chance of making a type I error. Hence, the probability that we reject the null hypothesis when it was in fact true is 0.01 or 1%.

Therefore, by probability the answer will be 1%.

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Answer: 118

Step-by-step explanation:

Angle ABC and Angle BCD add up to 180 degrees, because Line AB and line CD are parallel. Because of this, Angle BCD can be moved up the the angle above 3n-47. Because the two angles fall on to a straight line, we can say that (3n-47)+(n+7)=180. Solving, n=55, so angle ABC equals 118 degrees.

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Answer:

B. 46.

Step-by-step explanation:

First we set up the equation A(n)=-172 and substitute the given equation for A(n), giving us -172=8+(n-1)(-4). Simplifying, we get -180=(-4n+12), or -4n=-192, or n=48. However, n represents the number of terms in the sequence, and since the sequence starts with n=1, we need to subtract 1 from our answer to get the term number corresponding to A(n)=-172. Therefore, the answer is B) 46.

The net change in the value of this stock for the week is $2.12.

The total change in the value of the stock is  $4.38.

We have,

a)

The net change in the value of the stock for the week is the difference between the closing price on Monday and the closing price on Friday.

Net change expression.

= $6.40 - $4.28

= $2.12

b)

The total change in the value of the stock is the sum of the absolute changes from day to day.

Total change expression.

= |$5.17 - $4.28| + |$4.79 - $5.17| + |$7.15 - $4.79| + |$6.40 - $7.15|

= $0.89 + $0.38 + $2.36 + $0.75 = $4.38

Thus,

The net change in the value of this stock for the week is $2.12.

The total change in the value of the stock is  $4.38.

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Steven ran more distance, and the difference is 5.6 units.

Rebbeca ran 3 times across the center of a circle whose diameter is 40 units, then the distance that she ran is 3 times that:

distance for Rebbeca = 40*3 = 120 units.

While Steven ran one time across the circumference, remember that the circumference is 3.14 times the diameter, so the distance that he ran is:

Distance for Steven = 3.14*40 = 125.6 units.

So Steven ran more, and the difference is:

125.6 - 120 = 5.6 units.

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There is only one solution. The measurements of the angles are ;

B = 54. 6 degrees

C = 41. 6 degrees

Option B

To determine the value of the angle, we need to know the law of sines.

It is represented as;

sin A/a = sin B/b

Such that;

From the information given, we have;

sin 83.8/11.1 = sin B/9.1

cross multiply the values, we get

sin B = 9. 0467/11.1

Divide the values

sin B = 0. 8150

find the inverse

B = 54. 6 degrees

Note that the sum of the angles in a triangle is 180

C = 180 - 138. 4 = 41. 6 degrees

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The measures of the angles add up to 180°, using that we can see that x = 10.

Here we can see that the two vertical lines are parallel, thus, the angles in both intersections are equal.

Now, notice that the 75° angle would be an adjacent angle to (11x - 5)°, then their measures add up to 180°, then we can write:

75° + (11x - 5)° = 180°

We can solve that for x.

75 + 11x - 5 = 180°

70 + 11x = 180

11x = 180 - 70 = 110

x = 110/11

x = 10

That is the value of x.

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The calculated value of the number of different outcomes in the sample space is 24

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Colors = 3

Clasps = 2

Locations = 4

So, we have

Outcomes = Colors * Clasps * Locations

Substitute the known values in the above equation, so, we have the following representation

Outcomes = 3 *2 * 4

Evaluate

Outcomes = 24

Hence, the number of different outcomes in the sample space is 24

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Answer:

Step-by-step explanation:

The situation that can be represented by the given equation 340 + 5x - 650 - 8x is:

Sierra started with savings of $340 and spends $8 of her savings every week. Brian started with savings of $650 and adds $5 to his savings every week. The equation represents the difference in savings between Sierra and Brian after x weeks. The term "340 + 5x" represents the total savings of Sierra after x weeks, where she starts with $340 and adds $5 per week. The term "- 650 - 8x" represents the total savings of Brian after x weeks, where he starts with $650 and subtracts $8 per week. By equating the two expressions, we can find the value of x, which represents the number of weeks needed for Sierra and Brian to have the same amount of savings.

The ratio of the cost price and the printed price of the book is 1.2444.

We have,

Let's assume the printed price of the book = P.

As per the problem, the shopkeeper is selling the book at a discount of 10% on the printed price. So the selling price of the book.

= (P - 0.1P)

= 0.9P.

The shopkeeper earns a profit of 12% on selling the book.

So, the selling price of the book is also 112% of the cost price.

That is,

0.9P = 1.12C

where C is the cost price of the book.

Now, let's find the ratio of the cost price and the printed price of the book:

C/P

= (C/0.9P)/(P/0.9P)

= 1.12/0.9

= 1.2444

Therefore,

The ratio of the cost price and the printed price of the book is 1.2444.

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The actual distance between City C and City D is approximately 647.06 miles.

We can use the given information to determine the scale of the map, which relates distances on the map to actual distances in the real world. Let x be the actual distance between City C and City D in miles. According to the map, the distance between City C and City D is represented by 4.42 feet. We can write this relationship as:

250 miles / 1.7 feet = x miles / 4.42 feet

Solving for x, we get:

x = (4.42 feet * 250 miles) / 1.7 feet = 647.06 miles

The key concept used in this problem is the idea of scale. Maps are often drawn to a specific scale, which allows us to relate distances on the map to actual distances in the real world. In this case, we used the scale of the map to convert the distance between City C and City D on the map (measured in feet) to the actual distance between the cities (measured in miles).

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Answer:

answer is 0.25

Step-by-step explanation:

2.50/10

there is only one zero in 10 so we move the decimal one digit towards left.

which then the decimal ends up in front of 2.

An equation for the line that passes through (-14, 14) and whose slope is undefined is x = -14.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-14, 14) and an undefined slope, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 14 = undefined(x - (-14))

y - 14 = undefined(x + 14)

x = -14

In conclusion, the equation of a line that has an undefined slope represents a vertical line that crosses the x-axis only i.e x = -14.

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Answer:

80 miles per hour.

Step-by-step explanation:

120 - 80 = 40 Because 40 is half than 80.

The fraction is simplified to -2/3

A fraction can be defined as a mathematical expression representing a part of a whole number, element or variable.

There are different types of fractions. They are listed thus;

Examples of improper fractions are; 3/2, 4/3

Examples of proper fractions are; 1/2 3/4

From the information given, we have that;

7/12 - 5/12

Find the lowest common denominator

7 - 15/12

Subtract the values

-8/12

-2/3

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The amount of commission Mr. A received last month is C = $ 417.62

Given data ,

Let the amount of commission earned be C

Now , the equation is

The first $1,500 in sales are eligible for a commission rate of 21%, so the commission on this portion of his sales is:

0.21 x $1,500 = $315

The remaining portion of his sales is:

$2,233 - $1,500 = $733

This amount is eligible for a commission rate of 14%, so the commission on this portion of his sales is

On simplifying the equation , we get

0.14 x $733 = $102.62

To find Mr. A's total commission, we add the commission on the first $1,500 to the commission on the remaining $733

$315 + $102.62 = $417.62

Hence , Mr. A earned a commission of $417.62 last month

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Answer:

The cost of one share of the stock on Friday is $41.45

Step-by-step explanation:

The initial cost of one share of the stock on Monday is $41.45.

On Tuesday, the cost goes up by $0.58, so the cost becomes:

$41.45 + $0.58 = $42.03

On Wednesday, the cost goes down by $0.26, so the cost becomes:

$42.03 - $0.26 = $41.77

On Thursday, the cost also goes down by $0.26, so the cost becomes:

$41.77 - $0.26 = $41.51

Finally, on Friday, the cost goes down by $0.06.

So the expression to represent the cost of one share of the stock on Friday is:

$41.51 - $0.06

To evaluate this expression, we simply subtract $0.06 from $41.51:

$41.51 - $0.06 = $41.45

Therefore, the cost of one share of the stock on Friday is $41.45

By completing squares, we can rewrite the quadratic equation as:

(x + 9)^2 = -9

Remember the perfect square trinomial:

(a + b)^2 = a^2 + 2ab + b^2

Here we have the quadratic equation:

x^2 + 103 = -18x + 13

We can rewrite this as:

x^2 + 18x = 13 - 103

x^2 + 18x = -90

x^2 + 2*9*x = -90

We can add 9^2 and subtract 9^2 to get:

x^2 + 2*9*x + 9^2 - 9^2= -90

(x^2 + 2*9*x + 9^2) - 9^2= -90

(x + 9)^2 - 81 = -90

(x + 9)^2 = -90 + 81

(x + 9)^2 = -9

That is the equation we wanted to get.

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Answer:

12

Step-by-step explanation:

The square root of 144 is 12. This is because when a number is squared, it means it is multiplied by itself. So, 12 multiplied by 12 is equal to 144. Therefore, the square root of 144 is the value that, when multiplied by itself, gives the result of 144. This value is 12. The square root of 144 is also a perfect square, which means it is a whole number that can be generated by multiplying two equal integers.

The total distance El had biked when he finally reached the library is 119/20 miles

Given that Eli biked for [tex]1\frac{1}{10}[/tex] miles two times extra as he missed a book at home.

The distance between the Elis house and library is [tex]3\frac{3}{4}[/tex] miles

We have to find the total distance Eli biked

Total distance  = [tex]1\frac{1}{10} +1\frac{1}{10} +3\frac{3}{4}[/tex]

=11/10+11/10+15/4

20 is LCM of 10, 10 and 4

= 22+22+75/20

=119/20 miles

Hence, the total distance El had biked when he finally reached the library is 119/20 miles

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The value of test statistics is -0.87.

We have,

n=25, mean= 24.4, s=9.2 and a=.05

As t = (x - [tex]\mu[/tex])/(s/√(n))

t = (24.4 - 26)/(9.2/√(25))

t = -0.8695652173913

t = -0.87

The sample size is n = 25, so df= 25 - 1= 24

So, the probabilities for the one tailed test are 0.20 and 0.15 respectively.

The p-value is between 0.15 and 0.20

The p-value is not less than α.

So, we can't reject the null hypothesis H0

We fail to reject the null hypothesis H0

Thus, the mean age of the prison population in cone city is 26 years.

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The measure of the missing vaule of x in the diagram is 43

From the question, we have the following parameters that can be used in our computation:

The circle

Using the theorem of sum of angles on a circumference, we have

2x + 122 + 152 = 360

Evaluating the like terms, we have

2x = 360 - (122 + 152)

So, we have

2x = 86

Divide by 2

x = 43

Hence, the missing vaule of x in the diagram is 43

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