What number is equal to 13 ones and 62 hundredths

The value of the variable t of the exponential equation [tex]-5\cdot e^{10\cdot t} = - 30[/tex], t = (1 / 10) · ㏑ 6 (EXACT), t = 0.179 (APPROXIMATE).

In this problem we need to clear the variable t of an exponential equation with one variable, this can done by means of relationship of exponential and logarithmic functions, logarithm properties and algebra properties.

Now we proceed to present the complete procedure for the solution to the exponential equation:

[tex]-5\cdot e^{10\cdot t} = - 30[/tex]

[tex]e^{10\cdot t} = 6[/tex]

10 · t = ㏑ 6

t = (1 / 10) · ㏑ 6

t = 0.179

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Answer:

  10.  x = 4

  11. UT = 44

Step-by-step explanation:

You want the value of x and the length of segment UT that bisects chord PR at point U into halves marked UP = (9x -3) and UR = (7x +5). The radius of circle T is 55 units.

Point U is the midpoint of chord PR, so ...

  UP = UR

  9x -3 = 7x +5

  2x = 8 . . . . . . . . . add 3-7x

  x = 4 . . . . . . . . divide by 2

Segments UP, UT and TP form a right triangle with one leg ...

  UP = 9(4) -3 = 33

and hypotenuse 55.

We observe that the ratio of these measures being 33/55 indicates triangle PUT is a 3-4-5 right triangle, with scale factor 11. That means UT is 4·11 = 44 units.

  UT = 44 units

__

Additional comment

Recognizing triangles made from Pythagorean triples, such as {3, 4,5}, {5, 12, 13}, {7, 24, 25}, or {8, 15, 17} can save a lot of work. If you don't recognize these, you can find the missing side length from ...

  TP² = UP² +UT²

  UT = √(TP² -UP²) = √(55² -33²) = √1936 = 44

<95141404393>

The shape of the fence is a rhombus.

Option C is the correct answer.

We have,

To determine the shape of the fence with the given coordinates, we can analyze the properties of different quadrilaterals.

Square: All four sides are equal in length, and all angles are right angles.

Rectangle: Opposite sides are equal in length, and all angles are right angles.

Rhombus: All four sides are equal in length, but the angles are not necessarily right angles.

Trapezoid: At least one pair of opposite sides are parallel.

Let's analyze the given coordinates to determine the shape of the fence:

Side 1: Distance between (-16, 1) and (-6, 5) = √(((-6) - (-16))² + (5 - 1)²) = √(10² + 4²) = √(116)

Side 2: Distance between (-6, 5) and (4, 1) = √((4 - (-6))² + (1 - 5)²) = √(10² + (-4)²) = √(116)

Side 3: Distance between (4, 1) and (-6, -3) = √((-6 - 4)² + (-3 - 1)²) = √((-10)² + (-4)²) = √(116)

Side 4: Distance between (-6, -3) and (-16, 1) = √((-16 - (-6))² + (1 - (-3))²) = √((-10)² + 4²) = √(116)

We can see that all four sides of the fence have equal lengths, which means it is either a square, rectangle, or rhombus.

To further differentiate between these shapes, we need to consider the angles.

The angle between side 1 and side 2:

tan(angle) = (5 - 1)/(-6 - (-16)) = 4/10 = 0.4

angle ≈ 21.8°

The angle between side 2 and side 3:

tan(angle) = (1 - 5)/(4 - (-6)) = (-4)/10 = -0.4

angle ≈ -21.8°

The angle between side 3 and side 4:

tan(angle) = (-3 - 1)/(-6 - (-16)) = (-4)/10 = -0.4

angle ≈ -21.8°

The angle between side 4 and side 1:

tan(angle) = (1 - (-3))/(-16 - (-6)) = 4/10 = 0.4

angle ≈ 21.8°

All four angles are approximately 21.8° or -21.8°. This indicates that the fence is a rhombus since its sides are equal in length but its angles are not right angles.

Therefore,

The shape of the fence is a rhombus.

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Answer:

A. Using the commutative property

Step-by-step explanation:

Because there is no use of commutative property in the solution process.

Answer:

A) Using Commutative property

Step-by-step explanation:

In step 1, it used distributive property when the number 5 is distributed inside of the equation in the parenthesis.

In Step 4, dividing both sides by 10 to further simplify the equation

In step 2, you combined like terms and it results to the equation in step 3

The value of x will be 16.

Given ,

Parallelogram with two sides:

side 1 = 3x + 20

side 2 = 5x - 12

In parallelogram the opposite side are equal and parallel.

Thus,

side 1 and side 2 will be equal and parallel.

Equating both sides to get the value of x,

3x + 20 = 5x - 12

x = 16

Hence the value of x can be found out by property of parallelogram.

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The surface area of Grace's shipping box is 664 square inches.

We have,

The box can be divided into six rectangles, each of which represents the face of the box.

To find the surface area of the box, we need to find the area of each face and then add them all up.

The top and bottom of the box are both 10 inches by 14 inches, so the area of each of these faces is:

= 10 x 14

= 140 square inches

The sides of the box are both 14 inches by 8 inches, so the area of each of these faces is:

= 14 x 8

= 112 square inches

The front and back of the box are both 8 inches by 10 inches, so the area of each of these faces is:

8 x 10

= 80 square inches

To find the surface area of the whole box, we add up the areas of all six faces:

= 2(140) + 2(112) + 2(80)

= 280 + 224 + 160

= 664 square inches

Therefore,

The surface area of Grace's shipping box is 664 square inches.

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The interest rate for the first period is $287.22

To obtain the first period interest, we use simple interest formula;

Simple Interest = Principal * Rate * Time

Given:

Principal = $45,687.23

Annual interest rate = 7.555%

Interest period = Monthly

Convert the annual interest rate to a monthly interest rate.

Monthly interest = Annual interest/ 12 = 7.555/12 = 0.6295%

Interest = Principal * Monthly interest rate * Time

Since it's the first period, the time is 1 month:

Interest = $45,687.23 * 0.62958333% * 1

Interest = $45,687.23 * 0.0062958333

Interest ≈ $287.22

Therefore, the first period interest is $287.22.

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If Each card corresponds to a sample point with a 1/52 probability then the  sample points in the event an ace is selected is S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}

In a standard deck of 52 playing cards, there are four aces.

Each ace corresponds to a different suit: clubs, diamonds, hearts, and spades.

So, when we talk about the event of selecting an ace, we are referring to the act of choosing one of these four specific cards from the deck.

The sample points in the event "an ace is selected" are the individual cards that match this criteria.

Therefore, the sample points in this event are:

S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}

These four cards are the possible outcomes when we randomly select a single card from the deck, focusing only on the event of selecting an ace.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$850\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 850\left(1+\frac{0.026}{4}\right)^{4\cdot 5}\implies A=850(1.0065)^{20} \implies A \approx 967.60[/tex]

The probability that either event will occur is 0.62

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

Event A = 6 + 6 = 12

Event B = 20 + 6 = 26

Both A and B = 6

Other Events = 20

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

Total = A + B + C + Others - Both

So, we have

Total = 12 + 26 - 6 + 20

Evaluate

Total = 52

So, we have

P(A) = 12/52

P(B) = 26/52

Both A and B = 6/52

For either events, we have

P(A or B) = (12 + 26 - 6)/52

Evaluate

P(A or B) = 0.62

Hence, the probability that either event will occur is 0.62

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Answer:

15*8*10-7*8*11=584

Step-by-step explanation:

The value of x, considering the Pythagorean Theorem, is given as follows:

x = 9.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The sides for the problem are given as follows:

15 and 8 (segment of 8 is the radius, which is the distance from the center to a point on the circumference of the circle).

Hence the hypotenuse is obtained as follows:

h² = 15² + 8²

h² = 289

h = 17.

Hence the value of x is obtained as follows:

x = 17 - 8

x = 9.

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The best estimate of the number of centimeters (cm) in 1 yard is; Yard ⇒ feet ⇒ inches ⇒ centimeters

If we have to determine the number of centimeters in 1 yard, the best way is;

Here we convert  yard to feet = 1 yard = 3 ft

Then, we convert ft to inches = 1 ft = 12 inches

                                                  3 ft = 3 × 12 = 36 inches

Now, we convert inches to centimeters = 1 inch = 2.54 cm

                                            36 inches = 36 × 2.54 = 91.44 cm

Therefore, the best path is Yard to feet to inches to centimeters

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Using similar side theorem, the side with equivalent proportion to the given side is RQ/SQ

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

In this problem, we can use this same theory to find the equivalent side of the given proportion.

OQ / PQ = RQ / SQ

The equivalent side is RQ/SQ

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The number of ways to draw the socks in each case is given as follows:

a) 90 ways.

b) 48 ways.

c) 42 ways.

The Fundamental Counting Theorem states that if there are m ways for one trial and n ways for another trial, then there are m x n ways in which the two trials can happen simultaneously.

This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual trial, according to the equation presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For item a, we have that there are no restrictions, hence there are 10 options for the first sock and 9 for the second, hence:

10 x 9 = 90.

For item b, we need one of each, hence the possible combinations are:

Hence:

6 x 4 + 4 x 6 = 48.

For item c, we can take 6 then five(two blue) or 4 then 3(two white), hence:

6 x 5 + 4 x 3 = 42.

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The required sample size for the confidence interval and given margin of error is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

[tex]\pi = 0.5[/tex]

Then the sample size for M = 0.04 is obtained as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]

n = 1037.

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The calculated value of the mode(s) of the data is (a) 1

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

1, 0, 2, 2, 3, 0, 1, 1, 4, and 5

By definition, the mode of a data is the data that has the highest frequency

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

The data element 1 has the highest frequency of 3

Other data elements have lesser frequencies

Hence, the mode(s) of the data is (a) 1

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This is a linear equation problem with two variables. One way to solve it is by using the substitution method. Let x be the price of the tie and y be the price of the pair of pants. Then we have:

$$

\begin{aligned}

x + y &= 87.18 \\

x &= y - 2.12

\end{aligned}

$$

Substituting x into the first equation, we get:

$$

\begin{aligned}

(y - 2.12) + y &= 87.18 \\

2y - 2.12 &= 87.18 \\

2y &= 89.30 \\

y &= 44.65

\end{aligned}

$$

Therefore, the price of the pair of pants is $44.65. To find the price of the tie, we plug y into the second equation:

$$

\begin{aligned}

x &= y - 2.12 \\

x &= 44.65 - 2.12 \\

x &= 42.53

\end{aligned}

$$

Therefore, the price of the tie is $42.53.

Answer:

42.53

Step-by-step explanation:

write equation

tie + pants = 87.18

since ties cost 2.12 less than pants,

tie = pants -2.12

now substitute back into first equation

pants - 2.12 + pants = 87.18

solve for pants by adding 2.12 to the other side

divide by 2 since there are 2 pants on one side

find pants and then substitute value into the tie equation to find the price of the tie

After rotating the triangle counterclockwise by 270 degrees, the new coordinates of the vertices would be (3, -1), (-4, 2), and (3, 5).

To rotate a point counterclockwise around the origin by 270 degrees, we can use the following transformation rules:

[tex]New_x = -y[/tex]

[tex]New_y = x[/tex]

Let's apply these rules to each vertex of the triangle and find the new coordinates:

For the first vertex (-3, 1):

[tex]New_x = -1[/tex]

[tex]New_y = -(-3) = 3[/tex]

So, the new coordinates for the first vertex after rotating counterclockwise by 270 degrees are (3, -1).

For the second vertex (2, 4):

[tex]New_x = -4[/tex]

[tex]New_y = 2[/tex]

The new coordinates for the second vertex after rotating counterclockwise by 270 degrees are (-4, 2).

For the third vertex (5, -3):

[tex]New_x = -(-3) = 3[/tex]

[tex]New_y = 5[/tex]

The new coordinates for the third vertex after rotating counterclockwise by 270 degrees are (3, 5).

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Answer:

  (3) 60°

Step-by-step explanation:

You want the measure of the third angle (E) in triangle EFG, given that two of the angles have measures 75° (angle F) and 45° (angle G).

The angle sum theorem tells you the sum of angles in any triangle is 180°. This means ...

  E + F + G = 180

  E + 75 + 45 = 180

  E = 60 . . . . . . . . . . . . . subtract 120 from both sides and simplify

The measure of angle E is 60°.

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Answer:

Step-by-step explanation:

76 RPMs

The actual length of the bus is given as follows:

45 feet.

The actual length of the bus is obtained applying the proportions in the context of the problem.

The scale drawing is of 0.5 inches to 5 feet, hence the length represented by each inch of drawing is given as follows:

5/0.5 = 10 feet.

The length of the drawing is given as follows:

4.5 inches.

Hence the actual length of the bus is given as follows:

4.5 x 10 = 45 feet.

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Answer:

Step-by-step explanation:

Answer:

------------------

There are 15 black pens out of total 80.

The probability of a black pen is:

The five number summary of the data set for the box plot would be :

First, order the numbers in ascending order:

2, 8, 9, 11, 14, 15, 17, 19, 20

The minimum is the smallest number which is 2. The maximum is the largest number which is 20.

The median is the number in the middle which is 19. The Q1 is the number in the middle of the first half of the numbers which is 9. The Q3 is the number in the middle of the second half which is 19.

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Answer:

min=2

1st quartile= 8.5

median=14

3rd quartile=18

max=20

Step-by-step explanation: