How do I solve this problem?

The quotient of the given problem using laws of exponents is; 6 * 10⁰

We want to express the quotient of the quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.

This is;

(30 * 10⁻²⁴)/(5 * 10⁻²⁴)

Now, we can break this down into like terms to get;

(30/5) * (10⁻²⁴/10⁻²⁴)

= 6 * 1

Now, 1 can also be written as;

10⁰ = 1

Thus, the solution of the given problem is; 6 * 10⁰

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Answer:

1728

Hope this helps :)

Answer: 207936 millimeters squared

Step-by-step explanation:

57 * 57 = 3249

3249 * 64 = 207936

Answer: 207936 millimeters^2

Step-by-step explanation: 57*57=3249

3249 64 times is 207936.

Answer:

Step-by-step explanation:

x + x + 16 = 90

2x +16 = 90

2x = 74

x = 37

The required radius and error in radius is 13.8 cm and ± 0.12cm

Given that,
A machinist is required to manufacture a circular metal disk with an area of 600cm².
(a) What radius produces such a disk is to be determined
(b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part is to be determined.

The area of a circle is given by the pie times square of the radius.

Area of circle = πr^2

Here,
a) The given area of disk = 600 cm²
   πr² = 600
   r = √600/3.14
   r = 13.8 cm

b) an error tolerance of ± 5 cm² in the area of the disk,
So the percentage of error is 0.84%
Now, 0.84% of radius = 0.84 *13.8/100 = 0.12
The required error in radius will be ±0.12 cm

Similarly,
c) limx→a f(x) = L
Where a is the area of the disk and L is length, and f(x) is function of area.

Thus, the required radius and error in radius is 13.8 cm and ± 0.12cm.

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The vehicle will get speed of approximately 15 mph and -210 mph.

Science's most important concept is measurement. Many measurable quantities are measured in fundamental or base units. One such measurable quantity is speed, which is defined as the ratio of an object's distance travelled to the time required to travel that distance. Let us learn about speed in depth during this session.

The ratio of distance to time taken to cover a distance is used to calculate speed. Because it only has one direction and no magnitude, speed is a scalar quantity.

Given the equation for gas mileage = 0.02x² + 3.9x  - 43 where x means speed

We have been asked to find x if gas mileage = 20 that is

0.02x² + 3.9x  - 43 = 20

Lets simplify

⇒ 0.02x² + 3.9x  - 43 = 20

⇒ x² /50 + 39x/10  - 63 = 0

⇒ x²/ 50 + 195x/50 - 3150 = 0

⇒ 1/50 (x + 195x - 3150 ) = 0

⇒ 1/50 (x + 210x - 15 x - 3150 ) = 0

⇒ 1/50 (x (x+210) −15 (x+210)) = 0

⇒ 1/50 (x−15)(x+210) = 0

⇒  (x−15)(x+210)  = 0 × 50

⇒ (x − 15)(x + 210)  = 0

⇒ x = 15, x = -210

So, try using 15 mph and -210 mph, that might work.

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The angle of depression of the meat from the top of the table is 40°

This situation makes a right-angle triangle with the height of table being the perpendicular to the right-angle triangle and the distance of meat from the foot of the table becomes the base of the imaginary right-angle triangle

to know the angle of depression of the meat from the top of the table

we need to find the ratio between the perpendicular and the base of the triangle to use trigonometry.

Tan  is the ratio of perpendicular and base of the triangle

which is = 96/114.4

          tan Ф=0.8392

To solve for Ф , a tan would move from the left-hand side to the right-hand side and would become tan inverse.

            Ф  = tan-1 0.8392

             Ф = 40°

 The correct question is a cat on a table 96cm views a piece of meat on the ground 114.4cm away from the foot of the table. find the angle of depression of the meat from the top of the table.

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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 &\$1024\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{half-yearly, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]A=1024\left(1+\frac{1}{2}\right)^{2\cdot 3} \implies A=1024(1.5)^6\implies A = 11664~\hfill \underset{earned~interest}{\stackrel{11664~~ - ~~1024}{10640}}[/tex]

The car will take 15 minutes to drive to the next stop which is 16 miles away.

As per the question statement, we are supposed to find the time taken by the car to drive to the next stop which is 16 miles away if it is driving on the interstate with cruise control on at a constant speed of 64 miles per hour.

Before solving the question, we need to know the concept of relation between time, distance and speed, which states that

[tex]speed=\frac{distance}{time}[/tex]

In the question [tex]speed = 64 mph\\distance = 16 miles\\time taken = t[/tex]

Substituting values in the formula above,

[tex]64=\frac{16}{t} \\t=\frac{16}{64} \\t=0.25 hours =0.25 *60\\t=15 minutes[/tex]

Hence the time taken by car  to drive to the next stop which is 16 miles away is 15 minutes or [tex]\frac{1}{4}[/tex] hours.

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Answer:

h=sqrt2*5i, h=-sqrt 2*5i

Step-by-step explanation:

Answer:

DNE

No real solutions

Step-by-step explanation:

This Quadratic Equation: 2h² + 100 = 0

Answer: 5

Step-by-step explanation:

After juggling for several minutes i.e., 2.5 minutes and [tex]1\frac{1}{3}[/tex] minutes (mixed fraction), the total number of bowling pins by clown is 37 pins

As per the question statement, a clown juggles 12 bowling for the first 2.5 minutes then he bump it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex]  minute (Mixed Fraction form)

We are supposed to find the total number if pins by the clown.

Let's calculate the total time first that will be 2.5 minutes + [tex]1\frac{1}{3}[/tex] minutes

[tex]1\frac{1}{3} =\frac{3*1 +1}{3} =\frac{4}{3} =1.34[/tex] minutes.

Therefore total time = 3.84minutes

Given that he bumps it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex]  minute so, the number of pins in the last  [tex]1\frac{1}{3}[/tex]  minute will be = [tex]18*1.34 = 24.12 = 25[/tex] (approx.)

So total number of bowling pins = [tex]12+25 = 37[/tex] pins

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Answer:

Step-by-step explanation:

-9x - 45 = -7x - 15  (Distribute -0.75 to (12x+60))        (x-8x = -7x)

-30 = 2x   (add 15 to both sides and add 9x to both sides)

-15 = x (divide both sides by 2)

The solution set of the inequality for R is given by [tex]-\frac{1172}{85} \leq x\leq \frac{1228}{55}[/tex] .

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.  It is frequently used to compare two numbers on the number line based on their sizes. Different types of inequalities are represented by a variety of notations such as < ,> ,≤ and ≥.

The modulus function takes the absolute value of a function.

To solve the given inequality we have simplify the inequality first.

[tex]x-\frac{7}{9} |(\frac{12}{5} -6x)|+50\ge -30[/tex]

[tex]or, x-\frac{7}{9}\times \frac{6}{5} |(2-5x)|+50\ge -30\\or,x-\frac{14}{15}|2-5x|\ge-80\\[/tex]

Now we separate the inequalities:

[tex]x-\frac{14}{15}(2-5x)\ge-80[/tex]  for 2x-5 ≥ 0

[tex]x-\frac{14}{15}(-(2-5x))\ge-80[/tex]  for 2x-5 ≤ 0

Now we will solve the two inequalities separate and find the intersection.

[tex]x-\frac{14}{15}(2-5x)\ge-80\\or,15x-28+70x\ge-1200\\or,x\ge -\frac{1172}{85}[/tex]

Again

2x-5 ≥ 0

or, [tex]x\le\frac{2}{5}[/tex]

hence [tex]-\frac{1172}{85}\le x\le\frac{2}{5}[/tex]

Similarly solving the other inequality we get

[tex]\frac{2}{5}\le x\le\frac{1228}{55}[/tex]

Now we find the intersection of the two inequalities:

[tex]-\frac{1172}{85}\le x\le\frac{1228}{55}[/tex]

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Answer:

The equation in slope-intercept form is: [tex]y=5x+32[/tex]

Step-by-step explanation:

To calculate the slope, [tex]m[/tex], we use the formula [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1} }[/tex] where [tex]y[/tex] are the [tex]y[/tex]-values of the points and [tex]x[/tex] are the [tex]x[/tex]-values.

Pugging our numbers into the formula, we get [tex]\frac{(-3)-12}{-7-(-4)}[/tex]. This simplifies to 5.

To calculate the [tex]y[/tex]-intercept, we first substitute one of our points into the formula. Substituting -4  and 12, we get [tex]12=5(-4)+b[/tex].

Then we can solve for [tex]b[/tex].

[tex]12=5(-4)+b[/tex]

[tex]12=-20+b[/tex]

[tex]32=b[/tex]

So, our slope is 32.

We can then plug these values into the slope-intercept form [tex]y=mx+b[/tex]

The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the cost of hamburger, y represent the cost of french fries and z represent the cost of soda, hence:

x + y = 13   (1)

Also:

x + 2z = 14    (2)

And:

x + y + z = 16    (3)

From the three equations:

x = 8, y = 5, z = 3

The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.

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The work in process(Job C) is $14,250

The finished goods(job B) is $23,000

The cost of goods sold(job A) is $31,500

What are work in process, finished goods and cost of goods sold in this case?

The work in process refers to the total costs incurred on Job C, since it was not completed at the end of the month, the finished goods refers to the costs incurred on job B which has been completed but not yet sold and cost of goods sold means the cost incurred on Job A which has been sold since it has been completed.

Job A:

Cost of job in process=$12,000

direct materials used=$2,000

direct labor=$10,000

number of direct labor hours=direct labor cost/ direct labor rate

number of direct labor hours=$10,000/$20=500 hours

Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour

Applied Manufacturing Overhead=500*$15=$7,500

cost of goods sold=$12,000+$2,000+$10,000+$7,500

cost of goods sold=$31,500

Job B:

Cost of job in process=$1,000

direct materials used=$8,000

direct labor=$8,000

number of direct labor hours=direct labor cost/ direct labor rate

number of direct labor hours=$8,000/$20=400 hours

Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour

Applied Manufacturing Overhead=400*$15=$6,000

finished goods=$1,000+$8,000+$8,000+$6,000

finished goods=$23,000

Job C:

Cost of job in process=$0

direct materials used=$9,000

direct labor=$3,000

number of direct labor hours=direct labor cost/ direct labor rate

number of direct labor hours=$3000/$20=150 hours

Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour

Applied Manufacturing Overhead=150*$15=$2,250

work in progress=$0+$9,000+$3,000+$2,250

work in progress=$14,250

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The area of the polygon is approximately 24.497 square units.

In accordance with the statement, we have a polygon with three vertices set on Cartesian plane, that is, a triangle. We need to find the side lengths first and later to calculate the area by Heron's formula. First, determine the lengths of each line segment by Pythagorean theorem:

JK = √[[4 - (- 3)]² + (4 - 4)²]

JK = 7

KL = √[(3 - 4)² + (- 3 - 4)²]

KL = √[(- 1)² + (- 7)²]

KL = 5√2

JL = √[[3 - (- 3)]² + (- 3 - 4)²]

JL = √85

Second, calculate the area of the triangle:

s = (JK + KL + JL) / 2

s = (7 + 5√2 + √85) / 2

s ≈ 11.645

A = √[s · (s - JK) · (s - KL) · (s - JL)]

A = √[11.645 · (11.645 - 7) · (11.645 - 5√2) · (11.645 - √85)]

A ≈ 24.497

The area of the polygon is approximately 24.497 square units.

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Answer: -4x²-11x-7

Step-by-step explanation:

[tex]-3x^2-3x-7-(x^2+8x)=\\-3x^2-3x-7-x^2-8x=\\-4x^2-11x-7[/tex]

The graphing is achieved as follows:

On the graph the third sign counting from the left is used.

This is placed on the first mark of the three marks between 3 and 4. This point equivalent to 3 1/4 or 3.25

Given data

the graph

and the equation  1/2 x - 3 < -1 3/8

solving for x gives

1/2 x - 3 < -1 3/8

1/2 x < 3 -11/8

x/2 < 13/8

x < 13 / 4

x < 3 1/4

On the graph the third sign counting from the left is used.

The arrow is facing left, this is to show the sign less than.

The tail has a hollow not a solid point to show that equality sign is not included.

This is placed on the first mark after point 3 as this is the point equivalent to 3 1/4 or 3.25

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[tex]\cfrac{12}{16}\implies \cfrac{4\cdot 3}{4\cdot 4}\implies \cfrac{4}{4}\cdot \cfrac{3}{4}\implies 1\cdot \cfrac{3}{4}\implies \boxed{\cfrac{3}{4}}~\hfill \cfrac{8\cdot 3}{8\cdot 4}\implies \boxed{\cfrac{24}{32}}[/tex]

Answer:

Quadratic Formula

Step-by-step explanation:

x^2-11x+10=

x^2-x-10x+10=

x(x-1)-10(x-1)=(x-10)(x-1)

Answer:

Your answer should be 90 degrees for angle one. For angle two, 58 and angle three 32.

Step-by-step explanation:

This is because they are supplementary angles! I hope this helps. Xx

Answer: ∠1 = 90°

Step-by-step explanation:

∠1 = ∠4

∠2 = ∠5

∠3 = ∠6

reason = vertically opposite angle

∠1 = 90°

∠2 = 58°

∠3 = 32°

checking :

total angles = 360°

360° = ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6

360° = 90° + 58° + 32° + 90° + 58° + 32°

360° = 360°

Based on the temperature readings, the average recorded temperature in the 20 days was 10.15°

The average temperature can be found by adding all the temperatures and then dividing by the number of temperatures taken which is 20.

The average is therefore:

= 24° + (−10°) +  9° +  18° +  23° +  27° +  8° +  17° +  3° +  7° + ( −2°) +  (−6°) +  2° + (−9°) +  (−8°) +  21° +  25° +  15° +  10° +  29°) / 20

= 203 / 20

= 10.15°

In conclusion, the average temperature was  10.15°.

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Answer: 15

Explanation:

The length of the segment is 10 plus 5 which is fifteen because you need to know how long it is. Just ignore the negatives.

Answer:

area of the arrow is 36inches^2

Step-by-step explanation:

Area of rectangle= lw

10x3=30

Area of triangle = bh/2

3x4=12/2=6

30+6=36 inches^2

Answer:

v = 13

Step-by-step explanation:

because they are supplementary angles they add up to 180

so

add them

and put them equal to 180

9v + 3 + 60 = 180

combine like terms

9v + 63 = 180

now subtract 63 to both sides

9v = 117

divide 9 to both sides

v = 13

that is your answer

The value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.

A function can be defined as an expression, rule or law that shows the relationship between a dependent and an independent variable.

Given the function;

f(x) = |x+3|

To determine f(6)

Substitute the value of x as 6

We have;

f(6)  = | 6 + 3 |

f(6) = 9

To determine f(-10)

Substitute the value of x as - 10

We have;

f(-10) = | -10 + 3 |

f(-10) = | -7|

f(-10) = 7

To determine f(0)

Substitute the value of x as 0

We have;

f(0) = | 0 + 3|

f(0) = 3

Thus, the value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.

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Answer- D = (equal sign)

Explanation-

When you see two straight lines in math | | with number inside, regardless if the number inside is positive or negative, the outcome will be positive. This is called the absolute value. After we solve our absolute value however, there is a negative on the outside, which means that 61 will become negative again. Our equation is now -61 _____ -61. Your correct choice will be the equal sign, since -61 is equal to -61.

HOPE THIS HELPS GOOD LUCK!