Give the greatest common divisor of $6^3$ and $3^6$.

Work Shown:

y = (4/5)x + 3

5y = 4x + 15 ... multiply all terms by 5 to clear out the fraction

0 = 4x + 15 - 5y  ... subtract 5y from both sides

4x-5y+15 = 0 .... rearrange terms

The equation is in standard form Ax+By+C = 0 where A = 4, B = -5, C = 15.

Some books use Ax+By = C to represent standard form. It's effectively the same thing just with C on the other side.

Answer:

729 emails

Step-by-step explanation:

The pattern is to multiply by 3

3*3 = 9

9*3 = 27

27*3 = 81

81*3 = 243

If the pattern continues, Martin will sent on monday:

243*3 = 729

729 emails

Answer:

729

Step-by-step explanation:

Answer:

V=11*7*9=693

Step-by-step explanation:

V=Bh ( B is the base area ( base*height) , and h is the height of the prism)

find B=base*h

B=11*7=77 in²

V=B*h=77*9=693 in³

The volume of the triangular prism is 174.25 in³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, the triangular base has a base of 11 inches and height of 7 inches.

The formula for finding the volume of a triangular prism is V = (base area x height) / 2.

In this case, the base area of the triangle can be calculated using the formula A = (1/2)bh, where b is the base length and h is the height.

In this case, b = 11 inches and h = 7 inches, so the base area is A = (1/2)(11)(7) = 38.5 inches squared.

Now that we have the base area, we can calculate the volume of the triangular prism: V = (38.5 inches² x 9 inches) / 2 = 174.25 in³.

Therefore, the volume of the triangular prism is 174.25 in³.

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Answer:

288 in²

Step-by-step explanation:

The formula used to solve this question is :

Lateral Surface Area = s( P1 + P2)

Where s = slant height = 2 inches

P1 and P2 = Perimeter of the bases

Perimeter of base 1 = 4 × length of the end of the small square

4 × 17 inches = 68 inches

Perimeter of base 2 = 4 × length of the end of the large square

4 × 19 inches = 76 inches

Lateral Surface Area = 2 × (68 + 76)

= 2 × 144

= 288 in²

Answer:

scale factor = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Consider the ratio of corresponding sides, image to original, that is

scale factor = [tex]\frac{T'V'}{TV}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

Answer:

The market price of the article is Rs. 978.72

Step-by-step explanation:

Let x represents the market price.

Let y represents the selling price.

Let z represents the cost price.

if an article is sold with 20% discount then there will be a profit of 15%.

SP = CP+Profit =z+0.15z=1.15z

ATQ

[tex]0.80x = 1.15z\\0.80x- 1.15z = 0[/tex]

If it is sold at 10% discount then there will be a profit of Rs.200

ATQ

[tex]0.9x - z = 200[/tex]

Now we are supposed to find the market price of an article.

[tex]0.9x - z= 200[/tex]

Multiplying 1.15 both sides

[tex]0.9x \times 1.15 - 1.15z = 200 \times 1.15\\1.035x - 1.15z = 230[/tex]

We know that[tex]1.15z = 0.80x[/tex]

[tex]1.035x - 0.80z = 230\\0.235x = 230\\x = \frac{230}{0.235}\\x= Rs. 978.72[/tex]

Hence The market price of the article is Rs. 978.72

Answer:

Step-by-step explanation:

[tex] \frac{26}{25} \times ( - \frac{16}{63} )[/tex]

Multiplying a positive and a negative equals a negative[tex]( + ) \times ( - ) = ( - )[/tex]

[tex] = - \frac{26}{25} \times \frac{16}{63} [/tex]

Multiply the fractions:

[tex] = - \frac{416}{1575} [/tex]

Hope this helps..

Best regards!!

Answer:

x = 73

Step-by-step explanation:

The measure of the sum of the arcs in a circle = 360°.

Sum the given arc measures and equate to 360, that is

95 + 52 + 67 + 2x = 360

214 + 2x = 360 ( subtract 214 from both sides )

2x = 146 ( divide both sides by 2 )

x = 73

Answer:

0

Step-by-step explanation:

First let's solve for the value in the parentheses.

[tex]0.35 \cdot 100 = 35[/tex]

We know this is correct because if we multiply a value by 100, the decimal point is moved 2 places to the left.

35 - 35 = 0, so the value of this expression equals out to be 0.

Hope this helped!

Answer:

Colin is wrong

Step-by-step explanation:

The question is incomplete because the chart or the table which shows the data is not given. I have attached the full question at the bottom. Consult it for better understanding.

We can clearly see in the chart the number of lates in January is 30, while the number of lates in March is 20.

As the half of 30 is 15, not 20, we can say that the statement of Colin is wrong, because the number of lates in March should be 15 to prove his statement true

Answer:

[tex]P(Brown\ or\ Green) = \frac{13}{25}[/tex]

Step-by-step explanation:

Given

[tex]n(Brown) = 20[/tex]

[tex]n(Green) = 6[/tex]

[tex]n(Blue) = 17[/tex]

[tex]n(Hazel) = 7[/tex]

Required

Determine the probability of Brown or Green eyes

First, the total number of respondents have to be calculated;

[tex]Total = 20 + 6 + 7 + 17[/tex]

[tex]Total = 50[/tex]

The events described above is a mutually exclusive event and as such, the required probability will be calculated by;

[tex]P(Brown\ or\ Green) = P(Brown) + P(Green)[/tex]

Calculating P(Brown)

[tex]P(Brown) = \frac{n(Brown)}{Total}[/tex]

Substitute 20 for n(Brown) and 50 for Total

[tex]P(Brown) = \frac{20}{50}[/tex]

Calculating P(Green)

[tex]P(Green) = \frac{n(Green)}{Total}[/tex]

Substitute 6 for n(Green) and 50 for Total

[tex]P(Green) = \frac{6}{50}[/tex]

So;

[tex]P(Brown\ or\ Green) = P(Brown) + P(Green)[/tex]

[tex]P(Brown\ or\ Green) = \frac{20}{50} + \frac{6}{20}[/tex]

Take LCM

[tex]P(Brown\ or\ Green) = \frac{20+6}{50}[/tex]

[tex]P(Brown\ or\ Green) = \frac{26}{50}[/tex]

Divide the numerator and denominator by 2

[tex]P(Brown\ or\ Green) = \frac{13}{25}[/tex]

Answer:

13/25

Step-by-step explanation:

Total number of people = 50

Probability of choosing a person with brown eyes [P(A)] = 20/50

Probability of choosing a person with green eyes [P(B)] = 6/50

Using the addition rule of mutual exclusive events (since they have specified brown OR blue, we use this formula):

P(A U B) = P(A) + P(B)

=> P(A U B) = 20/50 + 6/50 = 26/50 = 13/25

Therefore the probability of a person choosing a group that has brown or green eyes = 13/25

Also I got it right on edge haha, if you're still worried!!!!!!!!

Hope this helps :))))))))))))))

Answer: 0.127 feet by 0.090 feet

Step-by-step explanation:

Given that :

The USA's flag dimension = 19feet by 10feet

Union's (blue rectangle in the top left corner) dimension = 7 5/8 feet by 5 3/8 feet.

Union dimension for the shoulder patch of the USA flag used by astronauts for the Apollo mission has a scale factor of 1/60

Therefore, dimension of the union patch ;

1/60 * ( 7 5/8 feet by 5 3/8 feet)

1/60 * (61 / 8 feet by 43/8 feet)

61/480 feet by 43/480 feet

0.127 feet by 0.0895 feet

0.127 feet by 0.090 feet

Answer:

The distance between the plane and the observer is 16,659.18ft

Step-by-step explanation:

Complete question:

(An observer (O) spots a plane flying at a 42° angle to his horizontal line of sight. If the plane is flying at an altitude of 15,000 ft, what is the distance between the observer and the plane)

Hello,

The question above requires us to find the distance between an observer and a plane. This is very much easy because we are given the angle at which the observer makes with the plane. To solve this question correctly, we need a pictorial representation of the situation.

See attached document for better illustration

In the diagram, we need to find x.

Since the observer and the plane makes a right angled triangle with the distance apart them, we can use SOHCAHTOA

In this case, we have to use Tangent

Tanθ = opposite/ adjacent

θ = 42°

Opposite = 15,000

Adjacent = x

Tan42 = 15000 / x

x = 15000 / tan42

x = 15000 / 0.90

x = 16,659.18ft

The horizontal distance between the observer and the plane is 16,659.18ft

Answer:

I am not too sure but I know it is not 10,035, or 16,648, nor 20,188 because I put that and it wasn’t right so the last option would be.

22,417

Answer:

[tex]\large \boxed{\sf \ \ y=(x-4)^2-1 \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]y = x^2-8x+15\\ \\\text{*** we need to complete the square ***} \\ \\y=(x-4)^2-4^2+15=(x-4)^2-16+15=(x-4)^2-1[/tex]

And then the vertex is (4, -1) and as a > 0 the vertex is a minimum.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

x ≤5

Step-by-step explanation:

Pointing to the left means less than or less than or equal to

x ≤5

Answer:

[tex]\boxed{x \leq 5}[/tex]

Step-by-step explanation:

[tex]\sf Arrow \ pointing \ to \ the \ left \ on \ a \ number \ line \ means \ that[/tex]

[tex]\sf \ the \ value \ is \ either \ less \ than \ or \ less \ than \ or \ equal \ to.[/tex]

[tex]\sf{Graph}[/tex] [tex]x\leq 5[/tex] [tex]\sf{on \ the \ number \ line.}[/tex]

Answer:

the trig function you would use to find x would be cosine becuase its adjacent/ hypotenuse.

solving it would give you 49 becuase its cosine(x)=13/20 and you have to multiply by the inverse of cosine

to solve for y you would use sine of y which would be opposite/ hypotenuse = 13/20

Answer:

x intercept (10.5,0)

y intercept (0, -21)

Step-by-step explanation:

y=-2x-21

there are two intercept for a line

x intercept, the point of given equation of  line which lies on x axis.

For x intercept corodinate of y is o

Thus, value x intercept is form (x,0)

putting these value in y=-2x-21, we find x intercept

0=-2x-21

2x = 21

x = 21/2 = 10.5

Thus, x intercept (10.5,0)

Y intercept, the point of given equation of  line which lies on y axis.

For Y intercept coordinate of x is o

Thus, value y intercept is form (0,y)

putting these value in y=-2x-21, we find y intercept

y = -2*0 -21

y = -21

Thus, y intercept (0, -21)

Answer:

Hey there!

To solve this problem, you want to divide 22 by 3, which is about 7.33 feet.

We can check this by seeing 7.33 times 3=22

Hope this helps :)

Answer:

[tex]\large \boxed{\sf \ \ \ a\cdot b= 6 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex](a-bi)^2 = 13 - 12i\\\\<=> a^2+(bi)^2-2abi = 13-12i\\\\<=>a^2-b^2-2abi=13-12i[/tex]

Imaginary term must be the same so

-2ab=-12

2ab = 12

ab = 12/2 = 6

So the product of a and b is 6

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Let's solve the given equation step by step to find the product of a and b. Initially,

let's expand the left side of the equation: [tex](a - bi)^2 = (a - bi)(a - bi) = a^2 - abi - abi + b^2i^2 = a^2 - 2abi + b^2(-1) = a^2 - 2abi - b^2[/tex] We are given that this result is equal to[tex]13 - 12[/tex]i, so we can set up the following equation: [tex]a^2 - 2abi - b^2 = 13 - 12i[/tex] By comparing the real and imaginary parts of both sides, we can form two equations:

Equation [tex]1: a^2 - b^2 = 13[/tex]  (Equating real parts) Equation [tex]2: -2ab = -12[/tex](Equating imaginary parts) From Equation 2, we can deduce that ab = 6. To proceed further and find the product of a and b, we need more information. The current given equation has infinite possible solutions for a and b.

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Answer:

cos(theta/2) = sqrt((1+x)/2)

Step-by-step explanation:

From the double angle formula

cos^2(t)-sin^2(t) = cos(2t)  ...................(1)

cos^2(x)+sin^2(x) = cos(t-t) =1...............(2)

Add (1) and (2)

2cos^2(t) = 1+cos(2t)

cos^2(t) = (1+cos(2t))/2

cos(t) = sqrt((1+cos(2t))/2)

substitute t = theta/2

cos(theta/2) = sqrt((1+cos(theta))/2)

substitute cos(theta) = x

cos(theta/2) = sqrt((1+x)/2)

Answer: C

Step-by-step explanation:

"w" represents the number of weeks. If she adds $10 per week, the equation will include 10w. Because she starts out with $60 already, the complete equation would be:

[tex]T=60+10w[/tex].

Hope this helps!

The equation that describes the amount she has after 'w' weeks is

C : T = 60 + 10w.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, Sally wants to save for a new cell phone. She opens a bank account with $60 and adds $10 each week.

Assuming the total amount to be 'T' and no. of weeks to be 'w'.

∴ The equation that represents the amount of money she has is,

T = 60 + 10w.

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Answer:

z = 44

Step-by-step explanation:

26/z = 13/22

Using cross products

26 * 22 = 13*z

Divide each side by 13

26/13 * 22 = 13z/13

2 *22 =z

44 =z

Answer:

Z=44

To solve this proportion, you have to isolate z. You have to do what you do on one side of the equal sign to the other as well.

Answer:

moves it up 6 units

Step-by-step explanation:

y = f(x) + C C > 0 moves it up

f(x) = f(x) + 6 moves it up 6 units

Answer:

Vertical shift, 6 up.

Step-by-step explanation:

The entire function f(x) has a value of six added to it. That means that regardless of where f(x) was plotted on the coordinate plane, after the translation f(x) + 6, every single point would increase its value by six. Since all points would increase their values by six, the entire function would shift 6 up.

Answer:

366 minutes

Step-by-step explanation:

divide 15000 by 41

Answer:

[tex]\large \boxed{87.5 \, \%}[/tex]

Step-by-step explanation:

            Let x = the original number of books

Then 0.375x = the total number of biographies

 and 0.20  x = the original number of biographies

[tex]\text{Percent increase} = \dfrac{\text{ New number - Old number }}{\text{Old number }} \times 100\, \%\\\\= \dfrac{0.375x - 0.20x}{0.20x} \times 100\, \% = \dfrac{0.175x}{0.20x} \times 100\, \% = 0.875 \times 100\, \% = \mathbf{87.5 \, \%}\\\\\text{The number of biographies has increased by $\large \boxed{\mathbf{87.5 \, \%}}$}[/tex]

Answer:

50

Step-by-step explanation:

The value of P(A|B) = 0.50 which is correct option(B)

What is independent events?

Independent events is defined as an event that is not affected by other events.

A and B are independent events.

P(A) = 0.50

P(B) = 0.20

P(A|B) = P(A∩B)/P(B)

P(A|B) = P(A).P(B)/P(B)

P(A|B) = P(A)

Substitute the value of P(A) = 0.50,

P(A|B) = 0.50

Hence, the value of P(A|B) = 0.50

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Answer:

The answer is 12

Step-by-step explanation:

Trust me, kay? Please mark Brainliest!!!!

Answer:

12.8

Step-by-step explanation:

16% of 80

[tex]\frac{16}{100}[/tex] × 80

[tex]\frac{16}{10}[/tex] × 8

[tex]\frac{16}{5}[/tex] × [tex]\frac{4}{1}[/tex]

16 × 4

5

12[tex]\frac{4}{5}[/tex] = 12.8

Answer:

Between all these pairs of numbers,a rational number can be found in all the 3 pairs

Step-by-step explanation:

PAIR1: -10 and -9

Rational numbers are: -10.5,-10.6,-10.1,etc (there are way more)

PAIR2: 5.91 and 5.92

Rational numbers:- 5.915,5.916,etc(there are way more)

PAIR3:2/3 and 4/5

LCM= 15

2/3=10/15

4/5=12/15 between these two (10/15 & 12/15)

Rational numbers: 11/15, 11.5/15(because it's result would be a recurring/repeating decimal),etc