Mandy competed in a race that included running and biking.Mandy ran 1 3/4 and bicycled 3.6 miles. Mandy total time was 0.7 hour what was Mandy approximate average speed on miles per hour. A. 3.75 miles per hour. B. 6.87 miles per hour. C. 7.06 miles per hour. D. 7.64 miles per hour

Answers

Answer 1

Answer:

1 3/4 = 7/4 = 1.75 miles (ran);

1.75 + 3.60 = 5.35 miles ( ran and bicycled);

average speed = 5.35 / 0.7 = 7.64 miles per hour;

The correct answer is D.

Step-by-step explanation:



Related Questions

Find the slope between the following 2 coordinate points. (-3,6) and (-1,-8)

Answers

the slope formula is y2-y1 divided by x2- x1 so -8-6=-14 and -1+3=2
-14/2 =-7

Answer:

-7

Step-by-step explanation:

Use slope equation m=y2-y1/x2-x1 aka m=rise/run.

Insert in the correct values.

-1-(-3)=2=run

-8-6=-14=rise

SO, -14/2=m

Simplify:-14/2=-7

m=-7

Which set of three numbers could be the side lengths of a triangle?

A. 2, 4, 8
B. 2, 4. 6
C. 3, 5, 7
D. 3, 5, 9

Answers

Answer:

The correct option is C.

Step-by-step explanation:

In a triangle, then sum of two smaller sides is greater than the length of third greatest side.

Let, in a triangle ABC, If the length of sides are [tex]a<b<c[/tex], then

[tex]c<a+b[/tex]

In option A,

[tex]8\nless 2+4[/tex]

Therefore option A is incorrect.

In option B,

[tex]6\nless 2+4[/tex]

Therefore option B is incorrect.

In option C,

[tex]7<3+5[/tex]

Therefore option C is correct.

In option D,

[tex]9\nless 3+5[/tex]

Therefore option D is incorrect.

Answer:

C. 3, 5, 7

Step-by-step explanation:

We know that in a triangle, 'the sum of lengths of two sides is always greater than the length of the third side'.

So, according to our options:

A. In 2, 4, 8. We have 2 + 4 = 6 < 8

B. In 2, 4, 6. We see that, 2 + 4 = 6

C. In 3, 5, 7. We see that, 3 + 5 = 8 > 7

D. In 3, 5, 9. We see that, 3 + 5 = 8 < 9.

Therefore, only option C satisfies the property of the triangle stated above.

Hence, 3, 5, 7 are the side lengths of a triangle.

Which angle has a positive measure ?

Answers

Hi, I can't see the other choices so here is the information to choose the answer.The angles with an arrow that move in the counter clockwise direction have positive measure

The given angle is measured clockwise with respect to {+x} axis. So, it has negative measure.

What is angle?

An angle is formed when two rays have the same end point. The common end point is called vertex.

Given is to identify the positive angle.

Any angle measured clockwise with respect to + x axis is negative. Similarly, any angle measured anti - clockwise with respect to + x axis is negative.

Since only one angle is shown in the image, we will describe about it. It can be seen that the angle is measured clockwise with respect to + x axis. Hence, it is negative.

Therefore, the given angle is measured clockwise with respect to {+x} axis. So, it has negative measure.

To solve more questions on angles, visit the link below-

https://brainly.com/question/18166236

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estimate and then record the product 3×46=

Answers

Answer:

Estimate is 150 and actual product is 138.

Step-by-step explanation:

To estimate products, we round the numbers to nearest unit place, 10th, 100th, 1000th, and so on.

Given are the numbers 3 and 46.

We can round 46 ≈ 50.

So Estimation would be 3 x 46 ≈ 3 x 50

3 times 5 is 15 and we can add zeros after it.  

So estimation is 3 x 46 ≈ 150.

Now actual product would be...

3 times 6 is 18, so we note down 8 and 1 goes to carry over 4.

3 times 4 is 12 and carry 1 will be added in it, so 12 + 1 = 13.

It means the actual product is 3 x 48 = 138.

MATH IS HARD. HELP
Change the following into a single fraction: 1− (a+b/a−b)

Answers

Answer:

-2b/(a-b)

Step-by-step explanation:

1− (a+b/a−b)


We need to get a common denominator of a-b

1 = (a-b)/(a-b)

Replace 1 with (a-b)/(a-b)

(a-b)/(a-b) - (a+b)/(a-b)

Put over the common denominator

(a-b) - (a+b)

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

(a-b)


Distribute the minus sign.

(a-b) - a-b)

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

(a-b)

a-a-b-b

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

a-b


-2b

----------

a-b

Meg deposited a $3,000 bonus check in a new savings account. The account has an interest rate of 3% for 5 years. The interest is compounded daily. How much money did Meg have at the end of the account term? (Round your answer to the nearest dollar.)

Answers

Answer:

The $3485.52 money did Meg have at the end of the account term.

Step-by-step explanation:

Formula for compounded monthly

[tex]Amount = P(1+\frac{r}{365})^{365n}[/tex]

Where P is the principle , r is the rate of interest in the decimal form and n is the number of years.

As given

Meg deposited a $3,000 bonus check in a new savings account. The account has an interest rate of 3% for 5 years.

Principle = $3000

3% is written in the decimal form

[tex]= \frac{3}{100}[/tex]

= 0.03

Time = 5 years

Put in the formula

[tex]Amount = 3000(1+\frac{0.03}{365})^{365\times 5}[/tex]

[tex]Amount = 3000(1+\frac{0.03}{365})^{1825}[/tex]

[tex]Amount = 3000(1+\frac{0.03}{365})^{1825}[/tex]

[tex]Amount = 3000(1+ 0.0000822)^{1825}[/tex]

[tex]Amount = 3000(1.0000822)^{1825}[/tex]

[tex]Amount = 3000\times 1.16184[/tex]

Amount = $ 3485.52

Therefore the  $ 3485.52  money did Meg have at the end of the account term.




Answer:

The Answer is $3,485 btw

Step-by-step explanation:

Answer C

on a scale drawing with a scale of 1 in: 5 ft, a tree is in. tall. How tall is the actual tree?

Answers

Final answer:

The question about the height of a tree on a scale drawing did not provide enough information for a certain answer. However, given a hypothetical height for the drawn tree, the actual height can be determined by multiplying this by the scale factor.

Explanation:

The subject of this question is mathematics, specifically dealing with ratios and proportions related to scale drawings. Given that the scale of the drawing is 1 in: 5 ft, this means that 1 inch on the drawing corresponds to 5 feet in real life. However, the specific height of the tree on the drawing in inches is not provided in the question, making it impossible to give a definite answer.

As an example to further explain, if the tree is drawn as 2 inches on the scale drawing, you would simply multiply by 5 (since the scale is 1 in: 5 ft) to find the actual height of the tree. So, for a 2 inch drawn tree, the actual tree would be 2 in * 5 ft/in = 10 ft tall.

But given the current information, a definite height cannot be provided. Please provide the height of the tree in inches on the scale drawing.

Learn more about Scale Drawing Ratio here:

https://brainly.com/question/18289648

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53° 78° x° find the value of x

Answers

Answer:

I would say 49 is your answer

Step-by-step explanation:

53 plus 78 qould equal 131

subtract 131 from 180 and you get 49

add up all your numbers including x then they should all equal 180

Solve for the variable 2(3x+1)=3

Answers

Answer:

x = 1/6

Step-by-step explanation:

2(3x+1)=3

Distribute.


6x + 2 = 3


Subtract 2 from both sides.


6x = 1


Divide by 6 on both sides.


x = 1/6

Hello there!

Question:-

[tex]\sf \longmapsto2(3x+1)=3[/tex]

We need to find the value of x.

Solution:-

[tex]\sf \longmapsto2(3x+1)=3[/tex]

Distribute:-

[tex]\sf \longmapsto \: (2)(3x)+(2)(1)=3[/tex]

On Simplification:-

[tex]\sf \longmapsto \: 6x + 2 = 3[/tex]

Subtract 2 from both sides :-

[tex]\sf \longmapsto 6x+2 - 2=3 - 2[/tex]

On Simplification:-

[tex]\sf \longmapsto6x + 0 = 3 - 2[/tex]

[tex]\sf \longmapsto6x = 1[/tex]

Divide the two sides by 6:-

[tex]\sf \longmapsto \: \dfrac{6x}{6} = \dfrac{1}{6} [/tex]

Cancel 6/6, leave x, answer is 1x. 1/6 can't be cancelled.

[tex]\sf \longmapsto \: \dfrac{ \cancel6x}{ \cancel6} = \dfrac{1}{6} [/tex]

[tex]\sf \longmapsto \: x = \dfrac{1}{6} [/tex]

In Decimal:-

[tex]\sf \longmapsto \: x = 0.16[/tex]

______________________________________

Henceforth,the value of x is :-

[tex]\boxed{\huge\tt x = \dfrac{1}{6}} [/tex]

[tex] \bold{OR,}[/tex]

[tex]\boxed{\huge\tt x = 0.16}[/tex]

_____________________________________

Please let me know if you have any questions.

~MisterBrian

how many lines can go through two points

Answers

Answer: 1


Step-by-step explanation:

Only one line segment can be drawn between two points. Any other line segments would be overlapping and the same segment

What is the negative x-intercept of the graph of the quadratic function f(x) = 5x2 + 4x - 1? A) - 7 5 B) - 2 5 C) - 1 5 Eliminate D) -1

Answers

Answer:

D

Step-by-step explanation:

The quadratic formula is

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].

It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions.  Using the formula will require less work than finding the factors if factorable. We will substitute a=5, b=4 and c=-1.

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-4+/-\sqrt{(4)^2-4(5)(-1)} }{2(5)}\\x=\frac{-4+/-\sqrt{16+20} }{10}[/tex]

We will now simplify and solve.

[tex]x=\frac{-4+/-\sqrt{36}}{10}\\x=\frac{-4+/-6}{10}[/tex]

x=-1 and x=0.2

The amount of sales tax on a clothing purchase is directly proportional to the purchase price of the clothing. The sales tax on a $60 sweater is $4.20. Determine the constant of variation (sales tax percentage). A) .05 B) .06 C) .07 D) .08

Answers

Answer:

C  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

4.20 ÷ 60 = 0.07

sales tax is 7% and this is your constant of variation

The answer is 0.07 hope this helps you ! :)

PLEASE HELP!! THANKS!

What is the 4th term in the sequence?

Answers

Answer:

- 405

Step-by-step explanation:

the recursive formula given allows us to find the next term in the sequence by multiplying the previous term by - 3

[tex]b_{2}[/tex] = [tex]b_{1}[/tex](- 3) = 15 × - 3 = - 45

[tex]b_{3}[/tex] = [tex]b_{2}[/tex](- 3) = - 45 × - 3 = 135

[tex]b_{4}[/tex] = [tex]b_{3}[/tex](- 3) = 135 × - 3 = - 405


$1,400 ,3.8%, 1 year

Answers

Answer:

$1453.2

Step-by-step explanation:

I assume you mean the accumulated value on a principal of $1400 with 3.8% interest in 1 year.

1400 * (100%+3.8%) = 1400 * 1.038 = 1453.2

How much water should we add to 35 kg of sugar syrup to change its concentration from 30% to 25%?

Answers

35kg - a mass of sugar syrup

30% of 35kg it's a mass of sugar

30% = 30 : 100 = 0.3

30% of 35kg = 0.3 · 35kg = 10.5kg - a mass of sugar

Add xkg water. Then we have (35 + x)kg of sugar syrup and still 10.5kg of sugar.

10.5kg is 25% of (35 + x)kg .

(35 + x) -- 100%

10.5  -- 25%     multiply both sides by 4

42   -- 100%

Therefore we have the equation:

35 + x = 42      subtract 35 from both sides

x = 7

Answer: We should add 7kg of water.

What is the value of x? Show your work to justify your answer.


2. What is the value of the exterior angle? Show your work to justify your answer please!

Answers

Answer:

[tex]x^{\circ}=56^{\circ};[/tex]

The exterior angle has measure [tex]116^{\circ}.[/tex]

Step-by-step explanation:

Angle QRP and angle with measure of (2x+4)° are supplementary, then

[tex]m\angle QRP+(2x+4)^{\circ}=180^{\circ},\\ \\m\angle QRP=180^{\circ}-(2x+4)^{\circ}.[/tex]

The sum of the measures of all interior angles of the triangle is equal to 180°, then

[tex]m\angle PQR+m\angle QRP+m\angle RPQ=180^{\circ},\\ \\x^{\circ}+180^{\circ}-(2x+4)^{\circ}+60^{\circ}=180^{\circ},\\ \\x^{\circ}-2x^{\circ}=-60^{\circ}+4^{\circ},\\ \\-x^{\circ}=-56^{\circ},\\ \\x^{\circ}=56^{\circ}.[/tex]

The exterior angle has measure

[tex](2\cdot 56+4)^{\circ}=116^{\circ}.[/tex]

Answer:

x=56 and the exterior angle is 116

Step-by-step explanation:

We will call the unknown angle in the triangle y.  Angle y and the angle (2x +4) form a straight line so they make 180 degrees.

y + 2x+4 =180

Solve for y by subtracting 2x+4 from each side.

y + 2x+4 - (2x+4) =180 - (2x+4)

y = 180-2x-4

y = 176-2x


The three angles of a triangle add to 180 degrees

x+ y+ 60 = 180

x+ (176-2x)+60 = 180

Combine like terms

-x +236=180

Subtract 236 from each side

-x+236-236 = 180-236

-x = -56

Multiply each side by -1

-1*-x = -56*-1

x=56

The exterior angle is 2x+4.  Substitute x=56 into the equation.

2(56)+4

112+4

116


Jamahl wants to celebrate his birthday by roller skating with his friends. He has a total of $45 to buy t tickets. Each ticket costs $5. Select the equation that matches this situation.

Answers

45 ÷ 5 = "t" amount of tickets Jamahl can buy.

Answer:

45=5t

Step-by-step explanation:

im doing it right now and got it right

What is the equation in point-slope form of the line that passes through the point (3, −2) and has a slope of 23 ?


Drag and drop the appropriate number, symbol, or variable to each box.

Answers

Answer:

y + 2 = 23(x - 3)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 23 and (a, b) = (3, - 2), hence

y + 2 = 23(x - 3) ← equation in point-slope form


Please help me answer this question

Answers

Answers:

The sign is 4 ft on a side

The poster is 2 ft on a side

================================================

Explanation:

s = side length of the sign

p = side length of the poster

The poster "has sides measuring 2 ft less than the sides of the square sign", so p = s-2. Whatever the value of 's' is, we subtract off 2 to get the value of p. For example, if the sign has side lengths of s = 10 ft, then p = s-2 = 10-2 = 8 ft is the side length of the poster

We don't know s or p right now, so they are simply placeholders for some numbers.

If s is the side length of the sign, then s*s = s^2 is the area

If p is the side length of the poster, then p*p = p^2 is the area of the poster. We can replace p with s-2 since p = s-2. So we end up with p^2 = (s-2)^2 = s^2 - 4s + 4 after using the FOIL rule

Now subtract the two areas and set that difference equal to 12. Solve for s

(area of sign) - (area of poster) = 12

(s^2) - (s^2 - 4s + 4) = 12

s^2 - s^2 + 4s - 4 = 12

4s - 4 = 12

4s - 4+4 = 12+4

4s = 16

4s/4 = 16/4

s = 4

The sign's side length is 4, so its area is 4^2 = 16

If s = 4, then p is

p = s-2

p = 4-2

p = 2

The poster's side length is 2, so its area is 2^2 = 4

Subtract the areas: 16 - 4 = 12

The answer is confirmed


Tony bought 3 packs of pencils for $4 each and a pencil box for $7. Mario bought 4 binders for $6 each and used a coupon for $6 off. Write and evaluate expressions to find who spent more money.

Answers

Answer:

Tony

Step-by-step explanation:

Tony:

3 Packs = 12 dollars

1 Pencil Box = 7 dollars


Mario:

4 Binders = 24 dollars

-6.


12+7= 19

24-6=18


Tony spent more money.

A bank offers an APR of 6.4% compounded daily. The annual percentage yield is what percentage?

Answers

Answer:

The annual percentage yield is 6.609%

Step-by-step explanation:

Let's assume

amount invested=$1

so, P=1

APR of 6.4% compounded daily

so, r=6.4%=0.064

n=365

t=1

now, we can use formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

now, we ca plug values

[tex]A=1(1+\frac{0.064}{365})^{365\times 1}[/tex]

we get

[tex]A=1.06609[/tex]

now, we can find APY

[tex]APY=\frac{A-P}{P}\times 100[/tex]

now, we can plug values

[tex]APY=\frac{1.06609-1}{1}\times 100[/tex]

we get

APY is 6.609%

Answer:

The annual percentage yield is 6.609%.

Step-by-step explanation:

The annual percentage yield is calculated by:

APY = [tex](1+\frac{r}{n} )^{n} -1[/tex]

where r is the percentage rate and n refers to the number of times compounded.

So, r = [tex]\frac{6.4}{100}[/tex] = 0.064

Since the APR is compounded daily,

n = 365

Now,

APY = [tex](1+\frac{0.064}{365} )^{365} -1[/tex]

= 6.609% approximately

For the equation 2x^3 -11x^2 + 12x + 9 = 0 , the root 3 has a multiplicity of
A. 1
B. 2
C. 3

Please explain!

Answers

Answer:

B. 2

Step-by-step explanation:

The multiplicity of a root is the number of times it occurs as a root.

We must solve the equation to find the number of times 3 occurs as a root.

Since we know that 3 is a root, we can use synthetic division to find the other roots.

f(x) = 2x³ -11x² + 12x + 9

3|2   -11     12     9

 |       6    -15    -9

  2   -5      -3      0

So, (2x³ - 11x² + 12x +9)/(x - 3) = 2x² - 5x – 3

=====

Let’s use synthetic division again to see if 3 is a root of this quadratic

3|2    -5    -3

 |       6      3

 2      1      0

So, 2x² - 5x – 3 = (x - 3)(2x + 1), and

2x³ - 11x² + 12x +9 = (x - 3)(x - 3)²(2x+1)

The factor x – 3 appears twice, so the root 3 has a multiplicity of two.

Help me. Please give explanation. Thanks

Answers

Answer: x < 3

Step-by-step explanation:

NOTE: [tex]\sqrt{(x+5)^2} = |x + 5|[/tex]

Rewrite the equation:

| x + 5 | < | x + 1 |

Remember that absolute value makes the "inside" value positive, so we need to solve for 2 case of x + 5 (inside is positive or negative) and 2 cases of x + 1.

± (x + 5) < ± (x + 1)

Case 1: +  +

x + 5 < x + 1

    5 < 1

  FALSE

Case 2: - -

-(x + 5) < -(x + 1)

 x + 5 > x + 1   divided both sides by -1

      5 > 1

     TRUE so this works when both "insides" are negative

⇒   x + 5 < 0     and      x + 1 < 0

          x < -5     and           x < -1

since it has to satisfy both, x < -5

Case 3: + -

x + 5 < -(x + 1)

x + 5 < -x - 1     distributed -1 on right side

2x + 5 < -1

2x       < -6

 x       < -3

Case 4: - +

-(x + 5) < x + 1

-x - 5 < x + 1     distributed -1 on left side

   -5 < 2x + 1

   -6 < 2x

   -3 < x

     x > -3

This is a contradiction of Case 3 so need to choose a test point.

TEST POINTS (I choose -6, -4, and -2)

 | -6 + 5 | < | -6 + 1 |

 |    -1     | < |    -5   |

          1   <   5

        TRUE so x < -5 is valid

 | -4 + 5 | < | -4 + 1 |

 |     1     | < |    -3   |

          1   <   3

        TRUE so x < -3 is valid

 | -2 + 5 | < | -2 + 1 |

 |     3     | < |    -1   |

          3   <   1

        FALSE so x > 3 is NOT valid

Note that x < -3 includes all the values of x < -5, so x < -3 is the answer.

*******************************************************************************

This is a faster way to solve it. Thank you @proner26 !

| x + 5 | < | x + 1 |

(| x + 5 |)² < (| x + 1 |)²

x² + 10x + 25 < x² + 2x + 1

       10x + 25 <       2x + 1

        8x + 25 <                1

        8x         <             -24

          x         <              -3

Answer: x < -3

Evaluate -tan²A + 1 + sec²A

Answers

Answer:


Step-by-step explanation: sec^2A-tan^2A+1

=1+1

=2


Answer:


Hello :

secA= 1/cosA

tanA = sinA / cosA

- tan²A + 1 + sec²A  = - (sinA / cosA)² + 1 + ( 1/cosA)²

                                 = - sin²A / cos²A  + 1 + 1 /cos²A

                                 = ( - sin²A  + cos²A +1)/cos²A

                                = ( 1 - sin²A + cos²A ) / cos²A

but : 1 - sin²A = cos²A   because : sin²A + cos²A = 1

so : - tan²A + 1 + sec²A  = ( 2 cos²A) / (cos²A)

- tan²A + 1 + sec²A  = 2



convert improper fractions such as 29/6

Answers

Answer:


Step-by-step explanation: to covert improper fractions to normal fractions.

29/6 would be 4 wholes and 5/6

You count how much 6’s are in the 29 which is 4. And then the left over would be 5 so 5/6


Last week kellie ran 28 miles. This week she ran 32 miles. What is the perecent of change in the number she ran?

Answers

Answer:

60%

Step-by-step explanation:

first do 28+32.

Next it equals 60. So change 60 to percentage form. It would be 60%

ANSWER:

14% increase.

The percent of change in the amount of miles Kellie ran last week and this week, rounded to the nearest whole number, is a 14% increase.

STEP-BY-STEP EXPLANATION:

Let % of change in Kellie's running distances from last weeks's 28 miles to this week's 32 miles = x

x = [ ( New amount - Original amount ) / Original amount ] × 100%

New amount = 32 miles

Original amount = 28 miles

THEREFORE:

x = [ ( 32 - 28 ) / 28 ] × 100%

x = ( 4 / 28 ) × 100%

x = ( 1 / 7 ) × 100%

x = 0.1428571429... × 100%

x = 14% ( rounded to the nearest whole number )

What is the initial value of the function represented by this table? (5 points)
x . y
0 . 5
1 . 9
2 . 13

Answers

Answer:

5 is the initial value

Step-by-step explanation:

From the table we can see that the values of y are increasing by 4

Lets use two points and find out slope

[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

we use points (0,5) (1,9)

[tex]slope = \frac{9-5}{1-0}=4[/tex]

slope m= 5

Now we use y=mx+b equation

m= slope and b= y intercept, plug in (0,5)  and find out b

y=4x+b

5= 4(0) +b

so b= 5

b=5 is the initial value of the function



Answer:

5 is the initial value

Step-by-step explanation:

From the table we can see that the values of y are increasing by 4

Lets use two points and find out slope

formula of slope

slope=m=[tex]\frac{y2-y1}{x2-x1}[/tex]

putting points (0,5) (1,9) in equation of slope

m=[tex]\frac{9-5}{1-0}[/tex]

slope m= 4

we know y=mx+b

m= slope and b= y intercept, plug in (0,5)  and find out b

b=?

x=0

m=4

y=5

putting these values in y=mx+b

y=4x+b

5= 4(0) +b

so b= 5

b=5 is the initial value of the function




The length of an aquarium, which has the form of a rectangular solid, is equal to 5 decimeters, and the width is 4/5 the length. When you put 40 liters of water into the aquarium, it was full to 2/3 its volume. What part of the length makes up the height of the aquarium? (1 liter is equal by volume to 1 decimeter^3)

Answers

Answer:

The height of aquarium is [tex]\frac{3}{5}[/tex] of its length

Step-by-step explanation:

It is given that the length of rectangular aquarium is 5 decimeter

width of aquarium = [tex]\frac{4}{5}[/tex] of length

                              = [tex]\frac{4}{5} (5) = 4[/tex] decimeter

so we have

width of aquarium = 4 decimeter

Let us assume the height of aquarium be x decimeter

so the volume of the aquarium = length × width × height

Volume of aquarium = 5(4)(x)= 20x decimeter³

it is given that 40 liters of water is [tex]\frac{2}{3}[/tex] of volume of aquarium

also

1 liter = 1 decimeter³

Therefore, 40 liters = 40 decimeter³

now we have

[tex]\frac{2}{3}[/tex] of volume of aquarium = 40

[tex]\frac{2}{3}(20x)=40[/tex]

[tex]\frac{40x}{3} =40[/tex]

multiply both side by 3

[tex]40x= 3(40)[/tex]

[tex]40x=120[/tex]

divide both side by 40

[tex]x=\frac{120}{40}[/tex]

x = 3 decimeter

height of aquarium = 3 decimeter

comparing height and length

[tex]\frac{height }{length} =\frac{3}{5}[/tex]

[tex]height = \frac{3}{5} length[/tex]

hence the height of aquarium is [tex]\frac{3}{5}[/tex] of its length

how would you graph 4x+2y=16

Answers

Answer:


Step-by-step explanation:

There are several ways in which you could do this.  

One involves finding the x- and y-intercepts, plotting them and drawing a straight line through them.  Starting with 4x + 2y = 16, let x = 0 to find the y-intercept:  2y = 16, or y = 8.  The y-intercept is (0,8).  Next, let y = 0 in 4x + 2y = 16 and solve for x; this leads to the x-intercept.  4x = 16, so x = 4.  The x-intercept is then (4, 0).  Plot (4,0) and (0, 8) and draw a straight line through these two points.

Another involves solving 4x+2y=16 for y, obtaining the equivalent in slope-intercept form of this equation.  Subtracting 4x from both sides, we get 2y = 16 - 4x.  Dividing all terms by 2 results in y = -2x + 8.

As before, the y-intercept is (0,8).  Plot this point.  Now use the slope, m = -2, to find another point on this line:  Starting at (0,8), move 1 unit to the right (increasing x by 1) and then move 2 units down, arriving at (1, 6).  Plot this point.  Now draw a straight line through (1,6) and (0,8).  Your result should look the same as the previous graph you drew.


2)
Which question is a statistics question that anticipates variability?
A) What is my favorite number if choosing a number between 1 and 10?
B) What is an average person's favorite number if choosing a number between 1 and 10?
C) Which number is chosen the most by an average person when choosing a number between 1 and 10?
D) Which number is chosen the least by an average person when choosing a number between 1 and 10?

Answers

Answer:

B

Step-by-step explanation:

It's B.

Answer:

Step-by-step explanation:

its b

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