Coached Example
V
...
Tanya walked 15 laps on an indoor track in 30 minutes. What was Tanya's avera
speed in laps per minute?
The speed formula is r = _
The distance is _ laps.
The time is minutes.
Substitute the known values into the speed formula.
r=
Simplify the fraction.
r=
Tanya's average speed was
laps per minute.

Answer: 240 km

Step-by-step explanation:

From the graph :

50 miles = 80km

1 miles = 80/50 km

Therefore :

150 miles = 80/50 x 150

150 miles = 240 km

Answer:

15 shelves

Step-by-step explanation:

6 dvds = 1 shelf

89/6= 14.8333333333 shelves

But you cannot have 0.8333333333 shelves so you would round  0.8333333333 to 1

value of x is: [tex]x=\frac{-31}{12}[/tex]

Step-by-step explanation:

We need to solve the equation f(x)=g(x)

where [tex]f(x)=(\frac{1}{2})^2-3[/tex]

and [tex]g(x) = 3x + 5[/tex]

Solving to find f(x)=g(x)

Putting values of f(x) and g(x)

[tex]f(x)=g(x)\\(\frac{1}{2})^2-3=3x + 5\\\frac{1}{4}-3=3x + 5\\Subtarct\,\,5\,\,on\,\,both\,\,sides:\\\frac{1}{4}-3-5=3x + 5-5\\\frac{1}{4}-8=3x\\Taking\,\,LCm\,\,on\,\,left\,\,side\\\frac{1-8*4}{4}=3x\\\frac{-31}{4}=3x\\Divide\,\,both\,\,sides\,\,by\,\,3\\x=\frac{-31}{4*3}\\x=\frac{-31}{12}[/tex]

So, value of x is: [tex]x=\frac{-31}{12}[/tex]

The graph will be a straight line x= -2.58 or x = -31/12

Keywords: Composition of Functions

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Answer:

0/36

Step-by-step explanation:

Answer:

0/36

Step-by-step explanation:

It is impossible to roll two dice and get a sum less than 2.

(I'm assuming this is a 6 sided die, but either way if you have more than one die this is impossible.

The lowest you can roll would be 1+1 therefore adding up to a 2.

Answer:

[tex]x=-\frac{88}{3}[/tex]

Step-by-step explanation:

When a quantity "A" varies DIRECTLY with another quantity "B", we can write the proportionality equation as:

A = kB

Where k is the proportionality constant (to be found)

In this problem, it is given x varies DIRECTLY with y, so we can write:

x = ky

Also, given, x = 11, y = -3, so we plug these into the equation and first find k:

x = ky

11 = k(-3)

k = -11/3

Now, we need to find x when y = 8, so we substitute and find x:

[tex]x=ky\\x=(-\frac{11}{3})(8)\\x=-\frac{88}{3}[/tex]

To find x for a given value of y when x varies directly as y, determine the constant of proportionality using the provided pair of values. Then use this constant to calculate x for the new value of y.

Since x varies directly as y, we can write this as x = ky, where k is the constant of proportionality. To find the value of k, we use the given values: x=11 when y=-3. Substituting these values into the equation gives us 11 = k(-3), or k = -11/3.

To find x when y=8, we substitute y=8 and the value of k into the direct variation equation: x = (-11/3)(8) = -88/3 = -29.33. Therefore, x is approximately -29.33 when y=8.

Final answer:

To find sin 2θ when cos θ = 3/5, we first find sin θ using the Pythagorean identity and then apply the double angle formula, yielding sin 2θ = 24/25.

Explanation:

To find sin 2θ when given cos θ = 3/5 and θ is in the first quadrant, we can use the double angle formula for sine, which is sin 2θ = 2 sin θ cos θ. First, we need to find sin θ. Given that θ is in the first quadrant, all trigonometric functions are positive, and we can use the Pythagorean identity sin²θ + cos²θ = 1 to find sin θ. Since we know cos θ, cos²θ = (3/5)² = 9/25, which means sin²θ = 1 - 9/25 = 16/25. Taking the positive square root, since θ is in the first quadrant, sin θ = 4/5.

Now, we apply the double angle formula: sin 2θ = 2 × (4/5) × (3/5), which simplifies to sin 2θ = 24/25.

Answer: 200cm long

Step-by-step explanation:

Let the length of the rod be x

red = 1/4 of the rod , which means 1/4 of x

orange = 2/5 of x

The remainder = x - ([tex]\frac{x}{4}[/tex] +[tex]\frac{2x}{5}[/tex])

= x - ([tex]\frac{13x}{20}[/tex])

= [tex]\frac{7x}{20}[/tex]

yellow = 2/7 of the remainder , that is

yellow = 2/7 of [tex]\frac{7x}{20}[/tex]

yellow = [tex]\frac{x}{10}[/tex]

and it was given that the yellow section was 20cm long , that is

[tex]\frac{x}{10}[/tex] = 20cm

x = 20 x10

x = 200

Therefore the rod was 200cm long

To determine the length of a rod based on fractions of it being painted different colors, with the yellow section known to be 20cm, we set up a proportion based on the fractions of the rod painted and use this to solve for the total length of the rod, which is 200cm.

The subject of this question is Mathematics, and it is typically encountered at the Middle School level. To find the length of the entire rod when 1/4 is painted red, 2/5 is painted orange, and 2/7 of the remainder is painted yellow with the yellow section being 20cm, we need to set up an equation and solve for the total length of the rod.

First, we determine the fraction of the rod that remains after painting 1/4 red and 2/5 orange:

Let's start the calculations:

1. (1/4) + (2/5) = 5/20 + 8/20 = 13/20.

2. The remaining fraction = 1 - 13/20 = 7/20.

3. Let x be the total length of the rod. Since 2/7 of the remainder is 20cm, we can write the equation (2/7) * (7/20) * x = 20cm.

4. Simplify and solve for x:

(2/7) * (7/20) * x = 20cm,

(1/10) * x = 20cm,

x = 20cm * 10,

x = 200cm.

Therefore, the total length of the rod is 200cm.

Answer: 15

Step-by-step explanation: Linear equations can be written in the form

y = mx + b where the base "b" represents the y-intercept of the line.

So in this case, the y-intercept of the line would positive 15.

The equation can written as y = 4x + 15.

This equation is written in slope-intercept. y = mx + b

m = slope

b = y-intercept

In this equation the y-intercept (b) is 15.

_______

Best Regards,

Wolfyy :)

Answer:

160 ounces

Step-by-step explanation:

1 pound=16 ounces

so,

10 pounds=16 multiplied by 10= 160 ounces

Fun fact u spelled ounces at the very last.

pls can I have five star

The weight of the 10-pound package is 160 ounces.

There are 16 ounces in 1 pound. Juan is mailing a packet that weighs 10 pounds. To find the weight of the package in ounces, multiply the number of pounds (10) by the unit equivalence (16).

Therefore, the weight of the package is 160 ounces.

Answer:

I think it was warmer

Answer:

A

Step-by-step explanation:

If we take each small section to be "1" unit, we can say the large sections (for "2" and "5") are "2" units each. So in total there will be 8 sections.

Since 5 is "2" sections, we can say:

P(5) = 2/8 = 1/4

And 6 is "1" section, so we can say:

P(6) = 1/8

Definitely, Probability of landing a 6 is HALF that of probability of landing a 5. Also we can see this is the picture.

So, from the answer choices, A is right.

Answer:

A. $3,150

B. $2,100

Step-by-step explanation:

A. Given,

Trucks cost price = $40,000

Salvage Value = $8,500

Useful life = 10 years

Since there is no requirement, I am using straight-line depreciation method to calculate the depreciation expense.

We Know,

Depreciation Expenses = (Cost price - Salvage Value) / Useful Life

Therefore,

Depreciation expense = ($40,000 - $8,500)/10

Depreciation Expense = $31,500/10

Depreciation Expense = $3,150

Therefore, under the straight-line method, the depreciation expense will be = $3,150.

B. Given, (When the useful year is 15)

Trucks cost price = $40,000

Salvage Value = $8,500

Useful life = 15 years

Since there is no requirement, I am using straight-line depreciation method to calculate the depreciation expense.

We Know,

Depreciation Expenses = (Cost price - Salvage Value) / Useful Life

Therefore,

Depreciation expense = ($40,000 - $8,500)/15

Depreciation Expense = $31,500/15

Depreciation Expense = $2,100

Therefore, under the straight-line method, the depreciation expense will be = $2,100

Answer:

120

Step-by-step explanation:

87.5% of what number is 105?

87.5%=0.875

105/0.875=120

Answer:

Standard Form : 3x+1y=35

Step-by-step explanation:

The equation of the line will be 3x+y-35=0

The equation of the line in standard form will be expressed by using the coefficient of x and coeficient of y which is given

ax+by+c=0

The equation of line which passes through two points will be

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)

So according to asked question,

x₁=10,y₁=5

x₂=13,y₂=-4

the equation of line will be

(y-5)/(x-10)=(-4-5)/(13-10)

⇒(y-5)/(x-10)=-9/3

⇒(y-5)/(x-10)=-3

⇒y-5=-3(x-10)

⇒y-5=-3x+30

⇒y+3x-5-30=0

⇒3x+y-35=0

Therefore the equation of the line will be 3x+y-35=0

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Answer:

16 is x<3

Step-by-step explanation:

4x-10<2

Add 10 to both sides

4x<12

Divide 4 from both sides and you get x<3

Answer:

I think the simplified answer is 7.69

Answer: X = 4.33

Step-by-step explanation:

cos angle = hypotenuse / opposite side

cos 30° = X/5

0.866 = X/5

X = 4.33

Answer:

Step-by-step explanation:

9/16=x/12

cross product

16x=9*12

16x=108

x=108/16

simplify

x=27/4

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

x-3/18=12/9

x=12/9+3/18

x=24/18+3/18

x=27/18

x=3/2

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

7/11=18/x+1

18/x=7/11-1

18/x=7/11-11/11

18/x=-4/11

x=18/(-4/11)=(18/1)(-11/4)=-198/4=-99/2

x=-99/2

Answer:

b)−1×2×−3×4×−5 has a negative value.

Step-by-step explanation:

Given expressions are a)−1×−2  b)−1×2×−3×4×−5 C) 1×−2×−3×−4×−5 d)1×−2×3×−4×5

Firstly we have to multiply the digits with digit then after minus sign.

So for a)−1×−2

Solution, [tex]1\times2\ =2[/tex]

When two negative signs are multiplied with each other it gives a positive sign.

Both digits have a negative sign that means it gives a positive sign.

So the solution for 1st expression is [tex]2.[/tex]

b)−1×2×−3×4×−5

Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]

Here three digits have negative sign, two negative gives positive and then multiplied by negative gives negative.

So the solution for 2nd expression is [tex]-120[/tex].

C) 1×−2×−3×−4×−5

Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]

Here four digits have negative sign, two negative gives positive and again two negative gives positive means positive multiplied with positive gives positive.

So the solution for 3rd expression is [tex]120[/tex].

d)1×−2×3×−4×5

Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]

Two digits have a negative sign that means it gives a positive sign.

So the solution for 4th expression is [tex]120[/tex].

Hence the correct option is b.

Answer:

B

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

because that are 11 pencils that are 6 inches or longer, that's what the picture says.

Answer:

Helpful piece of information - each x = 1 pencil

Step-by-step explanation:

If each x = 1 pencil, and their are 6 x's over the 6 inch mark, 2 x's over the 7 inch mark, and 3 x's over the 8 inch mark, how many pencils measure 6 inches or more?

11 pencils measure 6, 7, and 8 inches.

I hope this helps!

Answer:

No Solution.

Step-by-step explanation:

2(x-1)-y=-8

y=2x+8

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

2x-2-(2x+8)=-8

2x-2-2x-8=-8

2x-2x-2-8=-8

0-2-8=-8

-2-8=-8

-10=-8

no solution

Answer:

100 seconds

Erica and Amy are at distance of 1 km in 100 seconds

Step-by-step explanation:

They both are travelling in opposite directions so the sum of the distances they travel is the distance between them.

Let's take t as the total time taken to achieve a seperation of 1km

Distance traveled by Erica , (Speed of Erica - v1)

x1 = v1 * t

Distance travelled by Amy , (Speed of Amy - v2)

x2 = v2*t

Therefore sum of the distances they traveled is x1+x2 = x

x = v1*t + v2*t

x = t*(v1 + v2)

Here it is given that final seperation between Amy and Erica is 1km or 1000 m

Therefore x = 1000 m

Thus t = [tex]\frac{x}{v1+v2}[/tex]

Substituting given values v1 = 6 m/s v2 = 4 m/s

Therefore,

They are apart by exactly 1km in a time of 100 sec

Answer:

y=-3/4x-5/4

Step-by-step explanation:

use the formula y-y1=m(x-x1)

y-4=-3/4(x-(-7))

The total number of nails will decrease by 14 nails when Willa will use 7 nails on each side.

Step-by-step explanation:

Sides of one birdhouse = 7

Nails used on each side = 9

Nails used on one birdhouse = Nails per side * Sides of birdhouse

Nails used on one birdhouse = 9*7 = 63 nails

If she uses 7 nails on each side, then the number of nails used on one birdhouse;

No. of nails = 7 * 7 = 49 nails

Change = Nails used on one birdhouse - No. of nails

Change = 63 - 49 = 14

The total number of nails will decrease by 14 nails when Willa will use 7 nails on each side.

Keywords: multiplication, subtraction

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Each birdhouse needs 63 nails. If Willa uses only 7 nails on each side, she will need a total of 49 nails.

Each side of the birdhouse requires 9 nails, and there are 7 sides on the birdhouse. To find the total number of nails needed for each birdhouse, we can multiply the number of nails per side by the number of sides:

9 nails/side x 7 sides = 63 nails needed for each birdhouse.

If Willa only uses 7 nails on each side, the total number of nails she uses will change. The new total number of nails can be found by multiplying the new number of nails per side (7 nails) by the number of sides (7 sides):

7 nails/side x 7 sides = 49 nails in total.

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Answer: No

Step-by-step explanation: because

1/2 +1/4 +1/3 is larger than one bowl.

6+3+4/12 = 13/12

;. 1 ¹/12.

Therefore, 1 bowl can not carry it

No, One bowl can not carry all of the ingredients at one time.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Chad made a snack by combining 1/3 of a bowl of granola with ¼ of a bowl of chopped banana and ½ of a bowl of yogurt.

The total amount 1/2 +1/4 +1/3 is larger than one bowl.

6 + 3 + 4/12 = 13/12

also 1 ¹/12.

Therefore, No 1 bowl can not carry it.

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8 minutes is 2/15 of an hour when simplified, which is obtained by dividing both the numerator and denominator of the fraction 8/60 by the greatest common divisor of 8 and 60, which is 4.

To convert 8 minutes into a fraction of an hour, first understand that 1 hour is equivalent to 60 minutes. Therefore, to find what fraction 8 minutes is of an hour, you can create the ratio of 8 minutes to 60 minutes, which simplifies to:

8 minutes / 60 minutes = 8/60

This fraction can then be simplified by dividing both the numerator and the denominator by the greatest common divisor (GCD) of 8 and 60, which is 4, to obtain:

8/60 ÷ 4/4 = 2/15

Thus, 8 minutes is 2/15 of an hour in simplest form.

Answer:

about 160

Step-by-step explanation:

Answer:

1440 CUVs, approx.  Actual number would be slightly lower.

Step-by-step explanation:

To answer this question, multiply 4800 vehicles by (3/10) for an approximation of the number of CUVs sold:

4800        3

---------- * ------- = 1440 CUVs

    1            10

Answer:

96 is the answer maybe of it