To win a medal in a 5K race, a runner's time
must be less than 22 minutes. Write an
inequality to represent the times in minutes
m that would win a medal.

Answer:

2(m+2)

Step-by-step explanation:

[tex]=-6 + 3m + 2 - m + 8\\\\=4+2m\\\\=2m+4\\\\=2(m+2)[/tex]

[tex] \sf \dashrightarrow \: - 6 + 3m + 2 - m + 8[/tex]

[tex] \\ \\ [/tex]

[tex] \sf \dashrightarrow \: - 4 + 3m - m + 8[/tex]

[tex] \\ \\ [/tex]

[tex] \sf \dashrightarrow \: 3m - m + 4[/tex]

[tex] \\ \\ [/tex]

[tex] \sf \dashrightarrow \: 2m + 4[/tex]

[tex] \\ [/tex]

[tex] \sf \dashrightarrow \: 2(m + 2)[/tex]

Answer:

27

Step-by-step explanation:

x + y = 15 (gallons)      (1)

0.25*x + 0.10 * y = 0.15 * 15   (2)

Multiply 100 on (2):

25x + 10y = 15

Divede by 5

5x + 2y = 3     (3)

From (1) y = 15 - x

so 5x + 10*(15 - x) = 15

5x + 150 - 10x = 15

-5x = 15 - 150 = -135

x = 135/5 = 27 (gallons)

Hi!

I can help you with joy!

In order to solve a proportion, all you should do is cross-multiply:

Cross-multiplying is exactly what it sounds like.

In this case, we Multiply

4 times 7

5 times y

28=5y

Divide both sides by 5:

5.6

Hope it helps!

-Nature

Given in the question, [tex]\frac{4}{5} =\frac{y}{7} \\[/tex], using the concept of direct proportion, y = 5.6

Direct proportion is the concept of proportionality where one variable increases/decreases when another increases/decreases and vice versa. The rate of increase/decrease can be measured through the constant ratio. The two quantities which are directly proportional are related by a Direct Proportion symbol '∝'.

Given in the question,

[tex]\frac{4}{5} =\frac{y}{7} \\[/tex]

multiplying 7 on both sides,

[tex]\frac{4}{5}*7 = \frac{y}{7} *7\\ \\ \frac{28}{5} = y \\\\y = 5.6[/tex]

Learn more about direct proportion here

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Answer:

-7/4 or -1 3/4

Step-by-step explanation:

Step 1. Convert into improper fraction.

2 1/2 = 5/2

Step 2. Convert the fractions into common denominator.

5/2 = 10/4

Step 3. Subtract.

3/4 - 10/4 = -7/4

Probabilities are used to determine the chances of events

The probability the spy is able to unlock the smart phone on his first try is 0.00000001

The length of the password is given as:

L = 8

Each of the digit in the password can take any of digits 0 - 9 (i.e. 10 digits)

So, the number of possible password is:

[tex]n = 10^8[/tex]

The probability that the spy unlocks the phone is:

[tex]p =\frac 1n[/tex]

So, we have:

[tex]p = \frac 1{10^8}[/tex]

Simplify

[tex]p = 0.00000001[/tex]

Hence, the probability the spy is able to unlock the smart phone on his first try is 0.00000001

Read more about probability at:

https://brainly.com/question/25870256

Answer:

144/169

Step-by-step explanation:

There are 52 cards, 4 are aces, so the probability of not getting ace is 48/52, so we square it, or multiply it by itself to get 144/169

Answer:

364.46

Step-by-step explanation:

First we need the height of the cone

so we divide the cone to two equal parts that means the adjacent 5 inches will be divided into two to give 2.5

then we use get a triangle from the cone and that's how we find our height using pythagoras theorem

hypotenuse Square = opposite Square + adjacent Square

7^2 = x^2 + 2.5^2

therefore our height is 6.53

now to get the surface area of the cone we use the formula

pi×r( r + Square root of r^2 + h^2

Answer:

see below

Step-by-step explanation:

Answer:

x=3/2

Step-by-step explanation:

[tex]\cfrac{3x-1}{21} =\cfrac{2x-2}{12}[/tex]

[tex]36x-12=42x-21[/tex]

[tex]6x=9[/tex]

[tex]x=\cfrac{3}{2}[/tex]

Hope it helps! :)

Answer:

4

Step-by-step explanation:

the amplitude is the distance from the crest to the trough of one wave

in this case, from 2 to -2

See the attached picture for the answer:

Answer:

The maximum angle they can use the ladder is 65.38º

Step-by-step explanation:

Sine law allows sinA/a = sin B/b = sin C/c

Reference the drawing attached

sin 90/110m = sinB/100m

1/110m = sinB/100

multiply both sides by 100

100/110 = sinB

divide each side by 10

10/11 = sinB

find inverse sin of both sides

sin^-1(10/11) = B

65.38º = B

The first question answer is 4

Answer:

$33,350

Step-by-step explanation:

[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 &\$29000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=29000\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies A=29000(1.05)^3\implies A\approx 33571.13[/tex]

Answer:

x = 5

Step-by-step explanation:

Piece 1 has length 5 inches

Piece 2 has length 20 inches

Piece 3 has length 25 inches

total length:50 inches

Answer:

x < -6

Step-by-step explanation:

-5x - 8 > 22

Add 8 to both sides:  -5x > 30

Divide both sides by 5:  -x > 6

Divide both sides by -1 (reverse sign):  x < -6

Answer:

x < -6

Step-by-step explanation:

First we want to move all terms not containing x to the right side

-5x > 22 + 8

-5x > 30

Then we want to divide

-5x/5 < 30/-5

30/-5

x < - 6

Answer:

Step-by-step explanation:

C and D

because root(4) = 2

C = 2 1

      1 2

      2 1

Answer:

26/15

Step-by-step explanation:

13/x= 2/2-x

the next step from here is to cross multiply and when we do that it's looks like this

13(2-x)=2*x

then we multiply

26-13x=2x

we then collect like terms

26=15x

therefore x= 26/15

we can leave our answer in this format or convert it to mixed fraction or decimal but its best to leave it in this format

Two or more expressions with an Equal sign is called as Equation. Value of x is 26/15 for equation 13/x=2/(2-x)

Two or more expressions with an Equal sign is called as Equation.

The given equation is

13/x=2/(2-x)

Apply cross multiplication

13(2-x)=2x

Apply Distributive property on LHS side

13(2)-13x=2x

26-13x=2x

Add 13x on both sides

26-13x+13x=2x+13x

26=15x

x=26/15

Hence value of x is 26/15 for equation 13/x=2/(2-x)

To learn more on Equation:

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Answer:

cosine rule - cos = [tex]\frac{a}{h}[/tex]

Step-by-step explanation:

Here the ladder is acting as hypotenuse and base as adjacent.

Formula: cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex]

And we know

[tex]\\ \tt\hookrightarrow tan\theta=\dfrac{Perpendicular}{Base}[/tex]

[tex]\\ \tt\hookrightarrow tan47=\dfrac{P}{30}[/tex]

Answer:

C

Step-by-step explanation:

from converting the linear equation 6x - 2y = 12 and slope intercept form we have to transpose terms to get the value of y hence equation and slope intercept form is y = 3x - 6.

Answer:

Option A

Step-by-step explanation:

Given the following question:

[tex]9+(\frac{1}{2})^4\times48[/tex]

In order to find this, answer we use order of operations and solve.

[tex]9+(\frac{1}{2})^4\times48[/tex]
[tex]\frac{1}{2} ^4=\frac{1}{2} \times\frac{1}{2} \times\frac{1}{2} \times\frac{1}{2} =\frac{1}{16}[/tex]
[tex]9+\frac{1}{16} \times48[/tex]
[tex]\frac{1}{16} \times48=\frac{1}{16}\times\frac{48}{1} =\frac{3}{1} =3[/tex]
[tex]9+3[/tex]
[tex]9+3=12[/tex]
[tex]=12[/tex]

Which means your answer is option A or "12."

Hope this helps.

According to the situation described, we have that:

a) The arithmetic sequence that gives the number of seats in the nth row is given by:

[tex]a_n = 24 + 7n[/tex]

b) The 38th row has 290 seats.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

Item a:

The first row has 31 seats, the second has 38, the third has 45 and so on, hence:

Then, the rule is:

[tex]a_n = a_1 + (n - 1)d[/tex]

[tex]a_n = 31 + 7(n - 1)[/tex]

[tex]a_n = 24 + 7n[/tex]

Item b:

This is the nth row, for which [tex]a_n = 290[/tex], hence:

[tex]a_n = 24 + 7n[/tex]

[tex]290 = 24 + 7n[/tex]

[tex]7n = 266[/tex]

[tex]n = \frac{266}{7}[/tex]

[tex]n = 38[/tex]

The 38th row has 290 seats.

You can learn more about arithmetic sequences at https://brainly.com/question/26366645

keeping in mind that a function is a set that has no X-repeats, namely the x-coordinate on every pair is never repeated, let's check these ones.

Check the picture below.

Answer:

E

Step-by-step explanation:

because its going up by 1's and so it would be 5x6/2 =15

Answer:

114ab-108b2=

collect like terms

114-108=6

divide by the coefficient of the number

b÷2=b

=6÷2=3

b=3

Answer:

See below.

Step-by-step explanation:

-7x+2y=10

/2   /2    /2

-7/2x+y=5

+7/2x   +7/2x

y=7/2x+5

The y-intercept is 5.

-hope it helps

Step-by-step explanation:

let adults be x and childrens be y

a/q

11x + 5y = 270

14x + 9y = 370

→ x = -5/11y + 270/11 ; 14x + 9y = 370

→ 14(-5/11y + 270/11) + 9y = 370

→ y = 10

→ x = -5/11 × 10 + 270/11

→ x = -50/11 + 270/11

→ x = 20

therefore, we got

x = 20, y = 10

each adult have to pay 20 and each children have to pay 10

so,

2 × 20 = 40

3 × 10 = 30

40 + 30 = 70

for a family of 2 adults and 3 children they have to pay 70.

hope this helps you dear.

Divide the length of the scale drawing by the scale (2.5) then multiply that by the scale feet (3)

11 inches / 2.5 = 4.4

4.4 x 3 = 13.2 feet

Answer: 13.2 feet

Total 2.5in pairs

[tex]\\ \tt\hookrightarrow \dfrac{11}{2.5}[/tex]

[tex]\\ \tt\hookrightarrow 4.4[/tex]

So length=4.4(3)=13.2ft