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3 years ago

2 Justin has $110 to spend at the mall. He wants to buy a hat that costs $25 and a pair

Mathematics

1 answer:

Sonbull [250]3 years ago

8 0

Answer:

Option B If Justin buys the hat and the jeans, solving the inequality $12x+65\leq 110$ for x, will tell him the maximum number of bags of socks he can buy

Option D. If Justin buys the hat, jeans, and the maximum number of bags of socks, he will have enough money left to buy a belt that is on sale for $7.99

Step-by-step explanation:

Let

x ----> the number of bags of socks

we know that

The number of bags of socks that Justin can buy multiplied by it cost, plus the cost of the hat plus the cost of a pair of jeans, must be at most $110

The inequality that represent this situation is

$12x+25+40\leq 110$

solve for x

Combine like terms left side

$12x+65\leq 110$

subtract 65 both sides

$12x\leq 45$

Divide by 12 both sides

$x\leq 3.75$

The maximum number of bags of socks is 3

If Justin buys the hat but not the jeans, then the inequality that represent this situation is

$12x+25\leq 110$

<u><em>Verify each statement</em></u>

case A) If x is the number of bags of socks Justin can buy, then the inequality representing this situation is x < 3

The statement is false

The inequality that represent this situation is $x\leq 3.75$

The maximum number of bags of socks is 3

case B) If Justin buys the hat and the jeans, solving the inequality $12x+65\leq 110$ for x, will tell him the maximum number of bags of socks he can buy

The statement is true

see the explanation

case C) If Justin buys the hat but not the jeans, solving the inequality $12x+40\leq 110$ for x will tell him the maximum number of bags of socks he can buy

The statement is false

Because the inequality will be $12x+25\leq 110$

case D) If Justin buys the hat, jeans, and the maximum number of bags of socks, he will have enough money left to buy a belt that is on sale for $7.99

The statement is true

Because

The total cost is

$12(3)+25+40=\$101$

The amount of money left is $\$110-\$101=\$9$

$\$9 > \$7.99$

therefore

If Justin buys the hat, jeans, and the maximum number of bags of socks, he will have enough money left to buy a belt

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Answer:

Step-by-step explanation:

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a°=144° and b°=67°

144+67=211

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Equation of the line that goes through the points (0, -2) and (-5, 3).

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Step-by-step explanation:

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3 years ago

A cylindrical tank has a base of diameter 12 ft and height 5 ft. The tank is full of water (of density 62.4 lb/ft3).(a) Write do

saw5 [17]

Answer:

a. 71884.8 π lb/ft-s²∫₀⁵(9 - y)dy

b. 23961.6 π lb/ft-s²∫₀⁵(5 - y)dy

c. 99840π lb/ft-s²∫₀⁶rdr

Step-by-step explanation:

.(a) Write down an integral for the work needed to pump all of the water to a point 4 feet above the tank.

The work done, W = ∫mgdy where m = mass of cylindrical tank = ρA([5 + 4] - y) where ρ = density of water = 62.4 lb/ft³, A = area of base of tank = πd²/4 where d = diameter of tank = 12 ft.( we add height of the tank + the height of point above the tank and subtract it from the vertical point above the base of the tank, y to get 5 + 4 - y) and g = acceleration due to gravity = 32 ft/s²

So,

W = ∫mgdy

W = ∫ρA([5 + 4] - y)gdy

W = ∫ρA(9 - y)gdy

W = ρgA∫(9 - y)dy

W = ρgπd²/4∫(9 - y)dy

we integrate W from y from 0 to 5 which is the height of the tank

W = ρgπd²/4∫₀⁵(9 - y)dy

substituting the values of the other variables into the equation, we have

W = 62.4 lb/ft³π(12 ft)² (32 ft/s²)/4∫₀⁵(9 - y)dy

W = 71884.8 π lb/ft-s²∫₀⁵(9 - y)dy

.(b) Write down an integral for the fluid force on the side of the tank

Since force, F = ∫PdA where P = pressure = ρgh where h = (5 - y) since we are moving from h = 0 to h = 5. So, P = ρg(5 - y)

The differential area on the side of the tank is given by

dA = 2πrdy

So. F = ∫PdA

F = ∫ρg(5 - y)2πrdy

Since we are integrating from y = 0 to y = 5, we have our integral as

F = ∫ρg2πr(5 - y)dy

F = ∫ρgπd(5 - y)dy since d = 2r

substituting the values of the other variables into the equation, we have

F = ∫₀⁵62.4 lb/ft³π(12 ft) × 32 ft/s²(5 - y)dy

F = 23961.6 π lb/ft-s²∫₀⁵(5 - y)dy

.(c) How would your answer to part (a) change if the tank was on its side

The work done, W = ∫mgdr where m = mass of cylindrical tank = ρAh where ρ = density of water = 62.4 lb/ft³, A = curved surface area of cylindrical tank = 2πrh where r = radius of tank, d = diameter of tank = 12 ft. and h = height of the tank = 5 ft and g = acceleration due to gravity = 32 ft/s²

So,

W = ∫mgdr

W = ∫ρAhgdr

W = ∫ρ(2πrh)hgdr

W = ∫2ρπrh²gdr

W = 2ρπh²g∫rdr

we integrate from r = 0 to r = d/2 where d = diameter of cylindrical tank = 12 ft/2 = 6 ft

So,

W = 2ρπh²g∫₀⁶rdr

substituting the values of the other variables into the equation, we have

W = 2 × 62.4 lb/ft³π(5 ft)² × 32 ft/s²∫₀⁶rdr

W = 99840π lb/ft-s²∫₀⁶rdr

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3 years ago

The negative sign in 15t-2t belongs to the term____?

alexdok [17]

The expression 15t – 2t not equivalent to 2t – 15t because the negative sign in 15t – 2t belongs to the term 2t.

Solution:

Given expressions are 15t – 2t and 2t – 15t.

To determine 15t – 2t is equivalent to 2t – 15t or not.

Substitute t = 2 in above two expressions.

15t – 2t = 15(2) – 2(2)

= 30 – 4

= 26

2t – 15t = 2(2) – 15(2)

= 4 – 30

= –26

The values of the expressions are different when t = 2.

So, 15t – 2t is not equivalent to 2t – 15t.

Hence the expression 15t – 2t not equivalent to 2t – 15t because the negative sign in 15t – 2t belongs to the term 2t.

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3 years ago

Compute the mean, median, and mode for the following three sets of scores saved.

igor_vitrenko [27]

Answer/Step-by-step explanation:

Score 1:

3, 7, 5, 4, 5, 6, 7, 8, 6, 5

Mean = $\frac{3 + 7 + 5 + 4 + 5 + 6 + 7 + 8 + 6 + 5}{10} = \frac{56}{10} = 5.6$

Median: order the data from least to the greatest.

3, 4, 5, 5, 5, 6, 6, 7, 7, 8

The median is average of the fifth and sixth data value in the data set

Median = (5 + 6)/2 = 11/2 = 5.5

Mode = value with the highest frequency = 5

Score 2:

34, 54, 17, 26, 34, 25, 14, 24, 25, 23

Mean = sum of all values/10

Mean = 276/10 = 27.6

Median: order the data set from min to max.

14, 17, 23, 24, 25, 25, 26, 34, 34, 54

The median is average of the fifth and sixth data value in the data set

Median = (25 + 25)/2 = 50/2 = 25

Mode = 25 and 34 (both have frequencies of 2)

Score 3:

154, 167, 132, 145, 154, 145, 113, 156, 154, 123

Mean = sum of all values/10

Mean = 1443/10 = 144.3

Median: order the data set from min to max.

113, 123, 132, 145, 145, 154, 154, 154, 156, 167

The median is average of the fifth and sixth data value in the data set

Median = (145 + 154)/2 = 299/2 = 149.5

Mode = 154

8 0

3 years ago