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pentagon [3]
3 years ago
7

Mount Rainier is 14,410 feet high. Mount McKinley is 20,320 feet high. How much taller is Mount McKinley? If Babe Ruth averaged

46 home runs per year, how many home runs did he hit in 12 years? What’s the difference between paying $10,000 cash for a car or paying a loan of $200 per month for 60 months? Ken sold $700 worth of digital cameras, $2,394 worth of laptops, and $833 worth of vacuum cleaners. Digital cameras cost $175 each, laptops cost $399 each, and vacuum cleaners cost $119 each. If Ken earns a $35 commission for each sale, how much did he earn in commissions in all? A parking garage owner has spaces for 70 cars and charges each driver $6 per day for parking. If the garage is full, how much more would the garage owner make if he charged $8 per day? Regina has $25 to buy groceries. She needs 3 cans of dog food, a gallon of milk, 5 pounds of chicken, a box of cereal, and 6 rolls of paper towels. The prices of the items are as follows: dog food—$1.50 a can; milk—$4 a gallon; chicken—$1.55 a pound; cereal—$2.75 a box; paper towels—99 cents a roll. Will Regina have enough money for all the items she needs? If not, how much more will she need? (Note: Remember that there are 100 cents in a dollar.)
Mathematics
1 answer:
professor190 [17]3 years ago
8 0
A] <span>Mount Rainier is 14,410 feet high. Mount McKinley is 20,320 feet high. How much taller is Mount McKinley?
To solve the question we use the formula:
(height of Mt. McKinley)-(height of Mt. Rainier)
plugging the values in the formula and simplifying we obtain:
20320-14410
=5,910 ft

b]</span><span>If Babe Ruth averaged 46 home runs per year, how many home runs did he hit in 12 years?
The total number of home runs in 12 years will be given by:
(Average home runs)*(number of years)
plugging the values and simplifying we obtain:
46</span>×12
=552 home runs

c]<span>What’s the difference between paying $10,000 cash for a car or paying a loan of $200 per month for 60 months?
</span>The difference will be evaluated as follows:
total amount of installments will be:
(monthly payment)×(number of months) 
plugging the values we get:
200×60
=$12000
thus the difference will be:
12000-10000
=2000
thus the difference of paying cash and installment is that when you pay in installments you will end up paying $2000 more.

d]<span>Ken sold $700 worth of digital cameras, $2,394 worth of laptops, and $833 worth of vacuum cleaners. Digital cameras cost $175 each, laptops cost $399 each, and vacuum cleaners cost $119 each. If Ken earns a $35 commission for each sale, how much did he earn in commissions in all?
To solve the question we need to find the number of each item he sold.
Number of items=(total cost of items)/(price per item)
thus:
Number of cameras he sold will be:
700/175
=4 cameras

Number of laptops sold:
2394/399
=6 laptops

Number of vacuum cleaners sold will be:
833/119
=7 vacuum cleaners
thus the total number of items was:
4+6+7=17 items
thus the total commission he received will be:
(commission per item)</span>×(Total number of items)
17×35
=$595

e]<span>A parking garage owner has spaces for 70 cars and charges each driver $6 per day for parking. If the garage is full, how much more would the garage owner make if he charged $8 per day?
To solve the question we proceed as follows:
Amount=(number of cars)</span>×(parking cost)
Total amount received for charging $6 will be:
6×70
=$420
Total amount received for charging $8 will be:
8×70
=$560
the difference will be:
560-420
=$140
This means he made $140 more.

f] <span>Regina has $25 to buy groceries. She needs 3 cans of dog food, a gallon of milk, 5 pounds of chicken, a box of cereal, and 6 rolls of paper towels. The prices of the items are as follows: dog food—$1.50 a can; milk—$4 a gallon; chicken—$1.55 a pound; cereal—$2.75 a box; paper towels—99 cents a roll. Will Regina have enough money for all the items she needs? If not, how much more will she need?
Total cost of the item Regina bought is:
milk=4*1=$4
dog food=3</span>×1.5=$4.5
<span>Chicken=1.55</span>×5=$7.75
<span>cereal=2.75</span>×1=2.75<span>
Paper towels=0.99</span>×6=$5.94
<span>Total amount required for the items:
4+4.5+7.75+2.75+5.94
=$24.94

ii. Conclusion:
Given that Regina has $25, the she has enough cash to buy the items. This is because she has more than she requires for the items.</span>
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Number of 18-years old in the survey:

(We add all  frequency points for each line)

0 + 30 + 20 + 60 + 70 + 40 + 60 + 40 + 0 = 320 students

Number of 18 year old spending between 25 and 35 minutes: 40 + 65 = 105

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2 years ago
For which system of equations is (5, 3) the solution? A. 3x – 2y = 9 3x + 2y = 14 B. x – y = –2 4x – 3y = 11 C. –2x – y = –13 x
Alla [95]
The <u>correct answer</u> is:

D) \left \{ {{2x-y=7} \atop {2x+7y=31}} \right..

Explanation:

We solve each system to find the correct answer.

<u>For A:</u>
\left \{ {{3x-2y=9} \atop {3x+2y=14}} \right.

Since we have the coefficients of both variables the same, we will use <u>elimination </u>to solve this.  

Since the coefficients of y are -2 and 2, we can add the equations to solve, since -2+2=0 and cancels the y variable:
\left \{ {{3x-2y=9} \atop {+(3x+2y=14)}} \right. &#10;\\&#10;\\6x=23

Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6

This is <u>not the x-coordinate</u> of the answer we are looking for, so <u>A is not correct</u>.

<u>For B</u>:
\left \{ {{x-y=-2} \atop {4x-3y=11}} \right.

For this equation, it will be easier to isolate a variable and use <u>substitution</u>, since the coefficient of both x and y in the first equation is 1:
x-y=-2

Add y to both sides:
x-y+y=-2+y
x=-2+y

We now substitute this in place of x in the second equation:
4x-3y=11
4(-2+y)-3y=11

Using the distributive property, we have:
4(-2)+4(y)-3y=11
-8+4y-3y=11

Combining like terms, we have:
-8+y=11

Add 8 to each side:
-8+y+8=11+8
y=19

This is <u>not the y-coordinate</u> of the answer we're looking for, so <u>B is not correct</u>.

<u>For C</u>:
Since the coefficient of x in the second equation is 1, we will use <u>substitution</u> again.

x+2y=-11

To isolate x, subtract 2y from each side:
x+2y-2y=-11-2y
x=-11-2y

Now substitute this in place of x in the first equation:
-2x-y=-13
-2(-11-2y)-y=-13

Using the distributive property, we have:
-2(-11)-2(-2y)-y=-13
22+4y-y=-13

Combining like terms:
22+3y=-13

Subtract 22 from each side:
22+3y-22=-13-22
3y=-35

Divide both sides by 3:
3y/3 = -35/3
y = -35/3

This is <u>not the y-coordinate</u> of the answer we're looking for, so <u>C is not correct</u>.  

<u>For D</u>:
Since the coefficients of x are the same in each equation, we will use <u>elimination</u>.  We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:

\left \{ {{2x-y=7} \atop {-(2x+7y=31)}} \right. &#10;\\&#10;\\-8y=-24

Divide both sides by -8:
-8y/-8 = -24/-8
y=3

The y-coordinate is correct; next we check the x-coordinate  Substitute the value for y into the first equation:
2x-y=7
2x-3=7

Add 3 to each side:
2x-3+3=7+3
2x=10

Divide each side by 2:
2x/2=10/2
x=5

This gives us the x- and y-coordinate we need, so <u>D is the correct answer</u>.
7 0
3 years ago
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