MATHEMATICS HIGH SCHOOL

to multiply a number by 12, Carter likes to multiply the number by 10 and then multiply it by 2 and add the product. Write an expression with parenthesis how carter would solve 12×16

Answers

Answer 1

Answer:

Since carter multiplies by 10 and then by 2 and adds the two, here we have been given 16 * 12

Step 1: Carter would first multiply the number by 10. This would be = 16*10

Step 2: Carter would multiply the number by 2. This would be = 16*2

Step 3: He would add the two. This would be = (16*10) + (16*2)

Carter's solution would be:

=16*12

=(16*10) + (16*2)

= 160 + 32

= 192

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Find the third directional cosine (there are two of them with opposite signs) if it is known that two directional cosines are equal to 1/2 and 1/3

Answers

Answer:

To find the third directional cosine, we need to use the property that the sum of the squares of the directional cosines is equal to 1.

Let's denote the three directional cosines as cosα, cosβ, and cosγ. Given that two directional cosines are equal to 1/2 and 1/3, we can set up the following equations:

cosα = 1/2

cosβ = 1/3

To find cosγ, we can rearrange the equation for the sum of the squares of the directional cosines:

cos²α + cos²β + cos²γ = 1

Substituting the given values, we have:

(1/2)² + (1/3)² + cos²γ = 1

Simplifying the equation, we get:

1/4 + 1/9 + cos²γ = 1

To solve for cos²γ, we can combine the fractions:

(9/36) + (4/36) + cos²γ = 1

(13/36) + cos²γ = 1

Now, we can solve for cos²γ by subtracting 13/36 from both sides:

cos²γ = 1 - 13/36

cos²γ = 23/36

Taking the square root of both sides, we find:

cosγ = √(23/36)

Since we are looking for the third directional cosine, there are two possible solutions, one positive and one negative. So, the third directional cosine can be either √(23/36) or -√(23/36).

In conclusion, the third directional cosine, cosγ, is either √(23/36) or -√(23/36).

A 32 oz bottle of water costs $1.92. What is the cost per ounce?A. $0.53/oz

B. $5.33/oz

C. $0.60/oz

D. $0.06/oz

Answers

Answer:

cost per ounce is 0.06 per ounce

Step-by-step explanation:

A 32 oz bottle of water costs $1.92.

we need to find the cost of one ounce.

To find the cost of 1 ounce , we need to divide the total cost by 32 oz

cost of 1 oz= $(1.92)/(32) =0.06$

0.06 is the unit price

So, the cost per ounce is 0.06 per ounce

Answer is D. As price of 32 oz bottle is $1.92 so to find the price of 1 oz, we will divide $1.92 by 32. 1.92/32 = 0.06 So our answer will be 0.06$ per oz

Madison wants to buy a car for $9000. She will borrow money and repay the total in 3 years. The required monthly payment on her credit card would be $300. The monthly payment for a personal loan would be $278. How much money would Madison save if she chose the personal loan instead of the credit card?

Answers

Madison would save $264 if she chose the personal loan

. Write the equation in slope intercept form for the line that goes through point (−10, 8) with slope =6.

Answers

y = mx + b is slope intercept form

x = -10
y = 8
m = 6

1. Solve for b

8 = (6)(-10) + b
b = 68

2. Plug m and b back into your slope intercept equation

y = 6x + 68

Steve can complete the 100m dash in 10 seconds while Paul can run it in 12 seconds. How does Steve's time compare to Paul's?A. Steve is 5∕6 as fast as Paul
B. Steve is 5∕6 slower than Paul
C. Steve is 1∕2 as fast as Paul
D. Steve is 1∕2 slower than Paul

a survey in which 400 people were asked to identify the TV channel on which they preferred to watch the evening news.

How many more people preferred WWCN with 41% than WANR with 22%?
A. 164
B. 76
C. 236
D. 68

Answers

So, Steve's time in a ratio to Paul's time:

$(Steven's time)/(Pauls's time) = (10)/(12) = (5)/(6) .$ So Steven's time is $(5)/(6)$ times shorter, that is
"Steven is $(5)/(6)$ times faster than Paul (I find the phrasing "as fast as" problematic though)

In the second question 41% of 400, which is 4*41=164 people chose WWCN and 22% chose WANR, that is 22%*400=4*22=88.

And the difference is 76 people! ( 164-88=76)B)

Answer:

Q-1 The correct option is A) Steve is 5∕6 as fast as Paul

Q-2 The correct option is 76.

Step-by-step explanation:

Consider the provided information.

Q-1

Steve can complete the 100m dash in 10 seconds while Paul can run it in 12 seconds.

Since, the distance for both are same,

$\frac{\text{Steve's time}}{\text{Paul's time}}=(10)/(12)=(5)/(6)\n\text{Steve's time}=(5)/(6)\text{ of Paul's time}}$

Hence, Steve's time is 5⁄6 of the time taken by Paul.

Therefore, the correct option is A) Steve is 5∕6 as fast as Paul

Q-2 a survey in which 400 people were asked to identify the TV channel on which they preferred to watch the evening news.

WWCN got 41% and WANR got 22%

For WWCN

41% of 400 is: $(41)/(100) * 400=164$

That means 164 people preferred WWCN.

For WANR

22% of 400 is: $(22)/(100) * 400=88$

That means 88 people preferred WANR.

We need to find how many more people preferred WWCN

For this subtract both the values: 164-88=76

Thus, 76 more people preferred WWCN

Hence, the correct option is 76.

Yves bought 420 tropical fish for a museum display. He bought 6 times as many parrotfish as angelfish. How many of each type of fish did he buy? Which is a system of equations to model the problem if x represents the number of angelfish Yves bought and y represents the number of parrotfish he bought?

A.
x + y = 6
y = 420x

B.
x + 6y = 420
y = 6x

C.
x – y = 420
y = 6x

D.
x + y = 420
y = 6x

Answers

Given:
420 tropical fishes
angel fish = x
parrot fish = 6x

x + y = 420
y = 6x Choice D.

x + y = 420
y = 6x

x + 6x = 420
7x = 420
x = 420 / 7
x = 60 number of angelfish

y = 6x
y = 6(60)
y = 360 number of parrot fish

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A student answered 46 problems on the test correctly and received a grade of 88%. how many problems were on the test if all problems we wear the same number of points?

2y+4=2(y+2) find the y

Can someone please explain each step in solving this?