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garik1379 [7]
3 years ago
9

Which expression correctly represents "twice the sum of four and a number"?

Mathematics
1 answer:
Lesechka [4]3 years ago
7 0

Answer:

2(4+x)

Step-by-step explanation:

"Twice the sum of" tells us it will be the equation times two

"the sum of four and a number" is easy, thats 4 + x

The second number is x because the number is not specified so we need a place holder, x in this case, to tell us that the number is not given.

All this put together = twice the sum of four and a number, or <u>2(4+x)</u>

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Josh and Lucy share some money in the ratio of 3 : 7 they share 84 in total how much money does Josh receive
Ann [662]
27.30 is the answer
7 0
2 years ago
Lenny and Lisa have obtained a 30-year, fixed rate mortgage for $675,250 with a 7.25% interest rate. They purchased 3 points and
Vikentia [17]

Answer:

119 months

Step-by-step explanation:

In this question, we are asked to calculate the amount of time it would take for a break-even point on a mortgage, if there is a factoring in the cost of points.

We proceed to answer the;

Mathematically,

The Break Even Point = Amount Paid for purchasing Discount Points divided by Monthly savings in the interest payments

We lost out the important values given in the question as follows:

Amount of Mortgage - $675,250

Tenure - 30 Years

The Rate of interest without points = 7.25%

The number of points = 3 points

The rate of interest with the 3 points = 6.875%

The amount to be paid for purchasing the discount point is now calculated below;

Since 1 discount point = 1% of mortgage value;

Therefore, 3 discount points = 3% of mortgage value

The amount paid is thus = 3% of $675,250 = $20,257.5

To calculate Monthly payment without points, we use the mathematical formula;

M = P[r(1+r)^n/((1+r)^n)-1)]

Where M

Is monthly payment, r is the interest rate, n is the number of months.

According to the question M = 675,250, r = 7.25% = 7.25/100 = 0.0725 , n= 30 * 12 months = 360 months

M = 675,250[0.0725(0.0725+1)^30/(1+0.0725)^360)-1) = $4606.40

To get the monthly payment with points, we simply use the formula again but this time interest rates will be 6.875% = 0.06875 I.e r = 0.06875

Inputting the terms in the formula will yield a value of $4435.91. This means monthly payment with discount will be $4435.91

Savings in monthly payments after purchasing the discount points = $4,606.40 - $4,435.91 = $170.48

Break Even = Purchase cost of Discount Points / Monthly savings

= $20,257.5 / $170.48

= 119 Months

Hence, the number of months it will take Lisa and Lenny to break-even point on their mortgage will be 119 months

6 0
3 years ago
The SAT is standardized to be normally distributed with a mean µ = 500 and a standard deviation σ = 100. What percentage of SAT
Aliun [14]

Answer:

34.134%

68.268%

Step-by-step explanation:

Given that:

Mean (m) = 500

Standard deviation (s) = 100

Percentage between 500 and 600

P(500 < x < 600)

P(x < 600) - P(x < 500)

Z = (x - m) / s

P(x < 600)

Z = (600 - 500) /100 = 1

P(x < 500)

Z = (500 - 500) / 500 = 0

P(Z< 1) - P(Z < 0)

0.84134 - 0.5

= 0.34134

= 0.34134 * 100%

= 34.134%

B.) Between 400 and 600

P(x < 400)

Z = (400 - 500) /100 = - 1

P(x < 600)

Z = (600 - 500) / 500 = 1

P(Z< 1 ) - P(Z < - 1)

0.84134 - 0.15866

= 0.68268

= 0.68268 * 100%

= 68.268%

8 0
2 years ago
How long will it take for an investment of $2000 to double in value if the interest rate is 7.25%
lesya692 [45]

Answer:

t = ln2/0.075

t = 9.24 years.

hope this helps

3 0
3 years ago
The value of the fraction 3c+2/4 one less than the value of the fraction 5c-1/3.
Viefleur [7K]

Answer:

7/8 > 5/6

Step-by-step explanation:

A) 7/8

We can compare this as follows.

Lets say both are equal.

Cross multiplying these we get 40=42

We get 40<42. In fraction we get

In case if you want to convert this to decimal, we get;

5/6 = 0.833 and 7/8 = 0.875

We get 5/6<7/8

B) 4/5

Similarly we get 4/5 = 0.8 and 5/6 = 0.833

Here 4/5<5/6

C) 3/4

we get 3/4 = 0.75 and 5/6 = 0.833

3/4<5/6

D) 2/3

we get 2/3 = 0.66 and 5/6 = 0.833

2/3<5/6

Step-by-step explanation:

5 0
2 years ago
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