A boy weighs 22.5 kilograms. How much does he weigh in pounds? Use the following conversion: 1 kilogram is 2.2 pounds.

A $5000 principal is invested in two accounts, one earning 1% interest and the another earning 6% interest. If the total interes

algol [13]

Answer: in the 1% account we have $2600 and in the 6% account we have $2400.

Step-by-step explanation:

We have two amounts A and B such that:

Where A is the amount invested in the 1% earning interest account and B is the amount invested in the 6% earning interest account.

A + B = $5000,

If the interest is yearly, then we have that, after one year, the interest is:

A*(1%/100%) + B*(6%/100%) = $170

A*0.01 + B*0.06 = $170

So we have two equations:

A + B = $5000

A*0.01 + B*0.06 = $170

In the first equation we can isolate A and get:

A = $5000 - B

and replace it in the other equation:

($5000 - B)*0.01 + B*0.06 = $170

$50 + B*0.05 = $170

B*0.05 = $120

B = $120/0.05 = $2400

Then A = $5000 - $2400 = $2600.

4 0

3 years ago

Can someone explain this to me

Hatshy [7]

6+7+3 =16
7+9+7 =23
9+6+7=22
6+8+1=15

6 0

3 years ago

If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight au

Marta_Voda [28]

Answer:

$P(X \geq 7) = P(X=7) +P(X=8)$

And we can find the individual probabilities using the probability mass function

$P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826$

$P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305$

And replacing we got:

$P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:

$X \sim Binom(n=8, p=0.9)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And for this case we want to find this probability:

$P(X \geq 7) = P(X=7) +P(X=8)$

And we can find the individual probabilities using the probability mass function

$P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826$

$P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305$

And replacing we got:

$P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131$

7 0

4 years ago

Read 2 more answers

What is the simplified value of the expression below

viktelen [127]

Answer:

Step-by-step explanation:

Combine like terms and then solve for X

24-12-2x3.2

12 -0.4x^3

8 0

3 years ago

X2 2 ab ab to b The diagian K n shows rectangle. The shade Find x.

Norma-Jean [14]

Answer:

x = 28 cm

Step-by-step explanation:

Given:

Area of link shaded regions = 84 cm²

Required:

The value of x (diameter of the semicircle/length of the rectangle)

Solution:

Diameter of the semicircle = 2r = x

Length of rectangle (L) = 2r = x

Radius of semicircle (r) = ½x

Width of rectangle (W) = radius of semicircle = ½x

Use 3.14 as π

Area of the link shaded regions = area of rectangle - area of semicircle

Thus:

Area of the link shaded regions = (L*W) - (½*πr²)

Plug in the values

84 = (x*½x) - (½*3.14*(½x)²)

84 = x²/2 - (1.57*x²/4)

84 = x²(½ - 1.57/4)

84 = x²(0.5 - 0.3925)

84 = x²(0.1075)

Divide both sides by 0.1075

84/0.1075 = x²

781.4 = x²

√781.4 = x

27.9535329 = x

x = 28 cm

5 0

3 years ago