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Mathematics College

Bernard weighs 7.5 pounds at birth. assuming his development proceeds normally, he should weigh about _____ pounds by his first birthday. 22.5 24.5 20.5 18.5

2 months ago

Solution 1

Guest #4815

2 months ago

Given Bernard weighs 7.5 pounds at birth.The question is asking us to assume that Bernard development proceeds normally.We need to find Bernard birth after a year.

It is observed that birth of a child triples or is thrice (3 times ) the weight at birth.As Bernard is weighing 7.5 pounds so he will triple or be 3times of this weight.

Bernard weight after a year= 3x7.5=22.5 pounds.

Solution 2

Guest #4816

2 months ago

25 i sthe answer to your ridiculous question

📚 Related Questions

Question

If the perimeter of a rectangle is 52 cm and the area is 165 square cm, then what are the dimensions of the rectangle?

Solution 1

Answer:

11 cm by 15 cm

Step-by-step explanation:

The perimeter is double the sum of length and width, so that sum is 26 cm. The area is the product of length and width, so you want to find two numbers whose product is 165 and whose sum is 26.

165 = 1·165 = 3·55 = 5·33 = 11·15

The numbers in the last factor pair total 26. These are the dimensions.

The dimensions are 11 cm by 15 cm.

Question

Assuming boys and girls are equally likely, find the probability of a couple having a baby boy boy when their fourth fourth child is born, given that the first three three children were all boys all boys.

Solution 1

I am assuming the gender of each child is independent of the other.

Then the information about the first three children is irrelevant.

So then the probability of fourth child being boy is 1/2, since boys and girls are equally likely.

Hope this helps.

Question

A tank initially contains 40 ounces of salt mixed in 100 gallons of water. a solution containing 4 oz of salt per gallon is then pumped into the tank at a rate of 5 gal/min. the stirred mixture flows out of the tank at the same rate. how much salt is in the tank after 20 minutes ?

Solution 1

The amount of salt that is in the tank after 20 minutes is;

A(20) = 267.56 Oz

We are given;

Initial amount of salt in tank; A(0) = 40 Ounces

A solution containing 4 oz salt per gallon is pumped into the tank at a rate of 5 gal/min.

This means rate in oz/min = 4/1 × 5/1 = 20 oz/min

Now, the rate at which the initial amount in the tank changes will be;

A'(t) = 20 - [(A(t)/(100)) × 5/1]

A'(t) = 20 - A(t)/20

Rearranging gives;

A'(t) + A(t)/20 = 20

Since this is a linear equation, the integrating factor will be; $e^{t/20}$

Multiplying through by the integrating factor gives;

A'(t) $e^{t/20}$ + (A(t)/20) $e^{t/20}$ = 20 $e^{t/20}$

Thus, the solution will be;

A(t) $e^{t/20}$ = 400 $e^{t/20}$ + C

Divide through by $e^{t/20}$ to get;

A(t) = 400 + C $e^{-t/20}$

At initial condition of A(0) = 40, we have;

40 = 400 + C

C = -360

Thus; at time (t), the amount of salt left is given by;

A(t) = 400 - 360 $e^{-t/20}$

After 20 minutes;

A(20) = 400 - 360 $e^{-20/20}$

A(20) = 400 - 132.44

A(20) = 267.56 Oz

Read more at; brainly.com/question/17003995

Solution 2

Let $A(t)$ be the amount of salt in the tank at time $t$ . We're given that $A(0)=40$ . The rate at which this amount changes is given by

$A'(t)=\dfrac{5\text{ gal}}{1\text{ min}}\cdot\dfrac{4\text{ oz}}{1\text{ gal}}-\dfrac{5\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ oz}}{100+(5-5)t\text{ gal}}$

$A'(t)+\dfrac{A(t)}{20}=20$

$e^{t/20}A'(t)+e^{t/20}\dfrac{A(t)}{20}=20e^{t/20}$

$\bigg(e^{t/20}A(t)\bigg)'=20e^{t/20}$

$e^{t/20}A(t)=400e^{t/20}+C$

$A(t)=400+Ce^{-t/20}$

Since $A(0)=40$ , we get

$40=400+C\implies C=-360$

so that the amount of salt at time $t$ is

$A(t)=400-360e^{-t/20}$

After 20 minutes, the tank contains

$A(20)=400-360e^{-20/20}\approx267.56\text{ oz}$

Question

The life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. what is the probability that a battery you buy lasts at most 100 hours? standardize the variable. x = 100 is equivalent to z =

Solution 1

We have been given that

mean, $\mu = 128$

standard deviation $\sigma = 16$

$x=100$

Let us evaluate the z score using the below mentioned formula

$z=\frac{x-\mu}{\sigma}$

On substituting the given values, we get

$z=\frac{100-128}{16} \\
\\
z=-1.75$

Thus, the value of z is -1.75.

Now, we find the probability that a battery you buy lasts at most 100 hours.

We will find the value for z= -1.75 using the z score table.

$P(z=-1.75)= .04006$

Hence, the required probability is 0.04006

Solution 2

-1.75 is the answer.

Question

The population standard deviation of the numbers 3, 8, 12, 17, and 25 is 7.563 correct to 3 decimal places. what happens if each of the five numbers is multiplied by 3

Solution 1

Let's figure this out as though we have no idea what the answer would be.

Step One
Find the new five numbers.
3*3, 8*3, 12*3, 17*3, 25*3
9 , 24 , 36, 51, 75

Step 2
Find the average
(9 + 24 + 36 + 51 + 75)/5 = 195/5 = 39

Step 3
Subtract the individual numbers from the average
(39 - 9) = 30
(39 -24) = 15
(39 - 36) = 3
(39 - 51) = - 12
(39 - 75) = -36

Step 4
Square the results from Step 3
30^2 = 900
15^2 = 225
3^2 = 9
(-12)^2 = 144
(-36)^2 = 1296

Step 5
Take the average of the results from step 4
(900 + 225 + 9 + 144 + 1296)/5
2574 / 5 = 514.8

Step 6
Take the square root of the result from step 5
deviation = sqrt(514.8)
deviation = 22.689

Step seven
Compare the two standard deviations.
s2/s1 = 22.689 / 7.563 = 3

Conclusion
If you are given 1 set of numbers to find a population standard deviation and you multiply each member by a, then the result will be a * the standard population deviation of the first set of numbers.

Note
Your calculator will do this as well, but you have to know how to enter the data into your calculator. That requires that you follow the directions carefully.

Question

Identify all of the root(s) of g(x) = (x2 + 3x - 4)(x2 - 4x + 29)

Solution 1

Answer:

x=-4,1,2+5i,2-5i

Step-by-step explanation:

Given is an algebraic expression g(x) as product of two functions.

Hence solutions will be the combined solutions of two quadratic products

$g(x) = (x^2 + 3x - 4)(x^2 - 4x + 29)\\$

I expression can be factorised as

$(x+4)(x-1)$

Hence one set of solutions are

x=-4,1

Next quadratic we cannot factorize

and hence use formulae

$x=\frac{4+/-\sqrt{16-116} }{2} =2+5i, 2-5i$

Solution 2

Answer:

The answer above is correct:

B. 1

C. 4

E. 2+5i

F. 2-5i

Step-by-step explanation:

I got this right on Edg. 2021

Question

Suppose that the demand equation for a certain item is 1p+1x2−160=0. evaluate the elasticity at 65:

Solution 1

The required value of elasticity at x = 65 is -0.007.

Given that,

The demand equation for a certain item is $1p + 1x^{2} -160 = 0$ .

We have to determine,

The value of elasticity at 65.

According to the question,

The price elasticity of demand is calculated as the percentage change in quantity divided by the percentage change in price.

Therefore,

Price of elasticity = $\frac{dp}{dx}$

Calculate change by differentiation with respect to p:

$\dfrac{d(p+x^{2} -160)}{dx}\\\\1 + 2x\frac{dp}{dx} = 0\\$

Then,

$E(x) = \frac{dp}{dx} = \frac{-1}{2x}$

Therefore, The elasticity at x = 65 is ,

$E(65) = \frac{-1}{2(65)} = -0.007$

Hence, The required value of elasticity at x = 65 is -0.007.

For more information about Elasticity click the link given below.

brainly.com/question/14547451

Solution 2

Price elasticity is defined as $\frac{\Delta(quantity)}{\Delta(price)}$ .

Here, the question has omitted to define variables, so we will ASSUME
p=price
x=variable,
and we're given
p+x^2-160=0

We calculate
$\delta{x}/\delta{p}$ by implicit differentiation with respect to p:
1+2x (dx/dp)=0
=>
E(x)=(dx/dp)=-1/(2x)

Therefore the price elasticity at x=65 is
E(65)=1/(2*65) =-1/130 (approximately -0.00769)

Question

Number of per month__number of moviegoers more than 7____________96 5-7_______________ ___180 2-4__________________219 less than 2____________205 total _________________700 Use the frequency table. Find the probability that a person goes to the movies at least 2 times a month. Round to the nearest thousandth. A. 0.138 B. 0.707 C. 0.137 D. 0.394 sorry for the poor graph up top,,,,:/

Solution 1

Answer:

B. 0.707

Step-by-step explanation:

The frequency table is given by,

Number of months Number of movie goers

More than 7 96

5 - 7 180

2 - 4 219

Less than 2 205

Total 700

Since, Probability of an event is the ratio of favorable events to the total number of events.

As, the number of people going to movies atleast 2 times a month = 96 + 180 + 219 = 495

The probability that a person goes to the movies atleast 2 times a month = $\frac{495}{700}=0.707$ .

Thus, option B is correct.

Solution 2

Leave out those who went less than twice to get those who went at least twice
pr = (700 - 205)/700 = 0.7071 <-------

So answer is B

Question

Without doing any computation, decide which has a higher probability, assuming each sample is from a population that is normally distributed with mu equals100 and sigma equals 15. explain your reasoning. (a) p(90less than or equals x overbarless than or equals110) for a random sample of size nequals 10 (b) p(90less than or equals x overbarless than or equals110) for a random sample of size nequals 20

Solution 1

A has a higher probability bcecause its distributation is larger in magnitude

Question

Solve for y in terms of x. 2/3y - 4 = x Please help . Time is critical for me in school rn

Solution 1

Answer:

$y=\frac{3}{2}(x+4)$

Step-by-step explanation:

We are given

$\frac{2}{3}y-4=x$

Since, we have to solve for y

so, we will isolate y on anyone side

Firstly, we add both sides by 4

$\frac{2}{3}y-4+4=x+4$

$\frac{2}{3}y=x+4$

Multiply both sides by 3

$3\times \frac{2}{3}y=3\times(x+4)$

$2y=3\times(x+4)$

now, we can divide both sides by 2

and we get

$y=\frac{3}{2}(x+4)$

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