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3 years ago

What is the process to find the product of 6x107 for 5th grade

1 answer:

7 0

Line it up vertically...
107
 6

...then multiply 7 by 6, and carry the 4:
107
 6
 2

Then multiply the 0 by 6 and add the carried 4 to the product of the 0 and 6:
107
 6
 42

Then multiply 1 by 6:
107
 6
642

You might be interested in

Jane and Sammie are making decisions about their bank accounts. Jane wants to deposit

prisoha [69]

Answer:

Sammie

Step-by-step explanation:

Jane

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 550.00(1 + 0.05/4)(4)(10)

A = 550.00(1 + 0.0125)(40)

A = $903.99

Sammie

First, convert R as a percent to r as a decimal

r = R/100

r = 7/100

r = 0.07 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 550.00(1 + 0.07/12)(12)(10)

A = 550.00(1 + 0.005833333)(120)

A = $1,105.31

3 0

3 years ago

A survey reported that 5% of Americans are afraid of being alone in a house at night. If a random sample of 20 Americans is sele

liq [111]

Answer:

5.96% probability that exactly 3 people in the sample are afraid of being alone at night.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they are afraid of being alone at night, or they are not. The probability of a person being afraid of being alone at night is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

5% of Americans are afraid of being alone in a house at night.

This means that $p = 0.05$

If a random sample of 20 Americans is selected, what is the probability that exactly 3 people in the sample are afraid of being alone at night.

This is P(X = 3) when n = 20. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596$

5.96% probability that exactly 3 people in the sample are afraid of being alone at night.

5 0

3 years ago

Which shows all the critical points for the inequality x2-4/x2-5x+6<0

Hoochie [10]

Answer:

x = ±2, 3 are the critical points of the given inequality.

Step-by-step explanation:

The given inequality is $\frac{(x^{2}- 4)}{x^{2}-5x+6}$

To find the critical points we will equate the numerator and denominator of the inequality to zero.

For numerator,

$x^{2}-4=0$

(x - 2)(x + 2) = 0

x = ±2

For denominator,

x² - 5x + 6 = 0

x² - 3x -2x + 6 = 0

x(x - 3) -2(x - 3) = 0

(x - 3)(x - 2) = 0

x = 2, 3

Therefore, critical points of the inequality are x = ±2, 3 where the sign of the inequality will change.

7 0

3 years ago

Two children, Ferdinand and Isabella, are playing with a water hose on a sunny summer day. Isabella is holding the hose in her h

wolverine [178]

Answer:

f = 0.84 or 84%

Step-by-step explanation:

Given:

- Original constant velocity of water v_o = 3.5 m/s

- The original diameter of the hose opening d_o = 1.5 cm

- The total vertical distance y(f) = 1.0 m

- The total range x(f) = 10.0 m

Find:

What fraction of the original area does Isabella has to reduce or pinch so the water can cover the entire range.

Solution:

- We will assume the flow of water as a stream of particles that follow a path of single point.

- Using second kinematic equation in the vertical direction and compute the time it takes the water to reach the ground:

y(t) = y(0) + v_y*t + 0.5*gt^2

Where, y(0) = v_y = 0,

1.0 = 0.5*g*t^2

t = sqrt ( 2*1 / 9.81 )

t = 0.4515 s

- Now we will use the second equation of motion for the x- direction motion:

x(t) = x(0) + v_x*t

Where, x(0) = 0,

10 = 0 + v_x*(0.4515)

v_x = 10 / 0.4515 = 22.1 m/s

- We have calculated the minimum velocity required to reach the range from isabella and ferdinand.

- We will use the continuity equation to compute the area required for the velocity calculated v_x = 22.1 m/s:

A_f*v_x = A_o*v_o

A_f = A_o*v_o / v_x

A_f = pi*0.015^2*3.5 / 4*22.1

A_f = 1.12 * 10^-4 m^2

- The fraction f of the reduction of area is:

f = (A_o - A_f) / A_o

f = (7.068*10^-8 - 1.12*10^-4) / (7.068*10^-8)

f = 0.84 or 84%

4 0

3 years ago

A poker hand consisting of 9 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactl

Andrew [12]

Answer: $\dfrac{^{12}C_{6}\times^{40}C_3}{^{52}C_9}$ or $\dfrac{228}{91885}$ .

Step-by-step explanation:

Given : A poker hand consisting of 9 cards is dealt from a standard deck of 52 cards.

The total number of cards in a deck 52

Number of faces cards in a deck = 12

Number of cards not face cards = 40

The total number of combinations of drawing 9 cards out of 52 cards = $^{52}C_9$

Now , the combination of 9 cards such that exactly 6 of them are face cards = $^{12}C_{6}\times^{40}C_3$

Now , the probability that the hand contains exactly 6 face cards will be :-

$\dfrac{^{12}C_{6}\times^{40}C_3}{^{52}C_9}$

$=\dfrac{\dfrac{12!}{6!6!}\times\dfrac{40!}{3!37!}}{\dfrac{52!}{9!\times43!}}\ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{228}{91885}$

Hence, the probability that the hand contains exactly 6 face cards. is $\dfrac{228}{91885}$ .

6 0

3 years ago