Write 0.0123 in dcientific notation

Which of the following choices is equivalent to the equation below?

mrs_skeptik [129]

Answer:

2x-1 = 5x-14

Step-by-step explanation:

5(2x−1) = 5(5x−14)

Divide each side by 5

5/5(2x−1) = 5/5(5x−14)

2x-1 = 5x-14

7 0

3 years ago

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The Groves basketball team did not record how many baskets were made by each player during the last game. Daniel remembers that

bixtya [17]

Answers:

Ben = 6
Max = 12
Mitchell = 2
Christion = 2
Daniel = 18

Each count above refers to the number of baskets made for the given player.

====================================================

Explanation:

For each player, let the following variables represent how many baskets were made

B = Ben
M = Max
T = Mitchel
C = Christion
D = Daniel

So for example, if D = 10, then this means Daniel made 10 baskets. Though for now, we're not sure what number replaces D or any given letter.

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"Daniel remembers that he made three times as many baskets as Ben" tells us that D = 3B is one equation

We know another equation is M = B+6 since Max made six more baskets than Ben

Another equation is C = T because these two students (Christion and Mitchell) made the same number of baskets.

We also know that T < B since Mitchell made fewer baskets compared to Ben.

Altogether the boys made 40 baskets total, so B+M+T+C+D = 40

-------------------

We have these five mathematical statements

D = 3B
M = B+6
C = T
T < B
B+M+T+C+D = 40

Let's focus on the last equation

B+M+T+C+D = 40

B+M+T+C+3B = 40 .... plug in D = 3B

4B+M+T+C = 40

4B+M+T+T = 40 .... plug in C = T

4B+M+2T = 40

4B+B+6+2T = 40 .... plug in M = B+6

5B+6+2T = 40

5B+2T = 40-6

5B+2T = 34

Now let's solve for T

5B+2T = 34

2T = 34-5B

2T = -5B+34

T = (-5B+34)/2

T = (-5B)/2 + 34/2

T = -2.5B + 17

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We've eliminated everything but two variables at this point.

Let's say that x replaced B and y replaces T

We get the equation y = -2.5x + 17

If you graph this equation along with y = x, you'll find that the two equations intersect at roughly (4.857, 4.857)

Since we want T < B, this means we want y < x to be the case. The line y = -2.5x+17 goes downhill as we move from left to right. If x is smaller than 4.857, then x >= y. Otherwise, if x is larger than 4.857, then y < x

Furthermore, looking at a table of values for this equation shows that only (x,y) = (6,2) is a point on y = -2.5x+17 such that both x and y are positive and x is the larger value, and they are both integer coordinates.

All of this means that when B = 6, this pairs with T = 2. No other number pair is possible for these two students.

We then use this to find the other player's basket count

D = 3B = 3*6 = 18
M = B+6 = 6+6 = 12
C = T = 2

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So we have the following results

B = 6
M = 12
T = 2
C = 2
D = 18

As a check,

B+M+T+C+D = 6+12+2+2+18 = 40

which confirms our answers.

7 0

3 years ago

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A campus program evenly enrolls undergraduate and graduate students. If a random sample of 5 students is selected from the progr

Bezzdna [24]

Answer:

The answer is "0.03125".

Step-by-step explanation:

Two types of undergraduates exist. Its chance for selecting the very first person who is part of degree studies will be 1/2. The probability will also be 1/2 for the 2nd person, as well as, the 3rd, 4th, and 5th person. For 5 random samples, the probability of the graduate therefore is

$\to \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{32}=0.03125$

4 0

3 years ago

The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a norma

kotegsom [21]

Answer:

Test statistic = 3.1587

Step-by-step explanation:

We are given that the Toy-lot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A).

Also, a sample of eleven motors was tested, and it was found that the mean current was x = 1.20 A, with a sample standard deviation of s = 0.42 A.

So, Null Hypothesis, $H_0$ : $\mu$ = 0.8 { claim of 0.8 A is not low}

Alternate Hypothesis, $H_1$ : $\mu$ > 0.8 { claim of 0.8 A is too low}

Now, the test statistics used here will be;

T.S. = $\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, X bar = sample mean = 1.20 A

s = sample standard deviation = 0.42 A

n = sample size = 11 motors

So, Test statistics = $\frac{1.20 - 0.8}{\frac{0.42}{\sqrt{11} } }$ ~ $t_1_0$

= 3.1587

At 1% level of significance, t table gives a critical value of 2.764 at 10 degree of freedom. Since our test statistics is higher than the critical value so we have sufficient evidence to reject null hypothesis .

Therefore, we conclude that Toy-lot claim of 0.8 A is too low.

8 0

4 years ago

3x^3(4x^4)=?<br> i need this plz

sladkih [1.3K]

Answer:

$12 x^{7}$

Step-by-step explanation:

3 0

3 years ago

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