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3 years ago

Express 75 as a product of its prime factors

Mathematics

2 answers:

uranmaximum [27]3 years ago

6 0

Answer:

Step-by-step explanation:

The prime factor of the product 75:

Factors of 75

1,3, 5, 15, 25, 75

or for the prime factorization of 75

3 x 5 x 5, which can also be written 75 = 3 x 5².

Hope this help :)

Lena [83]3 years ago

6 0

Answer:

3 × 5 × 5

I hope this helps!

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A dog breeder would like to know how many Dalmatian puppies are typically born in a litter. He conducts some research and select

podryga [215]

Answer:

c. 6.2 ± 2.626(0.21)

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 101 - 1 = 100

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 100 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$ . So we have T = 2.626

The confidence interval is:

$\overline{x} \pm M$

In which $\overline{x}$ is the sample mean while M is the margin of error.

The distribution of the number of puppies born per litter was skewed left with a mean of 6.2 puppies born per litter.

This means that $\overline{x} = 6.2$

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.626\frac{2.1}{\sqrt{101}} = 2.626(0.21)$

In which s is the standard deviation of the sample and n is the size of the sample.

Thus, the confidence interval is:

$\overline{x} \pm M = 6.2 \pm 2.626(0.21)$

And the correct answer is given by option c.

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3 years ago

What should you do first in order to reconcile your checkbook register?

Anarel [89]

First, you need to have your bank statement and your check register.

Then, compare all your deposits from your checkbook register to your bank statement credits to determine the amount of deposit not yet credited by the bank, which is called your Deposit in Transit.

Next, compare all your disbursements from your checkbook register to all the debits in your bank statement to determine the amount of disbursements not yet debited by the bank.

Also, you need to check for any bank charges already debited to your bank account but not yet recorded.

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3 years ago

The line perpendicular to y= (-3/2)x -4 and goes through (1,4)

Paladinen [302]

Answer <u>(assuming it is allowed to be in point-slope format)</u>:

$y-4 = \frac{2}{3}(x-1)$

Step-by-step explanation:

1) First, determine the slope. We know it has to be perpendicular to the given equation, $y = -\frac{3}{2} x-4$ . That equation is already in slope-intercept form, or y = mx + b format, in which m represents the slope. Since $-\frac{3}{2}$ is in place of the m in the equation, that must be the slope of the given line.

Slopes that are perpendicular are opposite reciprocals of each other (they have different signs, and the denominators and numerators switch places). Thus, the slope of the new line must be $\frac{2}{3}$ .

2) Now, use the point-slope formula, $y-y_1 = m (x-x_1)$ to write the new equation with the given information. Substitute $m$ , $x_1$ , and $y_1$ for real values.

The $m$ represents the slope, so substitute $\frac{2}{3}$ in its place. The $x_1$ and $y_1$ represent the x and y values of a point the line intersects. Since the point crosses (1,4), substitute 1 for $x_1$ and 4 for $y_1$ . This gives the following equation and answer:

$y-4 = \frac{2}{3}(x-1)$

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3 years ago

Solve 12x-5>-2 please

Stells [14]

Answer:

$x > \frac{1}{4}$

Step-by-step explanation:

$12x - 5 > - 2$

Lets add +5 in both the sides.

$= > 12x - 5 + 5 > - 2 + 5$

$= > 12x > 3$

Now lets divide 12 on both the sides.

$= > \frac{12x}{12} > \frac{3}{12}$

$= > x > \frac{1}{4}$

8 0

3 years ago

let a,b,c,d be four integers (not necessarily distinct) in the set {1,2,3,4,5}. the no. of polynomials x^4+ax^3+bx^2+cx+d which

Eddi Din [679]

By either long or synthetic division, it's easy to show that

$\dfrac{x^4+ax^3+bx^2+cx+d}{x+1}=x^3+(a-1)x^2+(-a+b+1)x+(a-b+c-1)-\dfrac{a-b+c-d-1}{x+1}$

The quartic will be exactly divisible by $x+1$ when the numerator of the remainder term vanishes, or for those values of $a,b,c,d$ such that

$a-b+c-d-1=0$

I'm not sure how to count the number of solutions (software tells me it should be 80), but hopefully this is a helpful push in the right direction.

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3 years ago

Express 75 as a product of its prime factors ​

Express 75 as a product of its prime factors