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3 years ago

What must be true about two integers thst combine to equal zero?

Mathematics

1 answer:

katrin2010 [14]3 years ago

3 0

Answer:

If two integers combine to equal 0, they are additive inverses of each other

Step-by-step explanation:

A is the additive inverse of B

B is the additive inverse of A

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If the ratio of the length to the breadth of a rectangle be 5:3 and its perimeter is 144m find the length of the rectangle

Kamila [148]

Answer:

length=45 m (2 sides = 90m)

Step-by-step explanation:

5x +3x=144

8x=144

x=18 (each of the 8 parts of 144 measure 18m)

5(18) + 3(18)=144

90 +54=144

90/2=45 (1 length side)

54/2=27 (1 width side)

The rectangle= 45+45 +27+27 = 144

5 0

3 years ago

A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A ran

mart [117]

Answer:

a) The 95% confidence interval would be given (0.070;0.121).

b) "increase the sample size n"

"decrease za/2 by decreasing the confidence"

Step-by-step explanation:

Notation and definitions

$X=48$ number of vehicles classified as sports utility.

$n=500$ random sample taken

$\hat p=\frac{48}{500}=0.096$ estimated proportion of vehicles classified as sports utility vehicles.

$p$ true population proportion of vehicles classified as sports utility vehicles.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

(a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your answers to three decimal places.)

The confidence interval would be given by this formula :

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.5=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.096 - 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.070$

$0.096 + 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.121$

And the 95% confidence interval would be given (0.070;0.121).

We are confident (95%) that about 7.0% to 12.1% of vehicles in California are classified as sports utility .

(b) How can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy? (HINT: There are two answers. Select all that apply.)

For this case we just have two ways to increase the accuracy one is "increase the sample size n" since if we have a larger sample size the estimation would be more accurate. And the other possibility is "decrease za/2 by decreasing the confidence" because if we decrease the confidence level the interval would be narrower and accurate

7 0

3 years ago

Is this set of numbers a Pythagorean triple? yes or no

Kaylis [27]

Answer:- No.

Explanation :-

Substitute these numbers in pythagoras theorem to check if the set of numbers is a pythagorean triplet.

Pythagoras theorem :- sq. of hypotenuse (longest side) is equal to the sum of sq.s of other two sides.

Here,

hypotenuse = 12 (as it is the longest side)

and other two sides are 6 and 9.

----> 6^2 + 9^2 = 12^2

----> 36 + 81 = 144

----> 117 = 144

Since, LHS is not equal to RHS, this set of numbers is not a pythagorean triplet.

8 0

3 years ago

Help............................

Lyrx [107]

Answer: convex

Step-by-step explanation:A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon. Equivalently, it is a simple polygon whose interior is a convex set.

8 0

3 years ago

John works as a tutor for an hour and as a waiter for an hour. This month, he worked a combined total of hours at his two jobs.

liberstina [14]

Correct Question:

John works as a tutor for $12 an hour and as a waiter for $8 an hour. This month, he worked a combined total of 86 hours at his two jobs.

Let be the number of hours John worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.

Answer:

Total hours = 86

Let t is the hours he spent on tutoring

then (86-t) is hours spent on waiting

Let Y is the total amount in dollars which is required .

Now;

y = (tutoring hours x 12$) + (waiting hours x 8$)

Y = 12t + 8(86-t)

6 0

3 years ago