MATHEMATICS COLLEGE

Is the product of opposites always 1

Answers

Answer 1

Answer:

Answer:

yes

Step-by-step explanation:

hope it helps!

Answer 2

Answer:

Answer:

Yes, the product of a number and its opposite is always 1, and the opposite of a negative number is always a positive number.

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Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 139 millimeters, and a variance of 49. If a random sample of 34 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 1.8 millimeters

Answers

The probability that the sample mean would differ from the population mean by more than 1.8 millimeters is approximately 0.0668.

What is the standard deviation?

A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.

The standard deviation of the population is $√(49) = 7$ millimeters. The standard error of the sample mean is then

$(7)/(√(34)) = (7)/(5.874) \approx 1.2$ millimeters.

The probability that the sample mean would differ from the population mean by more than 1.8 millimeters is the probability that it falls outside of the interval $(139 - 1.8, 139 + 1.8)$ . We can use the standard normal distribution to approximate this probability.

First, we need to convert the difference between the sample mean and the population means to standard units.

The difference of 1.8 millimeters is :

$(1.8)/(1.2) = 1.5$ standard units.

Then, we can use the standard normal distribution to find the probability that the sample mean falls outside of this interval.

This probability is equal to $1 - 2\Phi(-1.5) \approx 0.0668$ ,

where $\Phi$ is the standard normal cumulative distribution function.

Therefore, the required probability is approximately 0.0668.

Learn more about the standard deviation here:

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Can you help me to do this please?Determine the inverse of the h(x)

Answers

Answer:

$h^(-1)(x)=x^3+6x^2+12x+7$

Explanation:

Given the below function;

$h(x)=\sqrt[3]{x+1}-2$

We'll follow the below steps to determine the inverse of the above function;

Step 1: Replace h(x) with y;

$y=\sqrt[3]{x+1}-2$

Step 2: Switch x and y;

$x=\sqrt[3]{y+1}-2$

Step 3: Solve for y by first adding 2 to both sides;

$\begin{gathered} x+2=\sqrt[3]{y+1}-2+2 \n x+2=\sqrt[3]{y+1} \end{gathered}$

Step 4: Take the cube of both sides;

$\begin{gathered} (x+2)^3=(\sqrt[3]{y+1})^3 \n (x+2)^3=y+1 \end{gathered}$

Step 5: Expand the cube power;

Recall;

$(a+b)^3=a^3+3a^2b+3ab^2+b^3$

Applying the above, we'll have;

$\begin{gathered} (x+2)^3=y+1 \n x^3+3x^2\cdot2+3x\cdot2^2+2^3=y+1 \n x^3+6x^2+12x+8=y+1 \end{gathered}$

Step 6: Subtract 1 from both sides of the equation;

$\begin{gathered} x^3+6x^2+12x+8-1=y+1-1 \n x^3+6x^2+12x+7=y \n \therefore y=x^3+6x^2+12x+7 \end{gathered}$

Step 7: Replace y with h^-1(x);

$h^(-1)(x)=x^3+6x^2+12x+7$

What is the measure of ∠M?A.
53°

B.
65°

C.
81°

D.
98°

Answers

The shape is a quadrilateral, because it has four sides.

And sum of angles in a quadrilateral = 360 degrees.

The angle with no number but just a symbol = 90 degrees.

From the fourth angle been M:

Therefore: 90 + 62 + 127 + M = 360

279 + M = 360

M = 360 - 279

M = 81

M = 81°

Option C.

I hope this explains it.

Daniel's mom deposits $80 into his savings account for the year. Daniel decides to upgrade his game account which costs $7 per month. How many months will Daniel be able to pay for his game account if his mom doesn't deposit any more money into his savings account?

Answers

Answer:

11.43

Step-by-step explanation:

80÷7= 11.428571428571428571428571428571

i hope this helps

The population of bacteria M after X minutes is represented by the function M(x)=51(1.03)^x.whqt is the approximate difference between the populations after 3 minutes

Answers

The difference between the populations after 3 minutes is 5.

Population of bacteria

According to the question, the population of bacteria is modeled by the function; $M(x)=51(1.03)^x$ . We have to recall that x refers to the time taken to have an M number of bacteria.

Initially, x = 0 so;

$M(x)=51(1.03)^0$ = 51

After 3 minutes, we have;

$M(x)=51(1.03)^3$ = 56

Difference between the populations after 3 minutes = 56 - 51 = 5

Hence, the difference between the populations after 3 minutes is 5.

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A community pool office two types of memberships monthly and annual memberships. At the beginning of the year the ratio of monthly annual memberships is 10 to 3. However the pool offered an incentive to have members move the annual membership. After the incentive the ratio is 5 to 8. If there are 50 monthly members after the incentive and how many monthly members were there before?

Answers

Answer:

The number of monthly memberships before the incentive was 100

Step-by-step explanation:

Remember that

The total memberships after the incentive is equal to the total memberships before the incentive

step 1

Find out the annual memberships after the incentive

Let

x -----> monthly memberships after the incentive

y -----> annual memberships after the incentive

we know that

-----> equation A

substitute the value of x in equation A

step 2

Find out the total memberships after the incentive

step 3

Find out the monthly members before the incentive

Let

x -----> monthly memberships before the incentive

y -----> annual memberships before the incentive

we know that

-----> equation A

-----> equation B

substitute equation A in equation B and solve for x

therefore

The number of monthly memberships before the incentive was 100

Final answer:

Initially, there were 100 monthly members at the community pool, before the incentives were offered.

Explanation:

We start with the information that the ratio of monthly to annual memberships was initially 10 to 3, and then became 5 to 8. After the incentive, we're told there are now 50 monthly members.

To solve this problem, we set up a proportion. Since each part of the new ratio equals 10 members (50 monthly members/5 parts = 10 members per part), we can infer that before the incentive there were 10*10=100 monthly members.

Learn more about Proportions here:

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