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3 years ago

How many positive integers not exceeding 1000 are not divisible by either 4 or 6?

1 answer:

7 0

$\left\lfloor\dfrac{1000}4\right\rfloor=250$

$\left\lfloor\dfrac{1000}6\right\rfloor=166$

$\left\lfloor\dfrac{1000}{\mathrm{lcm}(4,6)}\right\rfloor=\left\lfloor\dfrac{1000}{12}\right\rfloor=83$

$250+166-83=333$

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What is the value of the underlined digit

xxMikexx [17]

The value of the underlined digit depends on the place the number that is underlined is. For the first digit, it would be ones. The second digit is 10s. The third is 100s and the fourth is thousands and the fifth is ten thousands and the 6 is hundred thousands, and the seventh is million, and so on.

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3 years ago

Mary, who is sixteen years old, is four times as old as her brother. how old will mary be when she is twice as old as her brothe

mojhsa [17]

Mary is 2x = 2*12 = 24 years old.

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2 years ago

the temperature at noon was -27 degrees . the temperature increased by 13 degrees by 2pm . what was the temperature at 2pm

Aleks [24]

First, you would create an equation for this problem.
-27 + 13

Now, all you would have to do is solve it.
-27 + 13 = -14

By 2 pm the temperature was -14 degrees.

I hope this helps!

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2 years ago

Read 2 more answers

Pleaseeeeeeeeee help meeee I don’t rlly get it

ella [17]

the correct answer is c

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3 years ago

A biologist is studying the growth of a particular species of algae. She writes the fall inclusion to show the radius of the alg

horrorfan [7]

Answer:

Part A)

A reasonable domain to plot the growth function is:

$0\leq d \leq 12$

Part B)

The y-intercept represents that when the biologist started her study, the radius of the algae was five millimeters.

Part C)

The average rate of change from d = 4 to d = 11 was about 0.11. This means that from the 4th day to the 11th, the radius of the algae grew, on average, at a rate of 0.11 mm per day.

Step-by-step explanation:

The radius of the algae f(d) in millimeters after d days is given by the function:

$f(d)=5(1.02)^d$

Part A)

We know that the radius of the algae was approximately 6.34 mm when the biologist concluded her study. To find the reasonable domain, we can substitute 6.34 for f(d) and solve for d. Therefore:

$6.34=5(1.02)^d$

Divide both sides by five:

$(1.02)^d=1.268$

Take the log of both sides with base 1.02:

$\displaystyle d=\log_{1.02}1.268$

Using the Change of Base Property, evaluate for d:

$\displaystyle d=\frac{\log 1.268}{\log 1.02}=11.9903...\approx 12$

So, the biologist concluded her study after 12 days.

Therefore, a reasonable domain to plot the growth function is:

$0\leq d\leq 12$

Part 2)

The y-intercept of the function is when d = 0. Find the y-intercept:

$f(0)=5(1.02)^{(0)}=5(1)=5$

Since d represent the amount of days after the study had begun, the y-intercept represents the radius of the algae on the initial day.

So, when the biologist started her study, the radius of the algae was five millimeters.

Part 3)

To find the average rate of change for a nonlinear function, we find the slope between the two endpoints on the interval.

We want to find the average rate of change of f(d) from d = 4 to d = 11.

Find the endpoints:

$f(4)=5.4121...\text{ and } f(11)=6.2168...$

And find the slope between them:

$\displaystyle m=\frac{f(11)-f(4)}{11-4}=0.1149...\approx 0.11$

Since f(d) measures millimeters and d measures days, this tells us that, on average, the radius of the algae grew by about 0.11 mm per day from the 4th day to the 11th day.

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2 years ago