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iVinArrow [24]
2 years ago
7

Frank has a 2-digit number on his baseball uniform. The number is a multiple of 10 and has 3 for one its factors. What three num

bers could Frank have on his uniform?
a. What do you need to find?
b. What information do you need to use?
c. How can you solve the problem?
d. Complete the sentence. Frank has a __________ his uniform. The number is a multiple of ____________ One factor of the number is ____________ Frank could have ____,____, or _____ on his uniform.
Mathematics
1 answer:
umka2103 [35]2 years ago
6 0
2 digits number

x <100   because 2digit

x/10  ∈ { 1, 2, 3, 4, 5, 6, 7, 8, 9}

x/3  ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9 }

max number divide by 10 is 90
max number divided by 3 is 99

because we know that numer is divided by 10 so our collections looks like:

{10, 20, 30, 40, 50, 60, 70, 80, 90}

we look from this collections only numbers witch will divided by 3:

30, 60, 90 = this is solutions

a) we need a natural number divided by 3 and 10 lower than 100
b) i need to use lenght of number and what numbers divides them
c) as above
d) baseball, 3 and 10, 3, 30,60,90





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Kayson mixes 300300300 milliliters (\text{mL})(mL)left parenthesis, start text, m, L, end text, right parenthesis of spinach, 20
Georgia [21]

Answer:

Total, T = (300s+200b+42d) mg

Step-by-step explanation:

Given that,

Kayson mixes 300 mL spinach, 200 mL of berries, and 42 mL of dressing to make a salad.

There are s mg of vitamin C per mL of spinach, b mg per mL of berries, and d mg per mL of dressing.

In 300 mL of spinach vitamin C is = (300 s)mg

In 200 mL of berries vitamin C is = (200 b)mg

In 42 mL of salad vitamin C is = (42 d)mg

It means that, total mg of vitamin C is :

Total, T = (300s+200b+42d) mg

Hence, this is the required solution.

4 0
2 years ago
The equation h(t) = -16t² + 80t + 64 represented the height, in feet, of a potato t seconds after it has been launched.
Lyrx [107]

Answer:

Part A) The potato hit the ground at t=5.70 seconds (see the explanation)

Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

we have

h(t)=-16t^2+80t+64

where

h(t) is the height of a potato in feet

t is the time in seconds

Part A)  Write an equation that can be solved to find when the potato hits the ground. Then solve the equation

we know that

When the potato hit the ground, the value of h(t) must be equal to zero

so

For h(t)=0

-16t^2+80t+64=0

Solve the quadratic equation

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-16t^2+80t+64=0

so

a=-16\\b=80\\c=64

substitute in the formula

t=\frac{-80\pm\sqrt{80^{2}-4(-16)(64)}} {2(-16)}

t=\frac{-80\pm\sqrt{10,496}} {-32}

t=\frac{-80+\sqrt{10,496}} {-32}=-0.70

t=\frac{-80-\sqrt{10,496}} {-32}=5.70

therefore

The potato hit the ground at t=5.70 seconds

Part B) Write an equation that can be solved to find when the potato is 40 feet off the ground. Then solve the equation

For h(t)=40 ft

substitute in the quadratic equation

-16t^2+80t+64=40

-16t^2+80t+24=0

Solve the quadratic equation

we have

a=-16\\b=80\\c=24

substitute in the formula

t=\frac{-80\pm\sqrt{80^{2}-4(-16)(24)}} {2(-16)}

t=\frac{-80\pm\sqrt{7,936}} {-32}

t=\frac{-80+\sqrt{7,936}} {-32}=-0.28

t=\frac{-80-\sqrt{7,936}} {-32}=5.28

therefore

The potato is 40 feet off the ground at the time t=5.28 seconds

3 0
2 years ago
A commercial laundry charges $5.25 per load. You have $31.50. Write and solve an inequality to find the greatest number of loads
4vir4ik [10]

Charges per load = $5.25

Total money = $31.50

As the situation says that charges are 5.25 and one has a total money of 31.50 so lets suppose the total load one has be 'w'

so equation becomes:

5.25w\leq31.50

solving it we get, w\leq6

So, option C is the correct answer.


5 0
2 years ago
Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of
kifflom [539]

Looks like we have

\vec F(x,y,z)=z^2x\,\vec\imath+\left(\dfrac{y^3}3+\sin z\right)\,\vec\jmath+(x^2z+y^2)\,\vec k

which has divergence

\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(z^2x)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial z}=z^2+y^2+x^2

By the divergence theorem, the integral of \vec F across S is equal to the integral of \nabla\cdot\vec F over R, where R is the region enclosed by S. Of course, S is not a closed surface, but we can make it so by closing off the hemisphere S by attaching it to the disk x^2+y^2\le1 (call it D) so that R has boundary S\cup D.

Then by the divergence theorem,

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(x^2+y^2+z^2)\,\mathrm dV

Compute the integral in spherical coordinates, setting

\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi

so that the integral is

\displaystyle\iiint_R(x^2+y^2+z^2)\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^1\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{2\pi}5

The integral of \vec F across S\cup D is equal to the integral of \vec F across S plus the integral across D (without outward orientation, so that

\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\iint_D\vec F\cdot\mathrm d\vec S

Parameterize D by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath

with 0\le u\le1 and 0\le v\le2\pi. Take the normal vector to D to be

\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=-u\,\vec k

Then we have

\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^1\left(\frac{u^3}3\sin^3v\,\vec\jmath+u^2\sin^2v\,\vec k\right)\times(-u\,\vec k)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{2\pi}\int_0^1u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac\pi4

Finally,

\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\left(-\frac\pi4\right)=\boxed{\frac{13\pi}{20}}

6 0
2 years ago
The number of messages that arrive at a Web site is a Poisson distributed random variable with a mean of 6 messages per hour. Ro
QveST [7]

Answer:

a) There is a 16.0623% probability that 5 messages are received in 1 hour.

b) There is a 11.5880% probability that 10 messages are received in 1.5 hours.

c) There is a 22.4042% probability that 2 messages are received in 0.5 hours.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

In this problem, we have a mean of 6 messages per hour.

(a) What is the probability that 5 messages are received in 1 hour?

Find the value of P when x = 5 and \mu = 6

So

P(X = 5) = \frac{e^{-6}*(6)^{5}}{(5)!} = 0.160623

There is a 16.0623% probability that 5 messages are received in 1 hour.

(b) What is the probability that 10 messages are received in 1.5 hours?

The mean is 6 messages in one hour.

For 1.5 hours, the mean is 6*1.5 = 9 messages.

So

We have to find the value of P when x = 10 and \mu = 9.

P(X = 10) = \frac{e^{-9}*(9)^{10}}{(10)!} = 0.115880

There is a 11.5880% probability that 10 messages are received in 1.5 hours.

(c) What is the probability that less than 2 messages are received in 1/2 hour?

The mean is 6 messages in one hour.

For 0.5 hours, the mean is 6*0.5 = 3 messages.

So

We have to find the value of P when x = 2 and \mu = 3.

P(X = 10) = \frac{e^{-3}*(3)^{2}}{(2)!} = 0.224042

There is a 22.4042% probability that 2 messages are received in 0.5 hours.

6 0
2 years ago
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