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charle [14.2K]
2 years ago
7

The students in math class use square tiles to make arrays. Celia says they can make more arrays with 8 tiles than with 9 tiles

because 8 has more factors. Is Celia correct?
Mathematics
2 answers:
Marizza181 [45]2 years ago
6 0
Yes
8=1,2,4,8,
9=1,3,9
Cerrena [4.2K]2 years ago
5 0

The students in math class use square tiles to make arrays. If they

  • use 8 (8=1·2·2·2) tiles, then they can form arrays of the length in 1 tile, 2 tiles, 4 tiles and 8 tiles;
  • use 9 (9=1·3·3) tiles, they can form arrays of the length in 1 tile, 3 tiles and 9 tiles (one array less).

So, you can conclude that Celia is correct.

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in 2016 the average Raleigh driver spent 18 hours in traffic jams, which accounted for 6% of their total driving time. How many
castortr0y [4]

Answer: 300 hrs

The time spent behind the wheel by the average Raleigh driver in 2016 is  300 hrs

Step-by-step explanation:

Given that;

Raleigh driver spent 18 hours in traffic jams

And it accounts for 6% of their total driving time

Now

let total driving time be = x hrs

so

6% of total driving time = 18 hrs

6/100 × x = 18hrs

6x = 1800 hrs

x = 1800/6

x = 300 hrs

∴ The time spent behind the wheel by the average Raleigh driver in 2016 is  300 hrs

5 0
2 years ago
The 3rd degree Taylor polynomial for cos(x) centered at a = π 2 is given by, cos(x) = − (x − π/2) + 1/6 (x − π/2)3 + R3(x). Usin
Otrada [13]

Answer:

The cosine of 86º is approximately 0.06976.

Step-by-step explanation:

The third degree Taylor polynomial for the cosine function centered at a = \frac{\pi}{2} is:

\cos x \approx -\left(x-\frac{\pi}{2} \right)+\frac{1}{6}\cdot \left(x-\frac{\pi}{2} \right)^{3}

The value of 86º in radians is:

86^{\circ} = \frac{86^{\circ}}{180^{\circ}}\times \pi

86^{\circ} = \frac{43}{90}\pi\,rad

Then, the cosine of 86º is:

\cos 86^{\circ} \approx -\left(\frac{43}{90}\pi-\frac{\pi}{2}\right)+\frac{1}{6}\cdot \left(\frac{43}{90}\pi-\frac{\pi}{2}\right)^{3}

\cos 86^{\circ} \approx 0.06976

The cosine of 86º is approximately 0.06976.

8 0
2 years ago
TravelEz sells dollars at a rate of ($1.40)/(1 euro) and buys dollars at a rate of ($1.80)/(1 euro). At the beginning of a trip,
Natalija [7]

Answer:

Sophie will get <u>$56</u> in exchange.

Step-by-step explanation:

Given:

TravelEz sells dollars at a rate of ($1.40)/(1 euro).

And dollars they buy at a rate of ($1.80)/(1 euro).

Sophie exchanged $540 to get 300 euros, at the beginning of trip.

And, she is left with 40 euros at the end of trip.

So exchanges the euros back to dollars.

Now, to find the dollars Sophie will get in exchange.

Let the dollars Sophie will get in exchange be x.

The rate at which TravelEz sells dollars = \frac{\$1.40}{1\ euro}

Number of euros Sophie is left with = 40.

Now, to get the dollars she will get we set proportion:

<em>As, </em>\$1.40<em> is equivalent </em>1\ euro<em>.</em>

<em>So, </em>x<em> is equivalent to </em>40\ euros<em>.</em>

Thus,

\frac{1.40}{1} =\frac{x}{40}

By cross multiplying we get:

56=x

x=\$56.

Therefore, Sophie will get $56 in exchange.

5 0
2 years ago
In a sample of 100 steel canisters, the mean wall thickness was 8.1 mm with a standard deviation of 0.5 mm. Someone says that th
Travka [436]

Answer:

This statement can be made with a level of confidence of 97.72%.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 8.1 mm

Standard Deviation, σ = 0.5 mm

Sample size, n = 100

We are given that the distribution of thickness is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

Standard error due to sampling:

=\dfrac{\sigma}{\sqrt{n}} = \dfrac{0.5}{\sqrt{100}} = 0.05

P(mean thickness is less than 8.2 mm)

P(x < 8.2)

P( x < 8.2)\\\\ = P( z < \displaystyle\frac{8.2 - 8.1}{0.05})\\\\ = P(z < 2)

Calculation the value from standard normal z table, we have,  

P(x < 8.2) =0.9772 = 97.72\%

This statement can be made with a level of confidence of 97.72%.

8 0
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At smith mountain lake boat rentals, it costs $25 per hour to rent a pontoon boat, plus a one-time charge for cleaning. The Beng
ludmilkaskok [199]

Answer:

The given equation  in slope intercept form is

226.50  = 7.5 (25) + 39  

Step-by-step explanation:

The SLOPE INTERCEPT form of a equation is y = m x + c

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Let us assume the one time cleaning charge = $  k

The boat is booked from 11 am : 6 : 30 pm

So, the number of hours boat was used   =  7 . 5 hours

Hence, the cost for engaging boat for 7.5 hours

= 7.5 (cost per hour )  = 7.5( $25)  = $187 . 5

Total amount paid by the family = $226. 50  =  Fixed cleaning charge  +  rate for 7.5 hours

⇒The cleaning fee paid by the family =    $226. 50 - $187 . 5  = $39

According to question:

Total amount paid  =  Number of hour x (cost per hour )  + Cleaning fee

Hence, the given equation  in slope intercept form is

226.50  = 7.5 ($25) + $39

8 0
1 year ago
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