All categories

3 years ago

james trained for the boston marathon for 3(1/2) hours every day. how many hours did he train each week?

Mathematics

1 answer:

iVinArrow [24]3 years ago

4 0

Y = 3.5x
24= 3.5x
the train will be ride 6 times each day
and there are 7 days in a week
so multiply 6 and 7
=42

You might be interested in

Element X decays radioactively with a half life of 9 minutes. If there are 610grams of

Nookie1986 [14]

A half-life of 9 minutes corresponds to a decay factor k such that

$\dfrac12=e^{9k}\implies k=-\dfrac19\ln\left(\dfrac12\right)$

Then the time it takes for the substance to decay from 610 g to 124 g is time t such that

$124\,\mathrm g=(610\,\mathrm g)e^{kt}$

Solve for t :

$\dfrac{62}{305}=e^{kt}$

$\ln\left(\dfrac{62}{305}\right)=kt$

$t=\dfrac1k\ln\left(\dfrac{62}{305}\right)\approx20.686$

so it takes about 20.7 min for the 610 g sample to decay down to 124 g.

4 0

3 years ago

The cost of buying salad from a salad bar is at least $4.50 per pound. Which inequality represents the price per pound of salad?

Oduvanchick [21]

The cost of buying salad per pound) is more than or equal to $4.50
Step-by-step explanation:
We know from the problem that the salad is going to cost at least $4.50 per pound. Therefore, it is entirely possible for the cost to exceed $4.50, but it cannot be lower than $4.50 because then it would not be equal to $4.50.
So, there would be a greater-than sign pointing toward the s (which I seemingly cannot depict on here for some reason...)

6 0

3 years ago

A garden is shaped in the form of a regular heptagon (seven-sided), MNSRQPO. A circle with center T and radius 25m circumscribes

Alenkinab [10]

The relationship between the sides MN, MS, and MQ in the given regular heptagon is $\dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}$

The area to be planted with flowers is approximately 923.558 m²

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

Required;

The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

$A = \dfrac{7}{4} \cdot a^2 \cdot cot \left (\dfrac{180 ^{\circ}}{7} \right )$

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

$\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}$

$s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69$

$The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52$

The area of the heptagon MNSRQPO is therefore;

$A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94$

$MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times 21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08$

By sine rule, we have

$\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}$

$sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})$

$\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}$

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

$Area \ of \Delta MSQ = \dfrac{1}{2} \times 43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}$

The area of the of the garden plated with flowers, $A_{req}$ , is given as follows;

$A_{req}$ = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

$A_{req}$ = 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, $A_{req}$ ≈ 923.558 m²

Learn more about figures circumscribed by a circle here:

brainly.com/question/16478185

6 0

3 years ago

. A landscaping company charges $40 to mow a lawn and $15 per hour to weed garden beds. The

Murljashka [212]

The landscape company charges 30+15x

7 0

3 years ago

Brian invests £2500 into his bank account.

klio [65]

2.5% per year multiplay by 5 equals 12.5% then multiple 2500 with 12.5 equals 312.5

5 0

3 years ago