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2 years ago

Find the length of side s to the nearest tenth.

Mathematics

1 answer:

bulgar [2K]2 years ago

5 0

Answer:

10.3

Step-by-step explanation:

The triangle can be solved from one side and two angles by using the angle sum theorem to find the third angle, then using the Law of Sines to find the remaining sides.

The angle at T is ...

180° - 119° -36° = 25°

The law of sines tells us side s will be ...

s/sin(S) = t/sin(T)

s = sin(119°)×5/sin(25°) . . . . multiply by sin(S)

s ≈ 10.34763

s ≈ 10.3

Additional comment

u/sinU = t/sin(T)

u = sin(36°)×5/sin(25°) ≈ 6.95409

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Find the product -a^4(7a^5- 5a+ 5)

Nostrana [21]

$-a^4(7a^5- 5a+ 5) = - 7a^{9} +5 a^{5} -5 a^{4}$

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3 years ago

A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has i

bija089 [108]

Answer: $\bold{a)\ P(t)=P_o\cdot e^{t\cdot ln(2.7)}}$

b) 5314

c) ln 2.7

d) 4.6 hrs

Step-by-step explanation:

$P(t) = P_o\cdot e^{kt}\\\\\bullet \text{P(t) is the number of bacteria after t hours} \\\bullet P_o\text{ is the initial number of bacteria}\\\bullet \text{k is the rate of growth}\\\bullet \text{t is the time (in hours)}\\\\\\270=100\cdot e^{k(1)}\\2.7=e^k\\ln\ 2.7=\ln e^k\\\boxed{ln\ 2.7=k}\\\\\text{So the equation to find the number of bacteria is: }\boxed{P(t)=P_o\cdot e^{t\cdot ln(2.7)}}\\\\\\P(4)=100\cdot e^{4\cdot ln(2.7)}\\.\qquad =\boxed{5314}$

$10,000=100\cdot e^{t\cdot ln(2.7)}\\100=e^{t\cdot ln(2.7)}\\ln\ 100=ln\ e^{t\cdot ln(2.7)}\\ln\ 100=t\cdot ln(2.7)\\\dfrac{ln\ 100}{ln\ 2.7}=t\\\\\boxed{4.6=t}$

4 0

3 years ago

Mrs. Adesso wants to take her class on a trip to either the science center or natural history museum. The science center charges

BartSMP [9]

Answer:

Step-by-step explanation:

When we write expressions for the total cost of each field visit and set them equal, we find the solution to be the ratio of the difference in fixed cost to the difference in variable cost.

y = 75 +7x . . . . . cost for x students to visit the science center

y = 50 +8x . . . . cost for x students to visit the natural history museum

Subtracting the first equation from the second, we get ...

0 = -25 +x

25 = x . . . . . add 25; the number of students such that costs are equal

The cost will be the same either place for 25 students.

Additional comment

Here, the fixed cost difference is 75-50=25, and the variable cost difference is 8-7=1. The ratio of these costs is ...

$25/($1 /student) = 25 students.

This relationship only holds when the higher fixed cost is associated with the lower variable cost. Charges are such that one place caters to larger numbers of students (science center), and one prefers fewer students (natural history museum).

4 0

2 years ago

Shauna makes 24 cupcakes per hour. She has already made 48 cupcakes. Let x represent the amount of time Shauna spends making the

GalinKa [24]

Y=24x+48

24 per hour (x) plus the 48 she already made would equal a total (y).

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3 years ago

The probability of randomly selecting a female from a group of 25 elementary school teachers is . Which of the following describ

nirvana33 [79]

Answer:

it is likely that a female will be picked

Step-by-step explanation:

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7 0

3 years ago