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3 years ago

Another way to write 9 x 200

Mathematics

2 answers:

Katyanochek1 [597]3 years ago

6 0

200+200+200+200+200+200+200+200+200

djyliett [7]3 years ago

6 0

Answer:

Since, Multiplication is a shortcut for addition.

Use of Distributive Property is the most familiar alternative way to write 9 x 200.

Distributive Property states that when a number is multiplied by the sum of two numbers, then the first number can be distributed to both of those numbers and multiplied by each of them separately i.e,

$a \times (b+c) =a\times b +a\times c$

9 x 200

First replace 200 as 100+100 then, we have

$9 \times (100+100)$

Now, using distributive property above:

9 x 200 = $9 \times (100+100) =(9 \times 100)+ (9 \times 100)$ = 900+900 =1800.

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Part of the area under this ramp serves for storage. Items can be stored only in the unshaded part of the ramp

Mekhanik [1.2K]

Answer:

48.1 m³ available, 2.5m³ not available

Step-by-step explanation:

Tan(X) = 4.5/(5.8+1.7)

Tan X = 3/5

Hypotenuse² = 3² + 5² = 34

Sin X = 3/sqrt(34)

X = 30.96

1/sinX = 1.7/SinY

Y = 61.003°

Third angle: 180 - X - Y = 88.037

Volume

= ½ × 1.7 × 1 × sin(88.038) × 3

= .

= 2.548

= 2.5m³

Available for storage:

½×4.5×7.5×3 - 2.548

= 48.077 = 48.1 m³

7 0

3 years ago

Uninhibited growth can be modeled by exponential functions other than A(t) =Upper A 0 e Superscript kt. For example, if an i

laila [671]

The question is incomplete. Here is the complete question.

Uninhibited growth can be modeled by exponential functions other than $A(t)=A_{0}e^{kt}$ . for example, if an initial population P₀ requires n units of time to triple, then the function $P(t)=P_{0}(3)^{\frac{t}{n} }$ models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below.

a) If the population triples in 30 days, and 50 insects are present initially, write an exponential function of the form $P(t)=P_{0}(3)^{\frac{t}{n} }$ that models the population.

b) What will the population be in 47 days?

c) When wil the population reach 750?

d) Express the model from part (a) in the form $A(t)=A_{0}e^{kt}$ .

Answer: a) $P(t)=50(3)^{\frac{t}{30} }$

b) P(t) = 280 insects

c) t = 74 days

d) $A(t)=50e^{0.037t}$

Step-by-step explanation:

a) n is time necessary to triple the population of insects, i.e., n = 30 and P₀ = 50. So, Exponential equation for growth is

$P(t)=50(3)^{\frac{t}{30} }$

b) In t = 47 days:

$P(t)=50(3)^{\frac{t}{30} }$

$P(47)=50(3)^{\frac{47}{30} }$

$P(47)=50(3)^{1.567}$

P(47) = 280

In 47 days, population of insects will be 280

c) P(t) = 750

$750=50(3)^{\frac{t}{30} }$

$\frac{750}{50}=(3)^{\frac{t}{30} }$

$(3)^{\frac{t}{n} }=15$

Using the property Power Rule of logarithm:

$log(3)^{\frac{t}{30} }=log15$

$\frac{t}{30}log(3)=log15$

$t=\frac{log15}{log3} .30$

t = 74

To reach a population of 750 insects, it will take 74 days

d) To express the population growth into the described form, determine the constant k, using the following:

A(t) = 3A₀ and t = 30

$A(t)=A_{0}e^{kt}$

$3A_{0}=A_{0}e^{30k}$

$3=e^{30k}$

Use Power Rule again:

$ln3=ln(e^{30k})$

$ln3=30k$

$k=\frac{ln3}{30}$

k = 0.037

Equation for exponential growth will be:

$A(t)=50e^{0.037t}$

3 0

3 years ago

A dressmaker needs to cut 9-inch pieces of ribbon from rolls of ribbon that are 6 feet

Nikolay [14]

It will be 14 we calculated

8 0

3 years ago

Need help with 6 dont know it

pickupchik [31]

Answer:

It should be 42.25 instead

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Roberta has $10,540 to invest. She plans to invest her money in certificates of deposit (CDs) that have 2.1% interest, a stock p

ira [324]

Answer:

The amount invested in CDs is $1,340

The amount invested in the stock portafolio is $6,900

The amount invested in the saving accounts is $2,300

Step-by-step explanation:

Let

x ---->the amount invested in CDs at 2.1%

y ---> the amount invested in the stock portfolio at 2.5%

z ---> the amount invested in the savings account at 1.5%

$x+y+z=10,540$ ----> equation A

$z=\frac{1}{3}y$ ----> equation B

substitute equation B in equation A

$x+y+\frac{1}{3}y=10,540$

$x+\frac{4}{3}y=10,540$

$x=10,540-\frac{4}{3}y$ ----> equation C

we know that

The total interest earned by the three amount must be equal to $231.69

$0.021x+0.025y+0.015z=231.69$ ----> equation D

substitute equation B and equation C in equation D

$0.021(10,540-\frac{4}{3}y)+0.025y+0.015(\frac{1}{3}y)=231.69$

solve for y

$221.34-0.0315y+0.025y+0.005y=231.69$

$0.0015y=231.69-221.34$

$0.0015y=10.35$

$y=\$6,900$

Find the value of x

$x=10,540-\frac{4}{3}(6,900)$

$x=\$1,340$

Find the value of z

$z=\frac{1}{3}(6,900)$

$z=\$2,300$

7 0

3 years ago