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3 years ago

Find the volume of the composite figure. please!

Mathematics

2 answers:

Alecsey [184]3 years ago

8 0

3times2times1equals 6
7times6times1equals 42

Irina-Kira [14]3 years ago

3 0

Volume= Length * width ( aka Base ) * height

Break up the figure into easier figures, a small square and a bigger square.

Small square- 3*2*1 = 6 cm

Large Square- 7*6*1 = 42 cm

42 + 6 = 48 cm. But wait! You have to take one more step, which is minus-ing 6 from 48. Why? Notice that there is a little area where a side of the small square meets the bigger square. That little area is worth 3 cm ( length is 3, height is 1 cm ) times 2 ( 3 cm is one side, another 3 cm is the other side from the other square ) = 6 cm.

Your total answer should be 42. ( or 48, if your teacher doesn't count the area where the squares meet/join together ).

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Please help provide the product in standard form !!

astraxan [27]

Answer:

x^3+4x^2+5x+2

Step-by-step explanation:

8 0

2 years ago

Each day, a factory produces a total of 280 containers of ice cream. The flavors are vanilla, chocolate, and strawberry. Each da

GalinKa [24]

Answer:

The correct equation in terms of s is: 4s=260

The number of strawberry ice cream produced per day, s=65.
The number of chocolate ice cream produced per day ,c=130.
The number of vanilla ice cream produced per day ,v=85.

Step-by-step explanation:

Let the number of containers of strawberry ice cream produced per day=s

Let the number of containers of vanilla ice cream produced per day=v

Let the number of containers of chocolate ice cream produced per day=c

Total Number of Ice Cream Containers=280

s+v+c=280

Given:

The factory produces twice as much chocolate ice cream as strawberry ice cream. This is written as:

c=2s

The factory produces 20 more containers of vanilla ice cream than strawberry ice cream. This is written as:

v=s+20

Therefore substituting c=2s and v=s+20 into the first equation: s+v+c=280

s+s+20+2s=280

4s=280-20

4s=260

Divide both sides by 4

s=65

The number of strawberry ice cream produced per day is 65.

The number of chocolate ice cream produced per day =2s=2(65)=130.

The number of vanilla ice cream produced per day =s+20=65+20=85.

3 0

3 years ago

Solve the system by graphing <br><br> Y=x+2<br> X=-3

Ainat [17]

the answer will be y=-1

6 0

3 years ago

Karen collects 6/7 quart of rainwater. She uses 1/2 of the water to clean her bicycle and uses the remaining water equally for 3

quester [9]

Water collected - 6/7
Water used for cleaning bicycle = 1/2 × 6/7 = 6/14
Water used for each houseplant =>6/14 ÷ 3 = 2/14 = 1/7

3 0

2 years ago

John, Sally, and Natalie would all like to save some money. John decides that it

brilliants [131]

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2) $y=100x+300$

Part 3) $\$12,300$

Part 4) $\$2,700$

Part 5) Is a exponential growth function

Part 6) $A=6,000(1.07)^{t}$

Part 7) $\$11,802.91$

Part 8) $\$6,869.40$

Part 9) Is a exponential growth function

Part 10) $A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

Part 11) $\$13,591.41$

Part 12) $\$6,107.01$

Part 13) Natalie has the most money after 10 years

Part 14) Sally has the most money after 2 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

$m=\$100\ per\ month$

The y-intercept or initial value is

$b=\$300$

$y=100x+300$

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

$10\ years=10(12)=120 months$

For x=120 months

substitute in the linear equation

$y=100(120)+300=\$12,300$

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

$2\ years=2(12)=24\ months$

For x=24 months

substitute in the linear equation

$y=100(24)+300=\$2,700$

Part 5) What type of exponential model is Sally’s situation?

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$P=\$6,000\\ r=7\%=0.07\\n=1$

substitute in the formula above

$A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}$

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) How much money will Sally have after 10 years?

For t=10 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{10}=\$11,802.91$

Part 8) How much money will Sally have after 2 years?

For t=2 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{2}=\$6,869.40$

Part 9) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$P=\$5,000\\r=10\%=0.10$

substitute in the formula above

$A=5,000(e)^{0.10t}$

Applying property of exponents

$A=5,000(1.1052)^{t}$

therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

$A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

see Part 9)

Part 11) How much money will Natalie have after 10 years?

For t=10 years

substitute

$A=5,000(e)^{0.10*10}=\$13,591.41$

Part 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

$A=5,000(e)^{0.10*2}=\$6,107.01$

Part 13) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

3 0

3 years ago