An office girl buys 12cent and 8cent stamps. It she spends
$9.00 and buys 100 stamps, how many of each sort did
she buy? (Let the number of 12cent stamps be x. Using x write down how many 8¢ stamps there were. Now make
an equation and find x).
​

Answer:

The simplified result is: [tex]\frac{5a^3}{3}[/tex]

Step-by-step explanation:

[tex]a^2.\frac{a^{3}+a^2b }{5a}.\frac{25}{3b+3a}[/tex]

We need to solve the above equation.

We take a^2 common from a^3+a^2b

and we take 3 common from 3b+3a

Solving,

[tex]a^2\:\frac{a^2\left(a+b\right)\:}{5a}\frac{25}{3\left(b+a\right)}[/tex]

Since a+b = b+a we can cancel them with each other.

[tex]=a^2\:\frac{a^2}{5a}\frac{25}{3}\\=a^2\:\frac{a^2}{a}\frac{5}{3}\\=a^2\:a\:\frac{5}{3}\\=\frac{5a^3}{3}[/tex]

So, The simplified result is: [tex]\frac{5a^3}{3}[/tex]

The simplified expression is (5(a + b)) / (3a(b + 1)).

To simplify the given expression, we'll perform the indicated operation step by step:

a² * [(a³ + a²b) / 5a] * [25 / (3b + 3a)]

Step 1: Cancel common factors within each fraction:

a² * [(a³ + a²b) / (5a)] * [25 / (3(b + a))]

Step 2: Simplify further:

(a³ + a²b) * [25 / (5a * 3(b + a))]

Step 3: Factor out common terms:

(a²(a + b)) * [25 / (15a(b + a))]

Step 4: Cancel common factors between numerators and denominators:

(a + b) * (25 / (15a(b + a)))

Step 5: Simplify further:

(25(a + b)) / (15a(b + a))

Step 6: Factor out common terms again:

(25(a + b)) / (15a * a(b + 1))

Step 7: Cancel common factors:

(5(a + b)) / (3a(b + 1))

So, the simplified expression is (5(a + b)) / (3a(b + 1)).

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so we are using some conversions here

so first convert 30,360ft=?miles

we are going to use

division like SBD

silly babies dancing an example ofc so it means small to big,divide so,

30,360ft÷5,280=5.75miles

5,280 is how many ft are in a mile.:)

so no,Morgan wasn't over 6 miles

To determine if Morgan was over 6 miles above the ground, we must convert the altitude from feet to miles by dividing by 5,280 (the number of feet in a mile). This computation shows us that Morgan was indeed over 6 miles high.

Yes, Morgan was over 6 miles above the ground. In order to solve this problem, we need to know that 1 mile equals 5,280 feet. Thus, first, we have to convert the altitude in feet into miles. We do this by dividing the number of feet by the number of feet in a mile.

30,360 feet / 5,280 feet per mile = 5.75 miles

Hence, Morgan was indeed flying at an altitude greater than 6 miles above the ground.

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The answer is:

The total time traveled  by the cabin cruiser is equal to 9 hours.

To solve the problem, we need to write two equations using the given information about the travel upstream and downstream.

Then, we need to write two equations:

Let be "x" the speed of the cabin cruiser (12 mph in still water)

Let be "y" the speed of the current (4 mph).

So,

For the travel against the current (upstream), we have:

[tex](x-y)*t_{upstream}=48miles\\\\(x-y)*t_{upstream}=48miles\\\\(x-4mph)*t_{upstream}=48miles[/tex]

For the travel with the current (downstream), we have:

[tex](x+y)*t_{downstream}=48miles\\\\(x+y)*t_{downstream}=48miles\\\\(x+4mph)*t_{downstream}=48miles[/tex]

Also, we know from the statement that the speed of the cabin cruise traveling in still water is equal to 12mph.

So,

Calculating the time traveled upstream, we have:

[tex](x-4mph)*t_{upstream}=48miles(12mph-4mph)*t_{upstream}=48miles(8mph)*t_{upstream}=48milest_{upstream}=\frac{48miles}{8mph}=6hours[/tex]

Calculating the time traveled downstream, we have:

[tex](x+4mph)*t_{downstream}=48miles(12mph+4mph)*t_{downstream}=48miles(16mph)*t_{downstream}=48milest_{downstream}=\frac{48miles}{16mph}=3hours[/tex]

Now that we know the time traveled upstream and downstream, we need to calculate the total time traveled using the following equation:

[tex]TotalTime=t_{upstream}+t_{downstream}\\\\TotalTime=6hours+3hours=9hours[/tex]

Therefore we have that the total time traveled is equal to 9 hours.

Have a nice day!

If it was asking for one can you would put 42.41 because it is (pi)(1.5)^2(6)

But then you times it by 6 cans and you get 254.47inches cubed

The total volume of juice in a six-pack, with each can being 6 inches tall and having a diameter of 3 inches, is 254.34 cubic inches. This is calculated using the volume formula for a cylinder.

The question asks for the total volume of juice in a six-pack of cans, where each can is 6 inches tall and has a diameter of 3 inches. To find the volume of one can, we use the formula for the volume of a cylinder: V = πr^2h, where V is volume, r is radius, and h is height. First, we find the radius of the can by dividing the diameter by 2, which gives us 1.5 inches. The volume of one can is therefore calculated as V = π(1.5)^2(6), which simplifies to V = π(2.25)(6) = 42.39 cubic inches. To find the total volume for a six-pack, we multiply this volume by 6: 42.39 in^3  × 6 = 254.34 in^3. Therefore, the total volume of juice in the six-pack is 254.34 cubic inches.

Answer:

57 4/5

Step-by-step explanation:

Add 5 and 14

5+14 = 19

Triple the sum

3 * 19 = 57

The add 4/5

57 + 4/5

57 4/5

Answer:

Part 1) The length of each side of the square is about 4.47 units

Part 2) The length of its diagonal is about 6.32 units

Step-by-step explanation:

Part 1)

Find the length of each side of the square

In the right triangle TPQ

Applying the Pythagoras Theorem

[tex]TQ^{2}=PQ^{2}-TP^{2}[/tex]

substitute the given values

[tex]TQ^{2}=6^{2}-4^{2}[/tex]

[tex]TQ^{2}=36-16[/tex]

[tex]TQ^{2}=20[/tex]

[tex]TQ=2\sqrt{5}\ units[/tex] -----> exact value

[tex]TQ=4.47\ units[/tex] -----> approximate value

Part 2)

Find the length of the diagonal of the square

Applying the Pythagoras Theorem

[tex]TR^{2}=TQ^{2}+QR^{2}[/tex]

we have

[tex]TQ=QR[/tex]

[tex]TQ=2\sqrt{5}\ units[/tex]

substitute

[tex]TR^{2}=(2\sqrt{5})^{2}+(2\sqrt{5})^{2}[/tex]

[tex]TR^{2}=40[/tex]

[tex]TR=2\sqrt{10}\ units[/tex] -----> exact value

[tex]TR=6.32\ units[/tex] ----> approximate value

Answer:

First box is 4.5 units and the second box is 6.3 units.

Step-by-step explanation: Correct Plato answer.

Answer:

x = √41  units

Step-by-step explanation:

Half the base length

= 8 ÷ 2

= 4

x² = 4² + 5²

x² = 16 + 25

x² = 41

x = √41

Answer:

x = sqrt(41)

Step-by-step explanation:

We have a right triangle with height 5 and a base that is 1/2 of 8 = 4

We can use Pythagorean theorem

a^2 + b^2 = c^2 to find the length of the hypotenuse

5^2 + 4^2 = x^2

25+16 = x^2

41 = x^2

Take the square root of each side

sqrt(41) = x

Answer:

2. the second alternative is correct

3. 24

Step-by-step explanation:

2.

In flipping a coin once, we can either land Heads, H or Tails, T. The sample space is thus;

{H,T}

In rolling a number cube labelled 1 to 6, we can roll a 1, 2, 3, 4, 5, or a 6. The sample space is thus;

{1, 2, 3, 4, 5, 6}

When we flip the coin and roll the number cube we shall combine the above sample spaces using the following logic;

We can roll the number cube and obtain a 1. When we flip the coin, we can land Heads or Tails. This gives a possible combined outcome of;

H-1, T-1

We can roll the number cube and obtain a 2. When we flip the coin, we can land Heads or Tails. This gives a possible combined outcome of;

H-2, T-2

Going on and on, we can roll the number cube and obtain a 6. When we flip the coin, we can land Heads or Tails. This gives a possible combined outcome of;

H-6, T-6

We shall have a total of ;

6*2 = 12 possible outcomes

Therefore, the second alternative is correct

3.

The number of different lunch combinations that can be made from 3 sandwich choices, 2 side item choices and 4 beverage choices  if you choose one sandwich, one side and one beverage is ;

3*2*4= 24

We simply find the product of the number of choices under each category.

Answer:

1/2, 5/4, 7/8

Step-by-step explanation:

to find it you can divide it on a calculator and then see the decimals and decide from least to greatest or you can reduce the fraction to its simplest form and then do the least fo greatest by looking at the denominator only

Answer:

1/2, 7/8, 5/4

Step-by-step explanation:

Answer:

0.00247

Step-by-step explanation:

Answer:

[tex]\large\boxed{2.47\times10^{-3}=0.00247}[/tex]

Step-by-step explanation:

METHOD 1:

[tex]\text{Use:}\ 10^{-n}=\dfrac{1}{10^n}\\\\2.47\times10^{-3}=2.47\times\dfrac{1}{10^3}=2.47\times\dfrac{1}{1000}=\dfrac{2.47}{1000}\\\\=\dfrac{2.47\times100}{1000\times100}=\dfrac{247}{100000}=0.00247[/tex]

METHOD 2:

[tex]a\times10^n\\\\\text{If}\ n<0\ \text{then move the comma n places to the left.}\\\text{If}\ n>0\ \text{then move the comma n places to the right.}[/tex]

[tex]\text{Therefore}\ 2.47\times10^{-3}=0\underbrace{.002}_{\leftarrow3}47[/tex]

Answer:

75 degrees

Step-by-step explanation:

The two marks on the triangle sides mean they are the same length (congruent).  Because of the Isosceles Triangle Theorem, the angles across from those two congruent sides are also congruent.  That means that angle C also measures 3x.  Because all the sides of a triangle add up to equal 180, then (x+5) + 3x + 3x = 180.  7x + 5 = 180, and 7x = 175.  That means that x = 25.  Take that 25 and sub it into 3x to get 3(25) = 75 degrees.

Answer:

Step-by-step explanation:

This is a geometric sequence. The general formula for any term is

t_n = a*r^(n-1)

t1 = 3

r = 3

t_n = 3* 3^(n - 1)

t_4 should be 81

t_4 = 3*3^(n - 1)

t_4 = 3*3^3

t_4 = 3 * 27

t_4 = 81

Answer:

an = 3 * (3)^ (n-1)  or

an = 3^n

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first term

9/3 = 3

To verify take the third term and divide by the second

27/9 =3

Since this is a geometric sequence, it is of the form

an = a1*r^(n-1)  where a1 is the first term and r is the common ration

an = 3 * (3)^ (n-1)

Since the first term is the same as the term inside the parentheses, we can combine

an = 3^1 * 3 ^ (n-1)

   = 3^ (1+n-1)

  = 3^ (n)

Answer:

50

Step-by-step explanation:

first the power 5^2 = 25 then the multiply 7*3 = 21 and then the addition

25+21+4= 25+25 = 50  

Hey there!

5^2 + 7 * 3 + 4

= 5 * 5 + 21 + 4

= 25 + 21 + 4

= 46 + 4

= 50

Therefore, your answer is: 50

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Could you comment the question so I could see it closer?

Answer:

A

Step-by-step explanation:

A shift along the x-axis is the opposite in the graph than in the equation. Rather than the x-intercept(s) being negative if the equation is x - n, they become positive; likewise for the other way around. A is the only answer that follows this rule. However, the y-intercept is y = n, so if n is negative, y gets shifted down rather than up.

Answer:

x=2.5

Step-by-step explanation:

First, you need to expand the brackets.

51x-19.5=108

Next, you need to add 19.5 to both sides giving:

51x=127.5

Then finally, you need to divide both sides by 51.

x =2.5

x equal to 2.5 in this equation

An algebraic equation is a mathematical statement that contains two or more algebraic expressions that are set equal to each other. The algebraic expressions can contain variables, constants, and operators.

We have:

3(17x – 6.5) = 108

We can solve for the value of x as follow:

3(17x – 6.5) = 108

17x(3) - 6.5(3) = 108

51x - 19.5 = 108

51x = 108 + 19.5

51x = 127.5

x = 127.5/51

x = 2.5

Therefore, x equal to 2.5 in this equation

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X=15

30/42=X/21

Cross multiply.

42x=630

Divide.

630/42= 15

x=15

I know its kind of confusing, it took me a while to get geometry down too.

But I hope this helps :)

Answer:

x = 15

Step-by-step explanation:

Since the triangles are similar, we can say that the ratio between the respective sides of the first triangle and the 2nd is constant.

Basically, VW / ST = VU/SR = WU/TR = k, where k is a positive real number

Solving for k is simple:

k = VU/SR = 42/21 = 2

So we found out that the 1st triangle is the 2nd triangle but scaled up 2 times.

We use this to find x.

ST * 2 = VW

2x = 30

x = 15

Answer:

7 times

Step-by-step explanation:

5 times 5 is 25 so 5 times 7 is 35 and thats the answer

Solve the equation by inserting 7 for x.

Our equation is now y=2.5(7)-1.5

Multiply.

Y=17.5-1.5

Subtract

Y=16

The answer is D. 16

Hope this helps!

Answer:

Saving account: A = 500(1 + 0.023t)

CD account: A = 500(1 + 0.018/12)^(12t)

Future value of saving account is $730

Future value of CD account is $716.47

She should choose the saving account

Step-by-step explanation:

* Lets revise the rules of simple and compound interest

- Simple Interest Equation (Principal + Interest)

 A = P(1 + rt)

- Where:

• A = Total amount (principal + interest)  future amount

• P = Principal Amount

• I = Interest Amount

• r = Rate of Interest per year in decimal; r = R/100

• t = Time Period involved  

- Compound interest can be calculated using the formula

 A = P (1 + r/n)^(nt)

Where:

• A = the future value of the investment, including interest

• P = the principal investment amount (the initial amount)

• r = the annual interest rate (decimal)

• n = the number of times that interest is compounded per unit t

• t = the time the money is invested for

* Now lets solve the problem

- Saving account:

# P = $500

# r = 2.3/100 = 0.023

# t = t

∴ A = 500(1 + 0.023t) ⇒ (1)

- CD account:

# P = $500

# r = 1.8/100 = 0.018

# n = 12

# t = t

∴ A = 500(1 + 0.018/12)^(12t) ⇒ (2)

* In case t = 20 years

- In equation (1)

# A = 500(1 + 0.023 × 20) = $730

- In equation (2)

# A = 500(1 + 0.018/12)^(12 × 20) = $716.47

* The future value of saving account is greater than the CD account

∴ She should choose the saving account

Answer:

0.45

Step-by-step explanation:

Brainiest please!

Answer: A.Lauren and Christy sold cookies for $0.50 each and glasses of lemonade for $1.10 each.

To get $17.20 you have to multiply the price of cookies by how many cookies you sold plus the cost of lemonade by how many glasses of lemonades were sold. Hope this helps!

Answer:

In 1981, the Australian humpback whale population was 350

Po = Initial population = 350

rate of increase = 14% annually

P(t) = Po*(1.14)^t

P(t) = 350*(1.14)^t

Where

t = number of years that have passed since 1981

Year 2000

2000 - 1981 = 19 years

P(19) = 350*(1.14)^19

P(19) = 350*12.055

P(19) = 4219.49

P(19) ≈ 4219

Year 2018

2018 - 1981 = 37 years

P(37) = 350*(1.14)^37

P(37) = 350*127.4909

P(37) = 44621.84

P(37) ≈ 44622

There would be about  44622  humpback whales in the year 2018

Final answer:

To predict the Australian humpback whale population, an exponential growth model is used with equation P(t) = 350  [tex]imes (1 + 0.14)^t.[/tex] By substituting t with the number of years since 1981, we can estimate the population for any given year.

Explanation:

To write the equation for a function you could use to predict the number of humpback whales, we can use an exponential growth model because the population increases by a constant percentage rate each year. The general form of an exponential growth model is [tex]P(t) = P0 imes (1 + r)t,[/tex]where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the number of years since the initial time.

Given that the initial population in 1981 was 350 whales and the growth rate is 14% or 0.14, and taking t to be the number of years since 1981, the function to predict the number of whales in year t is:

[tex]P(t) = 350 imes (1 + 0.14)t[/tex]

For the number of whales in the year 2000, we substitute t with 19 (since 2000-1981=19), and for the year 2018 it would be 37 (since 2018-1981=37).

To predict the number of humpback whales in the year 2018, we use the function with t=37:

[tex]P(37) = 350 imes (1 + 0.14)37[/tex]

Calculating this, the result is rounded to the nearest whole number giving us the approximate whale population in 2018.

Answer:

The individuals are observed the exact way they act in real life.

Step-by-step explanation:

There are two main types of studies in research; one is controlled or experimental and the other is observational.

In observational studies, the individuals participating in study are not manipulated or intervened or controlled in any way by the researcher.

Hence the statements best describes a characteristic of an observational study is the individuals are observed the exact way they act in real life !

Answer:

[tex]\large\boxed{r_{y-axis}(x,\ y)\to(-x,\ y)}[/tex]

Step-by-step explanation:

[tex]L(-6,\ 2)\to L'(-(-6),\ 2)\to L(6,\ 2)\\\\M(-5,\ 4)\to M'(-(-5),\ 4)\to M'(5,\ 4)\\\\N(-3,\ 2)\to N'(-(-3),\ 2)\to N'(3,\ 2)\\\\\bold{Conclusion:}\\\\r_{y-axis}(x,\ y)\to(-x,\ y)[/tex]

The rule of reflection for the triangle is Ry ( x , y ) → ( -x , y )

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the triangle be represented as ΔMLN

Now , the coordinates of the triangle are

The coordinate of M = M ( -5 , 4 )

The coordinate of L = L ( -6 , 2 )

The coordinate of N = N ( -3 , 2 )

when the triangle is reflected across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse.

The reflection of point (x, y) across the y-axis is (-x, y).

So , the coordinate of M' = M' ( 5 , 4 )

The coordinate of L' = L' ( 6 , 2 )

The coordinate of N' = N' ( 3 , 2 )

Hence , the rule of reflection is Ry ( x , y ) → ( -x , y )

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Answer:

2.4 ft = height

Step-by-step explanation:

The formula for the volume of a pyramid is V = (1/3)(base area)(height).

Here V = 20 ft² = (1/3)(base area)(height).

Since the base area is (5 ft)², or 25 ft²,   20 ft² = (1/3)(25 ft²)(height),

(height) = (20 ft³) / ( [25/3] ft², or    60 ft³ / (25 ft²) = 2.4 ft = height

For this case we have by definition, that the circumference of a circle is given by the following formula:

[tex]C = \pi * d[/tex]

Where:

d: Is the diameter of the circumference

So:

[tex]C = \pi * 25\\C = 78.5398[/tex]

Rounding to a decimal we have:

[tex]C = 78.5 \ yards[/tex]

ANswer:

[tex]C = 78.5 \ yards[/tex]

What’s a brainliest sorry I can’t help

This relation is a function because a function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs). So we have that:

[tex]\left[\begin{array}{cc}x & y\\1 & 0\\2 & 4\\3 & 8\\4 & 12\end{array}\right][/tex]

We have plotted all the points below. As you can see, this is a linear function. Therefore, with two points we can get the equation, so:

[tex]The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_{1},y_{1}) \ is:\\ \\ y-y_{1}=m(x-x_{1}) \\ \\ \\ y-0=\frac{4-0}{2-1}(x-1) \\ \\ y=4(x-1) \\ \\ y=4x-4 \\ \\ \\ Where: \\ \\ (x_{1},y_{1})=(1,0) \\ \\ (x_{2},y_{2})=(2,4)[/tex]

Finally, the equation is:

[tex]\boxed{y=4x-4}[/tex]

the answers is a) nucleus, cytoplasm and ribosomes

Answer:

Try using A for your answer

Step-by-step explanation:

Answer:

Volume of larger ball = 220,781.3 cubic centimeters

Step-by-step explanation:

Let's use ratios to solve for the diameter of the larger ball first (let the diameter of larger ball be L)

[tex]\frac{LargerBall}{SmallerBall}=\frac{15}{11}=\frac{L}{55}\\11*L=15*55\\11*L=825\\L=\frac{825}{11}=75[/tex]

So, the diameter of the larger ball is 75 cm. We know radius is half of diameter, so radius of larger ball is (1/2)(75) = 37.5 cm

Ball is in the shape of a sphere, which has a formula for volume as:

[tex]V=\frac{4}{3}\pi r^3[/tex]

where V is the volume and r is the radius

now we simply plug in 37.5 into r and use 3.14 as π:

[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}(3.14)(37.5)^3\\V=220,781.3[/tex]