What is the least common multiple (LCM) of 3 and 7?

Answer:

260 total stamps

Step-by-step explanation:

Marlee - 60

Xavier - 60

Nicki - 50

Cameron - 90

60+60+50+90= 260

The question involves setting up and solving an algebraic equation to find a number such that 12 less than 7 times this number equals 32 less than the product of -3 and the number. The solution to the equation 7x - 12 = -3x - 32 is x = -2.

The phrase '12 less than 7 times a number' can be represented as 7x - 12, where 'x' is the number in question. The phrase '32 less than the product of -3 and a number' translates to -3x - 32. Setting these two expressions equal to each other gives us the equation 7x - 12 = -3x - 32.

To solve for 'x', we can first add 3x to both sides of the equation, which will give us 10x - 12 = -32. Next, we add 12 to both sides to isolate the term with 'x', resulting in 10x = -20. Finally, we divide both sides by 10 to find the value of 'x', which yields x = -2.

Therefore, the number that satisfies the condition is -2.

Answer:

28 cupcakes and 12 muffins were sold.

Step-by-step explanation:

First identify what variable to use for cupcakes and muffins.

X→ Cupcakes

Y→ Muffins

Then you need to write two equations.

X+Y= 40

X= 4+2Y

Since you have the value of X you need to substitute.

(4+2Y)+Y= 40

Combine like terms.

4+3Y= 40

Now use Subtraction Property of Equality.

4+3Y= 40

-4           -4

Now you have 3Y= 36

You have to use Division Property of Equality now.

[tex]\frac{3Y}{3}[/tex]= [tex]\frac{36}{3}[/tex]

If done correctly you should get Y= 12

Afterwards you must get 12 and subtract it from 40.

40-12= 28

28 is the amount of cupcakes sold.

To check you can see that 28 is equal to 12×2+4.

Hope this helped!

The bake sale sold 28 cupcakes and 12 muffins. This was determined by setting up a system of two equations based on the problem details and solving for the number of cupcakes and muffins sold.

This is a problem of algebraic equations related to the real-world scenario of a bake sale. Here, we have two types of food items: cupcakes and muffins. According to the problem, the total number of cupcakes and muffins sold was 40. The information provided also states that the number of cupcakes sold was four more than twice the number of muffins sold.

To solve this problem, we need to set up a system of two equations. First, we know that the combined number of cupcakes (C) and muffins (M) is 40, so we can write this equation: C + M = 40. Secondly, we know that the number of cupcakes is four more than twice the number of muffins, giving us the second equation: C = 2M + 4.

Now, we can substitute the second equation into the first one, resulting in: 2M + 4 + M = 40. Simplifying this gives 3M + 4 = 40. Subtracting 4 from both sides gives 3M = 36. Dividing both sides by 3 then gives M = 12. Substituting M = 12 back into the first equation (C + M = 40), we find that C = 40 - 12 = 28.

So, the bake sale sold 28 cupcakes and 12 muffins.

https://brainly.com/question/953809

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Answer:

Let

x = the number of pepperoni added to the pizza.

y = the number of mushrooms added to the pizza.

z = the number of onions added to the pizza.

u = the number of olives added to the pizza.

Twice as many onions as pepperoni

z = 2*x

Half as many mushrooms as olives

y = u/2

There are 39 individual toppings on the pizza

x + y + z + u = 39

We are dealing with a system of equation with 4 unknowns and only three equations.

2*x - z = 0

y  - u/2 = 0

x + y + z + u = 39

This means that there are an infinite number of solutions for your problem

For example, here is one solution

x = 1

z = 2

1 + y + 2 + (2y) = 39

3y = 36

y = 12

u = 24

The number of ways a judge can award first, second, and third places in a contest with 10 entries is:

                                 720

We know that the choosing and arranging of r entries out of a total of n entries is given by the method of permutation and the formula is given by:

                   [tex]n_P_r=\dfrac{n!}{(n-r)!}[/tex]

Here we have to chose and arrange 3 people according to their ranks out of a total of 10 entries.

i.e. r=3 and n=10

Hence, the formula is given by:

[tex]{10}_P_3=\dfrac{10!}{(10-3)!}\\\\\\{10}_P_3=\dfrac{10!}{7!}\\\\\\{10}_P_3=\dfrac{10\times 9\times 8\times 7!}{7!}\\\\\\{10}_P_3=10\times 9\times 8\\\\\\{10}_P_3=720[/tex]

                  Hence, the answer is:

                             720 ways

Answer:

45 fish this year

Step-by-step explanation:

60 x .25 = 15

60 - 15 = 45

Answer:

True

Step-by-step explanation:

In general, when you compose a function [tex]f(x)[/tex] with its inverse [tex]f^{-1}(x)[/tex], you always get the identity function:

[tex]f(f^{-1}(x))=x[/tex]

The limitation [tex]-1\leq x \leq 1[/tex] is necessary because the arcsin function wouldn't be defined otherwise.

The statement 'sin(sin^-1 x) = x' is true for all real numbers x.

The statement 'sin(Sin^-1 x)=x for -1<=x<=1' is true. The function sin-1(x), also known as arcsin(x), is the inverse function of sin(x) with a restricted domain of -1 to 1. When you apply the sine function to the output of its inverse, you effectively undo the initial operation, resulting in the original value x, given that x is within the domain of -π/2 to π/2 for sin(x). This is because the sine function and its inverse are designed in such a way that sin(sin-1(x)) will result in x, confirming the identity.

Answer:

[tex]tan(x/2)=-4[/tex]

Step-by-step explanation:

we know that

The angle x belong to the III quadrant -----> given problem

step 1

Find the angle x

[tex]x=arctan(8/15)=28.07\°[/tex]

Remember that the angle x belong to the III Quadrant

so

[tex]x=28.07\°+180\°=208.07\°[/tex]

step 2

Find angle x/2

[tex]x/2=208.07\°/2=104.035\°[/tex]

step 3

Find tan(x/2)

[tex]tan(104.035\°)=-4[/tex]

[tex]b. \tan(x) = 2[/tex]

Answer:

A

Step-by-step explanation:

f^-1(x) is a common notation for the inverse of the function. An inverse of a function is a reflection over the line y=x. This results in the points (x,y) of the function becoming (y,x) for the inverse. Algebraically you find the inverse by switching the location of y and x in the equation of the function and solving.

y = -3x + 2

x = -3y + 2

x - 2 = -3y

-(x-2)/3 = y

-1/3x + 2/3 = y

The inverse of the function is a linear function because it follows the form y = mx+b for its equation. All lines are functions. The inverse is a function.

Answer:    a : f^1(x)= -1/3x +2/3 ; function

Step-by-step explanation:

Answer:X*2+4=y

Step-by-step explanation:Ok, so, we can pull four different points from this equation.

The monkey eats 4 apples each morning

The monkey eats 2 bananas for each 1 Tommy has

The number of bananas Tommy eats is marked as X

The number of fruits the monkey eats is marked as y

Let's start with Tommy.

X

Tommy eats X amount of bananas. Next the monkey.

X=y

The monkey eats y amount of bananas, but if you notice, he eats double to amount Tommy eats. So let's double Tommy's bananas.

X*2=y

You'll also notice, the monkey eats four apples everyday. Now, we're looking for the monkey's FRUIT intake, where as we're only looking at Tommy's BANANA intake. So, let's add that to the equation.

X*2+4=y

And there's the equation right there.

Answer:

Option B. n

Step-by-step explanation:

we know that

A regular polygon is a convex polygon whose angles are all congruent.The number of lines of symmetry in a regular polygon is equal to the number of sides a regular polygon has.

therefore

the answer is option B. n

[tex]X[/tex] is the random variable for lifespan of a protozoan and [tex]X\sim\mathcal N(48,10.2^2)[/tex]. Let [tex]\bar X[/tex] be the mean of a sample from this distribution, so that [tex]\bar X\sim\mathcal N\left(48,\left(\dfrac{10.2}{\sqrt{49}}\right)^2\right)[/tex].

For the sake of clarity, I'm denoting a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] by [tex]\mathcal N(\mu,\sigma^2)[/tex].

We have

[tex]P(\bar X\ge49)=P\left(\dfrac{\bar X-48}{\frac{10.2}{\sqrt{49}}\ge\dfrac{49-48}{\frac{10.2}{\sqrt{49}}\right)\approx P(Z\ge0.6863)\approx0.2463[/tex]

(where [tex]Z[/tex] follows the standard normal distribution)

To find the answer for this, it's a bit hard, but here is the formula

[tex](area \times 2) \div h[/tex]

We plug our numbers into the formula...

[tex](33 \times 2) \div 11[/tex]

66÷11=6

So the answer is 6mm

ANSWER

[tex]( \frac{g}{f} )(x) = \frac{1}{ 2x+3} [/tex]

The domain is:

[tex]x \ne1 \: or \: x \ne - \frac{3}{2}[/tex]

EXPLANATION

The given functions are:

[tex]f(x) = 2 {x}^{2} + x - 3[/tex]

and

[tex]g(x) = x - 1[/tex]

[tex]( \frac{g}{f} )(x) = \frac{g(x)}{f(x)} [/tex]

[tex]( \frac{g}{f} )(x) = \frac{x - 1}{2 {x}^{2} + x - 3 } [/tex]

Factor the quadratic trinomial in the denominator.

[tex]( \frac{g}{f} )(x) = \frac{x - 1}{2 {x}^{2} +3 x - 2x- 3 } [/tex]

[tex]( \frac{g}{f} )(x) = \frac{x - 1}{ x(2x+3) -1 (2x + 3 )} [/tex]

[tex]( \frac{g}{f} )(x) = \frac{x - 1}{ (2x+3) (x-1)} [/tex]

Cancel the common factors,

[tex]( \frac{g}{f} )(x) = \frac{1}{ 2x+3} \: where \: x \ne1 \: or \: x \ne- \frac{3}{2} [/tex]

Answer:

Its true ⇒ answer (a)

Step-by-step explanation:

* The solution of two linear equation means that this solution

  is a solution for each equation

* To check if the point is a solution of an equation

- Substitute its coordinates in the equation, if the left hand side

 is equal the right hand side, then the point is a solution

 of this equation

* Lets study our problem

- (-2 2) is the solution of two linear equations

- The slope of one equation is 3

- The slope of the second equation is the negative reciprocal

 of the slope of the first, means = -1/3

* Check the this conditions in the given equations

- In the equation y = 3x + 8 ⇒ the slope = 3

- In the equation y = -1/3 x + 4/3 ⇒ the slope = -1/3

* Now lets substitute the solution (-2 , 2) in the both equations

- First equation

∵ y = 2 ⇒ L.H.S

∵ 3(-2) + 8 = 2 ⇒ R.H.S

∵ L.H.S = R.H.S

∴ (-2 , 2) is a solution of the equation y = 3x + 8

- Second equation

∵ y = 2 ⇒ L.H.S

∵ (-1/3)(-2) + 4/3 = 2/3 + 4/3 = 6/3 = 2 ⇒ R.H.S

∵ L.H.S = R.H.S

∴ (-2 , 2) is a solution of the equation y = -1/3 x + 4/3

∴ (-2 , 2) is the solution of the two equations

* Its true

all positive real numbers

Answer:

C. All real numbers

Step-by-step explanation:

The domain refers to all values of x that makes the function define.

The given given graph represents a  linear function.

A linear function is a polynomial function.

Polynomial functions are defined for all real numbers.

The correct choice is C.

It is 5/8 because it is 5 per 8. You cut up the cookies and not the people. It does not reduce.

Final answer:

Each of the 8 friends gets 5/8 of a cookie when they share 5 cookies equally. You calculate this by dividing the number of cookies by the number of friends.

Explanation:

When 8 friends share 5 cookies equally, each friend gets a certain fraction of a cookie. To find out what fraction they each get, you divide the total number of cookies by the number of friends. In this case, you divide 5 cookies by 8 friends.

The calculation is 5 cookies ÷ 8 friends = 5/8 of a cookie for each friend.

Therefore, this means each friend gets 5/8 of a cookie. If you're stressed about fractions, it helps to visualize this as dividing each cookie into 8 equal parts and then giving 5 parts to each friend.

Answer:

$2.50

Step-by-step explanation:

just do 1 for the first hour then .5 for the next 2 then .5 for the remaining 49 minutes

Answer: $2.50

Step-by-step explanation: The formula to solve the cost of parking is $1 for the first hour + (3 x .5) for the additional three hours.

1 + (3 x .50) = 1 + 1.50 = $2.50 is the cost to park.

Answer:

Step-by-step explanation:

Answer:

Option A.

Step-by-step explanation:

we have

Derek's account

[tex]D(t)=500(1+2.5t)[/tex]

Susan's account

[tex]S(t)=500(1+1.8)^t[/tex]

Using a graphing tool

see the attached figure

At first Derek's account balance will be greater, but eventually Susan's account balance will be greater

area of parallelogram=base x height

= 30 x 20

= 600feet

Answer:

6 hours

Step-by-step explanation:

1. Divide the total miles (330) by the speed (55)

  330/55 = 6

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷The dots in between each term means multiply. First, we need to multiply all the like terms.

10 * 10 = 100

a * a = a^2

b = b

You can also multiply a number with a variable to get:

100a^2

You combine all terms together and you get:

100a^2 * b

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

Answer:

you can multiply them all

100ba^2

ANSWER

Q(5,-2),S(-3,4)

The given points have coordinates,

P(5,2) and R(-3,-4).

The mapping for a reflection across the x-axis is

[tex](x,y)\to (x,-y)[/tex]

This implies that,

[tex]P(5,2)\to Q( 5,-2)[/tex]

and

[tex]R(-3,-4) \to S(-3,4)[/tex]

The correct choice is A.

Answer:

The correct option is A.

Step-by-step explanation:

Answer:

Option b

Step-by-step explanation:

Since we are dealing with a question that deals with domain and range, it is best if we solve the problem graphically with the help of a calculator or any plotting tool.

Please, see attached image

We graph the equations and find the behavior of the graph

Domain

All reals except multiples of 2π

Range:

f(x) ∈  (-∞,-2] ∪ [2,∞)

Final answer:

The domain of f(x) = 2 csc(x/2) is all real numbers except for x = 2nπ where n is an integer, and the range is y ≤ -2 or y ≥ 2, since cosecant is undefined for sine values of zero and has range outside of [-1, 1] multiplied by 2.

Explanation:

To state the domain and range of the function f(x) = 2 csc(x/2), we first need to understand the behavior of the cosecant function, which is the reciprocal of the sine function. The sine function has a domain of all real numbers and a range of [-1, 1]. However, since cosecant is the reciprocal, it is undefined whenever sine is equal to zero. Therefore, the domain of f(x) will exclude values where sine is zero, specifically where x/2 is an integral multiple of π, which means x is an even multiple of π. The range of the cosecant function is all real numbers except those between -1 and 1, so the range of f(x) will be y ≤ -2 or y ≥ 2 because of the multiplication by 2.

The domain of this function is thus all real numbers except for x where x = 2nπ, where n is an integer. The range is all real numbers y such that y ≤ -2 or y ≥ 2.

Answer:

(a-b, c)

Step-by-step explanation:

The midpoints of the two diagonals are the same, so we have ...

(P + (-a, 0))/2 = (O +(-b, c))/2

Multiplying by 2 and subtracting (-a, 0), we get ...

P = (0, 0) +(-b, c) -(-a, 0)

P = (a-b, c)

Answer:-18

Step-by-step explanation:x in (-oo:+oo)

(1/2)*x = -9 // + 9

(1/2)*x+9 = 0

1/2*x+9 = 0 // - 9

1/2*x = -9 // : 1/2

x = -9/1/2

x = -18

x = -18

brainliest please

Answer:

$70

Step-by-step explanation:

$40x.75=30

30+40=$70