A woman is throwing a party and has $200 to spend on snacks. She is purchasing packages of chips, c, for $1 each and Oreos, o, for $3 each. She needs to have 100 packages of snacks total. How many packages of chips and Oreos should she buy if she spends exactly $200?

Use your words to explain how you would solve the question and express your answer.

Answer:

all real values of x except x=5

Step-by-step explanation:

If [tex]f(x) = x2 – 25 and g(x) = x – 5,[/tex]

Then the domain is all real values of x except [tex]x=5[/tex].

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.

Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5), and irrational numbers such as √3, π(22/7), etc., are all real numbers.

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Answer:

Step-by-step explanation:

2/5=6/15

1/3=5/15

Answer:

6/15 and 5/15

Step-by-step explanation:

multiply 2/5 by 3 and 1/3 by 5

Answer:

The vertex is (-4, -52), and it represents the minimum for the function.

Step-by-step explanation:

Answer:

4.2

Step-by-step explanation:

5.7-1.5=4.2

Answer: x = 4.2

Explanation: If we're asked to solve for x in the equation x + 1.5 = 7.5, what we're really being asked to do is get x by itself on one side of the equation.

So if we take a look at the left side of our equation, notice that 1.5 is being added to x so in order to get x by itself, we must subtract 1.5 from the left side of the equation. Now remember your first rule of solving equations. If we subtract 1.5 from the left side of the equation, we must also subtract 1.5 from the right side of the equation.

So on the left side our +1.5 and -1.5 cancel out and we're simply left with x. On the right side of the equation,

5.7 - 1.5 simplifies to 4.2 so our answer is x = 4.2.

The nice thing about solving equations is that you can always check your answer by plugging it back in to the original equation.

So here, we're gonna plug a 4.2 back in for x in the original equation and we get (4.2) + 1.5 = 5.7.

Since 4.2 + 1.5 = 5.7 is a true statement, our answer checks and we know that it's right.

The correct answer is 12

Hope this helped!

Jane has 4 number of 20 phones and 11 number of 15 phone cards.

It is given that 15 phone cards worth either $20 or $15

lets Jane has x number of 20 phones  and y number of 15 phone cards

Then by the problem we have

x+y=15....(1)

20x+15y=245....(2)

Solve one of the equations either for the variable x or y. Now, substitute the solution from step 1 to the other equation.

So by using substitution method we have,

from equation 1 we get

y=15-x

use this value in equation 2

[tex]20x+15(15-x)=245\\\\20x+225-15x=245\\\\5x+225=245[/tex]

[tex]5x=20\\x=4\\y=15-4\\y=11[/tex]

Therefore we get x=4 and y=11

Therefore,Jane has 4 number of 20 phones and 11 number of 15 phone cards.

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Answer:

530.66 cm^2

Step-by-step explanation:

[tex]area \: of \: circle = \pi{r}^{2} [/tex]

Using the above formula,

Area of plate= 3.14(13)^2 = 530.66 cm^2

(I replaced pi with 3.14 since the question said to use 3.14 for pi)

Answer:

the area of a circle

[tex] \pi{r}^{2} [/tex]π= 3.14

r=13

The circumference of circle P is 6π ft. This corresponds to option (b) in the choices provided.

Understanding the Problem: The problem provides the length of the line segment PA, which is considered the radius of circle P.

Circumference Formula: The circumference of a circle is the distance around its edge. The formula to calculate it is C = 2πr, where C is the circumference and r is the radius.

Identifying the Radius: In this problem, PA is given as 3 ft. This represents the radius of circle P.

Substituting Values into the Formula: We substitute the given radius into the circumference formula:

  C = 2π ˣ 3 ft

Calculating: We perform the multiplication to find the circumference:

C = 6π ft

Complete Question:

What is the circumference of circle P?

PA = 3 ft

Express your answer in terms of π.

a. 3π ft

b. 6π ft

c. 12π ft

d. 24π ft

Answer:

Eight plus twenty four equals thirty two

have an amazing day! (❁´◡`❁)

Step-by-step explanation:

The word equation for "eight more than the number of children is 24" can be written as:

Number of children + 8 = 24

Let's break it down step by step:

1. Identify the unknown: The unknown in this equation is the number of children. Let's represent it as "x".

2. Translate "eight more than the number of children" into mathematical language: "Eight more than" means adding 8 to the number of children.

3. Write the equation: The equation becomes x + 8 = 24.

To find the value of x, we need to isolate it on one side of the equation. We can do this by subtracting 8 from both sides:

x + 8 - 8 = 24 - 8

Simplifying further:

x = 16

Therefore, the number of children is 16.

It's important to note that the word equation can be translated into different mathematical expressions. For example, another way to represent "eight more than the number of children is 24" would be:

Number of children = 24 - 8

This equation would also yield the same answer: 16.

Remember, word equations help us represent real-life situations in mathematical form, allowing us to solve problems and find solutions.

-p - 4p > -10

-5p > -10

p < 2

Hope this helps! ;)

Answer:

next time please ask a real question

Thanks

Step-by-step explanation:

The question appears to explore historical texts or languages, likely suited for college-level English or History studies, focusing on linguistics, manuscript studies, or medieval literature.

Given the fragments provided, it's challenging to decipher a coherent question or subject matter directly. However, the content suggests a possible exploration of historical texts or languages, particularly those relevant to English or linguistics studies at the college level.

Understanding or translating ancient or cryptic texts can be a significant part of higher education in English, where students might delve into Old English literature, manuscripts, or historical documents.

The various fragments hint at texts that might be from different periods or contexts, suggesting a study that spans a range of historical documents, potentially requiring translation or interpretation skills. Such a task would be well-suited for college-level English or History students focusing on linguistics, manuscript studies, or medieval literature.

Answer:

y=4x-22

Step-by-step explanation:

y-y1=m(x-x1)

y-(-10)=4(x-3)

y+10=4x-12

y=4x-12-10

y=4x-22

Answer:

10

Step-by-step explanation:

Divide 40 by 4, and you get 10. 10 rows.

Answer:

The correct answer is: [tex]4\frac{3}{5}[/tex]

Step-by-step explanation:

According to the rule of BODMAS, division is done before addition.

So, in a + b ÷ c, we will first calculate,  b ÷ c

Given b =  [tex]2\frac{2}{5}[/tex] = [tex]\frac{12}{5}[/tex] , c = [tex]\frac{3}{4}[/tex] .

So, [tex]\frac{b}{c}[/tex] = [tex]\frac{12}{5}[/tex] ÷ [tex]\frac{3}{4}[/tex]

So, [tex]\frac{b}{c} = \frac{12}{5} \times\frac{4}{3}[/tex] , as the numerator and denominator gets reversed as division is changed to multiplication.

So, [tex]\frac{b}{c} = \frac{16}{5}[/tex] .

Next the value of a to  [tex]\frac{b}{c}[/tex]  , where, [tex]a = 1\frac{2}{5} = \frac{7}{5}[/tex], we get,

[tex]\frac{7}{5} +\frac{16}{5} = \frac{23}{5} = 4\frac{3}{5}[/tex].

Answer:

2/5+0.6=1 and 9/10+0.1=1

Step-by-step explanation:

1-2/5=3/5

3/5=0.6

1-9/10=1/10

1/10=0.1

Answer:

16

Step-by-step explanation:

Answer:

2-x=1

2-1=1

Step-by-step explanation:

1 + 1 - 1 x 1 / 1.

Uses all 4 basic symbols.

Answer:0.8

Step-by-step explanation:

Answer:

  37.0

Step-by-step explanation:

Half of x is the longer leg of the right triangle shown. That leg length can be found using the Pythagorean theorem:

  x/2 = √(24.6² -16.2²) = √(605.16 -262.44) = √342.72

  x ≈ 2×18.513 ≈ 37.025 . . . . . . rounding to 3 decimal places

  x ≈ 37.0

Basically, we are trying to find the equation that goes through the two points shown in the table. The points are: (5,30) and (10,55). The equation of a line is y=my+b where m is the slope and b is the y intercept. To find slope look for the change in y over the change in x.

Slope = (55-30)/(10-5)=5

We can stop here because the only answer choice with a slope of five is choice A.

Answer: A

Answer:

2) Option 9.4 is correct

Therefore the length of the given line segment is [tex]s=9.4[/tex] units

3) Option (1,1) is correct

Therefore the midpoint of the given line  segment is M=(1,1)

Step-by-step explanation:

2) Given that the line segment CD with endpoints C at (-3,1) and endpoint at D (5,6)

To find the length of the given line segment :

That is to find the distance of the end points using distance formula

[tex]s=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] units

Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the given points (-3,1) and (5,6) respectively

Substitute the points in the distance formula we have

[tex]s=\sqrt{(5-(-3))^2+(6-1)^2}[/tex] units

[tex]=\sqrt{(5+3)^2+(5)^2}[/tex] units

[tex]=\sqrt{8^2+5^2}[/tex]

[tex]=\sqrt{64+25}[/tex]

[tex]=\sqrt{89}[/tex]

[tex]=9.4[/tex]

Therefore [tex]s=9.4[/tex] units

Option 9.4 is correct

Therefore the length of the given line segment is [tex]s=9.4[/tex] units

3) Given that the line segment PG with point P at (-6,4) and point at G (8,-2)

To find the midpoint of the given line segment :

Midpoint formula is [tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the given points (-6,4) and  (8,-2) respectively

Substituting the points in the midpoint formula we get

[tex]M=(\frac{-6+8}{2},\frac{4-2}{2})[/tex]

[tex]=(\frac{2}{2}+\frac{2}{2})[/tex]

[tex]=(1,1)[/tex]

Therefore M=(1,1)

Therefore option (1,1) is correct

Therefore the midpoint of the given line  segment is (1,1)

Answer:

80 percent

Step-by-step explanation:

Answer:

80 percent

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

We want to set up an expression involving 1, -6, -7, -3.

-6*-3--7+1

We use BODMAS to simplify:

We multiply to get:

18--7+1

We now add to obtain:

18--6

Note that negative negative gives addition.

Therefore:

18+6

This finally simplifies to:

24

Answer:

72

Step-by-step explanation:

72 i did the math

Answer:

Therefore the price of an foundation drink is $ 3.20(approx).

Step-by-step explanation:

Let the price of one fountain drink be x and one beg of popcorn be y.

The Clayton family bought 4 fountain drinks and 3 begs of popcorn and paid $22.50. The Hanks family bought 5 fountain drinks and 2 begs of popcorn and paid $23.75.

According to the problem,

4x+3y=22.50..............(1)

5x+2y=23.75..............(2)

Equation (1)×5 - Equation (2)×4

20x+15y-(20x+8y)=112.5-91

⇔20x + 15y -20 x-8y=21.5

⇔7y=21.5

⇔y = 3.07

putting the value of y in equation (1)

4x+3×3.07 =22.50

⇔4x=22.50 -9.21

⇔x=3.20

Therefore the price of an foundation drink is $ 3.20(approx).

Answer:

B

Step-by-step explanation:

Given

2x + 10 = 6 ( divide all 3 terms by 2 )

x + 5 = 3 ← equivalent equation

The equation which is equivalent to 2x + 10 = 6 from the given options is x + 5 = 3.

Given the equation in the question:

2x + 10 = 6

Options:

A) 2x = 4

B) x + 5 = 3

C) x + 10 = 3

D) 2x + 6 = 10

To find the equation that is equivalent to 2x + 10 = 6, we check each of the options.

For A) 2x = 4

2x + 10 = 6

2x = 6 - 10

2x = -4

Option A is wrong.

For B) x + 5 = 3

2x + 10 = 6

Divide each term by 2:

2x/2 + 10/2 = 6/2

x + 5 = 3

Option B is correct.

For C) x + 10 = 3

2x + 10 = 6

Divide each term by 2:

2x/2 + 10/2 = 6/2

x + 5 = 3

Option C is wrong.

For D) 2x + 6 = 10

2x + 10 = 6

Subtract 6 and 10 from both sides:

2x + 10 - 10 - 6 = 6 - 6 - 10

2x - 6 = -10

Option D is wrong.

Therefore, x + 5 = 3 is equivalent  to the equation.

Option B) x + 5 = 3 is the correct answer.

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Answer:

6

4 squared= 16

16÷8=2

2×3=6

Answer: the answer is 6

Step-by-step explanation:

Answer:

The co-ordinates of A' is

A)  [tex](-2,\frac{14}{3})[/tex]

Step-by-step explanation:

Given point:

(-3,7)

The point is dilated with a scale factor  [tex]r=\frac{2}{3}[/tex]  with the center of dilation at the origin.

To find the co-ordinates of the dilated point A'.

Solution:

Any  point dilated with the center of dilation at the origin with a scalar factor [tex]k[/tex] is given by:

[tex]D(x,y)\rightarrow D(kx,ky)[/tex]

Thus, the point (3,-7) dilated with a scale factor  [tex]r=\frac{2}{3}[/tex]  with the center of dilation at the origin  is given as :

[tex]A(-3,7)\rightarrow A'(\frac{2}{3}\cdot -3,\frac{2}{3}\cdot 7)[/tex]

[tex]A(-3,7)\rightarrow A'(-2,\frac{14}{3})[/tex]

Thus, the co-ordinates of A' is [tex](-2,\frac{14}{3})[/tex].

Answer:201525

Step-by-step explanation:

In permutations, the order of items matters. The word 'TOY' can be arranged in 6 different ways, calculated using the formula: n!/(n-r)!.

The student is asking a mathematical question related to permutations. Permutations refer to the arrangements of items where the order is important. In this instance, the student is interested in arranging the letters in the word 'TOY'. To calculate the number of ways to arrange these letters, we use the formula: n!/(n-r)!. Here, 'n' is the total number of items and 'r' is the number of items to choose and arrange.

Since 'TOY' has three distinct letters, then 'n' would be 3 and 'r' would also be 3. Applied to the formula, this becomes 3!/(3-3)!. Once you calculate this, you get 6. Therefore, there are 6 possible arrangements of the word 'TOY'.

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The formula to find the volume of a cylinder is V = hπr², where h is the height of the cylinder and r is the radius of its base.

To find V, the volume of a cylinder in cubic inches, we can use the formula V = Ah, where A represents the cross-sectional area of the cylinder and h represents the height or depth of the cylinder. To find the cross-sectional area for a cylinder, the formula A = πr² can be used, where r is the radius of the cylinder's base. Substituting value of A in volume's formula will give V = hπr², which is commonly used formula to find the volume of a cylinder.

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To find the volume of a cylinder in cubic inches, use the formula V = πr²h, where r is the radius of the base of the cylinder and h is the height of the cylinder.

The equation for finding the volume V of a cylinder in cubic inches can be derived from the basic principle that the volume of a shape is equal to the area of its base multiplied by its height. For a cylinder, the base is a circle, and the area of a circle is given by the formula πr², where r is the radius of the circle.

Therefore, the volume of the cylinder is the area of its base times its height, which can be written as V = πr²h, where h is the height of the cylinder. By using this formula, you can calculate the volume of a cylinder if you know the radius of its base and its height.

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Cost of item of $ 310 including the sales tax is $358.05.

Convert the percentage rate of sales tax to a decimal by dividing the percentage by 100.

A 15.50% sales tax rate becomes 0.155 when converted to a decimal.

After performing the multiplication, you will get the amount of sales tax that needs to be added to the item's price. So, $310  x 0.155 = $48.05.

Therefore, the total cost of the item after sales tax would be the original price plus the amount of sales tax, which is $310 + $48.05 = $358.05.