Carl bought 19 apples or 2 different varieties to make pies. The total cost of apples was $51.00. Granny Smith apples cost $3.00 per pound and Gala apples cost $2.50 per pound. How man pounds of Granny apples did Carl buy?

Answer:

1.  52

2. 2.9

Step-by-step explanation:

To find the mean, we take all the numbers, add them up then divide by the number of numbers.

1.  mean height

mean = (50+54+52+56+48)/5

            =260/5

            =52

52 inches

2.  mean score

There are 5+3+12+2+6+6+4 students = 38 students

Multiply the number of students times the score and add together

total points =  (0*5+1*3+2*12+3*2+4*6+5*6+6*4)

        = 111

The mean is the total points  divided by the number of students

mean = 111/38

        =2.92

Answer:

[tex]\bar x = 52inch\\\bar x_w = 2.92[/tex]

Step-by-step explanation:

According to the data recorded in the table, the average of the students' heights is calculated with the expression for the arithmetic mean:

[tex]\bar x =\frac{1}{n} \sum x_i[/tex]

[tex]\bar x = \frac{1}{5}(48 + 50 + 52 + 54 + 56) = \frac{260}{5} = 52[/tex]inch.

In the same way, the weighted average must be used to find the average football score:

[tex]\bar x_w = \frac{\sum x_i * w_i}{\sum w_i}[/tex], where wi are the frequencies of each response.

[tex]\bar x_w = (0 * 5 + 1 * 3 + 2 * 12 + 3 * 2 + 4 * 6 + 5 * 6 + 6 * 4) / (5 + 3 + 12 + 2 + 6 + 6 + 4) = \frac{111}{38} = 2.92[/tex]

Answer:

8x^2 - 25x +7

Step-by-step explanation:

Substitute the polynomials in

A^2 - (B+C)

(3x-4)^2 - (x+7+x^2+2), simplify the equation

Using foil method, (9x^2-24x+16) - (x+7+x^2+2)

(9x^2-24x+16)-(x^2+x+9), distribute the minus/negative sign to the second parenthesis

(9x^2-24x+16) - x^2-x-9, combine like terms

8x^2 - 25x +7

You pess the thing that looks like a paperclip. Then you take a picture and crop it

Answer:96

Step-by-step explanation:

A; 480/16 = 30 students per classroom

B: 192/12 =16 students per classroom

we need x such that [tex]\frac{480-x}{16} = \frac{192+x}{12}[/tex]

which means

(480-x )* 12 should be equal to (192+x) * 16

5,760 - 12x = 3,072+16x

5,760 - 3,072 = 12x + 16x

2,688 = 28x

x = 96

For an equation to be linear, the slope has to be the same/constant.

To find the slope (m), you use the slope formula:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]  and substitute in 2 points

(1 , 60) [x₁ , y₁] and (5 , 70) [x₂ , y₂]

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]  

[tex]m=\frac{70-60}{5-1}[/tex]

[tex]m=\frac{10}{4} =\frac{5}{2}[/tex] or 2.5

Try a different point to see if the slope is the same:

(5, 70) and (20, 80)

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{80-70}{20-5}[/tex]

[tex]m=\frac{10}{15} =\frac{2}{3}[/tex] or 0.6666666

Since the slopes are different, a linear equation can not be used

Answer:

C.

Step-by-step explanation:

C is true because we already know g(0) is -2, and functions cannot repeat themselves with different numbers like that. A is not true because the range does not go that far down. B is not true because the domain does not go that far up.

Answer:

C is the answer

Step-by-step explanation:

C is the answer because

Answer:

C- 42

Step-by-step explanation:

there are 8 ounces in a cup so 12 x 8 = 96 oz

96/2.25 = 42.6666666667

Rounded back to 42

By using all the chocolate cream, at most the number of eclairs that can be made is:

                 C) 42

It is given that:

You have 12 cups of chocolate cream to fill eclairs.

Each eclair requires 2.25 ounces of filling.

We know that:

The universal conversion that is used is:

  1 cups=8 ounces

and hence,

12 cups= 12×8=96 ounces.

Hence, the number of ounces of chocolate cream to fill eclairs= 96 ounces

Also,

amount of filling required by 1 eclair= 2.25 ounces.

Hence, Number of eclairs that can be made is:

[tex]Number\ of\ eclairs=\dfrac{96}{2.25}\\\\i.e.\\\\Number\ of\ eclairs=42.67[/tex]

This means that:

Atmost the number of eclairs than can be made= 42

Answer:

2x=30 degrees

Step-by-step explanation:

Add up all of the angles and set them equal to 180 degrees, because triangles are always made up of angles with a sum of 180 degrees.

2x+4x+6x=180

12x=180

x=15

smallest angle is 2x

2(15)=30

Final answer:

To solve the given system of linear equations, the elimination method is used, resulting in the solution x = 63/26 and y = -97/26.

Explanation:

The system of equations presented by the student:

-4x + 5y = 8

6x - y = 11

belongs to the topic of algebra, specifically to solving systems of linear equations. To find the values of x and y that satisfy both equations, we can use methods like substitution or elimination. Let's use elimination in this case:

Multiply the second equation by 5 so that the y terms will cancel out when we add the two equations together. The second equation becomes 30x - 5y = 55.

Add the modified second equation to the first equation:

-4x + 5y = 8
+ 30x - 5y = 55

____________________

26x         = 63

Solving for x, we find that x = 63/26.

Substitute x into one of the original equations to find y.

Using 6x - y = 11:

6(63/26) - y = 11

378/26 - y = 11

y = 378/26 - 286/26

y = 92/26

Therefore, the solution to the system of equations is x = 63/26 and y = 92/26.

Answer:

2x– 3y = –18

3x + y = -5

Converting the equation in slope-intercept form

2x-3y= -18

-3y= -2x-18

-3y= -(2x+18)

3y=2x+18

y=(2x+18)/3

And for equation 2

y= -5-3x

For plotting the graph, the online graphing calculator desmos.com can be used.

The points can be calculated by putting negative and positive values of x in both equations.

The graph is attached as a picture.

As we can see from the graph that two lines intersect at (-3,4) so it is the solution of the given system of linear equations.

Answer:

[tex](-3,4)[/tex],

Step-by-step explanation:

The given system of equations is

[tex]\left \{ {{2x-3y=-18} \atop {3x+y=-5}} \right.[/tex]

To solve this system, we could multiply the second equation by 3, and solve for x:

[tex]\left \{ {{2x-3y=-18} \atop {9x+3y=-15}} \right.\\11x=-33\\x=\frac{-33}{11}=-3[/tex]

Now, we replace this value in a equation to find y-value:

[tex]3x + y = -5\\3(-3)+y=-5\\-9+y=-5\\y=-5+9\\y=4[/tex]

Therefore, the solution for the system is [tex](-3,4)[/tex], you can observe this in the graph attached.

The probability that a hat randomly chosen from Gina's inventory will be a helmet is 2 out of 12, which simplifies to 1 out of 6.

The subject of this question is probability, which is a branch of mathematics. Gina has 12 different hats, out of which 2 are helmets. The probability of an event happening is calculated as the number of ways the event can happen divided by the total number of outcomes.

So in this case, there are 2 helmets out of a total of 12 hats. So, the probability that a hat randomly chosen from Gina's inventory will be a helmet is 2 out of 12. You can also simplify this probability by dividing both the numerator and the denominator by the greatest common divisor, which is 2 in this case. Therefore, the simplified probability is 1 out of 6.

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The probability of choosing a randomly selected hat from Gina's inventory to be a helmet is 1/6.

To find the probability of selecting a helmet from Gina's inventory, we need to divide the number of helmets by the total number of hats in her inventory.

Gina has 12 hats, including 2 helmets, so the probability is

= 2 helmets / 12 hats

= 1/6.

Therefore, the probability of choosing a randomly selected hat from Gina's inventory to be a helmet is 1/6.

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The given expression simplifies to 0.

To simplify the expression (2√6÷√2+√3)+(6√2÷√6+√3)-(8√3÷√6+√3), we need to simplify each term and then combine like terms. Let's break it down step by step:

Simplify 2√6÷√2 by realizing that √6÷√2 is equivalent to √3. So, 2√3 remains.

In the second term, 6√2÷√6, √6÷√6 simplifies to 1, so we just have 6√2.

For the last term, 8√3÷√6, √3÷√6 simplifies to √(3÷6), which simplifies further to √(1÷2), or 8÷√2.

Combine like terms with the common denominator of √3, resulting in:
(2√3 + 6÷√3 - 8÷√3).

The terms with the square root denominators can be combined into (-2√3).

After combining, we have (2√3 - 2√3), which simplifies to 0. Therefore, the simplified expression is 0.

650000(0.025) = $16,250

Answer:

$16250 commission

($650,000 times .025 (2.5%) = $16250)

51 is the interquartile range for the set of data hope this helps;)

Answer:

Thank youuu

Step-by-step explanation:

Answer:

[tex]13.96\%[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]V=P(1-r)^{x}[/tex]  

where  

V is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$18,000\\r=?\\x=10\ years\\V=\$4,000[/tex]

substitute in the formula

[tex]\$4,000=\$18,000(1-r)^{10}[/tex]  

Simplify

[tex](2/9)=(1-r)^{10}[/tex]  

[tex](2/9)^{1/10}=(1-r)[/tex]  

[tex]r=1-(2/9)^{1/10}[/tex]  

[tex]r=0.1396[/tex]  

convert to percent

[tex]r=0.1396*100=13.96\%[/tex]  

it is the same as subtraction 34

50+(-34)=50-34

Answer:

No, the bolt won't fit into the hole

Step-by-step explanation:

We need to convert the diameter of the bolt into decimal by dividing:

2/9 = 0.222...

The hole has diameter of 0.2

Hence, 0.222 is larger than 0.2, so the bolt won't fit.

Answer:

£7,878

Step-by-step explanation:

she gets:

40p× 260 miles = 10,400p

she pays:

52 : 5.36= £9.70 per mile

260 x 9.70 = £2,522

to find out what she claimes more than she pays: 10,400 - 2,522 = 7,878

Amal claims £77.2 more than what she spends on petrol for a 260 miles journey for work.

To solve this problem, we need to calculate how much Amal earns for the journey and how much she pays for petrol.

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Answer:

The given equation 3x^2-4x+21 has no factors.

Step-by-step explanation:

[tex]3x^2-4x+21[/tex] We need to factorize this equation.

For factorization we split the middle term such that their sum is equal to middle term and product is equal to product of first and last term of the given expression.

in Our case : 63x^2

We need to find two factors of 63x^2 whose sum is equal to -4x

Factors of 63= 1,3,7,9,21,63

1* 63

3*21

7*9

None of the above factors sum is equal to -4.

So, the given equation 3x^2-4x+21 has no factors.

Answer:

No factors.

Step-by-step explanation:

The polynomial is not factorable with rational numbers. If you are on some advanced math, you would be able to be able to factor this.

3.5 cookies

Friend one: 3 Friend two: 3

One leftover cookie

Split in half give one to each and that makes 3.5

Each of the 2 friends gets 3.5 cookies when sharing 7 cookies equally.

When 2 friends share 7 cookies equally, you divide the total number of cookies by the number of friends. Here, you need to divide 7 cookies by 2 to find out how many cookies each person gets. The calculation would be:

Divide 7 by 2: 7 \/ 2 = 3.5

So, each friend gets 3.5 cookies. However, since you cannot share a cookie perfectly in half without changing its state, we assume this division is hypothetical. In a real-world scenario, they might have to decide how to divide the last cookie or simply share it equally, giving each friend half of the last cookie.

Answer:

(- 1, 3)

Step-by-step explanation:

To find the y- coordinate, substitute x = - 1 into the equation

y - 3 = 2(x + 1) ( add 3 to both sides )

y = 2(x + 1) + 3 ← substitute x = - 1

y = 2(- 1 + 1) + 3 = (2 × 0) + 3 = 0 + 3 = 3

Answer:

Step-by-step explanation:

Since this is not an equation, we're not looking to "solve."  Rather, we're to subtract the 2nd polynomial from the 1st one.

 -24x² + 18x + 6

-(               6x + 3)

------------------------------

-24x² + 12x   +3 (answer ... this is called a "difference" and is the

                              result of subtraction)

The simplified expression is 3( -8x² + 4x + 1).

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

(-24x² +18x+6) - (6x+3)

Now, simplifying the polynomial

= -24x² +18x+6 - 6x - 3

= -24x² + 12x + 3

= 3( -8x² + 4x + 1)

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$160 marked down 25% would be 40

When substituting x=2 and t=4 into the expression 1/8 (x^3 - 4)(t^2 + 8), it simplifies to 12.

If x=2 and t=4, to find the value of 1/8 (x3 - 4)(t2 + 8), we must substitute the values of x and t into the expression and simplify.

Firstly, calculate x3:

x^3 = 23 = 8

Then, calculate t2:

t^2 = 42 = 16

Now we substitute x^3 and t^2 into the expression:

1/8 (8 - 4)(16 + 8) = 1/8 (4)(24) = 1/8 * 96 = 12

Hence, the value of the expression is 12 when x = 2 and t = 4.

ANSWER

The discriminant is -3

EXPLANATION

The given quadratic equation is:

[tex] {x}^{2} + 3x - 6 = 0[/tex]

Comparing this equation to:

[tex]a {x}^{2} + bx + c = 0[/tex]

we have

a=1, b=3, and c=-6

The discriminant is calculated using the formula,

[tex]D = {b}^{2} - 4ac[/tex]

We substitute the values to get:

[tex]D = {3}^{2} - 4(1)(3)[/tex]

[tex]D = 9 - 12[/tex]

[tex]D = - 3[/tex]

Answer:

Discriminant = 33

Step-by-step explanation:

Solution of a quadratic equation ax² + bx + c = 0

Discriminant  = (b² - 4ac)

It is given that, x² + 3x - 6 = 0

To find the value of discriminant

x² + 3x - 6 = 0

Here a = 1, b = 3 and c = -6

Discriminant  = (b² - 4ac)

 =  (3² - 4 * 1 * (-6))

 = (9 +24) = 33

Therefore discriminant  of given equation is 33

Answer:

Y = 963

Step-by-step explanation:

The digits of Y add to 18.  The first digit is 3 times the third digit.  The second  digit is 2 times the third digit.  Y is a three digit number.​

Let Y a three digit number be: abc

First digit = a , Second digit = b, Third digit = c

Also given,

The digits of Y add to 18. => a+b+c = 18     eq(i)

The first digit is 3 times the third digit. => a = 3c     eq(ii)

The second digit is 2 times the third digit. => b = 2c     eq(iii)

Putting value of a and b in eq(i)

3c + 2c + c = 18

6c = 18

c= 18/6

c = 3

Putting value of c in eq(ii) and eq(iii)

a= 3c => a=3(3) => a= 9

b= 2c => b=2(3) => b = 6

Thus, Y = abc

Y = 963

Answer:

f(x) = x3 − 3x2 − 13x + 15    Factor:   x+3

f(x) = x4 + 3x3 − 8x2 + 5x − 25   Factor:  x+5

f(x) = x3 − 2x2 − x + 2     Factor:  x-2

f(x) = -x3 + 13x − 12  Factor:  x+4

Step-by-step explanation:

f(x) = x^3 − 3x^2 − 13x + 15

Solving:

We will use rational root theorem: -1 is the root of x^3 − 3x^2 − 13x + 15 so, factor out x+1

x^3 − 3x^2 − 13x + 15 / x+1 = x^2-2x-15

Factor: x^2-2x-15 =(x+3)(x-5)

So, factors are: (x+1)(x+3)(x-5)

Factor: (x+5)

f(x) = x^4 + 3x^3 − 8x^2 + 5x − 25

Solving:

We will use rational root theorem: -5 is the root of x^4 + 3x^3 − 8x^2 + 5x − 25, so factour out (x+5)

x^4 + 3x^3 − 8x^2 + 5x − 25 / x+5 = x^3-2x^2 +2x -5

So, factors are (x+5) (x^3-2x^2 +2x -5)

  Factor:  x+5

f(x) = x^3 − 2x^2 − x + 2    

Solving:

x^2(x-2)-1(x-2)

(x-2)(x^2-1)

(x-2) (x-1) (x+1)

Factor:  x-2

f(x) = -x^3 + 13x − 12

Solving:

-(x^3 + 13x -12)

We will use rational root theorem:

The 1 is a root of (x^3 + 13x -12) so, factor out x-1

Now solving (x^3 + 13x -12)/x-1 we get (x-3)(x+4)

So, roots are: - (x-1)(x-3)(x+4)

Factor (x+4)

Answer:

Polynomial 1 = x + 3

Polynomial 2 = x + 5

Polynomial 3 = x - 2

Polynomial 4 = x + 4

Step-by-step explanation:

We are given with Polynomials and and some factors.

We have to match the correct Pair.

We Map the polynomials on the graph then check which factors matches.

Polynomial 1).

x³ - 3x² - 13x + 15

factors are ( x + 3 ) , ( x - 1 ) , ( x - 5 )

Polynomial 2).

[tex]x^4+3x^3-8x^2+5x-25[/tex]

factors are ( x + 5 )

Polynomial 3).

[tex]x^3-2x^2-x+2[/tex]

factors are ( x + 1 ) ,( x - 1 ) , ( x - 2 )

Polynomial 4).

[tex]-x^3+13x-12[/tex]

factors are ( x + 4 ) ,( x - 1 ) , ( x - 3 )

Therefore,

Polynomial 1 = x + 3

Polynomial 2 = x + 5

Polynomial 3 = x - 2

Polynomial 4 = x + 4

Answer:

The approximate value of the area is [tex]153.86\ m^{2}[/tex]

Step-by-step explanation:

we know that

The area of the circle (landing pad) is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=7\ m[/tex]

substitute

[tex]A=\pi (7)^{2}[/tex]

[tex]A=49\pi\ m^{2}[/tex] ----> exact value of the area

Find the approximate value

assume [tex]\pi=3.14[/tex]

[tex]A=49(3.14)=153.86\ m^{2}[/tex] ------> approximate value of the area

Answer:

Area of Circular landing pad = 307.72 m^2

Step-by-step explanation:

Area of Circular landing pad = 2πr^2

where r = radius of circular landing pad = 7m

π = 22/7 = 3.14

by placing all these value in the formula

Area of Circular landing pad = 2*3.14*(7^2)

Area of Circular landing pad = 6.28*49

Area of Circular landing pad = 307.72 m^2

Answer:

-0.01851851851

Step-by-step explanation:

Answer:

[tex]-\dfrac{3}{2}[/tex]

Step-by-step explanation:

[tex]\dfrac{\frac{2}{3} }{\frac{4}{-9} } [/tex]

[tex]= \dfrac{2}{3} \div \dfrac{4}{-9}[/tex]

[tex]= \dfrac{2}{3} \times \dfrac{-9}{4}[/tex]

[tex]= \dfrac{-18}{12}[/tex]

[tex]= -\dfrac{3}{2}[/tex]

Answer:

Option B. [tex]-2x+30[/tex]

Step-by-step explanation:

we know that

The blue area is equal to the area of complete rectangle minus the area of the  white rectangle

so

[tex]A=(5+3x)(6)-(5)(4x)\\\\ A=(30+18x)-(20x)\\ \\A=-2x+30[/tex]