There are 40 flavors of ice cream at the local ice cream store. 37.5% of the flavors contain chocolate. Which proportion could be used to calculate the total number of ice cream flavors that contain chocolate?

QUESTION 1

The given inequality is

[tex]|m|-2>0[/tex]

We group like terms to get,

[tex]|m|>2[/tex]

This implies that,

[tex]-m>2[/tex] or [tex]m>2[/tex].

We simplify the inequality to get,

[tex]m<-2[/tex] or [tex]m>2[/tex].

We can write this interval notation to get,

[tex](-\infty,-2)\cup (2,+\infty)[/tex].

QUESTION 2

[tex]|x-4|-3\:>\:5[/tex].

We group like terms to get,

[tex]|x-4|\:>\:5+3[/tex].

[tex]|x-4|\:>\:8[/tex]

We split the absolute value sign to get,

[tex]-(x-4)\:>\:8[/tex] or [tex]x-4\:>\:8[/tex]

This implies that,

[tex]x-4\:<\:-8[/tex] or [tex]x-4\:>\:8[/tex]

[tex]x\:<\:-8+4[/tex] or [tex]x\:>\:8+4[/tex]

[tex]x\:<\:-4[/tex] or [tex]x\:>\:12[/tex]

We can write this interval notation to get,

[tex](-\infty,-4)\cup (12,+\infty)[/tex].

QUESTION 3

The given inequality is

[tex]|6+9x|\leq 24[/tex]

We split the absolute value sign to obtain,

[tex]-(6+9x)\leq 24[/tex] or [tex](6+9x)\leq 24[/tex]

This simplifies to

[tex]6+9x\ge -24[/tex] and [tex]6+9x\leq 24[/tex]

[tex]9x\ge -24-6[/tex] and [tex]9x\leq 24-6[/tex]

[tex]9x\ge -30[/tex] and [tex]9x\leq 18[/tex]

[tex]x\ge -\frac{10}{3}[/tex] and [tex]x\leq 2[/tex]

[tex]-\frac{10}{3}\leq x\leq2[/tex]

We write this in interval form  to get,

[tex][-\frac{10}{3},2][/tex]

QUESTION 4

The given inequality is

[tex]|1-5a|>29[/tex]

We split the absolute value sign to get,

[tex]-(1-5a)>29[/tex] or [tex]1-5a>29[/tex]

This simplifies to,

[tex]1-5a\:<\:-29[/tex] or [tex]1-5a\:>\:29[/tex]

This implies that,

[tex]-5a\:<\:-29-1[/tex] or [tex]-5a\:>\:29-1[/tex]

[tex]-5a\:<\:-30[/tex] or [tex]-5a\:>\:28[/tex]

[tex]a\:>\:6[/tex] or [tex]a\:<\:-\frac{28}{5}[/tex]

We write this in interval notation to get,

[tex](-\infty,-\frac{28}{5})\cup (6,+\infty)[/tex]

Answer:

4:1

Step-by-step explanation:

If the side length x is dilated to 2x, the area x² will dilate to (2x)² = 4x², which is 4 times the original x².

Answer:

1:4     C

Step-by-step explanation:

c) definition of midpoint

f) definition of congruency

g) property of rectangle (opposite sides are congruent)

h) SAS

i) CPCTC

Answer:

Let x represents the number of apple tree and y represents the number of pear tree and z represents the number of cherry tree in an orchard.

From the given statement: The number of apple trees is 8 more than twice the number of pear trees.

⇒ [tex]x = 2y + 8[/tex]                         .....[1]

Also, It is given that the number of cherry and pear trees combined is 11 more than the number of apple trees.

⇒[tex]y + z = x + 11[/tex]                    ......[2]

The farmer plants 143 trees total.

⇒[tex]x +y +z =143[/tex]                        .....[3]

Substitute equation [2] into [3] we get;

[tex]x + x + 11 = 143[/tex]

Combine like terms;

[tex]2x +11 = 143[/tex]

Subtract 11 on both sides we get;

2x + 11 -11 =143 -11

Simplify:

2x = 132

Divide both sides by 2 we get;

x = 66

Substitute the value of x in equation [1];

66 = 2y + 8

Subtract 8 on both sides we get;

[tex]66 -8 =2y + 8 -8[/tex]

Simplify:

58 = 2y

Divide by 2 on both sides we get;

y = 29

Substitute the value of x and y in equation [3];

we have;

29 + 66 + z = 143

95 + z =143

Subtract 95 on both sides, we get;

95+ z -95 = 143- 95

Simplify:

z = 48

The framer plant in the orchard =  66 apple trees , 29 pear trees and 48 cherry trees

Answer:

3

Step-by-step explanation:

I can see it in the demonstration graph

Answer:

3

Step-by-step explanation:

Male: 12

Female: 9

12 - 9 = 3

Hopes this helps

Answer:

24 dollars

Step-by-step explanation:

Linda spends $24 for two items that bought from the store.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

Given that,

Cost price of one time = $12.

Also, number of items that Linda bought = 2.

To find the total amount that Linda spends.

Use mathematical operations,

cost of 1 item = $12

Cost of 2 items = 12 x 2 = 24.

Hence, Linda spends $24 for 2 items.

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Answer:

all of your answers are correct

1.) 64

2.) x= -5+4i and x= -5-4i

3.) (4x+3iy)(4x-3iy)

Answer:

When we are completing squares, we need to divide by 2 the linear term and then find its square power, that's the term we need to add on both sides of the equality, as follows

[tex](\frac{16}{2})^{2} =(8)^{2}=64[/tex]

Basically, we need to add the number 64 both sides

[tex]x^{2} +16x+64=18+64[/tex]

The given equation is

[tex]x^{2} +10x+41=0[/tex]

We need to apply the quadratic formula to solve this equation

[tex]x_{1,2} =\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

Where [tex]a=1[/tex], [tex]b=10[/tex] and [tex]c=41[/tex]. Replacing these values, we have

[tex]x_{1,2} =\frac{-10(+-)\sqrt{10^{2}-4(1)(41) } }{2(1)}\\x_{1,2} =\frac{-10(+-)\sqrt{100-164 } }{2}=\frac{-10(+-)\sqrt{-64} }{2}[/tex]

There we need to use complex number, to transform the subradical number in a positive number

[tex]x_{1,2}=\frac{-10(+-)\sqrt{64}i }{2}=\frac{-10(+-)8i}{2}\\ x_{1,2}=-5(+-)4i[/tex]

Therefore, the complex solutions are

[tex]x_{1}=-5+4i\\ x_{1}=-5-4i[/tex]

The given expression is

[tex]16x^{2} +9y^{2}[/tex]

To solve this expression, remember that [tex]i=\sqrt{-1}[/tex]

First, we expresse both squares uniformly,

[tex]16x^{2} +9y^{2}=(4x)^{2}+(3y)^{2}[/tex]

But, we know that [tex]-(-1)=1[/tex], so

[tex](4x)^{2}+(3y)^{2}=(4x)^{2}-(-1)(3y)^{2}[/tex]

Then,

[tex](4x)^{2}-(-1)(3y)^{2}=(4x)^{2}-(3y)^{2}i^{2}[/tex], because [tex]i^{2}=-1[/tex]

Therefore, the expression with complex numbers is

[tex](4x)^{2}-(3iy)^{2}\\\therefore (4x+3iy)(4x-3iy)[/tex]

Answer is C 18%

Step-by-step explanation:

Answer:

If this is from TTM the answer is 10 cars.

Step-by-step explanation:

Answer:

The equation of the line would be y = 5x - 28

Step-by-step explanation:

First, we need to know that perpendicular lines have opposite and reciprocal slopes. Give that information, we know that the new line will be the reciprocal and opposite of -1/5. This would be 5. Now that we have that information, we can use it along with a point to fill in the point-slope form of the equation.

y - y1 = m(x - x1)

y - 2 = 5(x - 6)

Then we must solve for y.

y - 2 = 5(x - 6)

y - 2 = 5x - 30

y = 5x - 28

The domain of the function for one week of work is all values of x that are less than or equal to 50.

The domain of a function represents the set of all possible input values for that function. In this situation, the function represents the daily cost of hiring a plumber for x hours of work, and the maximum number of hours the plumber works per week is 50. Therefore, for one week of work, the domain of the function is the set of all values of x that are less than or equal to 50.

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Answer:

The percent error of Jocelyn's estimate is 2.14 .

Step-by-step explanation:

Formula

[tex]Percentage\ error = \frac{Error\times 100}{exact\ value}[/tex]

Where

[tex]error = \left | approx\ value - exact\ value \right |[/tex]

As given

Jocelyn estimates that a price of wood measures 5.5 cm.

If it actually measures 5.62 cm.

approx value =  5.5 cm

exact value = 5.62 cm

Put in the error formula

[tex]error = \left | 5.5 - 5.62 \right |[/tex]

[tex]error = \left | -0.12\right |[/tex]

error = 0.12

Put in the formula

[tex]Percentage\ error = \frac{0.12\times 100}{5.62}[/tex]

[tex]Percentage\ error = \frac{12}{5.62}[/tex]

Percentage error = 2.14 (Approx)

Therefore  the percent error of Jocelyn's estimate is 2.14 .

Answer:

The combined speeds of the trains equals 800 miles per 4 hours or

200 miles per hour.

This averages out to 100 miles per hour for each train.  

Westbound train is 18 mph faster so  

109 mph = Westbound

91  mph = Eastbound

That seems to be right except trains speeds of 91 mph and 109 mph seem to be VERY fast.

Step-by-step explanation:

36?

Bc if you divied 130/5 (girls) you get 36? Im sorry this may not be right, I'm not for sure :P

Answer:

8  1/4

Step-by-step explanation:

Answer:

B) 538, 650

Step-by-step explanation:

Given:

Errors on tax returns filed manually  = 20%

Errors on tax returns filed electronically  = 0.05%

Tax return filled in each way = 2.7 million

Manual filing:

2,700,000 x 20% = 2,700,000*0.2 = 540,000

Electronic filing:

2,700,000 x 0.05% = 2, 700,000*0.0005 = 1,350

Error difference = 540,000 - 1,350 = 538,650

There will be 538,650 more erroneous tax returns filed manually than there are filed electronically.

Thank you.

The difference between manually filed return and the electronically filed return is [tex]\boxed{538650}[/tex]. Option (b) is correct.

Further Explanation:

Explanation:

The total tax return is 2.7 million.

The errors on the tax return for electronic filling are [tex]0.05\%.[/tex]

The errors on the tax return for manual filling are [tex]20\%.[/tex]

Number of errors in filing tax return manually can be calculated as follows,

[tex]\begin{aligned}{\text{Errors in manual filling}} &= 2700000 \times 20\%\\ &= 2700000 \times \frac{{20}}{{100}} \\&= 540000\\\end{alignd}[/tex]

Number of errors in filing tax return electronically can be calculated as follows,

[tex]\begin{aligned}{\text{Errors in electronically filling}} &= 2700000 \times 0.05\% \\&= 2700000 \times \frac{{0.05}}{{100}} \\&= 1350 \\\end{aligned}[/tex]

The difference in the errors can be calculated as follows,

[tex]\begin{aligned}{\text{Difference}} &= 540000 - 1350 \\&= 538650 \\\end{aligned}[/tex]

The difference between manually filed return and the electronically filed return is [tex]\boxed{538650}[/tex]. Option (b) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Tax and Returns

Keywords: Tax, returns, filed, tax return, 20%, chance, errors, electronically, 0.05%, containing errors, chance, same, 2.7 million, each way, manually, manually filed, erroneous, 270575, income tax, salary, tax on salary.

Answer: choice C, y = 0.014x+0.85

==============================

Explanation:

Each column of the table represents an (x,y) pair of values

x = number of pages

y = cost

If we look at the first two columns, we see the two points (50,1.55) and (100,2.25). The x value is listed first. Let's compute the slope of the line through these two points

m = (y2-y1)/(x2-x1)

m = (2.25-1.55)/(100-50)

m = 0.7/50

m = 0.014

So far, we see the answer is between A,B or C as they have the slope of 0.014

Use this slope value, and one of the points -- say (x,y) = (50,1.55) -- to find the y intercept b

y = mx+b

y = 0.014x+b .... plug in the slope found earlier

1.55 = 0.014*50+b ... plug in the point (x,y) = (50,1.55)

1.55 = 0.7+b

1.55-0.7 = 0.7+b-0.7 ... subtract 0.7 from both sides

0.85 = b

b = 0.85

With m = 0.014 as the slope and b = 0.85 as the y intercept, we can say that y = mx+b turns into y = 0.014x+0.85. That narrows the answer down to choice C.

Answer:

105

Step-by-step explanation:

first, the printer print 15  (75/5) pages per minutes,

next, 7×15=105

Answer:

The correct option is C.

Step-by-step explanation:

From the given figure it is noticed that the coordinates of B are (-5,-7).

If ABC is reflected across x = 1, then

[tex](x,y)\rightarrow(1-(x-1),y)[/tex]

[tex](x,y)\rightarrow(2-x,y)[/tex]

[tex](-5,-7)\rightarrow(2+5,-7)[/tex]

[tex](-5,-7)\rightarrow(7,-7)[/tex]

If ABC is reflected across y =-3.

[tex](x,y)\rightarrow(x,-3-(y-(-3)))[/tex]

[tex](x,y)\rightarrow(x,-6-y)[/tex]

[tex](7,-7)\rightarrow(7,-6-(-7))[/tex]

[tex](7,-7)\rightarrow(7,1)[/tex]

Therefore option C is correct.

Answer: point Q is located in (3,4)

Step-by-step explanation: the ratio of SQ:QT is 5:2, and for every two units (up two, right two) it is one ratio. go up two, right two five times that leads a ratio between 5:2.

Answer:

562 + x ≥ 650

x ≥ 88

Step-by-step explanation:

He has 562 points.  He needs x points to get an A.  He must get at least 60 points to get an A.

562 + x ≥ 650

To solve this, we subtract 562 from each side

562-562 + x ≥ 650-562

x  ≥ 650-562

x ≥ 88

Answer:

0.25 pints of raspberries do you get per dollar.

Step-by-step explanation:

Unit rate defined as the rates are expressed as as a quantity of 1, such as 3 feet per second or 4 miles per hour, they are called unit rates.

As per the given statement: A farm lets you pick 3 pints of raspberries for $12.00.

⇒ for $12 a farm lets you pick 3 pints of raspberries.

then by unit rate definition,

Unit rate per dollar = [tex]\frac{3}{12} = \frac{1}{4} = 0.25[/tex] pint

Therefore, 0.25 pints of raspberries do you get per dollar.

Answer:0.25

Step-by-step explanation: hope I helped !

Answer:

95

Step-by-step explanation:

We have been given a diagram triangle in which measurement of few angles in terms of x are given.

Using those we need to find the exterior angle but before that we need to find the value of x.

We know that exterior angle is equal to sum of two distant interior angles of that triangle so we can write:

(8x+15)=(3x+20)+(4x+5)

8x+15=3x+20+4x+5

8x+15=7x+25

8x-7x=25-15

x=10

Now plug x=10 into exterior angle 8x+15

8x+15=8*10+15=80+15=95

Hence final answer is 95.

Hey There!

The answer is going to be the answer is

mEFC=253°

To find the answer you must find the value of mEF  which is

mEF,mFEC,mDC,mED

You subtract each of them  and you should get 73.

Then  add 180 and your final choice should be 253

Answer:

253

Step-by-step explanation:

Answer:

(-3,3)

Step-by-step explanation:

3x=36-15y and 11x =-78+15y

We move all x  and y terms to the left hand side of the equation , so that we can apply elimination method

3x=36-15y , Add 15 y on both sides , 3x + 15y = 36

11x =-78+15y, subtract 15y on both sides, 11x -15y = -78

Now we add both equations

3x  + 15y = 36

11x -15y = -78

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

14x  = -42

divide both sides by 14

x= -3

Now Plug in -3 for x in any one of the given equation

3x=36-15y

3(-3) = 36 - 15y

-9 = 36 - 15y

Subtract 36 on both sides

-45 = -15y

Divide both sides by -15

So y= 3

Answer is (-3,3)

Answer:

4,910 seconds

Step-by-step explanation: