Given that x is a nonnegative number, a student conjectured that x + 3 < x2.
Which value of x is a counterexample to the student's conjecture?
A: x= -1/3
B: x= -3
C: x= 2
D: 3

The number of cookies prepared from 1.33 cups of butter are 48.

A ratio in mathematics signifies how many one number appears to contain another. For instance, when there are eight oranges as well as six lemons in a fruit bowl the orange-to-lemon ratio is eight to six, or 8:6, which really is similar to the proportion 4:3.

Now, as per the given question.

In this item, we have been asked to calculate the total number of cookies that may be made by having;

Let 'x' be the cookies made by 1.33 cups of butter.

When, six dozen cookies with 2 cups of the butter = 72 cookies with 2 cups of the butter.

We will use the ratio & proportion formula to solve this problem:

a/b = c/d

Let us now enter the values:

72 cookies/ 2 cups of butter = x / 1.33 cups of butter

Cross multiplying the equations;

72 cookies × 1.33 cups of butter = x × 2 cups of butter

Thus,

x = (72 cookies × 1.33 cups of butter)/2 cups of butter

x = 48

Thus,  48 cookies will be made in proportion to 1.33 cup butter.

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The complete question is-

You are making cookies and are missing a key ingredient eggs. You have most of the other ingredients needed to make the cookies, except you have only 1.33 cups of butter and no eggs. You note that the recipe calls for two cups of butter and three eggs (plus the other ingredients) to make six dozen cookies. You call a friend and have him bring you some eggs. If you use all the butter (and get enough eggs), what number of cookies will you make?

Mr. Lopez spread the stones at a pace of 0.059 cubic yards per hour.

A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

"Per unit of time" is a frequent sort of rate, and examples include speed, heart rate, and flux. Exchange rates, literacy rates, and electric field ratios are examples of ratios with a non-time denominator (in volts per meter).

The word "per" is used to denote the division of the units of the two measurements that make up a rate when discussing its units (for example a heart rate is expressed "beats per minute"). A rate that is defined using two numbers of the same units will provide a dimensionless quantity that can be stated as a percentage (for instance, the global literacy rate in 1998 was 80%), fraction, or multiple. Examples of these rates include tax rates and literacy rates.  

2/34 = 0.0588 equals to 0.059 ( approximately).

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Answer:

3x² + x

Step-by-step explanation:

collect the like terms first:

2x² + x² - 4x + 5x + 1 - 1

3x² + x

Answer:

the last answer. 3x to the second power + x

Step-by-step explanation:

Answer: where's the pic?

Answer:

x = 5

Step-by-step explanation:

Given:

[tex]2 \frac{2}{7}:(0.6x)=\dfrac{4}{21}:0.25[/tex]

Convert the mixed number into an improper fraction by multiplying the whole number with the denominator of the fraction, adding it to the numerator of the fraction, and placing it all over the denominator of the fraction:

[tex]\implies 2\frac{2}{7}=\dfrac{2 \times 7+2}{7}=\dfrac{16}{7}[/tex]

Therefore:

[tex]\implies \dfrac{16}{7}:(0.6x)=\dfrac{4}{21}:0.25[/tex]

[tex]\implies \dfrac{\frac{16}{7}}{0.6x}=\dfrac{\frac{4}{21}}{0.25}[/tex]

Cross multiply:

[tex]\implies \dfrac{16}{7} \times 0.25 = \dfrac{4}{21} \times 0.6x[/tex]

[tex]\implies \dfrac{16\times 0.25}{7} = \dfrac{4\times 0.6x}{21}[/tex]

[tex]\implies \dfrac{4}{7} = \dfrac{2.4x}{21}[/tex]

Cross multiply again:

[tex]\implies 4 \times 21=2.4x \times 7[/tex]

[tex]\implies 84=16.8x[/tex]

Divide both sides by 16.8:

[tex]\implies \dfrac{84}{16.8}=\dfrac{16.8x}{16.8}[/tex]

[tex]\implies 5=x[/tex]

[tex]\implies x=5[/tex]

Answer:

The value of x is 5.

Step-by-step explanation:

Let's solve for the value of x,

→ 2 2/7 : (0.6x) = 4/21 : 0.25

→ 16/7 : (0.6x) = 4/21 : 0.25

→ (16/7) × 0.25 = (4/21) × 0.6x

→ 4/7 = (2.4x)/21

→ 2.4x × 7 = 4 × 21

→ 16.8x = 84

→ x = 84/16.8

→ [ x = 5 ]

Hence, the value of x is 5.

The first five terms of a geometric sequence in which the second term is 6 and fourth term is 54 are 2, 6, 18, 54, 162. Thus, the correct option is option D.

A Geometric progression may be defined as a series of terms in which the ratio between each succeeding term and the preceding term of the series is constant.

It is given that the second term of the series is 6 and the fourth term is 54.

The first five terms of geometric sequence are given by a, ar, ar², ar³ and ar⁴.

Thus, ar = 6                                                            ......(1)

ar³ = 54                                                                  ......(2)

Divide equation (2) by (1)

ar³/ar = 54/6

r² = 9

=> r = 3

Putting value of r in equation (1)

ar = 6

=> a×3 = 6

=>a = 2

Now, substituting the values of a and r the terms of Geometric progression are given by:

a = 2, ar = 6, ar² = 18, ar³ = 54 and ar⁴ = 162.

Thus, the first five terms of Geometric sequence are given by 2, 6, 18, 54, 162.

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Answer:

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

The two given angles form a linear pair.

Sum of the two angles is 180°, set equation and solve for e:

50 students of the 200 students in the school would favor a new dress code.

We will use simple cross multiplication here

For first case

no. of students surveyed = 20

no. of student agreed for a new dress code = 5

This gives us 5/20

For second case

no. of students surveyed = 200

no. of student agreed for a new dress code = x

This gives us x/200

Lets us cross multiply

5/20 = x/200

20x = 200×5

x = (200×5)/20

x = 50

Given an equation between two fractions or rational expressions in mathematics, particularly in primary arithmetic and elementary algebra, one might cross-multiply the equation to make it simpler or get the value of a variable.

The technique can be used to remember which things to multiply together by drawing lines that resemble the outline of a heart. It is also sometimes called as "cross your heart" technique.

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Using distance formula, distance between two points is √61 unit

Let's us consider an example first -

What is the the distance between A and B

Let A = (3,2) and B (9,7)

Given A (3,2) and B( 9,7) are the two points on a plane

We have find to distance between A and B

Put the distance formula in two points as we know -

Distance= d√(x^2-x^1)^2 + (y^2-y^1) ^2

Here X1= 3

         X2 =9

         Y1=2

         Y2=7

Thus putting all these value x and y formula

d= √(9-3)^2+(7-2)^2

d=√(6^2+5^2)

d=√(36+25)

d=√61 unit

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Answer:

$29.05

Step-by-step explanation:

First, you have to multiply $19.95 by 2 since he bought 2 shirts that were the same price. 19.95 times 2 is a total of $39.90. It says that he saved $9.10 on both shirts so, in order to see the original price of the shirts, you would have to multiply $9.10 times 2 which is $18.20. Now you need to add 39.90 to 18.20 which is $58.10. You just need to divide that by 2 which will give you $29.05.  Each shirt's orignial price was $29.05

Hope that helps you out :D

2x+6-4x-1=13

2x+5=13

2x=8

x=4

Answer:

y = -0.6x - 1.6.

Answer:

27

Step-by-step explanation:

Say the youngest sibling is a. Anna would be a+1, and the oldest would be a+2. If the sum of all of them are 81, then 3a+3 = 81. minus three on both sides, and you get 78. So 3a = 78/3 = 26. if the youngest is 26, then Anna will be a + 1 so 27.

The age of Anna where she is the middle of three siblings is 27 years.

Given data:

Let's represent Anna's age as "x." Since Anna is the middle sibling, the ages of her siblings would be x - 1 and x + 1, since they are consecutive integers.

According to the information given, the sum of their ages is 8181:

x + (x - 1) + (x + 1) = 81

Now, combine like terms:

3x = 81

Divide both sides by 3:

On simplifying the equation:

x = 81/3

x = 27

Hence, Anna's age is 27 years.

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The complete question is attached below:

Anna is the middle of three siblings whose ages are consecutive integers. If the sum of their ages is 81, find Anna's age.

The quotient is 10/3 .

Sharing something equally is one way to view division.

Whatever we all equally share in this problem must be a part, not a whole. What are some examples of things we typically consider to be parts? We do, however, discuss food in casually.

3/4  of a pan of brownies or 2 1/2slices of pizza could be included. Additionally, we weigh some goods in division of a pound, notably bulk foods and sweets.

There are some materials that we purchase in division of a whole, such as lengths of fabric, rope, or ribbon that are sold in units of a yard. Any of those objects could be divided into equal portions as part of your word puzzle. Here are two illustrations:

At the supermarket, Dayana and her 3/4 friends purchased a candy bag weighing 2 1/2  lb. How much candy will each individual receive if they decide to divide it equally?

(2 1/2)/(3/4)= (5/2)/(3/4)= (5[tex]\times[/tex]4)/(3[tex]\times[/tex]2)=20/6=10/3

The quotient is 10/3 .

This means that after Dayana cuts each piece of board, its length will be  10/3 yards.

Therefore, the quotient is 10/3.

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Solving the given equation y = x(ab/a - b) for a, we have: a = by/(y - bx).

To solve an equation for a given variable is to make the variable the subject of the formula. To do this, isolate the variable to one side of the equation using appropriate properties of equality.

Given the equation,

y = x(ab/a - b)

Multiply both sides by 1/x

y/x = ab/(a - b)

Multiply both sides by (a - b)

y/x × (a - b) = ab/(a - b) × (a - b)

y(a - b)/x = ab

(ay - by)/x = ab

ay - by = abx

ay - by + by = abx + by

ay = abx + by

ay - abx = abx + by - abx

ay - abx = by

a(y - bx) = by

Divide both sides by (y - bx):

a(y - bx)/(y - bx) = by/(y - bx)   [division property of equality]

a = by/(y - bx)

Thus, solving the given equation y = x(ab/a - b) for a, we have: a = by/(y - bx).

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A pair of shoes gives us 48 different outfits.

What is a linear equation?

We will employ the basic counting principle, which states that if one task can be completed in method A and another in way B, then both tasks may be completed in way A*B.

If mom buys 1 shirt, then total shirts(A) = 6+1 =7, total pants(B) = 2 and total shoes (C) = 3

By basic counting principle, number of outfits = A*B*C = 7*2*3 = 42 outfits possible

and

If mom buys 1 pair of shoes, then total shirts(A) = 6, total pants(B) = 2 and total shoes (C) = 3+1 = 4

By basic counting principle, number of outfits = A*B*C = 6*2*4 = 48 outfits possible

hence, buying a pair of shoes gives us 48 different outfits.

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Answer:

Step-by-step explanation:

x=4 is a vertical line.

horizontal line through (-6,5): y=5

y=6 is a horizontal line.

vertical line through (-6,5): x=-6

The equation of line parallel to y = -( 1/3 )x + 4 and passing through the point P ( 6 , 5 ) is y = -( 1/3 )x + 7

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = -( 1/3 )x + 4

Let the first point be P ( 6 , 5 )

Slope m = -1/3

The parallel lines have the same slope , so the point-slope form of the equation of a line to find the equation of the line passing through P(6,5) with slope -1/3 is

y - 5 = ( -1/3 ) ( x - 6 )

Adding 5 on both sides , we get

y = ( -1/3 )x + 2 + 5

y = -( 1/3 )x + 7

Hence , the equation of line is y = -( 1/3 )x + 7

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The complete question is attached below :

What is the equation of the line that is parallel to the line y = -1/3x + 4 and passes through the point (6, 5)?

A) y = -1/3x + 3

B) y= -1/3x + 7

C) y= 3x - 13

D) y= 3x + 5

The maximum income the doctor can get in a day is $1280

Time required for routine office visits = 15 minutes

Time required for physical visits = 45 minutes

Maximum physical visits possible in a day = 10

Maximum routine visits possible in a day = 12

Available hours for appointment = 9 hours or 540 minutes

Cost of routine appointment = $60

Cost of physical appointment = $70

In order to maximize income, she should do maximum possible routine visits as it gives more return in less time and the remaining time can be used to do physical visits, therefore:

No. of routine visits the doctor should do = 12

Time consumed in 12 visits = 12*15 = 180 minutes

Time remaining = 360 minutes

No. of physical visits she should do = 8

Time consumed in 8 physical visits = 8*45 = 360 minutes

Total income the doctor will generate in a day  = 12*60 + 8*70

= 720 + 560 = $1280

Hence, the maximum income of the doctor will be $1280

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Answer:

b=5

Step-by-step explanation:

Here,

b + 13 = 18

or, b = 18 - 13

or, b = 5

Hence, b=5

Answer:

B = 5/b, b  0

Step-by-step explanation:

Bb+13=18

Subtract 13 from both sides.

Bb=18−13

Subtract 13 from 18 to get 5.

Bb=5

The equation is in standard form.

bB=5

Divide both sides by b.

b

bB

​

=

b

5

​

Dividing by b undoes the multiplication by b.

B=

b

5

​

The average (division) change of the price of one share per one day is $7.896

The given parameters are

Total = $39.48

Number of days =  5 days

The average (division) change of the price of one share per one day is calculated as

Average = Total/Number of days

So, we have

Average = $39.48/5

Evaluate the quotient

Average = $7.896

Hence, the average (division) change of the price of one share per one day is $7.896

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1, 3, and  5 are true

Answer:

y = -4x -4

Step-by-step explanation:

we need to get two points to calculate the gradient

points chosen are (-2,3) and (-3,7)

Gradient = change in y coordinates/ change in X coordinates

G = (7-3)/(-3- -2)

= 4/-1

= -4

to write the equation in slope -intercept form we need one known point (-2,3) and one unknown point (X,y) and the gradient.

G = ∆y/∆x

-4 = (y - 3)/ (X - -2)

-4 = (y-3)/ (X+2)

we now cross multiply

-4(X + 2) = y - 3

-4x -8 = y-3

-4x -8+4 = y

y = -4x -4

Answer:

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

From the right triangle we get the sum:

From the exterior angle theorem we get the sum:

Subtract the first equation from the second to get:

Answer:

y = 25

Step-by-step explanation:

Solution 1:

The line X is on, is a supplementary angle.

180-115 is 65

There are two Xs

A triangle adds up to 180

180- 65- 65= 50

50/2= 25

Solution 2:

The line X is on is a supplementary angle.

180-115 is 65

180- 65 - 90 (right angle)= 25

These measurements are not identical due to confounding;

When the effects of two or more explanatory variables on a response variable cannot be distinguished from one another, confounding occurs in an experiment.

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The area of triangle ABC with vertices is 22 square units

The vertices are given as:

A(4, -3) B(9,-3) , and C(10, −11)

The area of the triangle is calculated using

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

This gives

Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|

Evaluate the sum of products

Area = 0.5 * |44|

Remove the absolute bracket

Area = 0.5 * 44

Evaluate

Area = 22

Hence, the area of ABC with vertices is 22 square units

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The average speed in meters per second is 10.4 m/s.

Average speed is the total distance travelled per time. Average speed can be determined by dividing total distance by

Average speed = total distance / total time

The first step is to convert kilometer to meter: 1000 meter = 1 kilometer

The second step is to convert hours to seconds:

1 hour = 60 minutes

1 minute = 60 seconds

1 hour = 60 x 60 seconds

1 hour = 3,600 seconds

Multiply the average speed by 1000 meters and divide by 3,600 seconds.

37.6 x (1,000 / 3,600)  = 10.44 m / s

10.4 m/s (1 d.p)

In order to round off to one decimal place, if the hundredth figure is less than 5, there is no change in the tenth digit. Digits that are less than the tenth digit are removed.

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Answer: 75%

Step-by-step explanation:

20-5=15 right handed  students

[tex]\displaystyle\\\frac{15}{20}*100\% =\\\\\frac{15*20*5}{20} \%=\\\\15*5\%=\\\\75\%\ -\ percentage\ of\ students\ are\ right\ handed[/tex]

Angle between hour and minute hand= 204°

a figure which is formed by two rays or lines that shares a common endpoint is known as Angle.

The hour hand has covered 2 h and 48 min from position 12 o'clock (reference position). And in case of minute hand 22 min from reference. Required angle is angle covered by minute hand minus the angle covered by hour hand (clearly minute hand has covered greater angle in comparison with hour hand).

For calculating angle covered by minute hand:

In 60 min the min hand covers 360°

60 min = 360°

1 min = 6° ; 48 min = 288°

For calculating angle covered by hour hand:

12 h ( of hour hand) = 360°

1 h = 30°

For [2 + (48/60)] h, the angle covered= [2 + (48/60)]*30° = 84°

Angle between hour and minute hand = (288–84)° = 204°

It is the acute angle between hour and minute hand. For finding reflex angle subtract the obtained acute angle from 360°. So the reflex angle will be 299°.

Angle between hour and minute hand= 204°

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