Wei Xun bought 8 pieces of chocolates and 10 lollipops for $17. The average price of a piece of chocolate was S$1. What was the average price of a lollipop?​

Answer:

[tex]11 - 2 {}^{3} [/tex]

[tex]11 - 8[/tex]

[tex]3[/tex]

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The correct option is B.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication, and non-negative exponentiation of variables involved.

Example:

 x² + 3x + 5

In order to find the values at which the given polynomial will have zeros of the function, we need to find the values at which f(x) changes from positive to negative or vice versa. Since this is the range at which the function must have crossed the x-axis on the graph.

As per the given table, the value of f(x) is changing from negative to positive and positive to negative are between 2.5 and 3.0 and between 4.0 and 4.5.

Hence, the correct option is B.

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Distance from the origin to the points  ≈ 0.41.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]  

Point A (5, 3, 4) and point B (−4, 2, 6) are located away from the origin (0,0,0), and the points from the origin to this points are expressed as OB - OA where;

Let OB is the distance from the origin to the point B

Let OA is the distance from the origin to the point A

Using the formula for calculating the distance between two points;

OA = √(z2-z1)²+(y2-y1)²+(x2-x1)²

OA = √(4-0)²+(3-0)²+(5-0)²

OA = √(16)+(9)+(25)

OA = √50

OA = 7.071

Similarly;

OB = √(6-0)²+(2-0)²+(-4-0)²

OB = √(6)²+(2)²+(-4)²

OB = √36+4+16

OB = √56

OB = 7.4833

Distance from the origin to the points = 7.4833 - 7.071= 0.4123

Distance from the origin to the points  ≈ 0.41

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Answer:

$63

Step-by-step explanation:

Alana has 4 units of the $171.

Brianna has 7 units of the $171.

Carla has 8 units of the $171.

Total units = 4 + 7 + 8 = 19

19 units = $171

1 unit  [tex]\frac{171}{19} \\= $9[/tex]

Brianna has 7 units, so she receives 7 x $9 = $63.

The shaded area for the inequality y > -3-(5/4)x is given below.

The inequality is the relation between two expressions showing the relationships such as greater than, lower than, greater than equals to, and lower than equals to.

The given inequality is -5x-4y<12

solving this inequality for y

-5x-4y<12

⇒ -4y<12+5x

⇒y > (12+5x)/(-4)

⇒y > -3-(5/4)x

the line y= -3-(5/4)x has y intersection at (0,-3) and  x intersection at (-12/5,0).

The inequality y > -3-(5/4)x show that this will be above the straight line y = -3-(5/4)x as if we put (0,0) in the inequality, the inequality will be 0>-3 which is true that shows that the region contains (0,0).

Therefore the shaded area for the inequality y > -3-(5/4)x is given below.

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The approximations of the mean and the standard deviation are 233.3 and 229.82, respectively

The table of values is given as:

Savings Lower Limit Upper Limit     Frequency

0-199         0         199                       345

200-399   200   399                         97

400-599   400   599                         52

600-799   600   799                         21

800-999   800   999                         9

1000-1199 1000  1199                         8

1200-1399 1200  1399                      3

Rewrite the table to include the class midpoint and the frequency

x               f

99.5         345

299.5        97

499.5        52

699.5        21

899.5        9

1099.5        8

1299.5        3

The mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{99.5* 345 + 299.5* 97 + 499.5* 52 + 699.5 * 21 + 899.5 * 9 + 1099.5 * 8 + 1299.5 * 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]

Evaluate

[tex]\bar x = 233.331775701[/tex]

Approximate

[tex]\bar x = 233.3[/tex]

Hence, the approximation of the mean is 233.3

The standard deviation is calculated as:

[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]

So, we have:

[tex]\sigma= \sqrt{\frac{(99.5-233.3)^2* 345 + (299.5-233.3)^2* 97 +...... + (1299.5 -233.3)^2* 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]

Evaluate

[tex]\sigma = 229.82[/tex]

Hence, the approximation of the standard deviation is 229.82

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Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Answer:  Choice A

[tex]\begin{pmatrix}-15 & 59 & -3\\16 & 61 & -83\\-45 & -99 & 106\end{pmatrix}[/tex]

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

Explanation:

In matrix A, the upper left corner is -3

Multiply this with -7 to get  -7*(-3) = 21

So we'll have 21 in the upper left corner of matrix -7A. The other entries will be handled in a similar fashion.

Meanwhile, the upper left corner of matrix B is 9. Multiply this with -4 to get 9(-4) = -36 which is the upper left corner entry of matrix -4B

Combine those products: 21 + (-36) = -15

The number -15 is the upper left corner entry in matrix -7A-4B

This points us to choice A as the final answer.

Answer:

True

Step-by-step explanation:

-77 is less than -76. Since the symbol refers to less than or equal to, this statement will be true.

The solution set for the given inequality is 3<x<5.

The given inequality is 6<x+3<8.

In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.

Now, solve the given inequality:

6<x+3<8⇒6<x+3 and x+3<8

6-3<x ⇒3<x

x+3<8⇒x<5

Thus, 3<x<5.

Therefore, the solution set is 3<x<5.

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Inequality and graph the solution set and a number line, express the Solution set in interval notation is 3 < x < 5

6<x+3<8

[tex]6 < x+3\quad \mathrm{and}\quad \:x+3 < 8[/tex]

[tex]\mathrm{If}\:a < u < b\:\mathrm{then}\:a < u\quad \mathrm{and}\quad \:u < b[/tex]

[tex]\mathrm{Combine\:the\:intervals}[/tex]

[tex]x > 3\quad \mathrm{and}\quad \:x < 5[/tex]

[tex]3 < x < 5[/tex]

Therefore the Inequality and graph of the solution set and a number line, express the Solution set in interval notation as 3 < x < 5.

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Answer:

D: (–∞, ∞); R: [–11, ∞)

Step-by-step explanation:

The domain of a quadratic function is all real numbers, so eliminate the third and fourth options.

Also, since the coefficient of [tex]x^2[/tex] is positive, we know the graph opens up and thus has a minimum.

This means that the first option must be wrong since the range has a maximum, not a minimum.

Therefore, the correct answer is Option 2.

Answer:

D: (–∞, ∞); R: [–11, ∞)

Step-by-step explanation:

I honestly don't know the answer but the other person said this so I'm putting it as my answer ill update this answer when i find out if its right or not.

update I GOT A 100% woop woop

Answer:

340 i am pretty sure

Step-by-step explanation:

Answer:

1 1/6 = 1
5/9 = 45/99

Step-by-step explanation:

When rounding, make sure that anything that's above half will be rounded up if anything is below half it will be rounded down.
e.g. Round to the nearest half or whole

1. 5/9
Answer: 45/99
Why: 5/9 is 4 units to 9 while 5/9 is half of a unit closer to 45/99

2. 8/10
Answer: 10/10 or 1
Why: 8/10 is 2 units from 10 while 8/10 is 3 units from 5

Hopefully this helped!

Answer:

The answer is either 30 degrees or 36 degrees.
You need a protractor to measure it.
Most probably, the answer is 30 degrees.
BUT PLEASE MEASURE THE ANGLE WITH A PROTRACTOR!

Answer:

d. 60°

Step-by-step explanation:

Since the clock is a full circle, it has a degree span of 360°.

∴ every 5-min interval on the clock

= 360° ÷ 12 five min intervals

= 30°

∴ acute angle formed by clock in figure

= two 5-min intervals

= 60°

[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]

★ Curved surface area of right circular cylinder is 4.4 m².

★ Radius of base of the cylinder is 0.7 m.

★ [tex]\tt \pi = \dfrac{22}{7}[/tex]

[tex]{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]

★ The height of cylinder.

[tex] {\large{\textsf{\textbf{\underline{\underline{Using \: Formula :}}}}}}[/tex]

[tex] \star \: \tt C.S.A \: of \: cylinder = \boxed{ \tt \pink{{ 2πrh}}}[/tex]

[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]

Let,

❍ The height of circular cylinder be [tex]h[/tex]

❍ Radius [r] of base of cylinder be 0.7 m

We know,

[tex] \star \: \tt C.S.A \: of \: cylinder = 2πrh[/tex]

Putting,

☆ [tex]\tt \pi = \dfrac{22}{7}[/tex]

☆ r as 0.7

[tex] \longrightarrow \tt 4.4 {m}^{2} = 2πrh[/tex]

[tex] \longrightarrow \tt 4.4 {m}^{2} = \bigg( 2 \times \dfrac{22}{7} \times 0.07 \times h \bigg)m[/tex]

[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( {2 }\times \dfrac{22}{ \cancel{7}} \times \dfrac{ \cancel{7}}{10} \times h \bigg)m[/tex]

[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( 44 \times \dfrac{ {1}}{10} \times h \bigg)m[/tex]

[tex] \longrightarrow \tt \dfrac{44}{ \cancel{10}} \times \cancel{10} \: m = \bigg( 44 \times 1 \times h \bigg)[/tex]

[tex] \longrightarrow \tt 44 m = 44h[/tex]

[tex]\longrightarrow \tt \dfrac{44}{44} m = h[/tex]

[tex]\longrightarrow \tt \red{ 1 m } = h[/tex]

Therefore, the height of cylinder = 1 m.

[tex]\begin{gathered} {\underline{\rule{290pt}{2pt}}} \end{gathered}[/tex]

The expression that represents this inequality must relate both temperatures, then it would look like this: -40°F < x < 140°F.

To express this situation in an inequality we must include the temperature values. Additionally, we must include the greater than (>) or less than (<) symbols to relate the values.

According to the above, the expression would look like this:

Note: This question is incomplete because some information is missing. Here is the information:

A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F.

Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form.

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Answer:

V = 9 in^3

Step-by-step explanation

Comment

The formula for a Pyramid of any B is V = B * h / 3. You have to be able to calculate the Base or just be given in it.

In this case the Base is a triangle. So the first thing needed is the area of the base.

Base

Area_triangle = base length * height / 2

Neither the Base length nor the height need to be the same as the B and h used for the volume of the Pyramid

Givens

b = 4 inches

h = 1.5 inches

Area_triangle = 4 * 1.5 / 2

Area_triangle = 2 * 1.5

Area_triangle = 3 inches^2

Solution

Base (triangle) Area = 3

h = 9

V = B * h / 3  

V = 3 * 9 / 3

V = 9 cubic inches

Answer V = 9 in^3

Answer:

yes.......................

Step-by-step explanation:

Answer:

x

Step-by-step explanation:

I got it right.........

Answer:

11,812.5

Step-by-step explanation:

25% = 0.25

(YEAR ONE)

[tex]28,000*0.25 -- > 21,000[/tex]

↓ (why?)

28,000 * 0.25 = 7,000

[tex]28,000 - 7,000 = 21,000[/tex]

(YEAR TWO)

[tex]21,000 * 0.25 -- > 15,750[/tex]

↓ (why?)

[tex]21,000 * 0.25 = 5250[/tex]

[tex]21,000 - 5,250 = 15,750[/tex]

(YEAR THREE)

[tex]15,750 * 0.25 -- > 11,812.5\\[/tex]

↓ (why?)

[tex]15,750 * 0.25 = 3,937.5\\15,750 - 3,937.5 = 11,812.5[/tex]

Answer = 11, 812.5

Step-by-step explanation:

[tex] {x}^{3} + 3x + 1 = 1 = = = > \\ {x}^{3} + 3x = 0 = = = > \\ x({x}^{2} + 3) = 0 \\ x = 0 \: or \\ {x}^{2} + 3 = 0 = = = > \\ {x}^{2} = - 3 = = = > x 1= \sqrt{ - 3} \: or \: i \sqrt{3} \\ x2 = - \sqrt{ - 3} = = = > x2 = - i \sqrt{3} [/tex]

[tex] {x}^{3} + 3x + 1 = 5 = = = > \\ {x}^{3} + 3x - 4 = = = > \\ (x - 1)( {x}^{2} + x + 4) = 0 = = = > \\ x - 1 = 0 = = > x1 = 1 \\ {x}^{2} + x + 4 = 0 = = = > \\ x2 = - 1 + i \sqrt{3} \\ x3 = - 1 - i \sqrt{3} [/tex]

[tex] {x}^{3} + 3x + 1 = 3 = = = > \\{ x}^{3} + 3x - 2 = 0 = = = > x = 0.6[/tex]

The values of the inverse of the function, f(x) = x³ + 3·x + 1, obtained from  graphing of the function are;

a. f⁻¹(1) = 0

b. f⁻¹(5) = 1

c. f⁻¹(3) ≈ 0.59607

An inverse function is a function that reverses the action of another function, such that the inverse function maps the output of the function to the corresponding input.

The inverse of the function can be found by graphing the function, f(x) = x³ + 3·x + 1, using technology and then using inverse or table function to find the values of the inverse functions at the specified points

a. The value of the inverse function, f⁻¹(1), is the x-value, on the graph that corresponds to the point with a y-coordinate of 1.

The graph of the function indicates that at a y-value of 1, x = 0, therefore;

f⁻¹(1) = 0

b. Similarly, the graph indicates that a y-value of 5, x = 1, therefore;

f⁻¹(5) = 1

c. When the y-value = 3, we get;

x³ + 3·x + 1 = 3

x³ + 3·x - 2 = 0

Solving the above equation with an online tool, we get; x ≈ 0.59607

Therefore; f⁻¹(3) ≈ 0.59607

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The value of the length of the scaled up rectangle is 12.8 unit.

A rectangle is a polygon with four sides , the opposites are parallel and equal.

It is given in the figure that

A rectangle 4* 8 is scaled up and a new rectangle is formed α * 25.6

Scale factor = 25..6/8 =3.2

The value of the length therefore will be

4 * 3.2 = 12.8 unit

Therefore the value of the length of the scaled up rectangle is 12.8 unit.

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Answer:

Using the formula multiplicity, we find that the equation of the function will be [tex]f(x)=-(x+6)^{3} (x-2)^{4}[/tex]. The graph is in the attachment.

Step-by-step explanation:

Concept: Given that for -6, multiplicity is 3 and for 2 multiplicity is 4.

So, the equation of multiplicity is represented as:

[tex]f(x)=a(x-root)^{mutliplicity}[/tex]

This gives the following function

[tex]f(x)=a(x+6)^{3} (x-2)^{4}[/tex]

The equation has a negative leading coefficient.

This means that, the value of a is less than 0 i.e. a < 0

Assume any value of a (say a = -1), the equation becomes

[tex]f(x)=-(x+6)^{3} (x-2)^{4}[/tex]

The graph is in the attachment.

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Answer:

C

Step-by-step explanation:

trust bro

The x axis is labeled as Number of days.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

let x be the  number of days and y be money.

So, the equation is

y = -7x + 150.

Hence, the x axis is labeled as Number of days.

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