Adrian, Ben and Charlie share some sweets in the ratio of 8:5:10.
Charlie got 24 more sweets than Adrian.
Work out the total number of sweets.

Answer:

Domain: -6≤x<0 or 0<x≤2

Range: 1<x≤6

Step-by-step explanation:

Domain = The set of starting numbers - the x values.

Range = The set of numbers it becomes - the y values.

For the domain, it starts at -6, on the left and ends at 0; however, it doesn't include 0. Then is starts at 0, exclusive, and ends at 2.

For the range, it starts at 1, but doesn't include 1, and ends at 6, inclusive.

The domain of the given piecewise-defined function is -6≤x≤0 or 0. The domain of a function refers to the set of all possible input values or x-values of the function, while the range refers to the set of all possible output values or y-values of the function. In a piecewise-defined function, each piece has its own domain and range.

The domain of a function refers to the set of all possible input values or x-values of the function, while the range refers to the set of all possible output values or y-values of the function. In a piecewise-defined function, each piece has its own domain and range.

To determine the domain of the given piecewise-defined function, we need to identify the intervals on the x-axis where each piece of the function is defined. From the graph, we can see that the function is defined from -6 to 0, and also from 0 to 2. So the domain is -6≤x≤0 or 0

The range of the function is the set of all y-values that correspond to the x-values in the domain. Looking at the graph, we see that the function takes on values between 1 and 6, inclusive. So the range is 1≤y≤6.

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Answer:

The solutions of the equations are π/3 , 2π/3 , 4π/3 , 5π/3

Step-by-step explanation:

* Lets revise the four quadrant before solving the equation

# First quadrant the measure of all angles is between 0 and π/2

  the measure of any angle is α  

∴ All the angles are acute  

∴ All the trigonometry functions of α are positive  

# Second quadrant the measure of all angles is between π/2 and π

  the measure of any angle is π - α  

∴ All the angles are obtuse  

∴ The value of sin(π - α) only is positive ⇒ sin(π - α) = sinα  

# Third quadrant the measure of all angles is between π and 3π/2  

  the measure of any angle is π + α  

∴ All the angles are reflex

∴ The value of tan(π + α) only is positive ⇒ tan(π + α) = tanα

# Fourth quadrant the measure of all angles is between 3π/2 and 2π

  the measure of any angle is 2π - α  

∴ All the angles are reflex

∴ The value of cos(2π - α) only is positive ⇒ cos(2π - α) = cosα

* Now lets solve the equation

∵ 4 sin²Ф - 3 = 0 ⇒ the domain is 0 ≤ Ф ≤ 2π

- Add 3 for both sides

∴ 4 sin²Ф = 3 ⇒ divide the both sides by 4

∴ sin²Ф = 3/4 ⇒ take square root for both sides

∴ √(sin²Ф) = √(3/4)

∴ sinФ = √3/2 OR sinФ = -√3/2

- When the value of sinФ is positive

∴ The angle Ф is on the first or second quadrant

- When the value of sinФ is negative

∴ The angle Ф is on the third or fourth quadrant

- We have four values of Ф because 0 ≤ Ф ≤ 2π

- Lets find the measure of the acute angle α

∵ sinα = √3/2

∴ α = sin^-1(√3/2) = π/3

- If Ф is on the first quadrant

∴ Ф = α = π/3

- If Ф is on the second quadrant

∴ Ф = π - α = π - π/3 = 2π/3

- If Ф is on the third quadrant

∴ Ф = π + α = π + π/3 = 4π/3

- If Ф is on the fourth quadrant

∴ Ф = 2π - α = 2π - π/3 = 5π/3

* The solutions of the equations are π/3 , 2π/3 , 4π/3 , 5π/3

Answer:

5/12

Step-by-step explanation:

Since 1/2 is the same distance from zero and one, we can use it to judge whether a fraction is closer to 0 or 1.

Since 5/8 is greater than 4/8 which is 1/2, it is closer to 1.

Since 8/10 is greater than 5/10 which is 1/2, it is closer to 1.

Since 5/12 is less than 6/12 which is 1/2, it is closer to 0.

So our answer is C. 5/12

The value close 0 than 1 is 0.41667.

A fraction is a part of a whole number. for example, [tex]\bold{\dfrac{1}{4}}[/tex] represent a quarter of a number. Similarly, when we solve the fraction meaning [tex]\bold{\dfrac{1}{4}}[/tex]  in the decimal form we divide the numerator, therefore, 1 in this case with the denominator as 4 in this case. the value thereafter we get is known as the decimal form of a fraction.

for example,  = 0.25.

Also, to convert a decimal to a fraction we simply divide the number by a multiple of 10. the number will be depending upon the number of numbers are after the decimal.

for example, 0.25 will be written as [tex]\bold{\dfrac{25}{100}}[/tex] while 0.5 will be written as [tex]\bold{\dfrac{5}{10}}[/tex].

Now, solving the question,

Bring every fraction to decimal form,

[tex]\bold{\dfrac{5}{8}= 0.625}[/tex]

[tex]\bold{\dfrac{8}{10} = 0.8}[/tex]

[tex]\bold{\dfrac{5}{12} = 0.41\overline6}[/tex]

[tex]\bold{\dfrac{7}{14} = 0.5}[/tex]

Hence, the value close 0 than 1 is 0.41667.

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Answer:

B. g(x) = 3x^3.

Step-by-step explanation:

In general   a f(x)  stretches vertically the graph of f(x) by a factor a.

The new function after a vertical stretch of the cubic function F(x) = x^3 is G(x) = 3x³, which multiplies the output of the original function by 3.

When you apply a vertical stretch to the cubic function F(x) = x³, you multiply the output of the function, not the input. A vertical stretch by a factor of 3 would mean that each output value is tripled. Therefore, the correct equation for the new function would be G(x) = 3x³.

Option A is incorrect because (1/3x)³ represents a horizontal stretch by a factor of 3. Option C, (3x)³, represents a horizontal shrink by a factor of 1/3, and results in steeper slopes than the original function, which is the opposite effect of a vertical stretch. Option D, 1/3x³, would be a vertical compression by a factor of 1/3, not a stretch.

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Answer:

C. a paper clip

Step-by-step explanation:

An apple generally weighs more than 3 grams, and can go even into oz.

Depending on the type of material the backpack is made of, and also how big it is, the mass can vary, however, it is safe to say the backpack will be more than 3 grams.

A cat definitely weighs more than 3 grams. Any born cat that weighs only 3 grams will not survive.

~

For this case we have the following options:

An apple, it is known that the apple will never weigh 3 grams.

A backpack will not have that weight either.

A cat would never weigh 3 grams or be newborn.

To have an object of 3 grams, the object must be very light.

A paperclip is very likely to weigh 3 grams because it is a very small and extremely light object.

Answer:

Option C

Answer:

1-C, 2-B, 3-A, 4-E, 5-D

Step-by-step explanation:

It is convenient to let a graphing calculator or spreadsheet compute the standard deviations for you. (Some will compute sample standard deviation; some will compute population standard deviation. It makes no difference to the ordering, as long as the same computation is used for all data sets.)

The correct order of the data sets from smallest to largest standard deviation is: C, B, A, E, D.

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Answer:

Step-by-step explanation:

1. The problem statement tells you the function applies for year values (x) 2009 and later. The domain is real numbers greater than or equal to 2009.

__

2. We can use the distributive property to eliminate parentheses:

  3.2(x -2009) +206 = 3.2x -6428.8 +206

  = 3.2x -6222.8

__

3. Put 2025 in the equation and do the arithmetic

  g(2025) = 3.2·2025 -6222.8 = 257.2 . . . . mm

__

4. Put this value of level rise in the equation and solve for x.

  g(x) = 3.2x -6222.8

  500 = 3.2x -6222.8 . . put 500 mm where g(x) is in the equation

  6722.8 = 3.2x . . . . . . . add 6222.8

  x = 6722.8/3.2 = 2100.875

The water rise will be equal to about half a meter late in the year 2100.

Answer:

541.8 cm³

Step-by-step explanation:

Volume of a prism is the height times the area of the base.

V = hA

Area of a rectangle is width times length, so:

V = hwl

Given h = 8.8 cm, w = 4.7 cm, and l = 13.1 cm:

V = (8.8 cm) (4.7 cm) (13.1 cm)

V = 541.8 cm³

Answer:

[tex]541.8cm^{3}[/tex]

Step-by-step explanation:

V = Bh or V = lwh

substitute given measurements, then simplify.[tex]13.1cm * 4.7cm * 8.8cm = 541.8cm^{3}[/tex]

Answer:

  PPF, PFF

Step-by-step explanation:

There are several ways you can list all the possible combinations. A couple of my favorite are a) use a binary counting sequence; b) use a gray code counting sequence.

Using the first method, the binary numbers 000 to 111 can be listed in numerical order as 000, 001, 010, 011, 100, 101, 110, 111. Letting 0=P and 1=F, the ones missing from your list are the ones in italics in my list.

Using the second method, we change the right-most character, then the middle one, and finally the left-most character so there is one change at a time: 000, 001, 011, 010, 110, 111, 101, 100.

After you have a list of all possible combinations, it is a simple matter to compare the given list to the list of possibilities to see which are missing.

The correct outcome possibilities for the missing boxes in the given scenario are:

1. PPP (all three tires pass)

2. PPF (two tires pass, one fails)

3. PFP (two tires pass, one fails)

4. FPP (two tires pass, one fails)

5. FFP (two tires pass, one fails)

6. FPF (two tires pass, one fails)

7. FFF (all three tires fail)

To determine the missing outcomes, we must consider all possible combinations of passes (P) and failures (F) for three tires. Since each tire can either pass or fail, there are [tex]2^3 = 8[/tex] possible outcomes. We already have five of these outcomes listed, and we need to find the remaining two.

The missing outcomes must include all combinations of passes and failures that have not been listed yet. Since we have all combinations with exactly two passes and one fail, and we have the combination with three passes and three fails, the remaining combinations must have exactly one pass and two fails. These combinations are:

- PFF (one tire passes, two fail)

- FPF (one tire passes, two fail)

Therefore, the complete list of outcomes is:

1. PPP (all three tires pass)

2. PPF (two tires pass, one fails)

3. PFP (two tires pass, one fails)

4. FPP (two tires pass, one fails)

5. FFP (two tires pass, one fails)

6. FPF (two tires pass, one fails)

7. PFF (one tire passes, two fail)

8. FFF (all three tires fail)

Each of these outcomes represents a distinct possibility when testing three tires, and together they account for every possible result of the wear and tear test for the three tires.

Answer:

21.1 percent

Step-by-step explanation:

Total balls after -1 red ball=7+5+4+3=19

Prob of purple ball= purple ball/total balls

= 4/19

=0.2105...

percentage:21.1%

The probability of selecting a red ball and then a purple one without replacement from a box containing 8 red, 5 brown, 4 purple, and 3 green balls is approximately 8.4%.

In probability, there are two events of interest here: selecting a red ball and then selecting a purple ball. Since the total number of balls changes after picking the red ball, these are dependent events. The probability of the first event (selecting a red ball) is 8 out of 20 (total balls). Then, with a red ball removed and not replaced, the probability of the second event (selecting a purple ball) is 4 out of 19. To find the overall probability, we multiply the probabilities of these two events.

To convert the probability to a percentage, multiply the result by 100. By doing this, the probability rounds to approximately 8.4%.

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2 * 10^2

Divide the first numbers, which are 6 and 3, to get 2. Then, subtract the powers of the exponents, which are 5 and 3, to get 2.

Answer:

x = 31

Step-by-step explanation:

The sides of an isosceles trapezoid are the same length, so ...

5x -32 = 2x +61

3x = 93 . . . . . . . . add 32-2x

x = 31 . . . . . . . . . . divide by 3

Answer:

b.

Step-by-step explanation:

x-intercepts are found by factoring.  We will use standard factoring here since this one is straightforeward and has real zeros as its solutions.  

In our equation,

a = 2

b = 2

c = -4

The rules are to take a * c and then find the factors that number, determine which combination of those factors will give you the linear term (the term with the single x on it), and rearrange those signs accordingly.  Let's start with that:

Our a * c is 2 * -4 = -8.

We need the factors of |-8|:  1,8 and 2,4

Some combination of those factors needs to give us a +2x.  2,4 will work as long as the 4 is positive and the 2 is negative.

Now we put them back into the equation, the absolute value of the larger number first:

[tex]2x^2+4x-2x-4=0[/tex]

Now group the terms in sets of 2 without moving any of them around:

[tex](2x^2+4x)-(2x-4)=0[/tex]

In each set of parenthesis, pull out what is common to both terms.  In the first set, the 2x is common, and in the second set, the 2 is common:

[tex]2x(x+2)-2(x+2)[/tex]

Now what is common between both terms is the (x + 2), so pull that out, grouping what is remaining in its own set of parenthesis:

[tex](x+2)(2x-2)=0[/tex]

To find the zeros, remember that the Zero Product Property tells us that for that equation above to equal zero, one of those factors has to equal zero, so:

x + 2 = 0 or 2x - 2 = 0.  Solve both for x:

x = -2 so the coordinate is (-2, 0)

2x - 2 = 0 and

2x = 2 so

x = 1 so the coordinate is (1, 0)

Answer:

A. 16.12 ft  B.  9.64 ft

Step-by-step explanation:

For both of these, you need Pythagorean's Theorem because we have right triangles.  In part A, we are given 2 legs and are asked to find the length of the hypotenuse:

[tex]14^2+8^2=PR^2[/tex] and

[tex]196+64=PR^2[/tex]

and PR = 16.12 ft

In part B, we are given the length of the hypotenuse and side PQ remains the same:

[tex]14^2+QR^2=17^2[/tex] and

[tex]196+QR^2=289[/tex]

[tex]QR^2=289-196[/tex] so

QR = 9.64 ft

Answer:

Option C is correct.

Step-by-step explanation:

The given equation or function is linear if the variables x and y have degree zero or 1.

The given equation is 5x^4+5y =9

here x has degree =4 and y has degree = 1, but for linear equation both x and y variables must have degree zero or 1.

So, Option C is correct.

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

P(A) = 0.5

P(B) = 0.5

P(C) = 0.15

P(D) = 0.7

P(E) = 0.15

We need to find the independent events.

When we consider,

P(A∩D) = P(Event A and Event D) = 0.35

and

P(A) × P(D) = 0.7 × 0.5 = 0.35

We get that

P(A∩D)= P(A) × P(D) = 0.35

All other options are not satisfying the conditions of "Independent events".

Hence, Option 'B' is correct.

Answer:

option b would be the correct answer

Step-by-step explanation:

Answer:

1. 22 in

2. 11.304 units

Step-by-step explanation:

Formulas for the circumference are

C = 2πr

C = πd

___

1. Put the given numbers in the appropriate formula:

C = 2·(22/7)·(7/2 in) = 22 in

__

2. Put the given numbers in the appropriate formula:

C = 3.14·3.6 = 11.304 . . . units

Answer:

4

Step-by-step explanation:

[tex] 16a+32b+16c= 4*(4a+8b+4c)[/tex]

Answer:

If 4a+8b+4c=1, then 16a+16c+32b = 4

Step-by-step explanation:

To answer the question, a rule of three can be raised:

4a + 8b + 4c --------------- 1

16a + 16c + 32b --------- X

X = (16a + 16c + 32b) ÷ (4a + 8b + 4c)

This is equivalent to the division of the two polynomials, 16a + 16c + 32b by 4a + 8b + 4c.

Before dividing we organize the first polynomial,

16a + 16c + 32b = 16a + 32b + 16c

Dividing the two polynimials, we have

16a + 32b + 16c   | 4a + 8b + 4c  

-16a - 32b - 16c            4

       = 0 =

The exact quotient is 4, since the residue is 0

Hope this hepls!

Answer:

y=1/4x-1

Step-by-step explanation:

First step to determine the equation of a line is is to determine its slope.

We see the line passes through points (4,0) and (0,-1), that means its slope is:

S = (0 - -1) / (4 - 0) = 1/4

Since there's only one choice with a slope of 1/4, the choice is easy :-)

But we can also verify the equation by checking if it validates the given points. So, what's the value of y if x = 0?

y = (1/4)0 - 1 = 0 - 1 = -1  Validated.

And when x = 4?

y = (1/4)4 - 1 = 1 - 1 = 0  Validated too.

Answer:

[tex]x-4y=4[/tex]

Step-by-step explanation:

The given function passes through: (4,0) and (0,-1).

The equation is of the form;

y=mx+b

where b=-1 is the y-intercept.

The equation now becomes:

y=mx-1

We substitute the point (4,0) into the function to obtain;

0=m(4)-1

0+1=4m

1=4m

[tex]m=\frac{1}{4}[/tex]

Therefore the equation is:

[tex]y=\frac{1}{4}x-1[/tex]

Multiply through by 4 to get;

[tex]4y=x-4[/tex]

The equation in standard form is;

[tex]x-4y=4[/tex]

Answer:

B.   -1.5x − 3.5y = -31.5

Step-by-step explanation:

You forgot to provide the reference image which is essential to answer the question, but I managed to find it... and attach it to my answer.

In the given equation for AB, if we place the y term on the left and x term on the right, we see the slope of that line is 7/3 (y = (7x - 21.5)/3 ==> 7/3x).

We see on the image that the line PQ is perpendicular to AB.  That means that its slope is -3/7.

If we quickly check the slopes of each of the possible answers...

A. -3x + 4y = 3 ----> 4y = 3x - 3 ==> y = (3x-3)/4 => slope = 3/4

Not what we're looking for.

B. -1.5x - 3.5y = -31.5 ==> 3.5y = -1.5x + 31 ===> y = (-1.5x +31)/3.5

that gives us a slope of -1.5/3.5... We can simplify it... -3(0.5)/7(0.5) = -3/7

Exactly as predicted.

Since we have the point P (7,6), we can enter it in the equation to verify:

-1.5x - 3.5y = -31.5

-1.5 (7) - 3.5 (6) = -10.5 - 21 = -31.5  --- Verified

C. 2x + y = 20 ==> y = 20 - 2x ===> slope is -2, not what we want.

D. -2.25x + y = -9.75 ==> y = 2.25x - 9.75 ==> slop is 2.25 cannot be it.

Answer: B. -1.5x − 3.5y = -31.5

Step-by-step explanation:

Answer:

[tex]f(x)=x^2+16[/tex]

Step-by-step explanation:

By the conjugate rule, if -4i is a root, then so is +4i.  So we have 2 roots, thus, we have a second degree polynomial (namely, a quadratic).  If

x = -4i, then

x + 4i is a root.

If

x = 4i, then

x - 4i is a root.  

Having (x - 4i)(x + 4i) as roots, we can now FOIL them together to get a polynomial of least degree.

FOILing gives us

[tex]x^2+4ix-4ix-16i^2[/tex]

Notice that the +4ix and the -4ix cancel each other out, leaving you with

[tex]x^2-16i^2[/tex]

Since

[tex]i^2=-1[/tex]

we can make the substitution:

[tex]x^2-16(-1)[/tex]

which simplifies to

[tex]x^2+16[/tex]

In function notation form:

[tex]f(x)=x^2+16[/tex]

Final answer:

The polynomial function in standard form with the root -4i is f(x) = x² + 16. We derive this by realizing that the conjugate, 4i, is also a root and multiplying the factors (x + 4i)(x - 4i), simplifying to the quadratic polynomial.

Explanation:

To write a polynomial function with the given root -4i, we must take into consideration that complex roots come in conjugate pairs for polynomials with real coefficients. Hence, if -4i is a root, then its conjugate 4i must also be a root. The factors of the polynomial corresponding to these roots are (x + 4i) and (x - 4i).

We can find the polynomial by multiplying these two factors:

(x + 4i)(x - 4i)

Applying the difference of squares, we get:

x² - (4i)²

x² - (-16)

x² + 16

The polynomial function in standard form with the given root -4i is:

f(x) = x² + 16

Answer:

x=4,-2/3

Step-by-step explanation:

To solve for x, we first subtract 8 from both sides.

So 3x^2-10x-8=0

Using the quadratic formula, we get

X=(10+sqrt(100+96))/6 or x = (10-sqrt(100+96))/6

So x=(10+14)/6 or x=(10-14)/6

So x=4 or x=-2/3.

Answer:

x=4 or x=-2/3.

Step-by-step explanation:

Answer:

x=14

Step-by-step explanation:

4(x - 8)³ - 18 = 846

4(x - 8)³ = 864

(x - 8)³ =216

∛(x - 8)³ =∛216

x-8 = 6

x= 6+8

x=14

Answer:

x=14

Step-by-step explanation:

look this solution :

Answer:

55 degrees.

Step-by-step explanation:

We can use the postulate if two angles are congruent in both triangles than the triangle is congruent.

That means we can plug in 80 and 45 for triangle QRS.

Then, we can find angle 1 by subtracting the sum of those numbers from 180.

80 + 45 = 125

180 - 125 = 55

Answer:

It is D

Step-by-step explanation:

3.75 miles or 3 3/4 would be your answer

Answer:

  x = −3

Step-by-step explanation:

A zero of a function is a value that makes one of the factors be zero.

To make x+3 = 0, x = -3.

To make x-7 = 0, x = 7.

To make x+5 = 0, x = -5.

Of these values that make the factors zero, only x = -3 is on your choices list.

Answer:  The correct option is

(B) x = - 3.

Step-by-step explanation:  We are given to select the correct zero of the following polynomial function :

[tex]f(x)=(x+3)(x-7)(x+5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

The zeroes of the function f(x) are given by

[tex]f(x)=0\\\\\Rightarrow (x+3)(x-7)(x+5)=0\\\\\Rightarrow x+3=0,~~x-7=0,~~x+5=0\\\\\Rightarrow x=-3,7,-5.[/tex]

Therefore, the zeroes of the given function are

x = -3, x = 7 and x = -5.

Thus, the correct option is

(B) x = -3.

Answer:

21x^2 - 41x + 10

Step-by-step explanation:

The area of a rectange is length x width.

L = 7x-2

W = 3x-5

So, you would do (7x-2)x(3x-5).

To do this, you can do FOIL.

F (first times first) - (7x)(3x)=21x^2

O (outside times outside) - (7x)(-5)= -35x

I (inside times inside) - (-2)(3x)= -6x

L (last times last) - (-2)(-5) = 10

So, it is 21x^2 - 35x - 6x +10

Then you combine like terms giving you:

21x^2 - 41x + 10

Answer: 21x^2 - 41x + 10

Step-by-step explanation: If the lengths are even then the number would be angle.

Answer:

I believe it is "E"

Step-by-step explanation:

E-series can eat my memes

Kill me please I'm Swedish ree

Answer: The key feature in the experimental study is C. The treatment in the experiment must be applied to each of the individuals in the experimental group. This is because it is made sure that the variables and conditions in different correspondents are applied so that actual results may be concluded.

Step-by-step explanation:

Explanation:

A) For the function ...

f(x) = mx + b

the vertical translation by k makes the function ...

g(x) = f(x) + k = mx + b + k

This can be rewritten as ...

g(x) = m(x +k/m) +b = f(x+k/m)

That is, the vertical translation by k is equivalent to a horizontal translation by -k/m, where m is the slope of the linear function.

___

B) For a vertical translation of 3, the equivalent horizontal translation is ...

-k/m for k=3

= -3/m . . . . . where m is the slope of the function

_____

Please note that there is no equivalent for m=0.